CHARACTERIZATION OF A COLD FLOW NON-AXISYMMETRIC ...
CHARACTERIZATION OF A COLD FLOW NON-AXISYMMETRIC SUPERSONIC EJECTOR
by
DAVID M. LINEBERRY A DISSERTATION
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Mechanical and Aerospace Engineering to The School of Graduate Studies of The University of Alabama in Huntsville
HUNTSVILLE, ALABAMA 2007
UMI Number: 3272664
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In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree from The University of Alabama in Huntsville, I agree that the Library of this University shall make it freely available for inspection. I further agree that permission for extensive copying for scholarly purposes may be granted by my advisor or, in his/her absence, by the Chair of the Department or the Dean of the School of Graduate Studies. It is also understood that due recognition shall be given to me and to The University of Alabama in Huntsville in any scholarly use which may be made of any material in this dissertation.
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DISSERTATION APPROVAL FORM Submitted by David M. Lineberry in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering and accepted on behalf of the Faculty of the School of Graduate Studies by the dissertation committee. We, the undersigned members of the Graduate Faculty of The University of Alabama in Huntsville, certify that we have advised and/or supervised the candidate on the work described in this dissertation. We further certify that we have reviewed the dissertation manuscript and approve it in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering.
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ABSTRACT The School of Graduate Studies The University of Alabama in Huntsville
Degree
Doctor of Philosophy
College/Dept. Engineering/Mechanical and Aerospace Engineering . Name of Candidate David M. Lineberry . Title Characterization of a Cold Flow Non-Axisymmetric Supersonic Ejector .
Experimental investigations of dual and single nozzle non-axisymmetric strut based supersonic ejectors were carried out. The strut nozzles transitioned from a round throat to a square exit with an expansion ratio of 4.6. The ejector system entrained secondary air from the lab and exhausted to the lab at atmospheric pressure. The ejectors were operated at equivalent mass flow rates at primary chamber pressure to back pressure ratios ranging from 6.8 to 61.2 for the single nozzle strut and 3.4 to 30.6 for the dual nozzle strut. Under these conditions both struts demonstrated operation in three distinct regimes: mixed, saturated supersonic and supersonic.
Secondary flow choking was
demonstrated for both struts at equivalent primary mass flow rates. The mixing length was determined by pressure recovery or equalization with the back pressure. This length remained relatively constant at approximately 20 nozzle hydraulic diameters for the primary mass flow rates in the mixed regime. At higher mass flow rates, the pressure recovery length increased and appeared to be strongly affected by the primary nozzle exit pressure. Surveys of duct exit stagnation pressure indicated poor mixing at high mass flow rates with a supersonic core existing through the mixing duct. Shadow graph images revealed a complex shock structure in the recovery region of the mixing duct. Classical analytical models for axisymmetric ejectors were used to investigate the effect
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of non-axisymmetric geometry.
Preliminary CFD simulations were performed to
investigate ejector mixing.
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ACKNOWLEDGMENTS
The work documented in this dissertation would not have been possible without the assistance of several individuals. First I would like to thank Dr. Clark Hawk for his devotion to the students in the Propulsion Research Center. I would not be at this point in my life without his support. Second I would like to thank my dissertation advisor, Dr. Brian Landrum.
I would also like to acknowledge Dr. Marlow Moser for his
invaluable guidance in the experimental setup, and analysis of results. I would also like to thank Dr. Hugh Coleman, Dr. Kader Frendi, and Dr. C.P. Chen for their support of my research. In addition, a number of other individuals deserve mention for their assistance to my research. George Olden was a tremendous help in the lab in all aspects of the experiment from the beginning to the end of this work. A number of other individuals in the PRC should be recognized:
Balasubramanyam Madhanabharatam for the CFD
analysis, Tony Hall for his assistance with laboratory issues, Chris Linn and David Jackson for their help in the shadowgraph experiments, and finally Geri Gaeta for her assistance with the exit profile traces. I would also like to recognize the late Dr. Mark V. Bower. Dr. Bower was always available for consultation, and was supportive of me both in my academic pursuits and in my teaching endeavors at UAH. He will be greatly missed.
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TABLE OF CONTENTS
Page List of Figures .................................................................................................................... xi List of Tables ................................................................................................................... xvi List of Symbols ............................................................................................................... xvii Chapter 1.
INTRODUCTION....................................................................................................... 1 1.1
Introduction....................................................................................................... 1
1.2
Ejector Propulsion Applications ....................................................................... 1 1.2.1 Ducted Rockets....................................................................................... 2 1.2.2 Rocket Based Combined Cycle Engines ................................................ 3
2.
1.3
Principles of Ejector Operation......................................................................... 5
1.4
Ejector Flow Regimes....................................................................................... 8
1.5
Ejector Performance Characterization ............................................................ 10
1.6
Ejector Design Considerations........................................................................ 12
1.7
Ejector Analysis Techniques........................................................................... 14
1.8
Motivation....................................................................................................... 15
BACKGROUND....................................................................................................... 18 2.1
UAH Propulsion Research Center .................................................................. 18
2.2
Classical Ejector Research.............................................................................. 23 2.2.1 Fabri’s Ejector Model........................................................................... 23 2.2.2 Supersonic Regime............................................................................... 25 2.2.3 Saturated Supersonic Flow ................................................................... 28 2.2.4 Mixed Flow .......................................................................................... 28 2.2.5 Mixed Flow with Primary Separation .................................................. 31 2.2.6 Matching Fabri’s Models ..................................................................... 32 2.2.7 Addy’s Ejector Model .......................................................................... 34
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2.2.8 Supersonic Flow Regime Model .......................................................... 34 2.2.9 Mixed Flow Regime ............................................................................. 36 2.3
CFD Analysis.................................................................................................. 37
2.4
Current Experimental Work............................................................................ 39 2.4.1 Propulsion Engineering Research Center............................................. 39 2.4.2 Japan Aerospace Exploration Agency.................................................. 41 2.4.3 Aerojet .................................................................................................. 44 2.4.4 Small Scale Experimental Efforts ........................................................ 45
2.5 3.
Summary ......................................................................................................... 47
FACILITY AND EXPERIMENTAL SETUP .......................................................... 48 3.1
Facility ............................................................................................................ 48
3.2
Test Matrix...................................................................................................... 55 3.2.1 Mixing Duct Tests ................................................................................ 56 3.2.2 Exit Pressure Profiles ........................................................................... 58 3.2.3 Shadowgraph Visualizations ................................................................ 59
4.
UNCERTAINTY ANALYSIS AND DATA REDUCTION EQUATIONS ............ 62 4.1
Introduction..................................................................................................... 62
4.2
General Uncertainty ........................................................................................ 62 4.2.1 Single Variable Measurement Uncertainty .......................................... 63 4.2.2 Uncertainty for a Calculated Result ..................................................... 65 4.2.3 Uncertainty for a Collection of Results................................................ 66
4.3
Reducing Test Uncertainty Through Nominal Readings................................ 67
4.4
Pressure Transducers Calibration ................................................................... 68
4.5
Ejector Specific Uncertainty ........................................................................... 68 4.5.1 Mass Flow ............................................................................................ 69 4.5.2 Bypass Ratio......................................................................................... 71 4.5.3 Mach Number....................................................................................... 72 4.5.4 Pressure Ratios ..................................................................................... 73
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5.
EXPERIMENTAL RESULTS .................................................................................. 74 5.1
Introduction..................................................................................................... 74
5.2
Single Nozzle Strut ......................................................................................... 74 5.2.1 Mass Flow Augmentation .................................................................... 75 5.2.2 Mach Numbers ..................................................................................... 76 5.2.3 Strut Gap Pressures .............................................................................. 78 5.2.4 Mixing Section Static Pressure Distributions....................................... 82 5.2.5 Exit Pressure Profiles ........................................................................... 90
5.3
Dual Nozzle Strut............................................................................................ 97 5.3.1 Mass Flow Augmentation .................................................................... 98 5.3.2 Mach Numbers ..................................................................................... 99 5.3.3 Strut Gap Pressures ............................................................................ 100 5.3.4 Mixing Section Static Pressure Distribution ...................................... 103 5.3.5 Exit Pressure Profiles ......................................................................... 109
6.
DISCUSSION OF RESULTS ................................................................................. 116 6.1
Mass Flow and Bypass Ratio........................................................................ 116 6.1.1 Mass Flow Calculations ..................................................................... 119 6.1.2 Bypass Ratio....................................................................................... 122
6.2
Pressure Distribution..................................................................................... 125
6.3
Flow Visualization ........................................................................................ 131
6.4
Analytical Comparisons................................................................................ 136 6.4.1 Single Nozzle Strut............................................................................. 136 6.4.2 Dual Nozzle Strut ............................................................................... 138
6.5 7.
CFD Analysis................................................................................................ 141
CONCLUSIONS ..................................................................................................... 148 7.1
Flow Regimes ............................................................................................... 148
7.2
Mixing Duct Pressure Distributions.............................................................. 150
7.3
Mass Flow Entrainment ................................................................................ 153
7.4
Comparison to Analytical Models ................................................................ 154
7.5
CFD Analysis................................................................................................ 155 ix
7.6
Momentum Effects........................................................................................ 156
7.7
Future Work .................................................................................................. 158
APPENDIX A: Systematic Uncertainty Values ............................................................ 162 APPENDIX B: Regression Uncertainty Analysis for Calibration................................. 164 APPENDIX C: Mathcad Calculation Sheets ................................................................. 170 APPENDIX D: Test Results (Average Values)............................................................. 215 REFERENCES ............................................................................................................... 224
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LIST OF FIGURES
Figure
Page
1.1 Schematic of a ducted rocket [2]. ................................................................................ 3 1.2 Schematic of the Aerojet StrutJet Concept [3]. ........................................................... 4 1.3 Specific impulse for RBCC operating modes [3]. ....................................................... 5 1.4 Axisymmetric ejector diagram..................................................................................... 6 1.5 Depiction of shear layer between a high speed primary jet and a low speed secondary flow. ....................................................................................................... 7 1.6 Mass Flow and Bypass ratio for a supersonic ejector [10]. ...................................... 11 2.1 Sketch of PRC ejector facility.................................................................................... 19 2.2 PLIF images of the mixing between the turbine exhaust and the two rocket plumes from the dual nozzle strut [23].............................................................................. 20 2.3 Probe locations for pressure traces in the PRC ejector [24]. ..................................... 21 2.4 Sketch of an axisymmetric ejector with Fabri’s notation. ......................................... 24 2.5 Sketch of an axisymmetric ejector with Fabri’s notation for mixed regime analysis.29 2.6 Comparison of recreated model with data from Fabri’s model. ................................ 32 2.7 Mixed regime comparison of current model with Fabri’s model. ............................. 33 2.8 Ejector configuration for Kitamura’s experiments [33]............................................. 42 2.9 Pressure recovery comparison in rectangular and circular cross section ejectors [33]........................................................................................................................ 42 2.10 Surface flow patterns for a circular duct (a) and a rectangular duct (b) ejector [33]........................................................................................................................ 43 3.1 Schematic of PRC cold flow ejector facility.............................................................. 48 3.2 Ejector test rig cross section. ..................................................................................... 49 3.3 Ejector test rig end view. ........................................................................................... 50
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3.4 Dual and single nozzle ejector struts. ........................................................................ 51 3.5 PRC ejector top wall static pressure tap locations. .................................................... 52 3.6 PRC ejector side wall pressure tap locations. ............................................................ 53 3.7 Secondary flow Pitot probe location in strut fairing.................................................. 54 3.8 Probe trace locations for stagnation pressure traces across the duct exit plane......... 58 3.9. Schematic of shadowgraph setup for ejector facility................................................ 59 3.10. Region of interest for shadowgraphy [37]. ............................................................. 60 5.1 Single nozzle strut primary and secondary mass flow comparison. .......................... 75 5.2 Secondary flow Mach number ahead of the strut and mixed flow Mach number at duct exit centerline (single nozzle strut). .............................................................. 77 5.3 Single nozzle strut gap pressure ratios....................................................................... 79 5.4 Single nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 40.5, 47.3, 53.9, and 60.6)...................................................................... 80 5.5 Single nozzle strut pressure ratio at last static pressure tap in the strut gap (0.843 hydraulic diameters upstream).............................................................................. 81 5.6 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 6.5)................. 83 5.7 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 13.2)............... 83 5.8 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 20.2)............... 84 5.9 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 27.2).............. 84 5.10 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 33.8)............ 85 5.11 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 40.5)............. 86 5.12 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 47.3). ............. 87 5.13 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 53.9). .............. 88 5.14 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 60.6). ............. 88 5.15 Single nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).................................................................................. 92 5.16 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.5). . 92
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5.17 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.2). 93 5.18 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.8). 93 5.19 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.2). 94 5.20 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 33.8). 94 5.21 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 40.4). 95 5.22 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 47.1). 96 5.23 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 53.7). 96 5.24 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 60.3). 97 5.25 Dual nozzle strut secondary and primary mass flow. .............................................. 98 5.26 Dual nozzle inlet and exit centerline Mach numbers............................................... 99 5.27 Dual nozzle strut gap pressure ratios. .................................................................... 100 5.28 Dual nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 20.4, 24.0, 27.4, and 30.6). .......................................................................................... 101 5.29 Dual nozzle strut gap pressure ratios at last static pressure tap (0.843 hydraulic diameters upstream). ........................................................................................... 102 5.30 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 3.5)................. 104 5.31 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 6.8).................. 104 5.32 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 10.2)............... 105 5.33 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 13.5)............... 105 5.34 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 16.9)............... 106 5.35 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 20.5)............... 106 5.36 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 24.0)............... 107 5.37 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 27.4)............... 108 5.38 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 30.7)............... 108 5.39 Dual nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A). ............................................................................................... 110
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5.40 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 3.5).... 111 5.41 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.9).... 112 5.42 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 10.1).. 112 5.43 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.4).. 113 5.44 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 16.7).. 113 5.45 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.9).. 114 5.46 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 23.9).. 114 5.47 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.1).. 115 5.48 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 30.3).. 115 6.1 Secondary mass flow versus set point pressure ratio for single and dual nozzle struts.................................................................................................................... 117 6.2 Secondary mass flow comparison for both struts. ................................................... 118 6.3 Bypass ratio versus primary mass flow rate for single and dual nozzle struts. ....... 123 6.4: Bypass ratio versus pressure ratio for the dual and single nozzle struts with low pressure test data. ................................................................................................ 124 6.5: Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.3 lbm/s)........................................................................................ 126 6.6 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.7 lbm/s)........................................................................................ 126 6.7 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.05 lbm/s)...................................................................................... 127 6.8 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.39 lbm/s)...................................................................................... 127 6.9 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.74 lbm/s)...................................................................................... 128 6.10 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.1 lbm/s)........................................................................................ 129 6.11 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.45 lbm/s)...................................................................................... 130
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6.12 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.78 lbm/s)...................................................................................... 130 6.13 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 3.13 lbm/s)...................................................................................... 131 6.14. Series of images depicting chamber pressure ramp up for single nozzle strut: (a) Pc/Pb = 13.3, (b) Pc/Pb = 33.8, (c) Pc/Pb = 40.5, and (d) Pc/Pb = 47.2................ 133 6.15 Series of images depicting chamber pressure ramp up for dual nozzle strut: (a) Pc/Pb = 16.8, (b) Pc/Pb = 20.4, (c) Pc/Pb = 24.0, and (d) Pc/Pb = 30.6. ....................... 134 6.16. Plot of top wall pressure distribution with shadowgraph image (dual nozzle strut Pc/Pb = 30.6). ...................................................................................................... 135 6.17 One-dimensional model for axisymmetric ejector of equivalent geometry to single nozzle strut PRC ejector...................................................................................... 137 6.18 Comparison of theoretical symmetric ejector model with experimental data for non axisymmetric single nozzle ejector..................................................................... 138 6.19 Comparison of Fabri models with dual nozzle strut data. ..................................... 139 6.20 Theoretical bypass ratio for axisymmetric ejectors with geometry ratios equivalent to those in the single and dual nozzle PRC ejectors. .......................................... 141 6.21 Ejector strut gap sidewall pressure ratio (Pc/Pb = 40.4)......................................... 142 6.22 Ejector strut gap sidewall pressure ratio (Pc/Pb = 53.7) [44]. ................................ 143 6.23 3-D strut rocket nozzle exit Mach contours............................................................ 144 6.24 3-D strut rocket nozzle exit pressure contours........................................................ 144 6.25 Sidewall pressures in ejector mixing duct (Pc/Pb = 40.4). ..................................... 145 6.26 Sidewall pressures in ejector mixing duct (Pc/Pb = 53.7). ..................................... 145 6.27 3-D Pressure profiles at centerline of top-wall (Pc/Pb = 40.4)............................... 147
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LIST OF TABLES
Table
Page
3.1
Ejector Test Matrix............................................................................................... 56
A.1
Systematic uncertainty constants for instrumentation........................................ 163
D.1
Test averages for single nozzle strut................................................................... 216
D.2
Test averages for dual nozzle strut...................................................................... 220
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LIST OF SYMBOLS
a
speed of sound
a*
characteristic speed of sound
Aduct
mixing duct cross sectional area
Athroat
cross sectional area of the primary nozzle
B
systematic uncertainty
D
mixing duct diameter (Fabri’s model)
Dh
ejector rocket nozzle exit hydraulic diameter
f
skin friction factor
L
mixing duct length (Fabri’s model)
M
Mach number
M*
characteristic Mach number
m
mass flow
P
static pressure
Po
stagnation pressure
Rair
gas constant for air
S
sample standard deviation
S
standard deviation of the mean
T
temperature
To
stagnation temperature
U
total uncertainty
U
total uncertainty of the mean
w
width of ejector mixing duct
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Greek δ*
boundary layer displacement thickness
γ
ratio of specific heats
λ
ratio of the mixing duct area to the primary nozzle exit area (Fabri’s model)
λ*
ratio of the throat area to the primary nozzle exit area (Fabri’s model)
λ’
ratio of the duct area at the secondary flow inlet to the primary nozzle exit area. (Fabri’s model)
μ
ratio of secondary flow stagnation pressure to the back pressure
ν
ratio of the primary jet plume width at maximum expansion to the primary nozzle exit area. (Fabri’s model)
ρ
density
σ
ratio of the diffuser exit area to the mixing duct exit area
ω
bypass ratio
ξ
ratio of the lateral surface area to that of the transverse area (Fabri’s model)
Subscripts 1
primary flow conditions
2
secondary flow conditions
3
mixed flow conditions
b
exit flow conditions
c
chamber conditions
p
primary flow conditions
s
secondary flow conditions
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CHAPTER 1
INTRODUCTION
1.1
Introduction In the past several decades, the pursuit of a fully reusable launch vehicle has
driven interest in using airbreathing ejectors to provide thrust enhancement to traditional rocket propulsion devices.
Fundamentally, an ejector is a device which exchanges
momentum between a high velocity primary fluid stream and a low velocity secondary fluid stream. The momentum exchange occurs as a result of the viscous interaction between the two streams. As momentum is exchanged, the two streams mix until a single uniform mixture exists. The mixed stream will have a greater momentum than the initial primary stream and a higher pressure than the induced secondary fluid. Although the principles behind ejector operation are relatively simple, the fluid mechanics in even a simple ejector are not well understood.
1.2
Ejector Propulsion Applications Ejector-rocket devices have been studied in various forms over the past five
decades [1]. Concepts such as ducted rockets, ram-rocket, air-augment rockets, and rocket ejector nozzle engines, ejector ramjets, ejector scramjets and rocket based
1
2 combined cycle engines utilize the ejector effect. The augmented thrust comes from the entrainment of secondary flow from the atmosphere which can either add momentum to a primary flow exhaust or be combusted with a fuel to increase the total energy of the exhaust gases. By increasing the thrust without additional onboard propellant, a higher overall specific impulse for the vehicle is achieved. Although the devices mentioned have different performance considerations, they all operate under the same principles, a secondary air flow entrained by a primary flow stream. The simplest of these devices is the ducted rocket and the most complex is the rocket based combined cycle engine. The complexity comes from incorporation of many modes of operation, but the ejector physics in all of these systems is essentially the same.
1.2.1
Ducted Rockets Figure 1.1 shows a schematic of a ducted rocket. Here the rocket engine is
exhausted into a mixing duct with an open inlet and an open exit.
Air from the
surrounding atmosphere is ingested through the ejector action, mixes with the rocket exhaust, and can be used in a downstream combustion process. By utilizing the oxygen in the ingested air, the total onboard oxidizer required for the engine is reduced. In most ducted rocket concepts either the primary rocket is fuel rich or additional fuel is injected into the mixed flow stream for downstream combustion. Even without the downstream combustion, ducted rockets can offer a thrust increase over conventional rockets at low flight speeds.
In addition to increasing thrust, the ingested air for combustion can
significantly improve the specific impulse of the vehicle. At low Mach numbers, the specific impulse increase can be in the range of 10 to 20% even without combustion [2].
3 With the addition of combustion, the specific impulse can be augmented in the range of 200% [2]. Since the flow path for the engine is relatively simple, the thrust augmentation comes at a low design cost.
Fuel Injection
Primary Rocket
Air
Mixer
Combustor
Nozzle
Figure 1.1 Schematic of a ducted rocket [2].
1.2.2
Rocket Based Combined Cycle Engines Many organizations have studied reusable launch vehicles that use a Rocket
Based Combined Cycle, RBCC, engine as an alternative to carrying all the oxidizer onboard [3-6]. Generally an RBCC vehicle incorporates four modes of engine operation into a single duct or flow path. Figure 1.2 shows a diagram of the Aerojet StrutJet RBCC engine concept [3].
The ejector rocket mode is used for take off and the initial
acceleration to around Mach 2. As the vehicle passes Mach 2, the ejector rockets are no longer used, and the engine transitions to the ramjet operation mode. As the vehicle velocity passes approximately Mach 5, the engine transitions to scramjet operation. This mode is used until the vehicle ascends to the upper atmosphere where air breathing
4 engine operation is no longer viable. The engine transitions to a pure rocket mode to accelerate into space.
Figure 1.2 Schematic of the Aerojet StrutJet Concept [3].
By using four different modes of operation, the vehicle can operate in the mode which provides the highest specific impulse (ISP) for that flight regime. By utilizing atmospheric air as an oxidizer in the first three airbreathing modes, the propellant weight is significantly reduced. In theory, an RBCC vehicle can achieve overall mission ISP values which are significantly higher than those of a conventional pure rocket launch vehicle [3]. Figure 1.3 shows the potential ISP improvement of the operating modes of an RBCC vehicle over that of a chemical rocket propulsion system. The concept of an RBCC engine is relatively straightforward; however, development of such an engine is a complex task. The desired engine geometry for each
5 operational mode differs, so the transition from one mode to the next would also involve physical changes to as duct area, fuel injection location, and ignition location. The physical changes would also be accompanied by operational changes in the engine fuel and oxidizer flow rates, cooling flow rates, etc. Although there are many enabling technologies which must be developed to build and test an RBCC engine, the potential benefits of such an engine make it an attractive alternative to traditional propulsion methods.
7000 TURBOJETS
HYDROGEN FUEL
6000
5000 SPECIFIC IMPULSE (SECONDS)
RAMJETS
4000
3000
SCRAMJETS
Ducted Rockets
2000
ACCERERATION MODES (MANY CANDIDATES)
1000
0
2
4
6
8
ROCKETS
10
12
14
16
MACH NUMBER
Figure 1.3 Specific impulse for RBCC operating modes [3].
1.3
Principles of Ejector Operation As stated previously, an ejector is a momentum exchange device which is
designed to transfer momentum from a driven primary flow to an ingested secondary
6 fluid. The interaction along the boundary between the two jets transfers momentum from the primary jet to the secondary fluid by means of viscous effects and pressure interaction. The result of this interaction is a loss of momentum in the primary jet, lowering the jet velocity and pressure, and an increase of momentum to the ingested secondary fluid, increasing the secondary flow velocity and pressure. These two initially separate flow streams mix as the momentum is transferred and result in a fully mixed stream with a momentum that is higher than the momentum of the initial driven primary flow.
If the primary flow stream is supersonic, then the configuration is deemed a
supersonic ejector. A sketch of a typical axisymmetric supersonic ejector is shown in Figure 1.4. The primary stream is typically accelerated through a nozzle and exhausted into an openended duct. Upon leaving the nozzle, the primary stream is either turned inward through shock compression, exhausts parallel to the wall, or is turned outward through a free expansion. These modes are denoted as over expanded, ideally expanded, or under
Minimum Geometric Area (Aerodynamic Choke Location)
Mixing Duct
Secondary Flow Mixed Flow Primary Flow
Ejector Nozzle
Mass Addition Choke Location
Primary Jet Boundary
Figure 1.4 Axisymmetric ejector diagram.
Ejector Exit
7 expanded and refer to the exit pressure of the nozzle relative to the surrounding pressure. After the primary flow leaves the nozzle, viscous effects across the boundary between the primary flow and the secondary fluid cause the surrounding pressure to drop as the secondary fluid is “dragged” by the primary flow. This pressure reaches some minimum value once the steady state operation has been reached. The resultant lower pressure in the duct aids in the developing and maintaining the flow of the secondary fluid. The boundary between two flow streams of different velocities, as in the case of the secondary and primary flow streams in an ejector, is known as a free jet boundary. A continuous static pressure is maintained across this boundary. Between the two streams, a shear layer is established from the point where the two flows first contact. This layer becomes thicker as it progresses downstream. The shear layer acts to accelerate the secondary flow and impede the primary flow as shown in Figure 1.5. In addition to the velocity changes across this shear layer, mixing between the primary and secondary streams occurs across this layer.
Initial Stream Profiles
Subsequent Stream Profiles
US
US Shear Layer Boundary Dividing Streamline Shear Layer Boundary UP
UP
Figure 1.5 Depiction of shear layer between a high speed primary jet and a low speed secondary flow.
8 1.4
Ejector Flow Regimes In some of the earliest comprehensive studies of ejectors, Fabri established two
main regimes of ejector operation, the mixed regime and the supersonic regime [7, 8]. Although there are other subsets of these regimes, this classification has been used as a standard throughout ejector literature. These regimes are categorized by whether or not the secondary flow reaches a choke before significant mixing with the primary flow has occurred. For a given geometry and a fixed secondary flow stagnation pressure, the ejector operating regime is dependant primarily on the ratio of the stagnation pressure of the primary flow to the back pressure at the exit of the ejector (Pop/Pb). For low values of Pop/Pb the ejector operates in the mixed regime. The secondary flow remains subsonic throughout the ejector until it mixes with the primary stream. At these operating conditions the primary flow is typically over expanded and the flow is turned inward (towards the centerline of the ejector) through a series of shocks at the exit of the primary nozzle. In this regime, changes to Pop/Pb affect the amount of secondary mass flow ingested through the duct. As the pressure ratio decreases, the secondary mass flow will decrease until the limiting case of zero entrained mass flow is reached. Mixing between the primary and secondary streams begins immediately upon entering the mixing duct. The secondary flow pressure will be at a minimum value where the two flows converge and then begin to recover (increase) as the flow proceeds down the mixing duct. If the pressure at the nozzle exit reaches a critical pressure, the primary flow may separate from the nozzle wall. If separation occurs, the performance of the ejector is significantly reduced. This condition represents a special case of the mixed operating
9 regime. For most supersonic ejector propulsion applications, this critical pressure is lower than typical operating conditions. At high Pop/Pb values the ejector operates in the supersonic regime and the secondary flow chokes prior to mixing with the primary flow. The limiting case for this flow regime is the saturated supersonic regime where the secondary flow chokes at the minimum geometric area through which it flows. This type of choking mechanism is known as a traditional aerodynamic choke. In an ejector, this minimum area is typically the area of the duct between the primary nozzle and the duct wall (upstream of the mixing duct) as shown in Figure 1.4. The saturated supersonic regime can occur for pressure ratios at which the primary flow is either over expanded or ideally expanded. When the ejector is operating in this flow regime, the maximum amount of secondary mass flow that can be induced by the primary flow stream is entrained. Mixing between the two flow streams begins at the entrance to the mixing duct and there is an almost immediate pressure recovery. At Pop/Pb values above saturated supersonic flow regime values, the ejector enters the pure supersonic regime.
In this regime the secondary flow choke point moves
downstream from the minimum geometric area to the point of maximum expansion of the primary flow stream. This location is identified as the mass addition choke location in Figure 1.4. The primary flow plume acts as a physical restriction to the secondary flow and creates a minimum area smaller than the minimum geometric area in the strut gap region. This type of choke is known as a mass addition or Fabri choke. Between the primary nozzle exit plane and the mass addition choke point, the mixing between the two flow streams is minimal. The mass flow in the minimum
10 geometric area will be slightly less than that for the saturated supersonic regime flow conditions. Once the flow enters the supersonic regime, the secondary mass flow cannot be increased by changes to Pop/Pb [7, 8]. However, the secondary mass flow can be reduced if the primary flow stream stagnation pressure is increased or if the back pressure is reduced. Such variation would result in a greater expansion of the primary plume and thus a smaller minimum area for the mass addition choke. Downstream of the mass addition choke, the two flow streams mix and begin the recompression and pressure recovery process. Once the supersonic regime is reached, pressure ratio increases (which increases in the energy of the primary flow) serve to pump the mixed flow to a higher pressure rather than increase the entrained mass flow [9].
1.5
Ejector Performance Characterization In most ejector applications the performance is characterized by the secondary
mass flow entrainment per mass flow of primary fluid (the bypass ratio) and the pressure increase of the secondary fluid through the ejector (the compression ratio). Figure 1.6 shows a plot of the mass flow rates of the primary ( m 1 ) and secondary fluids ( m 2 ) and the bypass ratio plotted against the ratio of the stagnation pressures of the primary fluid (Pop) to that of the secondary fluid (Pos). The figure is from a constant area supersonic ejector study conducted by Bartosiewicz [10].
In the study, the primary chamber
pressure was varied while the secondary flow stagnation pressure remained constant. The bypass ratio and mass flows were measured over a range of ejector operational modes. Because the nozzle geometry is fixed, the primary mass flow for this ejector is
11 m2 /m1
m2, m1
Peak Bypass Ratio
0.016
24 0.011 19 14
0.006 Secondary Flow Choke
9 0.001
m1/m2 m 2 /m1 m1 m1
4
m m22
-1 3
5
7
9
11
Mass Flow (kg/s)
Bypass Ratio (m2/m1 (%))
29
-0.004 13
Stagnation Pressure Ratio (Pop /Pos)
Figure 1.6 Mass Flow and Bypass ratio for a supersonic ejector [10].
proportional to the primary chamber pressure, and increases linearly as Pop/Pos increases. The secondary mass flow (initially negative indicating zero induced mass flow) increases until it chokes. Once this choke point is reached, the ejector is in the supersonic regime. The bypass ratio, initially at zero (the limiting case for the mixed flow regime), increases to a peak value as the primary mass flow is increased. The bypass ratio then drops as the primary mass flow is increased. As can be seen in the figure, this choke represents the maximum amount of secondary flow which can be induced for a given set of operating conditions and further increases in the primary mass flow rate do not increase the secondary mass flow rate. For this data the choke pressure ratio is the same as the peak
12 bypass ratio. However, this is not the case for all supersonic ejectors and is dependent on the geometry of the ejector. Once the secondary mass flow chokes, the bypass ratio becomes inversely proportional to the primary mass flow (and hence the primary total pressure). For most ejector applications, maximizing the bypass ratio is desirable as this condition represents a high level of efficiency in the momentum exchange between the two fluids. Additionally if the peak bypass ratio occurs near the choke point for the secondary flow, as shown in Figure 1.6, then the ejector is operating not only at a maximum efficiency from a momentum exchange standpoint, but it is also inducing the maximum amount of secondary mass flow. However, the peak bypass ratio generally occurs at low pressure ratios. To achieve the necessary thrust for many propulsion applications, a higher primary chamber pressure must be used and the bypass ratio that is available for the operating chamber pressure can offer some enhancement to the engine performance.
1.6
Ejector Design Considerations Performance of an ejector is dependant on a number of thermodynamic and
geometric factors.
Figure 1.1 depicted an axisymmetric ejector, which is the most
commonly used in experimental studies because its simple geometry can be analytically modeled. The flow through an axisymmetric cross section is quasi-one-dimensional in nature with approximately uniform flow properties that vary only in the axial direction. Non-axisymmetric geometry introduces significant complexities to the flow field. In either the axisymmetric or non-axisymmetric case, the areas of the primary flow nozzle
13 exit, the secondary flow minimum geometric area, and the duct exit area influence the regime of ejector operation and hence influence the entrainment and the compression ratio. The primary nozzle area ratio influences the mass flow rate and the exit Mach number and pressure of the primary flow thus influencing the entrainment and the compression ratio for the ejector. The length of the mixing duct affects the flow mixing as well as the recompression process for the mixed flow.
In a propulsion application, this length is
important especially if the mixture is then to be combusted to provide additional thrust. The duct must be long enough for complete mixing, but not too long so that additional losses will drain energy from the mixed flow. The mixing duct is also where the pressure recovery must occur if there is no diffuser. A longer duct will allow for better pressure recovery and more complete mixing, but can also result in increased system frictional losses reducing the compression ratio and the momentum of the exit stream. This duct mixing length will have an impact on the overall vehicle design and thus an efficient mixing process will result in a shorter flow path and reduced overall vehicle size and weight. Thermodynamic properties of the gas influence the behavior of the ejector as well. The pressures at the exit of the duct as well as the stagnation pressures of the primary and secondary flow influence the ejector operation regime. The bypass ratio is strongly influenced by the pressures as well as the composition of the gasses (molecular weight) in the ejector and the stagnation temperatures of the flows. One of the difficulties with using ejectors in a propulsive application is that the geometry which simplifies analysis is not always the most practical for the overall launch
14 vehicle design. Many of the rocket based combined cycle vehicle concepts that use ejectors utilize non-axisymmetric geometries [3, 4, 11]. These geometries make for a simpler design from a packaging stand point. At best these geometries can be simplified to two-dimensional analysis, but more often a full three-dimensional analysis of the complex flow is required. In addition, there can be irreversibilities (shock structures, separation, viscous dissipation) in the flow, combustion effects, heat transfer effects, and turbulence effects which can be enhanced by the three-dimensional characteristics.
1.7
Ejector Analysis Techniques A number of analytical approaches have been taken to model propulsion ejector
operation. Models vary in complexity from a very simple balance of the governing equations for axisymmetric geometry and inviscid flow, to very complex computational fluid mechanics analysis for specific three-dimensional ejector configurations with downstream combustion. In general most of the simple analytical models rely on satisfying the three governing equations of continuity, momentum and energy. The model is generally closed by assuming symmetry, ideal gases, isentropic flow, and a viscous mixing model as needed. One of the complications in dealing with modeling an ejector is that depending on the operating regime (mixed or supersonic), the assumptions used to close the model differ slightly.
Almost all of the models rely on either
simultaneous solution of the governing equations or on an iterative solution. Several papers have been published with methods for determining operation of simple axisymmetric ejectors [7, 9, 10, 12-15].
Many of these models have shown good
agreement with experimental data for axisymmetric geometries. The most significant
15 problems with these models in terms of propulsive applications is their reliance on the one-dimensional forms of the governing equations and not adequately capturing the viscous effects in the duct. As the geometry of the flow becomes more complex, these models break down. A detailed discussion of classical one-dimensional modeling of ejectors is provided in Chapter 2. As an alternative to one-dimensional analytical modeling, computational fluid dynamics (CFD) simulation is becoming a viable alternative to experimental variation of ejector geometries. Several published works have focused on CFD analysis of ejector operation [10, 16-22]. These CFD models have typically focused on the one- or twodimensional ejector systems. While these simulations have provided some insight into flow behavior, there is a need to extend CFD models to three-dimensional ejectors to capture more complex flow phenomena. For this approach to be successful, meaningful experimental data from complex three-dimensional geometries must be readily available to validate the computer models.
1.8
Motivation Although ejector phenomena have been studied extensively from both an
experimental and analytical standpoint, the fundamental fluid mechanics of even simple ejector systems are not well understood. The interactions between the flow streams in an ejector occur at very high velocities and in turbulent regimes. The primary jet can undergo a complex shock train which recompresses the fluid, and the secondary flow can either be subsonic or supersonic. If sonic, the secondary flow choking mechanism may
16 either be geometric due to a minimum physical area or a mass addition choke due to the interaction with the primary jet. Ejector operation is dependent on several different parameters such as the composition of the fluids, the geometry of the nozzle and the mixing duct, operating pressures of the fluids, and the diffuser duct characteristics. Most experimental studies focus on only a few different variations of these parameters. Most of the analytical work performed on ejectors relies on either relatively simple one-dimensional models or on a full computational fluid dynamics approach. The simple one-dimensional approach can provide reasonable results for axisymmetric cases, but when the geometry is threedimensional, this model does not predict three-dimensional ejector performance characteristics well. CFD approaches can produce relatively good global results but do not reproduce the detailed fluid phenomena because of a lack of detailed experimental data for comparison.
To improve the modeling, a more extensive database of
experimental data is required. This dissertation presents an experimental investigation of a three-dimensional, non-axisymmetric, supersonic ejector, representative of what could be used in a rocket based combined cycle propulsion system. The experiment was carried out over multiple operating regimes and for two different non-axisymmetric nozzle configurations.
The
ejector was operated over a wide range of primary flow stagnation pressures. A rigorous analysis was performed to assess the experimental uncertainty associated with the measurements. The experimental results were then evaluated to determine the operating regimes, the choking mechanisms, the mass flow entrainment, and the mixing characteristics for the two system configurations.
17 Two analysis techniques were evaluated for application to the more complex three-dimensional geometry of this study. The theoretical results were compared to the experimental results to determine additional considerations that would improve the model. The experimental results were also compared with some simple two-dimensional CFD simulations performed in a parallel study to evaluate CFD turbulence modeling techniques for use in these complex flow systems. Finally, the experimental effort provides a benchmark of experimental data with uncertainty that can be used to further evaluate detailed three-dimensional CFD codes for use in ejector systems.
CHAPTER 2
BACKGROUND
2.1
UAH Propulsion Research Center The Propulsion Research Center (PRC) at the University of Alabama in
Huntsville has an ongoing research project dedicated to studying the fluid mechanics in ejector systems. The facility was developed in 1996 as part of a cooperative research effort with NASA and Aerojet. The ejector configuration was based on the AeroJet StrutJet concept [3].
The StrutJet utilized a non-axisymmetric design based on a
rectangular engine mounted underneath the vehicle body. The PRC test rig consisted of a 1/6th scale strut model mounted in a rectangular duct 4.0 inches tall by 3.5 inches wide. Figure 2.1 shows a sketch of the PRC test rig. In one of the first sets of experiments in the PRC cold flow facility, the mixing between a flow stream from a turbine exhaust slit and the primary flow streams from the main rocket nozzles in a dual nozzle strut was examined [23]. The ratio of the chamber pressure to the stagnation pressure of the turbine exhaust was varied for the experiments. The turbine exhaust slot was operated at a stagnation pressure of 275 psi for all tests and the pressure ratio was operated at set point ratios of 1, 1.5, and 2. The primary flow was
18
19
Figure 2.1 Sketch of PRC ejector facility.
also heated up to a temperature of 750 ºR so that the convective Mach number between the turbine exhaust and the rocket nozzles would match full scale conditions. The flow from the turbine exhaust slot was seeded with acetone and a Planar Laser Induced Fluorescence (PLIF) diagnostic method was used to observe mixing between the gases. Figure 2.2 shows images taken at various distances from the exit plane. The study showed that the mixing zone reached from the exit plane of the strut to a distance of about 20.45 hydraulic diameters (of the rocket nozzle exit) downstream. As the pressure ratio increased, the mixing between the streams was delayed but the overall mixing length did not vary significantly. Thus at higher chamber pressures, the mixing occurred slowly at first but became more rapid as the flow moved downstream. This study
20 provided a qualitative view of the mixing between streams in the duct, but little
Pressure Ratio (Pc /Poturbine)
quantitative information on the detailed flow field was recorded.
2.0
1.5
1.0 0.00 0.57
1.14 1.70 2.27
7.95
11.65
20.45
Distance from Exit Plane (L/Dh)
Figure 2.2 PLIF images of the mixing between the turbine exhaust and the two rocket plumes from the dual nozzle strut [23].
Additional studies with the ejector facility investigated pressure traces across the duct at various downstream locations to provide more insight into the pressure field [24]. Stagnation pressure traces were taken in the strut gap region at locations 3.88 in. (9.84 cm) and 3.0 in. (7.62 cm) upstream of the nozzle exit plane, at the nozzle exit plane, and 4.25 in. (10.8 cm) downstream of the nozzle exit plane in the mixing duct. Three probes were used in the pressure traces. Each probe was connected to a 300 psi
21 (2.07 MPa) pressure transducer and their vertical positions relative to the strut nozzles are shown in Figure 2.3.
Rocket Nozzle Turbine Nozzle Probe 1 Probe 2
2,58 in 2,0 in Probe 3
0.5 in
Figure 2.3 Probe locations for pressure traces in the PRC ejector [24].
For all tests the back pressure was equal to atmospheric pressure (approximately 14.7 psi 0.1 MPa). By varying the chamber pressure in the strut rockets, the ratio of the rocket chamber pressure to the back pressure was varied. Tests were conducted at pressure ratios of 13.6, 18.7, 24.9 and 37.4. The data showed the total pressure is very uniform across the center of the region but that there is a slight drop off of total pressure as the probes approached the side wall. Due to the geometry of the probes, the traces could only be moved within about 0.25 inches (6.35 cm) of the side wall, but were able to move very close to the strut. No uncertainty estimates were given for this data and the resolution of the pressure transducer was too low for the data recorded. However, these
22 plots indicate a boundary layer developing along the side wall of the duct. Although the data from these plots could not be used to reliably estimate the boundary layer thickness, they did indicate that the boundary layer thickness is significant and must be considered when determining the mass flow through this region. Pressure traces in the mixing duct showed the spreading of the primary jet plume and indicated the presence of a core flow at 4.25 inches downstream of the duct. Smith [25] upgraded the data acquisition capability of the PRC facility and performed a comprehensive study of the single nozzle strut. For this series of tests, the ratio of the chamber pressure to the back pressure was varied from 6.8 to 44.2. The duct was instrumented with pressure taps along the centerline of the top and side walls of the mixing duct to measure the wall pressure distributions. This study focused on the fluid mechanics of the ejector system specifically examining the choking mechanism, mass flow entrainment, and the mixing duct pressure distributions. A secondary mass choke was identified to occur at a pressure ratio (Pc/Pb) of 34, and Smith concluded that the choke persisted for pressure ratios between 34 and 40.8. He stated that the choke transitioned to an aerodynamic choke at a pressure ratio of 44.2. The bypass ratio was found to be highest at the lowest chamber pressure and decreased sharply with increasing chamber pressure until the choke point was reached. Once the secondary flow choked, the bypass ratio was inversely proportional to the chamber pressure.
The pressure
distribution indicated complex flow patterns in the first 10 inches (25.4 cm) of the mixing duct and it was concluded that the flow became fully mixed within a distance of 15 in. (38.1 cm) of the primary nozzle exit plane. Smith concluded that the asymmetric effects led to enhanced mixing effects.
23 2.2
Classical Ejector Research Many of the early works on ejectors focused on modeling axisymmetric ejector
systems using simple analytical approaches. As noted in Chapter 1 these approaches generally rely on balancing continuity, momentum, and energy equations, coupled with a wall friction and or a mixing model. Steady quasi-one-dimensional flow is generally assumed to simplify the governing equations. This type of analysis has generally showed very good agreement for global parameters such as the bypass ratio for axisymmetric ejectors.
2.2.1
Fabri’s Ejector Model One of the early works published on supersonic ejectors was by Fabri and
Siestrunk [8]. A simple one-dimensional axisymmetric ejector model was presented and the predicted results were compared with experimental data. Fabri outlined four flow patterns or regimes of operation for a supersonic ejector: mixed with separation, mixed, saturated supersonic, and supersonic. Each of these regimes was modeled separately depending on the significant flow features. Ejector performance was characterized by the bypass ratio, ω, and the ratio of the secondary flow stagnation pressure to the back pressure, μ.
Fabri listed the following major geometric influences on ejector
performance: mixing tube length, diffuser design, cross-sectional areas of the mixing duct, nozzle throat, nozzle exit, and the secondary flow mixing duct inlet area, and the geometric shape of primary nozzle.
In addition to these parameters, the ejector is
influenced by the thermodynamic state of the primary and secondary fluids, and the back
24 pressure on the ejector. Fabri’s model was able to accurately predict the effect that varying these parameters had on performance. Figure 2.4 shows a schematic of an ejector with Fabri’s geometric notation. The primary and secondary flows are represented by a prime (′) or a double prime (″) respectively. The area of the primary jet is taken as a unit area, S, and all other areas are referenced relative to this area. The dimensions given in Figure 2.4 are the ratios of the local area to the primary jet area. Thus the total area of the mixing duct is λS. In his analytical models, Fabri assumed quasi-one-dimensional flow, an axisymmetric primary nozzle with uniform supersonic flow at the exit, a cylindrical constant area mixing duct, a secondary flow entrance which establishes the minimum geometric area at the entrance to the mixing duct, uniform secondary flow at the entrance to the mixing duct, the primary and secondary fluids have the same composition (air), both streams act as perfect gases,
Secondary Flow Choke Location Supersonic Regime Secondary Flow
Primary Flow
λ’-υ
λ’-1
υ
1
λ/λ*
1
Nozzle Base Area
λ
e Jet Boundary
Figure 2.4 Sketch of an axisymmetric ejector with Fabri’s notation.
25 and both flows have the same stagnation temperatures. For individual models of the separate flow regimes, additional assumptions were added.
2.2.2
Supersonic Regime In the supersonic regime, the secondary flow achieves a choke in the mixing duct
at the location of maximum expansion of the primary flow, location e in Figure 2.4. Fabri modeled the primary and secondary flow as separate streams and neglected interaction between them until the point where the secondary flow chokes (location e). When the ejector is operating in this regime, the back pressure has no effect on the bypass ratio because the choked condition defines the mass flow for each stream. Each stream was modeled as one-dimensional isentropic flow between the inlet to the mixing duct, location 1, and the point where the secondary flow chokes, location e. Fabri’s model produced results which were very close to experimental data with one exception, as he noted, this model does not enforce equal pressure across the jet boundary. A second limitation to this model is that the effects of the base of the primary nozzle are not included except as a reduced area for the secondary flow. However, this did not cause significant deviation from the experimental data for Fabri’s experiment because the base area of the primary nozzle was small relative to the other inlet areas and to the mixing tube area. Fabri’s model for the supersonic regime consisted of five equations. The first two equations were mass balance equations for each of the two flow streams. When recast in terms of the characteristic Mach number (M*), these equations become
26
ν=
(M ) (M ) * p,e
( (
⎛m - M ⎜ 2 ⎜ m2 - M * p,e ⎝
2 * p,1
2
) )
⎞ ⎟ 2 ⎟ ⎠
2 * p,1
1 γ-1
,
(2.1)
and
( (
) )
( (
⎛ m2 - M * s,1 ⎜ 2 ⎜ m2 - M * s,e ⎝
* 2 s,1
M λ′ - ν = λ′ - 1 M *s,e
) )
1
⎞ γ-1 ⎟ . 2 ⎟ ⎠
2
(2.2)
Here the variable m is given by
m=
γ +1 , γ -1
(2.3)
where γ is the ratio of specific heats for the gas. Since both flows are assumed to be isentropic between the mixing duct inlet and the choke location, the pressures at these two points can be related using isentropic flow equations. In terms of the characteristic Mach number, these equations become
( (
) )
( (
) )
2 * Pp,e ⎛⎜ m - M p,e = Pp,1 ⎜ m 2 - M * p,1 ⎝
2 2
γ
⎞ γ-1 ⎟ , ⎟ ⎠
(2.4)
and * ⎛ 2 Ps,e ⎜ m - M s,e = Ps,1 ⎜ m 2 - M * s,1 ⎝
2 2
γ
⎞ γ-1 ⎟ . ⎟ ⎠
(2.5)
The fifth equation required for Fabri’s supersonic regime model is a momentum balance between the inlet section and the downstream choke point. For steady, inviscid flow with negligible body forces the momentum equation becomes
27
Pp,1
( ) + ( λ′ - 1) P 1+ ( M ) = - (M ) m - (M ) 1+ ( M ) νP + ( λ′ - ν ) P m -(M )
1+ M *p,1 m2
2
* 2 s,1
s,1
2 * p,1
* 2 s,1
2
2 * p,e
p,e
2
s,e
2
* p,e
( ) - (M )
1+ M m2
* 2 s,e
.
(2.6)
* 2 s,e
If the secondary flow at location e is assumed to be sonic, the local characteristic Mach number will be equal to one. With known conditions for the primary flow at the inlet, and a known geometry, Equations (2.1) through (2.6) represent 5 equations with 6 unknown quantities (ν, M *p,e , M *s,e , Ps,1 , Pp,e , Ps,e ). Thus, for every value of Ps,1 the remaining unknown variables can be determined by simultaneously solving these equations. Once the pressures and Mach numbers are known, the bypass ratio, ω, and the ratio of the secondary flow stagnation pressure to the back pressure, μ, can be determined according to
Po M v = ( λ′ - 1 ) s Po p M
* s,1 * p,1
( (
⎛ m2 - M * s,1 ⎜ ⎜ m2 - M * p,1 ⎝
) )
1
1
⎞ γ-1 To 2 ⎟ ⎛ p⎞ , 2 ⎟ ⎜⎝ Tos ⎟⎠ ⎠
2
(2.7)
and ⎛ Ps,1 ⎜ m2 μ= Pb ⎜ m 2 - M * s,1 ⎝
(
1
)
⎞ γ-1 ⎟ . 2 ⎟ ⎠
(2.8)
Here the stagnation pressure for either the secondary or primary flow is related to the static pressure according to γ
Po ⎛ m 2 ⎞ γ-1 =⎜ ⎟ . P ⎝ m 2 - M *2 ⎠
(2.9)
28 2.2.3
Saturated Supersonic Flow In the saturated supersonic flow regime, the secondary flow chokes in the
minimum geometric area of the duct between the primary nozzle and the duct walls at Section 1. The bypass ratio is strictly a function of the stagnation conditions of the flow. The back pressure has no influence on the bypass ratio if the ejector is operating in this regime. The secondary induced flow is independent of the primary mass flow rate. The performance of the ejector is thus strictly a function of the stagnation pressures and stagnation temperatures of the two flow streams, the primary flow Mach number at the nozzle exit, and the geometry of the duct. The bypass ratio in this regime is given by
P μ = v ( λ′ - 1 ) b Po p
(
⎛ 1 ⎜ m2 - 1 2 M *p,1 ⎜⎝ m 2 - M *p,1
)
(
1
)
1
⎞ γ-1 To 2 ⎟ ⎛ p⎞ . 2 ⎟ ⎜⎝ Tos ⎟⎠ ⎠
(2.10)
For given nozzle conditions (Pop, Mp), the primary mass flow can be calculated through isentropic equations and the secondary mass flow can be calculated from Equation (2.7). The remaining flow properties can be determined assuming isentropic flow with a given mass flow and area.
2.2.4
Mixed Flow In the mixed flow regime, the secondary flow remains subsonic throughout the
ejector. Unlike the supersonic regime, the entrained mass flow and thus the bypass ratio are dependent on the back pressure. Figure 2.5 shows a sketch of the ejector for the analysis of flow in this regime. The two flow streams begin mixing at the entrance to the mixing duct (Location 1). Since the back pressure influences the performance of the
29 ejector, the property changes through the diffuser, a mixing model, and a model for frictional losses in the duct must also be included
λ’-1 Secondary Flow Primary Flow
Mixing Duct
λ/λ*
Diffuser
λ
1
1
2
λσ
3
Figure 2.5 Sketch of an axisymmetric ejector with Fabri’s notation for mixed regime analysis.
The analysis of the flow in the mixed regime relies on some method of estimating the effects of the viscous interaction between the walls of the duct and the flow stream. Fabri modeled the associated pressure drop using
(a ) (M ) f×ρ * 2
δP = ∫
* 2
2
dξ ,
(2.11)
where f is the coefficient of friction, M* represents a mean value of the characteristic Mach number at any intermediate section, and ξ is the ratio of the area of the lateral surfaces to that of the transverse section. This ratio is given by
ξ=
4L , D
where L is the length of the mixing duct and D is the diameter of the mixing duct.
(2.12)
30 At the entrance to the diffuser, Location 2 in Figure 2.5, the two flow streams are completely mixed. Since the mixed flow is subsonic, the pressure at this point must be greater than or equal to the back pressure at the exit of the duct (Section 3). Thus, the back pressure limits the amount of secondary mass flow that can be entrained. Fabri’s mixed flow model consisted of five equations. The flow was broken into two sections, the mixing duct section and the diffuser section. The governing equations for the mixing duct are
Pp,1
(
M *p,1
a*p m 2 - M *p,12
Pp,1
)
+ ( λ′ - 1) Ps,1
a*p M *p,1 m 2 - M *p,1
(
* M s,1
* 2 a*s m 2 - M s,1
+ ( λ′ - 1) Ps,1 2
)
= λP2
a*m
(
M 2* , m 2 - M 2* 2
)
* * a*s M s,1 a*m M m,2 , = λP 2 * 2 m 2 - M *s,12 m 2 - M m,2
(2.13)
(2.14)
and
(
(
Pp,1 1+ M *p,1
(
m 2 - M *p,1
)
) 2
2
)+P
( ) ( )
2 ⎡ ⎤ 1+ M *s,1 λ - λ′ ⎥ ⎢ ( λ′ - 1 ) + 2 = s,1 2 2 * ⎢ m ⎥ m M p,1 ⎣ ⎦
⎛ fξ m 2 +1 ⎞ * 1+ ⎜ 1+ ⎟ M2 2 m2 ⎠ ⎝ λP2 2 m 2 - M 2*
( )
2
.
(2.15)
( )
The pressure and Mach number at the exit of the mixing duct (Region 2) are related to the pressure and Mach number at the end of the diffuser (Region 3) by
σ=
( P M (m 3
and
( )) , - (M ) )
P2 M 2* m 2 - M 2* * 3
2
2
* 2 3
(2.16)
31
(m
2
)( ) - (M )
+1 M *
m2
* 2
2
(
( ) ( )
2
m 2 1- M * f ⋅ dξ dσ = 2 2 σ m2 - M *
) dM
*
M*
,
(2.17)
where σ is the ratio of the exit area to the area at the end of the mixing duct. With no diffuser, σ is equal to 1 and dσ is equal to 0. For this case the expression simplifies to
( ) ( )
1- M 2* m2 +1 f ξ = ( d) m2 2 2 M 2*
2
2
( ) 2(M ) 1- M 3*
2
* 2 3
⎛ M* +ln ⎜ 2* ⎝ M3
⎞ ⎟, ⎠
(2.18)
where ξd is the ratio of the diffuser lateral area to the transverse cross-sectional area. Because the two flow streams are assumed to have the same composition and have equal stagnation temperatures, the energy equation is not needed for this model. For a chosen value of M 3* and known values of the primary jet and the back pressure, the equations can be solved for the pressure and Mach number in Section 2 and at the secondary flow mixing duct inlet (Section 1). The bypass ratio is then calculated according to Equation (2.10).
2.2.5
Mixed Flow with Primary Separation In this regime the primary pressure is low enough that the primary flow separates
from the nozzle wall prior to Section 1. The primary flow leaves this part of the nozzle parallel to the mixing duct walls and does not reattach within the nozzle. The portion of the nozzle which is not filled with the primary flow is assumed to be at the subsonic secondary pressure at Section 1. The equations for mixed flow in the previous section still generally hold, but they must be slightly modified to account for new effective areas at the inlet of the mixing duct. Fabri used an approximation for the point of separation in the nozzle. He assumed the flow separated when the ratio of the nozzle pressure to the
32 surrounding pressure ( Ps,2 ) was less than or equal to 2.5. The results for primary flow with separation were not as close to Fabri’s experimental results because of this assumption.
2.2.6
Matching Fabri’s Models The equations for the supersonic, saturated supersonic, and the mixed regime
were used to recreate Fabri’s ejector predictions for use in the current study. Figure 2.6 shows a comparison of the results for the supersonic and saturated supersonic model calculations compared with selected points extrapolated from Fabri’s original paper [8]. The model assumes a primary flow characteristic Mach number of 1.78, a primary nozzle exit area of 0.45 cm2, a mixing duct cross-sectional area of 0.95 cm2, and a exit to primary flow stagnation pressure ratio of 3.5. The current model calculations reasonably
Supersonic Regime 0.6
Saturated Supersonic Regime
Bypass Ratio
0.5 Fabri's Experimental Data
0.4
Supersonic Model
0.3
Saturated Supersonic Model
0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Pos/Pb
Figure 2.6 Comparison of recreated model with data from Fabri’s model.
33 match the points extracted from Fabri’s paper. It is believed that the slight discrepancies can be attributed to the extraction process as well as to the fact that Fabri’s work was performed in the 1950’s without the use of computers for computation and plotting. There could be some errors in Fabri’s computations due to rounding errors which grow through the analysis. Despite the discrepancies in the plotted data, the redeveloped model tracks the original model very well. Figure 2.7 shows a plot of the mixed regime flow model predictions, against mixed flow data predicted for Fabri’s ejector. For these predictions, a primary nozzle exit area of 0.45 cm2, a mixing duct exit to primary nozzle exit area ratio of 2.37, and pressure ratios of 4.5 and 3.5 were used. As can be seen in Figure 2.7, the recreated model once again tracks the extrapolated data very well but slightly over predicts the bypass ratio for a given bypass ratio. The slight discrepancies between the recreated
0.8
Fabri's Experimental Results (Pc/Pb = 4.5)
Bypass Ratio
0.7
Mixed Regime Model (Pc/Pb = 4.5)
0.6 0.5
Saturated Supersonic Regime Model (Pc/Pb = 4.5) Fabri's Experimental Results (Pc/Pb = 3.5)
0.4 0.3 0.2
Mixed Regime Model (Pc/Pb = 3.5)
0.1 0.0 0.0
0.2
0.4
0.6
0.8
1.0
Pos/Pb
Figure 2.7 Mixed regime comparison of current model with Fabri’s model.
34 model and the original data are believed to be to Fabri’s calculation accuracy and to the data extrapolation process.
2.2.7
Addy’s Ejector Model Similar to Fabri, Addy performed another set of experiments on axisymmetric
ejectors with a constant area mixing duct [26]. Addy developed models for both the mixed regime and the supersonic regime. As described in the following sections, the models were based on the same general assumptions as Fabri but with a couple of additional conditions for the specific regime models.
2.2.8
Supersonic Flow Regime Model In the saturated supersonic flow regime, Addy’s model was identical to Fabri’s,
although Addy’s model was recast to use different parameters. Addy’s bypass ratio was based on the maximum flow through the strut gap and through the primary nozzle. In this regime, the secondary flow is aerodynamically choked in the gap between the nozzle and the diffuser duct. For this condition, the bypass ratio is given by
ms A Pos , = s m p Ap Po p
(2.19)
where the ms is the secondary mass flow rate, mp is the primary mass flow rate, As is the inlet area to the mixing duct for the secondary fluid, Ap is the inlet area to the mixing duct for the primary flow, Pos is the secondary flow stagnation pressure, and Pop is the primary flow stagnation pressure. For the supersonic flow regime, Addy determined the flow between the inlet to the diffuser and the choke point by assuming an inviscid secondary and primary flow,
35 and then superimposing mixing along the boundary into the flow field. This mixing results in a higher secondary mass flow rate over that given by the inviscid interaction. For the inviscid two stream model, the secondary flow is considered to be onedimensional in nature, and the primary flow retains two-dimensional (axisymmetric) characteristics. The secondary stream is treated by conventional one-dimensional gas dynamic methods and the primary stream is solved using a method of characteristics for steady irrotational supersonic flow. The governing equations are simultaneously solved subject to the condition that the pressure along the boundary is continuous (a condition neglected by Fabri). The solution starts from a given flow geometry and primary Mach number. The ratio of the secondary static pressure to the primary stagnation pressure is selected such that the nozzle is under expanded. A finite subsonic secondary flow Mach number at the inlet to the mixing duct is selected. The flow field corresponding to the selected values of the pressure ratio and the trial Mach number is then calculated. Once the flow field has been established through the method described above, the viscous mixing along the boundary is determined. A plane two-dimensional flow model for turbulent constant pressure mixing of two uniform parallel streams is used. The mixing region is superimposed upon the inviscid two stream boundary under the assumption that for the case of over expanded primary flow, the mixing will not significantly influence the inviscid flow field because the secondary mass flow will be small. In the mixing model, Addy determines a displacement thickness for the boundary layer between the jets which results in a decrease in the available flow area for the secondary flow according to
ΔA = -2πR2 δ* ,
(2.20)
36 where ΔA is the area decrease, R2 is the radius of the secondary flow, and δ* is the displacement thickness. The corresponding increase in the mass flow ratio as a result of the mixing is given by Δms Po R δ* = -2 s *2 * , mp Po p R p R p
(2.21)
where R*p is the radius of the primary flow plume at the point of choking. The mixing displacement thickness is determined using the momentum and continuity equations on a control volume between undeflected streamlines of both the primary and secondary flow streams. The corrected bypass ratio is then given by
⎛ ms ⎜⎜ ⎝ mp
⎞ ⎛m ⎞ ⎛ Δms =⎜ s ⎟ +⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎠corrected ⎝ m p ⎠inviscid ⎝ m p
⎞ . ⎟⎟ ⎠ mixing
(2.22)
One of the significant limitations of Addy’s analysis is the assumption that the mixing effects do not significantly alter the inviscid flow field. If the secondary mass entrained due to mixing is of the same order of magnitude as the inviscid secondary mass flow, the assumption breaks down.
2.2.9
Mixed Flow Regime In the mixed flow regime Addy used a one-dimensional analysis technique similar
to Fabri’s model including frictional losses along the diffuser duct wall. For uniform inlet flow, the momentum and continuity equations were applied between the entrance section and the point downstream where the two flows are uniformly mixed and subsonic. Because the stagnation temperatures of the primary and secondary flows are equal, the energy equation was not required for Addy’s model.
37 The continuity and momentum equations were recast in terms of pressure ratios; the ratio of the secondary flow static pressure at the inlet to the primary flow stagnation pressure and the secondary flow Mach number are independent variables. For a selected pressure ratio, the subsonic exit Mach number and the static pressure at the entrance to the mixed region can be determined as functions of the secondary flow inlet Mach number. For long diffuser tubes, frictional effects were accounted for from the inlet to the mixed region to the exit of the duct using standard compressible Fanno flow relations with a coefficient of friction equal to 0.005. The final condition was matching the exit pressure to the ambient pressure using adiabatic flow relations (isentropic flow relations between Po, P and Mach number) recognizing that Po at the exit will be different from Po at point 2 due to friction effects. The value of Ms,1 can be determined from the specified Ps,1/Pop and Pb/Pop for a given ejector geometry. The secondary mass flow can then be established with P, T, and Ms,1. Addy compared the results of his model to that of Fabri. The two models showed good agreement for higher values of the secondary Mach number at the inlet to the mixing duct. For low values of the secondary flow Mach number (the mixed flow regime), Addy’s results which include viscous effects were much closer to the experimental data than Fabri’s model.
2.3
CFD Analysis Although the one-dimensional analytical models can reasonably predict global
parameters such as the bypass ratio, they do not provide a description of the flow field within the ejector duct or accurately capture the mixing between the flow streams. For
38 this more detailed information computational fluid dynamics (CFD) must be employed. Several efforts over the years have been made to validate CFD modeling techniques using experimental data and to use these CFD codes to evaluate the influence of various parameters in the ejector [1, 10, 16, 18, 19, 21, 27, 28]. The majority of the CFD studies have focused on one-dimensional or twodimensional ejector systems. The axisymmetric nature allows the geometry to be created in one or two dimensions and produces relatively fast model convergence. Like the lower-order analytical models, CFD models produce good results for global variables such as the mass flow entrainment and the compression ratio, but still do not predict the flow field details well [21]. As the distance from the primary nozzle increases, the unsteadiness of the flow increases and the predictions can deviate significantly from the actual flow behavior. Although many CFD models have been used to predict and validate fluid mechanics experimental work, there is not a consistent modeling approach for all ejector systems. Velazques presented a comprehensive survey of various CFD approaches which have been used to model ejector rockets [27]. He once again pointed out that the global quantities of engineering interest are reasonably predicted on the simple geometries; however, even on these geometries, the local flow details cannot be studied due to the large computational cost. A parametric study of a rocket based combined cycle engine in all rocket mode was carried out by Steffen, et al. [28]. The study evaluated the effect of four geometric and two flow field variables set at three levels each. Variations of the inlet areas of the primary and secondary flow, the mixing duct area and length, and the stagnation
39 properties of the primary and secondary flow were evaluated to determine the influence of these parameters on the predicted flow field and on the global performance of an axisymmetric ejector. Many of the CFD simulations have been used to predict hot fire experimental performance. However as noted earlier, there is no global modeling technique for even simple cold flow ejectors. The addition of an injected fuel with mixing and combustion further complicates the simulations. As with the cold flow cases, these models have been able to reasonably predict global parameters, but cannot predict local flow field details very accurately. Often the CFD studies can provide insight into characteristic flow behavior but cannot reproduce the experimental data.
2.4
Current Experimental Work Several universities and companies have performed experimental work on
ejectors and Rocket Based Combined Cycle vehicle concepts. Research in this area has varied from simple cold flow axisymmetric ejector systems to hot fire RBCC engine concepts. This section describes some of the research work that has been released in the open literature.
2.4.1
Propulsion Engineering Research Center The Propulsion Engineering Research Center (PERC) at The Pennsylvania State
University has conducted a series of experimental and analytical research efforts on a Rocket Based Combined Cycle system operating in ejector mode [19, 29, 30]. The PERC facility consists of a two-dimensional duct with slit type strut nozzles.
40 Experiments have been conducted in both a single and a twin thruster configuration. The facility utilizes a direct connect mode in which the inlet of the duct is connected to a blow down facility. Thus the mass flow rate and the stagnation pressure of the secondary (entrained) air can be controlled. The PERC facility is a hot fire facility which means the primary exhaust gases are products of combustion from the rocket chamber. The exhaust products are combusted with entrained air, and in some cases injected fuel in a downstream portion of the duct, and the products from this combustion are accelerated through a converging nozzle. The PERC research has focused on the mixing and combustion in the downstream region of the duct utilizing Raman Spectroscopy to determine species concentration at various locations. The nozzles for the dual and twin thruster configuration are half of the size of the single nozzle configuration so that the same primary mass flow rate is produced for the same chamber pressure. The cross-sectional area of the PERC duct is 15 in2 (96.8 cm2) and the total blockage area by the strut/s is 4.55 in2 (29.4 cm2). The area ratio of the strut nozzles is 3.3. For equivalent primary mass flow rates of the single and twin thruster configurations, the twin thruster configuration entrained more secondary mass flow than the single thruster. The average secondary mass flow rate was approximately 15% greater for the twin thruster configuration. As a result of increased shear area in the twin thruster configuration, the mixing between the flow streams was improved. The single thruster configuration required approximately twice as much duct for complete mixing. In addition, the overall static pressure in the duct was significantly higher for the twin thruster configuration [30].
41 2.4.2
Japan Aerospace Exploration Agency Aoki, Lee, Masuya, Kanda and Kudo performed a series of analyses and
experimental studies on a two-dimensional ejector for application in a single stage to orbit vehicle [4, 31, 32].
The ejector apparatus consisted of a two-dimensional
rectangular primary entrance and a rectangular secondary flow entrance. The secondary flow inlet area could be varied, and the primary flow inlet Mach number varied from 2.4 to 3.4. Additionally an area choke was located downstream of the mixing section to simulate the effects of thermal choking of the flow. The area of the secondary throat could also be varied. The experiment used air as the primary fluid and nitrogen as the secondary fluid. The total pressures of both the primary and secondary fluid were varied. Both one- and two-dimensional analytical models were developed. All of the models neglected friction drag, heat transfer to the walls, and base pressure effects. Additionally, the calculations assumed complete mixing in the test section and choking at a downstream throat. The models were able to predict the pressure recovery and the secondary mass flow fairly accurately. Working in conjunction with JAXA, Kitamura, et al. investigated the pressure recovery of rectangular and circular mixing ducts of ejector-ramjets [33]. Figure 2.8 shows a schematic of the ejector configurations for this study.
Three different
axisymmetrc primary nozzles were investigated in the experiment and these were operated over a chamber pressure range of 2.5 MPa to 5.5 MPa. The ingested air was controlled with venturi orifices. To simulate pressure increase due to combustion, plugs were used to modify the exit area. Figure 2.9 shows a plot of the pressure along the wall
42
Figure 2.8 Ejector configuration for Kitamura’s experiments [33].
Figure 2.9 Pressure recovery comparison in rectangular and circular cross section ejectors [33].
43 of both the circular and rectangular ducts for an operating pressure of 2.8 MPa and a bypass ratio of 0.33. As can be seen in the figure, the pressure recovery began in approximately the same downstream location; however, the total pressure recovery was about 5% lower for the rectangular duct. The recovery length for the rectangular duct was significantly longer than the length required for the circular duct. Flow fields in the ducts were visualized using a silicon oil and a fluorescent powder. After a test run, the ejector duct was disassembled and examined. Figure 2.10 shows a comparison of the flow patterns in the circular and rectangular ducts. The rectangular duct flow pattern appeared asymmetric with recirculating flow and separation. Kitamura concluded that the flow field was a result of the corner effects and flow separation in the duct.
Figure 2.10 Surface flow patterns for a circular duct (a) and a rectangular duct (b) ejector [33].
44 2.4.3
Aerojet The Aerojet Strutjet concept was originally developed for a reusable launch
vehicle to replace the current shuttle system. The Strutjet engine incorporates an ejector mode for take off and initial acceleration to ramjet speeds (around Mach 2.5). Figure 1.2 showed a diagram of the Strutjet engine concept. The research at Aerojet has made significant achievements towards a demonstratable vehicle concept [34], but several technologies must be matured before even ground test of flight configurations engines are possible. The Strutjet engine concept uses multiple struts with embedded rocket engines mounted in the engine duct. The ejector action of the exhausting rocket plumes entrains secondary air from the atmosphere through the gaps between the struts. The ejector pumping is complete much faster with the multiple struts than without struts utilizing a two-dimensional flow path [34]. The ducted rocket mode of the Strutjet provides some added specific impulse over an all-rocket engine up to Mach 2.5 where the ramjet mode would take over. In addition to engine performance studies, Aerojet has investigated the performance of a single stage to orbit concept powered by the Strutjet including multiple vehicle body configurations and sizes [3, 34]. The studies showed that the Strutjet concept has the potential to provide improved design margins over conventional rocket launch systems. The margins can be used to reduce operating costs through reduced maintenance activities of the highly reusable systems and the reduction in engine replacement cost possible through a significantly smaller vehicle and horizontal takeoff. The horizontal takeoff and landing concept vehicle offers gross takeoff mass that is
45 about 44% less than the all rocket design and the dry mass that is about 68% less than the all rocket design.
2.4.4
Small Scale Experimental Efforts On a smaller scale, many research efforts have focused on cold flow
experimentation on one-dimensional geometry ejectors [14, 15, 35, 36]. Young and Idem performed a series of cold flow experiments for air-air sonic and supersonic ejectors [35]. The study investigated the influence of the separation distance between the primary nozzle exit and the mixing tube radius.
Two primary nozzle configurations were
examined: a converging nozzle and a converging-diverging nozzle.
The distance
between the primary nozzle exit and the constant area mixing tube entrance was systematically varied. Equal stagnation temperatures for the primary and secondary flow were maintained and the mixing duct exit pressure was maintained at atmospheric pressure. The study showed for all cases that the bypass ratio decreased with increasing primary to secondary flow stagnation pressure ratios.
As the distance between the
primary nozzle exit and the mixing duct entrance was increased, the bypass ratio increased until a separation distance of 0.512 times the radius of the mixing tube was reached. As the separation distance was increased beyond this value, the bypass ratio was constant for a given stagnation pressure ratio. The study also showed that the mixing length was independent of the separation distance, but was dependent on the primary nozzle Mach number. As Mach number increased, the mixing length increased. Dutton, et al. performed an investigation of an axisymmetric supersonicsupersonic ejector configuration focusing on the compression ratio of the secondary
46 flow [14]. A one-dimensional model of the ejector similar to Fabri’s was developed to predict the performance. An overall control volume around the mixing duct was used and uniform velocity and pressure distributions were assumed at the entrance to the mixing duct with a fully mixed and uniform stream at the exit of the mixing duct. Both supersonic and saturated supersonic models were employed depending on the ejector operation regime. Comparison of the theoretical predictions with the experimental work showed that the predicted maximum ejector compression ratios were 15% to 22% higher than the measured values and that the ejector was susceptible to separation of the secondary stream at the point of confluence of the primary and secondary streams. A parametric study was performed for eight model parameters to determine their influence on the compression ratio. The eight parameters were the primary stream Mach number, the secondary stream Mach number, the specific heat ratios of the primary and secondary stream, the ratio of the stagnation temperatures of the primary and secondary streams, the ratio of the molecular weights of the primary and secondary flow streams, the ratio of the areas of the primary and secondary flow stream, and the ratio of the stagnation pressures of the primary and secondary flow streams. The most effective means for improving the ejector pressure recovery was to compress the secondary stream towards sonic conditions, either upstream of the ejector or in the mixing tube, and to operate near the matched static pressure point with a high Mach number, high stagnation temperature, low molecular weight primary gas [14]. If the pressure of the primary flow at the entrance to the mixing duct was higher than the secondary pressure at the same point, then separation of the secondary flow occurred, which degrades the ejector performance.
47 2.5
Summary Numerous other experimental studies and computational analyses of ejector
systems have been performed. Generally, these efforts focus on axisymmetric or twodimensional configurations at best.
These types of configurations may indicate
performance trends of non-axisymmetric geometries; however, the geometry will impart significant losses in the system. No simple analytical method has been found which accurately captures the global performance parameters for complex geometries like the current PRC test configuration. CFD results can predict global parameters reasonably well for relatively simple geometries and can provide insight into flow phenomena, but they cannot predict detailed flow field information. While a propulsion engine utilizing an ejector would have a portion of the flow field influenced by hot fire effects, a well established cold flow model which reasonably predicts detailed flow field information is needed to evaluate the majority of the ejector behavior which is not combustion related.
CHAPTER 3
FACILITY AND EXPERIMENTAL SETUP
3.1
Facility The PRC cold flow ejector facility is shown schematically in Figure 3.1. The
facility consists of an air supply system, the ejector test apparatus, and the data acquisition instrumentation. The air supply systems consist of a 500 ft3 (14.16 m3) air storage tank located outside of the facility and a 24 ft3 (0.68 m3) surge tank located in the test bay.
Both tanks were hydrostatically tested to 3500 psi (24.13 MPa).
Air is
compressed by a four stage piston compressor to a storage pressure of 2500 psi (17.24 MPa). The compressor has a purification system which cleans and dries the air
Flow Control Valve Air Tanks (524 ft3) Compressor
Ejector Duct
Figure 3.1 Schematic of PRC cold flow ejector facility.
48
49 before storage. The supply lines connecting the storage tank to the duct consist of seamless stainless steel tubing rated for high pressure applications.
The minimum
diameter of the lines connecting the tank to the ejector rig is 1.25 in (3.18 cm). A side view of the ejector duct is shown in Figure 3.2 and an end view is shown in Figure 3.3. The ejector consists of a constant area rectangular duct with a contoured inlet. The duct has 0.75 in. (1.91 cm) thick aluminum top and bottom walls, and 0.75 in. (1.91 cm) thick Plexiglas side walls. The constant area section of the duct is 3.5 in. (8.89 cm.) by 4.0 in. (10.16 cm.) tall. The contoured inlet is constructed of sheet metal and has a constant width of 3.5 in. (8.89 cm.). The inlet is elliptically contoured from 48 in. (121.92 cm.) tall at the entrance to 4.0 in. (10.16 cm.) tall where it attaches to the duct over a 5 ft. (1.524 m) length.
The inlet was designed to produce a uniform
secondary flow velocity profile into the constant area section of the duct.
17.0 in. 60.0 60.0”in.
45.5” 45.5 in.
17.0”
Contoured Inlet
Mixing Duct
Flow Direction
Fairing
Strut
Figure 3.2 Ejector test rig cross section.
50
Strut Primary Nozzles
4.0” 4.0 in.
3.5”
3.5 in.
Figure 3.3 Ejector test rig end view.
The primary flow for the ejector is driven through converging diverging nozzles which are embedded in a strut mounted approximately 45.5 in (115.57 cm.) upstream of the duct exit. Figure 3.4 depicts the two ejector struts used for this investigation. The struts are machined from carbon steel and have identical external dimensions. One strut has a single embedded nozzle and the other has two embedded nozzle.
The single
embedded nozzle exit is centered on the downstream face of the strut.
The two
embedded nozzles are located 1 in. apart and evenly spaced around the center of the downstream face of the strut. In addition, the dual nozzle strut has a vertical slit 0.1 in (0.254 cm). wide by 0.25 in (0.635 cm) high. This slit was designed to simulate exhaust from a turbine on the Aerojet Strutjet engine used in previous mixing studies [23]. For the current experiment, the slit was plugged with filler material, and sanded until the surface was smooth. The nozzles in both struts have the same geometry. The nozzles transition from a circular throat to a rectangular exit with an expansion ratio of 4.6 and a throat diameter of 0.46 in. (1.1684 cm).
Thus when operated at the same chamber
pressure, the dual nozzle strut will pass twice the mass flow of the single nozzle.
51 Pressure Tap
Thermocouple Location
Primary Feed
Primary Feed
Pressure Tap
Primary Feed
Thermocouple Location
Figure 3.4 Dual and single nozzle ejector struts.
The struts are designed to be installed in the duct assembly. An aerodynamic fairing is mounted on the upstream side of the strut.
The fairing was machined from
aluminum stock with a 0.5 in (1.27 cm) radiused leading edge and is 1.0 in (2.54 cm) wide by 5.0 in. (12.7 cm) long. This fairing provides a smooth transition from the inlet portion of the duct to the strut gap region. Air flow from the storage tanks to the strut is regulated by a pneumatically operated proportional-integral-derivative, PID, controller.
A pressure transducer
connected to the chamber in the embedded nozzles provides the feedback signal for the PID controller. In previous tests, the voltage for the chamber pressure set point was regulated by a manual control variable resistance potentiometer [25]. For the current set of experiments, this was replaced with software driven digital control. A desired pressure is set from the control software and the corresponding set point voltage is sent through the data acquisition card to the PID. The PID valve adjusts until the voltage signal from the pressure transducer in the strut chamber matches the set point voltage of the controlling software. Through this setup, the chamber pressure can be maintained within the desired pressure set point plus or minus 5 psi (34.5 kPa). A consistent chamber
52 pressure is thus maintained for equivalent runs, thus improving the repeatability of the experiment. Figure 3.5 shows a top view of the mixing duct identifying static pressure tap locations. Taps are mounted along the top wall and side wall of the mixing region of the duct (the region between the nozzle exit plane and the duct exit) and in the strut gap region (the region between the strut and the side wall). Forty-eight pressure taps are mounted along the centerline of the top wall. The first tap is located 0.25 in. (0.635 cm) downstream of the strut nozzle exit plane. The second tap is located 0.5 in. (1.27 cm) downstream of the nozzle exit plane. The next 20 taps are mounted on 0.5 in. (1.27 cm) centers starting from the second tap. The remaining 27 taps are mounted on 1 inch (2.54 cm) centers starting 1 inch (2.54 cm) downstream of the 21st tap and ending 7.0 in. (17.78 cm) upstream of the exit plane.
Nozzle Exit Plane Strut Gap Region
0.25 in. spacing 2 times
Mixing Duct Region
0.50 in. spacing 18 times
1.00 in. spacing 28 times
Figure 3.5 PRC ejector top wall static pressure tap locations.
Figure 3.6 shows a side view of the duct with static tap locations. Forty-eight pressure taps are mounted along the centerline of the sidewall of the duct in the mixing
53 region. The first tap is mounted in the same plane as the nozzle exit. The next 20 taps are mounted on 0.5 inch (1.27 cm) centers downstream of the first tap. The remaining 27 side wall pressure taps are mounted on 1 inch (2.54 cm) centers starting from the 21st pressure tap.
Nozzle Exit Plane Strut Gap Region
0.70 in. spacing 10 times
Mixing Duct Region
0.50 in. spacing 20 times
1.00 in. spacing 27 times
0.50 in.
Figure 3.6 PRC ejector side wall pressure tap locations.
With the exception of the first taps, the pressure taps on the top and side walls of the duct are mounted at the same distance downstream of the nozzle exit plane. These static pressure taps are read using a mechanical Scani-Valve pressure reader. The ScaniValve has two pressure transducers: one for the top wall pressure taps and one for the sidewall pressure taps. One additional pressure tap is mounted on the sidewall centerline 0.5 inches upstream of the duct exit plane. This tap measures the static pressure of the flow exiting the duct and is measured with an independent transducer. The static pressure taps in the strut gap region of the duct can be seen in Figure 3.6. The strut gap is the portion of the duct upstream of the nozzle exit plane, and
54 downstream of the aerodynamic fairing. Ten pressure taps are mounted on one sidewall in the strut gap region. It is assumed that the pressure distribution on the opposite side of the duct will be identical. The ten taps are evenly spaced over 7 inches (17.78 cm) starting 0.7 inches (1.78 cm) upstream of the nozzle exit plane. Two Pitot-static probes are used to measure the total pressure and static pressure of the secondary flow and of the exit flow.
The first Probe is mounted in the
aerodynamic fairing and protrudes approximately 1 inch upstream into the secondary flow. Figure 3.7 shows a drawing of this probe location. The second probe is mounted at the exit of the duct on a traversing mechanism so that the tip of the probe is just inside the exit plane. The traversing mechanism allows the probe to be moved across the duct in the horizontal plane.
Aerodynamic Fairing
Strut
Fairing Pitot Probe
Figure 3.7 Secondary flow Pitot probe location in strut fairing.
Two thermocouples are mounted in the duct. The first is located inside the strut nozzle chamber (see Figure 3.4). This thermocouple measures the total pressure of the
55 primary flow. The second thermocouple is mounted at the inlet of the constant section of the duct. This thermocouple measures the temperature of the secondary flow. The experiment is controlled using LabView® software. The code was developed for the experiments carried out by Smith [25] and was modified for the current set of experiments. A given set point chamber pressure and the lab atmospheric pressure are entered into the code. The code converts the set point pressure into a voltage and sends a signal to the PID controller valve. The PID controller valve then adjusts the size of the valve opening until the voltage from the strut nozzle chamber pressure transducer matches the desired set point. Once the chamber pressure reaches the desired set point pressure, the code begins to record data from the instrumentation through out the duct.
3.2
Test Matrix Numerous tests were carried out to investigate different performance
characteristics of the ejector. The set of experimental results presented in this dissertation is primarily from three specific types of tests and are summarized in Table 3.1. Each of the test types had a different focus and, because runtime was limited by the available stored air, not all of the regions of interest were examined in each test.
The
instrumentation for the tests was categorized into four groups: the rocket chamber, the mixing duct, the exit Pitot, and the entrance and strut gap.
The rocket chamber
measurement locations consist of the static tap in the rocket chamber and the thermocouple in the rocket chamber. Since chamber pressure was the control variable, this set of measurements was recorded for all tests. The mixing duct measurement group consists of the 48 top wall and 48 sidewall static pressure taps.
The exit Pitot
56 measurement group consists of the exit Pitot-static probe and the centerline sidewall exit pressure tap. The entrance and strut gap measurement group consists of the ten centerline sidewall strut gap pressure taps in the strut gap region as well as the fairing pitot static probe and the entrance thermocouple.
Table 3.1 Ejector Test Matrix Measurement Locations Entrance Number of Chamber Rocket Mixing Experiment Complete Exit Pitot and Strut Pressures (psi) Chamber Duct Focus Gap Tests
3.2.1
Single Nozzle Strut 100, 200, 300, 400, 500, 600, X 700, 800, 900
Mixing Duct Tests
10
Exit Profiles
1
100, 200, 300, 400, 500, 600, 700, 800, 900
Low Pressures
1
20, 25, 30, 35, 40, 45, 50, 55
X
X
X
X
X
X
X
X
X
X
Dual Nozzle Strut 50, 100, 150, 200, 250, 300, X 350, 400, 450
X
Mixing Duct Tests
10
Exit Profiles
1
50, 100, 150, 200, 250, 300, 350, 400, 450
X
X
X
Low Pressures
1
20, 30, 40, 50, 70
X
X
X
X
Mixing Duct Tests The first series of tests focused on the pressure distributions in the mixing duct.
As noted earlier, these taps are connected to a mechanically actuated Scani-Valve. To get
57 a complete set of readings for a single test, the Scani-Valve must step through each pressure tap, let the pressure equalize, record the voltage, then step to the next tap. The Scani-Valve steps through each of the 48 ports sequentially. For each port both a top and a side wall pressure measurement are taken. The controlling software reads the pressure at a given port then commands the Scani-Valve to step to the next port for each transducer. When the pressure is read at the 48th port, the Scani-Valve returns to the first port and begins the sequence again. At each port, the software waits approximately 0.1 sec. for the pressure to adjust before reading the transducer voltage.
Through
experimental analysis, it was determined that this delay was sufficient to allow the pressure to adjust and equalize from the last reading. Tests focusing on the mixing duct pressures require more runtime than tests focusing on other areas. For this series of tests, the ejector was brought up to steady state operation for each desired set point pressure ratio. Once the set point had been reached the stagnation and static pressure at the aerodynamic fairing, static and stagnation pressures at the duct exit, exit centerline sidewall pressure, the inlet temperature, the ejector rocket chamber temperature, the ejector rocket chamber pressure, and the static pressures for the first top wall and first sidewall static pressure taps were recorded. The Scani-Valve was then commanded to step to the second top wall and side wall positions and the aforementioned set of measurements was recorded again. The test was continued until the pressure at each of the 48 side wall and 48 top wall pressure taps was measured ten times.
58 3.2.2
Exit Pressure Profiles The second series of tests focused on the total pressure distribution at the exit of
the duct. Stagnation and static pressure measurements were made through out a quadrant at the exit of the duct using a Pitot-static probe mounted on a traversing mechanism. Symmetry was assumed across the horizontal and vertical centerline planes. Traces were taken at the five vertically distributed locations shown in Figure 3.8. Traces were taken starting at the center of the duct exit and traversing towards the wall and then returning to the center of the duct. The probe was then moved upward (towards the top wall) and a new set of pressure measurements was taken. For each trace, measurements were made at eleven locations across the horizontal line of motion.
At each location,
15 measurements of the exit stagnation and static pressures, exit centerline sidewall static pressure, rocket chamber pressure and temperature, strut gap pressures, inlet stagnation
h = 4.00 in.
w = 3.50 in.
Figure 3.8 Probe trace locations for stagnation pressure traces across the duct exit plane.
59 and static pressures, and inlet temperature were made over a 2 second time span as the probe paused. This gave a total of 22 measurements for each parameter at each of the eleven locations.
3.2.3
Shadowgraph Visualizations A third series of experiments was performed to capture shadowgraph images of
the PRC ejector system to visualize any shock structures and correlate them to the experimental results [37]. Reference [38] discusses various shadowgraph and Schlieren techniques and was the primary source of information for the shadowgraph setup used in this project.
For ease of construction, the simplest method, known as direct
shadowgraphy, was chosen. Figure 3.9 shows a diagram of the setup for the direct shadowgraph method. The only requirements for this system are a point light source, the flow region of interest, and a flat screen onto which the shadow is projected. Figure 3.10 shows the general region in the mixing duct that was imaged.
Light Source
Box to Reduce Light
Ejector Duct Screen
Observation Position
Figure 3.9 Schematic of shadowgraph setup for ejector facility.
60
Strut Ejector
Region of Shadowgraphy
Mixing Duct
≈ 10 in
Flow Direction
Figure 3.10 Region of interest for shadowgraphy [37].
Shadowgraphy was performed for both the single and dual nozzle struts. For the single nozzle strut, the set point pressure ratio (Pc/Pb) was varied from 6.8 to 60.5. For the dual nozzle strut, the set point pressure ratios were varied from 3.4 to 30.6. These chamber pressures provide approximately equivalent primary mass flow rates, i.e., a set point of 3.4 in the dual nozzle has an equivalent primary mass flow as a set point of 6.8 in the single nozzle strut. For these tests, only the rocket chamber measurement group parameters were recorded. The majority of the data presented in this dissertation is from the mixing duct tests.
For these tests, the set chamber pressure was achieved as described in the
preceding section. Once the steady state chamber pressure was reached, the pressure at each of the forty-eight side wall and top wall pressure taps was measured ten times. The pressures at other locations in the duct were measured 480 times during the same test. This test was repeated ten times with each test occurring on a different day.
61 The exit profile tests were used to determine the total pressure variation across a quadrant of the exit. Only one complete set of data from this test was collected. The Pitot-static probe was allowed to traverse across the exit of the duct recording the total pressure and static pressure at 10 different locations, then moved back towards the top wall stopping at the same locations to take ten more readings. When the probe returned to the center position, the test was stopped. The probe was then moved vertically closer to the top wall, and the test was conducted again traversing the probe toward the sidewall stopping at the same locations for readings. A total of 5 different locations was used from the center of the exit to the top wall. The low pressure tests were conducted to determine the maximum bypass ratio that could be achieved for this ejector. These tests were used for comparison purposes only. The tests were conducted in short runs, and 100 measurements were made from the rocket chamber, exit Pitot and entrance and strut gap measurement locations for a set chamber pressure. Since only one test was conducted at each chamber pressure the repeatability in these data points is not included. In addition to the tests listed in Table 3.1, a number of additional tests was used to test components of the facility setup. Tests were run to examine the repeatability of the digital chamber pressure control, to establish the minimum time for pressure equalization in the static pressure tap tubing, and single tests were run to obtain shadowgraph images.
CHAPTER 4
UNCERTAINTY ANALYSIS AND DATA REDUCTION EQUATIONS
4.1
Introduction This chapter presents a general discussion of uncertainty followed by specific
approaches used in the ejector experiments. The data reduction equations used for analysis will be presented. The uncertainty analysis methods outlined in Coleman and Steele [39] were used for this analysis.
The systematic uncertainty constants for
measured parameters are presented in Appendix A. An example of an analysis for the calculated quantity of secondary mass flow is presented at the end of the chapter.
4.2
General Uncertainty Measurement errors are divided into two categories, random errors and systematic
errors. A random error is one that contributes to scatter in the measured values, and thus can have a different magnitude for measurements of the same variable at steady state. A systematic error is one that is common to all of the measurements of the same variable, and thus has the same magnitude for all measurements of the same value at a steady state. The total error associated with a measured variable is the sum of the systematic error and random error components.
62
63 For the experiments presented in this dissertation, multiple measurements of the same variable were made at a presumed steady state. Because this experiments deals with high speed flow which can be turbulent, the measurement variation is associated with the turbulent fluctuations as well as the random measurement error.
Because
multiple tests at the same set point produced consistent average results, it is assumed that the measurements are statistically steady in time throughout the duct. The average measurements from multiple tests at the same set point are presented in this work. The variation of the test averages for the same set point composes the random uncertainty for the average result. The systematic uncertainties associated with the measurements were determined through an end to end calibration of the data acquisition system. That is, a known pressure was applied to the transducer, and values were recorded using the same data acquisition card and the same computer that were used for the experiment. Thus the calibration uncertainty combines systematic uncertainties of the transducer, the uncertainty in the “known” applied pressure, the data acquisition card, as well as other uncertainties associated with the setup of the system. The data from the calibration was applied to a regression uncertainty analysis to determine the scale and offset of the transducer and to determine the uncertainty associated with the reading. A sample of the regression uncertainty analysis is included in Appendix B.
4.2.1
Single Variable Measurement Uncertainty
For a sample containing N repeated measurements of a single variable (X). The sample standard deviation, SX, is given by
64
⎛ 1 SX = ⎜ ∑ Xi - X ⎝ N - 1 i=1 N
(
1 N
N
)
2
1 2
⎞ ⎟ , ⎠
(4.1)
where the average, X , is calculated as X=
∑X
i
,
(4.2)
i=1
and the standard deviation of the mean, S X , is given by SX =
SX . N
(4.3)
The random uncertainty is given by t ⋅ SX ,
(4.4)
and the random uncertainty of the mean is given by t ⋅ SX ,
(4.5)
where the factor t is a coverage factor and is obtained from the t-distribution [39]. The value of t depends on the combined number of degrees of freedom in the estimates of both systematic and random uncertainties. In all of the cases analyzed in this study, the combined number of degrees of freedom is greater than 9, so for 95% confidence uncertainty estimates, t is taken equal to 2.0 [39]. The total uncertainty, UX, for a single value is given by U X = 2 ⋅ S X 2 + BX 2 ,
(4.6)
and the total uncertainty of the mean, U X , is given by U X = 2 ⋅ S X 2 + BX 2 .
(4.7)
65 4.2.2
Uncertainty for a Calculated Result
Often a result is determined from several measured variables by using a data reduction equation (DRE). In general form, a DRE can be written as r = r ( X 1 , X 2 ,...X J ) ,
(4.8)
where r is the desired result, and X1 through XJ are the measured values from an experiment.
An uncertainty propagation equation can be used to determine the
systematic uncertainty in the result due to the uncertainties in the measured variables. For the general form of the DRE, the systematic uncertainty of the calculated result r is 2
2
2
⎛ ∂r ⎞ ⎛ ∂r ⎞ ⎛ ∂r ⎞ 2 2 2 Br 2 = ⎜ ⎟ BX J + ... ⎟ BX 1 + ⎜ ⎟ BX 2 + ... + ⎜ ∂ ∂ ∂ X X X ⎝ 1⎠ ⎝ 2⎠ ⎝ J⎠ , ⎛ ∂r ⎞ ⎛ ∂r ⎞ +2 ⎜ ⎟⎜ ⎟ BX i X k ⎝ ∂X i ⎠ ⎝ ∂X k ⎠
(4.9)
where the BX terms are the systematic uncertainties associated with the X variables and there is a correlated systematic uncertainty term (BXiXk) for each pair of variables that share a common error source [39]. The random uncertainty may be calculated using a similar error propagation equation; however, the correlated terms of the equation can be difficult to quantify in an experiment. These correlated errors can have a significant influence on the total random uncertainty [40]. Thus, the random uncertainty may be better estimated by computing a result for each set of measured variables at a single point in time. This produces a set of results for each set of measured values. The variation in the set of results may then be determined using Equation (4.1). By calculating the random uncertainty in this manner, the correlated effects are automatically captured. The random uncertainty of the result is then given by
66 2 ⋅ Sr ,
(4.10)
and the random uncertainty of the mean for the set of results is given by 2 ⋅ Sr .
(4.11)
U r = 2 ⋅ Sr 2 + Br 2 ,
(4.12)
In such a case, the total uncertainty in r is
and the uncertainty of the mean from the sample of results is calculated as 2
U r = 2 ⋅ S r + Br 2 .
4.2.3
(4.13)
Uncertainty for a Collection of Results
In the present experiment, multiple tests were taken at the same steady state set point. The desired results were calculated from each test and the associated uncertainties were determined. An average value of the result for each set point was determined from the test averages. This value is the reported result for that set point. To calculate the uncertainty of the collection of results, each test average value is treated as a single measurement value and the total uncertainty determined for a specific test is treated as the systematic uncertainty for a single data point value. That is, for test 1 at a set point of 100 psi chamber pressure, the secondary mass flow was determined to be 0.183 lbm/s and the total uncertainty was (Ums) ± 0.001 lbm/s. When all tests are examined and the average of the secondary mass flows at 100 psi chamber pressure is taken, The value of secondary mass flow from test 1 becomes data point one in the collection and the total uncertainty from test 1 (Ums)test1, becomes the systematic uncertainty associated with data point one in the set of secondary mass flow values (Bms)test1. The random uncertainty for
67 the collection of tests is determined by calculating the standard deviation of the data set using Equation (4.1), and then multiplying the standard deviation by a coverage factor using Equation (4.4) or (4.5).
4.3
Reducing Test Uncertainty Through Nominal Readings
A set of readings was taken at atmospheric conditions with no flow through the facility for all pressure transducers prior to and after each test run. An average pressure value was determined from the readings for each transducer. This value represents the nominal reading of the transducer. When a gauge pressure transducer is used to measure atmospheric pressure, the reading from the transducer should produce a pressure value of zero. However, as is often the case, the transducer can produce a value slightly more or slightly less than the zero value.
This slight deviation represents a portion of the
systematic uncertainty in the transducer. By subtracting the nominal transducer reading from the value measured during the test, some of this uncertainty can be eliminated from the experiment. Since the calibration of the transducer produced a scale and an offset, by subtracting the reading from a nominal reading, the offsets will cancel out. Thus the nominal reading becomes the offset. Thus in reality only the slope from the calibration is used. Additionally, since the same transducer measures both the nominal reading and the test reading, the readings share the systematic uncertainty of that transducer. As discussed earlier, when two readings share a common error source they are said to be correlated.
Because the nominal reading is subtracted from the test reading, the
derivatives of the data reduction equation with respect to the measured variable and the
68 nominal value of the measured variable will have opposite signs. This will result in a negative term in Equation (4.9), lowering the total systematic uncertainty.
4.4
Pressure Transducers Calibration
As stated earlier, an “end-to-end” calibration was preformed to estimate the systematic uncertainty associated with each of the pressure transducers. Each transducer was calibrated in place using either an air or a water based dead weight tester. For the calibration, the transducer is connected to the dead weight tester and the signal is read through the same data acquisition card using the same computer that is used for the actual test. By calibrating in this manner, the total systematic uncertainty determined from calibration will include uncertainties from both the calibration standard and the data acquisition system. Each transducer was calibrated in the positive range of pressure and a calibration curve extrapolated for the negative gauge pressures.
A regression
uncertainty analysis [39] was performed to determine the systematic uncertainty associated with the calibration. This type of analysis produces a second order curve of pressure uncertainty as a function of the voltage reading from the transducer. The uncertainty from the center of the pressure range is lower than the uncertainty at the end of the range. A sample of the regression uncertainty methodology, and the uncertainty expressions for each of the transducers is included in Appendix B.
4.5
Ejector Specific Uncertainty
The following section describes the specific data reduction equations and the specific uncertainty methods used for in the current experimental investigation. The
69 uncertainty for these equations was determined using the methods outlined in the previous sections. Sample calculation sheets are provided in Appendix C.
4.5.1
Mass Flow
The mass flow rates of the primary and secondary streams are determined from pressure and temperature measurements at various locations in the facility described in Chapter 3. The secondary mass flow rate is calculated from the centerline static and total pressure measurement at the aerodynamic fairing and the temperature measurement at the duct entrance. The secondary mass flow is calculated as γ-1 ⎡ ⎤ γ ⎢⎛ Po ⎞ γ ⎥, m = Aduct ⋅ P ⋅ 1 ⋅ ⎥ RairT γ - 1 ⎢⎜⎝ P ⎟⎠ ⎣ ⎦
2
(4.14)
where P is the static pressure, Rair is the specific gas constant for air (1716 ft-lbf/slug R), T is the temperature of the flow, γ is the ratio of specific heat for air (1.4), and Po is the
stagnation pressure of the flow. Aduct is the cross-sectional area of the duct at the location of the measurements. Because of the geometry of the duct, it was assumed that there could be significant boundary layer build up at the probe location. The area of the duct was corrected to account for the boundary layer using a simple flat plate boundary layer approach. The displacement thickness of the boundary layer was calculated using
⎡ ⎤ 1 .16 ⎥ ⎢ δ = ⋅x⋅ , 1 ⎥ ⎢ 8 7 ⎣⎢ Rex ⎦⎥ *
(4.15)
70 where δ* is the displacement thickness, x is the distance from the entrance of the duct constant area section, and Rex is the Reynolds number based on x. With the displacement thickness, the area of the duct at the probe location was calculated as Aduct = (l - 2 ⋅ δ* )(w - 2 ⋅ δ* ) ,
(4.16)
where h is the height of the duct and w is the width of the duct. The height and width are each reduced by 2 times δ* to account for boundary layers on both top and bottom, and the 2 side walls. The centerline velocity at the fairing was used along with the calculated density to calculate the Reynolds number. The mass flow calculation of Equation (4.14) assumes a uniform velocity profile across the duct with a boundary layer near the walls. For real flows, there will be some maximum centerline velocity. Thus these calculations are subject to some additional uncertainty because of the assumptions used for the calculation.
This uncertainty has not been quantified for this dissertation.
The
uncertainty presented with the results is associated with the measurements only. Since nominal pressures were used to lower the uncertainty, the full data reduction must include the nominal pressures. By subtracting the nominal reading from the test reading, all of the pressure values become gauge readings, so the atmospheric pressure must also be added to the pressure term in the data reduction equations. Thus the pressure terms must be replaced in all data reduction equations by P = Preading - Pnominal + Patmospheric .
(4.17)
In all of the equations presented in this analysis, the nominal and atmospheric pressure terms will not be shown in the equations, but it should be noted that the actual equation will included additional terms for each pressure value.
71 The primary mass flow is calculated assuming choked isentropic flow through the nozzle. The chamber pressure is assumed to be the stagnation pressure for the flow, and the chamber temperature is assumed to be the stagnation temperature. The mass flow is calculated according to γ+1
mp =
Pc Tc
Athroat
γ Rair
⎛ 2 ⎞ γ-1 ⎜ ⎟ , ⎝ γ +1 ⎠
(4.18)
where Pc is the stagnation pressure, Tc is the chamber temperature, and Athroat is the area of the nozzle throat (0.466 in2).
4.5.2
Bypass Ratio
The ratio of secondary mass flow rate to primary mass flow rate is known as the bypass ratio or the bypass ratio. This is a key parameter for RBCC applications as it can be used to determine the required onboard oxidizer. Combining Equations (4.17) and (4.18) yields the total data reduction equation for the bypass ratio, ω.
ω=
γ-1 ⎡ ⎤ 2 γ ⎢⎛ Pos ⎞ γ ⎥ Aduct × Ps × × ⎜ ⎟ - 1⎥ RairTs γ - 1 ⎢⎝ Ps ⎠ ⎢⎣ ⎥⎦
Pop Top
Athroat
γ Rair
⎛ 2 ⎞ ⎜ γ +1 ⎟ ⎝ ⎠
γ+1 γ-1
,
(4.19)
where the subscript s refers to secondary flow stream conditions, and the subscript p refers to primary flow stream conditions.
72 4.5.3
Mach Number
Mach numbers were calculated at two locations in the flow, ahead of the strut at the aerodynamic fairing, and at the exit of the duct. At the aerodynamic fairing, the flow was always subsonic allowing a straight forward calculation and uncertainty analysis to be performed. At the exit of the duct, the Mach number could either be supersonic or subsonic depending on the flow conditions. When the flow is supersonic, the Mach number calculation and the uncertainty analysis become increasingly complicated. When the flow is subsonic, the Mach number can be determined by γ-1 ⎛ ⎞ 2 ⎜ ⎛ Po ⎞ γ ⎟, M= 1 ⎜ ⎟ ⎟ γ -1⎜⎝ P ⎠ ⎝ ⎠
(4.20)
where Po and P are the stagnation and static pressures measured from the Pitot-static probe at the duct exit. The derivatives required for the systematic uncertainty equation can be calculated directly and applied to Equation (4.9). When the flow is supersonic, a Pitot probe inserted in the flow induces a shock wave to form on the nose of the probe. The measurement from the Pitot probe reflects the pressure on the downstream (subsonic) side of the shock wave [41]. The Mach number is determined by a process of iteration on the downstream Mach number using γ
⎡ γ - 1 2 ⎞ ⎤ γ-1 ⎛ 1+ M 1 ⎟⎥ ⎢ ⎜ ⎡ ⎤ Po2 2γ γ -1 2 = ⎢1+ M 12 - 1 ⎥ ⋅ ⎢1+ ⎜ ⎟⎥ , P1 2 ⎜ γ× M 2 - γ - 1 ⎟ ⎥ ⎣ γ +1 ⎦ ⎢ 1 ⎢⎣ ⎝ 2 ⎠ ⎥⎦
(
)
(4.21)
where Po2 is the stagnation pressure of the shocked flow measured by the Pitot-static probe, and P1 is the static pressure measured just upstream of the Pitot probe by a wall tap.
73 Because this is an iterative process, Equation (4.9) cannot be directly used to determine the systematic uncertainties for the result.
Therefore, a Monte Carlo
simulation was performed for each test in which supersonic flow was determined. Using measured values of Po2 and P1 with appropriate systematic uncertainties randomly generated, 10000 values of Mach number were calculated. The total uncertainty was determined using Equation (2.12). The drawback to this approach was that correlated errors were not accounted for in the simulation. The resulting uncertainties are therefore conservative, since in this case the correlated errors would have reduced the overall uncertainty.
4.5.4
Pressure Ratios
Many of the presented results are pressure ratios or functions of a pressure ratio. The pressure ratio is the absolute pressure divided by either the stagnation pressure of the secondary flow or the back pressure. For these experiments, both of these pressures are equal to the atmospheric pressure. As was noted earlier, nominal readings from the instrumentation at no-flow conditions were used to zero the measurement.
So the
pressures shown in the equations are actually the values given by Equation (4.17). The uncertainty calculation for the pressure ratio is straightforward, and will not be given further treatment.
CHAPTER 5
EXPERIMENTAL RESULTS
5.1
Introduction Cold flow experiments were carried out on both dual and single nozzle struts.
Aside from the number of strut nozzles, chamber pressure was the only control variable for the tests. The duct entrains air and exhausts air from the lab. Therefore the back pressure and the stagnation pressure of the secondary flow are equal to atmospheric pressure. For each chamber pressure set point, data points were determined as averages of ten tests conducted on separate days. A summary of the results with associated uncertainties is provided in Appendix D.
5.2
Single Nozzle Strut Experiments on the single nozzle strut were conducted at chamber pressure set
points of 6.5, 13.2, 20.2, 27.2, 33.8, 40.5, 47.3, 53.9, and 60.6. For mixing duct focused experiments, ten tests were conducted on separate days at each chamber pressure. For the exit profile experiments, a single series of tests at approximately the same chamber pressure set points was conducted.
74
75 5.2.1
Mass Flow Augmentation
Figure 5.1 shows the primary and secondary mass flow rates and the bypass ratio plotted against the set point pressure ratio (Pc/Pb). The primary mass flow is directly proportional to the chamber pressure. The secondary mass flow increase begins to level off around a value of 2.1 lbm/sec (0.95 kg/s) at a pressure ratio of 41. This corresponds to a primary mass flow of approximately equal mass flow, 2.1 lbm/sec (0.95 kg/s). The leveling off of the secondary mass flow trace is indication that the flow has become choked. The secondary mass flow can only be increased from this point by changing the stagnation conditions of the secondary flow. Thus the maximum amount of secondary flow that can be induced at standard atmospheric conditions is 2.1 lbm/sec (0.95 kg/s). The uncertainty bars in the plot account for both measurement uncertainty and the uncertainty associated with test-to-test set point variation.
Additionally, slight
Mass Flow (lbm/s)
Bypass Ratio (ms/mp)
3.5 3.0 2.5 Bypass Ratio Secondary Mass Flow
2.0 1.5
Primary Mass Flow
1.0 0.5 0.0 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.1 Single nozzle strut primary and secondary mass flow comparison.
76 differences in the measured values could be due to different atmospheric conditions at the time of each test. This uncertainty is also included in the bars indicated. The maximum measured bypass ratio occurs at the lowest chamber pressure set point. At a primary mass flow of approximately 2.1 lbm/sec (0.95 kg/s) and a pressure ratio of approximately 41, the secondary mass flow becomes constant. As the chamber pressure increases further, the bypass ratio becomes inversely proportional to the chamber pressure and there is no added mass benefit. For this ejector the peak bypass ratio did not occur at the same set point pressure ratio as the secondary flow choke. As noted in Section 1.4 an ejector is operating at a maximum efficiency when the peak bypass ratio and the choke point occur at the same set point.
The bypass ratio shown is not the peak bypass ratio for this ejector
configuration, rather it is the largest bypass ratio value measured for this series of tests. The maximum bypass ratio would occur at a lower set point then tested here. The bypass ratio is influenced by the duct geometry and the nozzle configuration. For this ejector configuration, changes to the geometry should shift the bypass ratio. However, these geometry changes would also affect the maximum secondary mass flow and in a propulsion engine application affect the overall size of the vehicle.
5.2.2
Mach Numbers
Figure 5.2 shows the Mach numbers of the secondary flow at the fairing and of the mixed flow at the center of the duct exit for each of the chamber pressures studied. The secondary flow Mach number was calculated using Equation (4.20). The secondary flow Mach number ahead of the strut peaked around a value of 0.29 at a primary pressure
77 ratio of approximately 41 and remained subsonic for all tests. As expected this is consistent with the secondary mass flow choking indicated in Figure 5.1. The exit Mach number was both subsonic and supersonic depending on the rocket chamber pressure. When the flow was subsonic, Equation (4.20) was used to calculate the Mach number. When the flow was supersonic, Equation (4.21) was used to calculate the Mach number. For supersonic flow, pressure fluctuations increased significantly which in turn increased the random uncertainty in the calculation. In addition, a Monte Carlo approach was used to determine the total uncertainty. The increased random uncertainty and the uncertainty analysis approach combine to significantly increase the uncertainty associated with the calculated Mach number. This behavior is illustrated by
1.4
Mach Number
1.2
Inlet Exit
1.0 0.8 0.6 0.4 0.2 0.0 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.2 Secondary flow Mach number ahead of the strut and mixed flow Mach number at duct exit centerline (single nozzle strut).
78 the large uncertainty bars on the exit Mach number data at high pressure ratios in Figure 5.2. The Mach number at the duct exit continued to increase with increasing chamber pressure.
Around a pressure ratio of 47, the rate of increase changed
dramatically. Above this chamber pressure, the primary and secondary flows will fully mix by the exit of the duct. This will be shown more clearly in the exit pressure profile plots. For the highest pressure ratio in this dataset, the exit pressure measurements indicated that the centerline exit flow was supersonic with a Mach number of approximately 1.11.
5.2.3
Strut Gap Pressures
While the plots of Figures 5.1 and 5.2 indicate that the secondary flow becomes choked, these plots do not indicate the type of choke that occurs. In order to determine the choking mechanism, the secondary flow static pressures in the strut gap were examined. If the choke is an aerodynamic choke, it will occur in this region of the duct. Figure 5.3 shows the ratio of the wall static pressure to the secondary flow stagnation pressure at each of the ten pressure tap locations in the strut gap. All of the chamber pressure set points for the single nozzle strut are shown in the figure. The location of the pressure taps are shown as the ratio of the distance from the nozzle exit plane divided by the hydraulic diameter of the nozzle exit area. The dashed line in Figure 5.3 shows the sonic limit (Ps/Pos = 0.528 for γ = 1.4). A pressure ratio at or below this point would indicate the presence of an aerodynamic choke.
79 Pc/Pb
Strut Gap Pressure Ratio (P/Pos)
1
6.5 0.9
13.2 20.2
0.8
27.2 33.8 40.5
0.7
47.3 53.9
0.6
60.6 Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.3 Single nozzle strut gap pressure ratios.
Figure 5.3 shows consistent trends through the strut gap at any set point. The pressure ratio decreases as the flow approaches the nozzle exit plane. This trend is consistent with pressure loss due to a growing boundary layer in the gap. The lowest pressure ratio occurs at the last pressure tap, 0.843 hydraulic diameters upstream of the nozzle exit plane. A complex behavior can be seen at set points between 40.5 and 60.6, the set points where the secondary flow is choked. At set point pressure ratios of 40.5 and 47.3, the strutgap pressure ratios are nearly identical and are within uncertainty of the sonic limit. As the pressure ratio is increased above 47.3, the strut gap pressure ratios increase (away from the sonic limit). Figure 5.4 is an expanded plot of the strut gap region for these pressure ratios to more clearly show the flow behavior.
80
Strut Gap Pressure Ratio (P/Pos)
0.65
Pc/Pb 0.6
40.5 47.3 53.9 60.6
0.55
Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.4 Single nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 40.5, 47.3, 53.9, and 60.6).
The change in behavior in the strut gap region can be more clearly seen by examining the pressure ratios at the last strut gap position only. Figure 5.5 is a plot of the strut gap pressure ratio at the final strut gap position versus the set point pressure ratio. As the set point increases, the strut gap pressure ratio decreases and approaches the sonic limit. Between set point pressure ratios of 40.8 and 47.6, the strut gap pressure ratios are within uncertainty of the sonic limit. When the set point pressure ratio increases above 47.3, the behavior as the pressure ratio begins to increase. The plot of secondary mass flow indicated an apparent choke of the secondary flow around a set point pressure ratio of 33.8. The strut gap pressure ratio for this set point has not yet reached the sonic limit. This indicates that if a choke has occurred it is a mass choke of the secondary flow in the mixing duct. As the set point is increased above 33.8, the minimum strut gap pressure
81 ratio continues to decrease. If a choke had occurred in the strut gap, the pressure ratio could not decrease any further. For the next two highest chamber pressure set points examined (40.5 and 47.3), the pressure ratio at strut gap position 10 appears to be within uncertainty of the sonic limit. This indicates that the secondary flow chokes in the strut gap for this range of set points. For set point pressure ratios higher than 47.3, the pressure ratio in the strut gap increases away from the sonic limit indicating the flow is no longer choked in the strut gap. The mass flow plot indicated that the flow remained choked at these higher set points, thus the choke location has moved downstream of the strut gap into the mixing duct.
Strut Gap Pressure Ratio (P/Pos)
1.0 0.9 0.8 0.7
Sonic Limit
0.6 0.5 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.5 Single nozzle strut pressure ratio at last static pressure tap in the strut gap (0.843 hydraulic diameters upstream).
82 5.2.4
Mixing Section Static Pressure Distributions
Static pressure measurements along the centerlines of the top and side walls of the duct are used to evaluate mixing of the primary and secondary flow streams. Figures 5.6 through 5.11 show plots of the top and sidewall pressures for chamber pressure set points varying from 6.5 to 33.8. The wall pressures in the figures have been normalized by the secondary flow total pressure measured at the fairing upstream of the strut (the lab atmospheric pressure). A pressure ratio of 1 indicates the primary and secondary flow have fully mixed at that point. The strut gap pressure ratios have been included with the sidewall pressures distribution. At the top of the plots is a cross section of the duct for positional reference. For chamber pressure ratio set points between 6.5 and 33.8, the pressure distribution plots indicate that the sidewall pressure ratio drops through the strut gap and then begins to recover in the mixing duct. As seen in Figures 5.1 and 5.2, secondary flow did not reach a choke for set point pressure ratios of 33.8 and lower. Thus for these plots the ejector is operating in the mixed regime. The lowest sidewall pressure ratio is found at the last position in the strut gap region. The first side wall pressure tap in the mixing duct region shows a value approximately equal to the last strut gap pressure ratio. The pressure ratio begins to recover from this point and has completely recovered to a pressure ratio of 1.0 by 20 hydraulic diameters. The top wall pressure taps show a similar trend to the sidewall taps. The first two taps are located immediately downstream of the strut. In this region, the flow separates and recirculates as the secondary flow tries to turn around the strut base. This results in a
83
1.2
Pressure Pressure Ratio Ratio (P/Po (P/Pos) s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2
Pc/Pb = 6.5
0.0 -10
0
10
20
30
40
50
Position Position(x/Dh) (x/Dh)
Figure 5.6 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 6.5).
1.2
Pressure Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 13.2
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.7 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 13.2).
84
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 20.2
0.0 -10
0
10
20 30 Position (x/D ) h Position (x/Dh)
40
50
Figure 2.8 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 20.2).
Pressure Ratio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 27.2
0.0 -10
0
10
20 30 Position (x/D ) Position (x/Dh)h
40
50
Figure 2.9 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 27.2).
85
1.2
(P/Pos) Pressure Ratio (P/Po s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 33.8
0.0 -10
0
10
20
30
40
50
Position (x/Dh) Position (x/Dh)
Figure 5.10 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 33.8).
pressure ratio of 1 at the first two top wall pressure tap locations. At approximately 1.2 hydraulic diameters downstream, the lowest top wall pressure ratio is found. The pressure ratio begins to recover from this position, and has fully recovered by 20 hydraulic diameters downstream of the strut nozzle exit plane.
This pressure
equalization is an indication that the two flows have mixed. For these pressure ratio set points, the chamber pressure had little influence on the length of duct required for pressure recovery and mixing. Figure 5.11 shows the top and side wall pressure distribution for a set point pressure ratio of 40.5. The side wall pressure ratio distribution slightly deviates from the other lower pressure distributions. The pressure ratio dropped in the strut gap region. However, the pressure ratio continued to drop once the flow passed the strut nozzle exit
86 plane.
The lowest pressure ratio was found approximately 1.2 hydraulic diameters
downstream of the strut nozzle exit plane. The sidewall pressure begins to recover from this point and has fully recovered by 22.9 hydraulic diameters downstream of the nozzle exit plane. The top wall pressure ratio distribution for this set point followed the same trend as the lower pressures. For this set point, the secondary flow has reached a choke in the strut gap region of the duct. As flow expands from the choke into the mixing duct, the flow experiences an acceleration which accounts for the pressure drop.
Pressure PressureRatio Ratio(P/Pos) (P/Pos)
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc = 40.5 psi
0.0 -10
0
10
20 30 Position(x/Dh) (x/Dh) Position
40
50
Figure 5.11 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 40.5).
The pattern of an initial pressure ratio drop to a low value, followed by a recovery region to pressure equalization, is identified as the “low pressure” trend. This trend will again be seen with the dual nozzle struts at low set point pressure ratios. It should be
87 noted that the trend appears to be mass flow driven as opposed to pressure driven. That is, the same trends are seen in the dual nozzle strut at the equivalent mass flow rates rather than the equivalent chamber pressures. However, the lower mass flow rates are results of lower chamber pressures in the strut rockets. This point will be discussed in more detail in a later section. Figures 5.12 through 5.14 show plots of the top and side wall pressure distributions for set point pressure ratios of 47.3, 53.9, and 60.6. The trends seen in these plots are significantly different from the “low pressure” trends observed in Figures 5.6 through 5.11. As seen in Figures 5.1 and 5.2, the secondary mass flow is choked at these set point pressure ratios. For these set points, there is a sharp drop in sidewall pressure ratios which begins at the strut nozzle exit plane and drops to a pressure ratio of
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 Side Wall
1.0
Top Wall 0.8 0.6 0.4 0.2 Pc/Pb = 47.3
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.12 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 47.3).
88
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0
Side Wall Top Wall
0.8 0.6 0.4 0.2 Pc/Pb = 53.9
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.13 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 53.9).
Pressure PressureRatio Ratio(P/Pos) (P/Pos)
1.2 1.0 Side Wall Top Wall
0.8 0.6 0.4 0.2 Pc/Pb = 60.6
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.14 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 60.6).
89 approximately 0.25 at 5.4 hydraulic diameters downstream of the nozzle exit plane. There is an apparent pressure ratio discontinuity at this location as the pressure ratio increases, then begins to drop to a value of 0.3. The pressure ratio appears relatively steady at this value until some point downstream where the flow begins to recover. The distance from the nozzle exit plane to this pressure recovery point increases with the setpoint pressure ratio. The side wall pressure ratio does not appear to completely recover to a value of 1 by the last pressure tap (44.6 hydraulic diameters downstream of the nozzle exit plane). This is an indication that the secondary and primary flows are not well mixed for these chamber pressures. The pressure ratio measurement uncertainty in the recovery region of Figures 5.12 through 5.14 is relatively large. This uncertainty is a reflection of the flow unsteadiness rather than instrumentation uncertainty. Each point is averaged from ten measurements from ten tests. The average values of the pressure ratios from each test were very close. However, the standard deviation of the ten measurements was very large because of pressure fluctuations due to the turbulent nature of the flow. The top wall pressure ratios in Figure 5.12 exhibit a slightly different trend from the side wall pressure ratios. The region of separation within the first half inch of duct downstream of the strut is still visible in the first two measurements of the top wall pressure trace. At 1.2 hydraulic diameters downstream, the top wall pressure ratio drops to an intermediate value between 0.4 and 0.5 depending on the set point pressure ratio. The pressure ratio then rises to a value of 0.55 and 0.66 around 3.6 hydraulic diameters downstream. The pressure ratio then steadily drops to a minimum value around 0.25 at 6.6 hydraulic diameters downstream.
Between 7.8 and 8.4 hydraulic diameters
90 downstream there is a sharp discontinuity in the pressure ratio which increases to a value around 0.45. The pressure ratio then drops again and continues to go through a series of steady decreases followed by discontinuous rises until the pressure ratio begins a steady recovery to atmospheric pressure. The recovery location for the top wall pressure ratio is the same as that of the side wall. As with the side wall, the recovery location appears to be dependent on the set point pressure and does not fully recover by the end of the instrumented duct (42 hydraulic diameters downstream of the exit plane). Because the embedded rocket nozzle is designed for optimum expansion at a chamber pressure around a pressure ratio set point of 44.2, the trend change of the pressure ratio distribution was originally theorized to be due to the transition in plume behavior from overexpanded to ideal and then underexpanded. However, tests of a dual nozzle strut indicate the trend is more likely due to primary mass flow addition. The sharp discontinuities found in the higher pressure ratio plots are caused by shock structure in the duct. The presence of the shocks was verified through shadowgraph flow visualization which will be presented in a later section.
5.2.5
Exit Pressure Profiles
Based on the wall profile plots (Figures 5.12 through 5.14), it was believed that at high chamber pressures the flow does not have time to mix within the length of the duct. Thus a high pressure core flow would exist at the exit. Figure 5.15 shows the results of one set of duct traces across the centerline horizontal plane (trace location A in Figure 3.8). The average stagnation pressure measurement with uncertainty for each position in the duct exit is given. When the secondary and primary flows are completely
91 mixed, the stagnation pressure should be constant across the duct exit plane. The data in Figure 5.15 indicate that the flow appears to be well mixed for set point pressure ratios up to 40.8. For these set points there is a slight drop off near the side wall (x/wexit = 0) which is believed to be attributed to a thickening boundary layer. This drop off becomes more pronounced as the set point pressure ratio is increased. At higher pressure ratio set points of 47.1, 53.7, and 54.4, a clear variation of the stagnation pressure exists across the exit plane. At the center of the duct, the stagnation pressure is at a maximum and drops as the side wall is approached. These data verify the presence of a high velocity core flow surrounded by a lower velocity secondary flow, and also show that complete mixing does not occur at these pressures. This agrees with trends in the corresponding top wall and side wall pressure data (Figure 5.10 and Figures 5.12 through 5.14). The stagnation pressure measurements at the high primary chamber pressures exhibited large variations in the measured steady state values which is indicative of turbulent flow. This was also noted for the mixing duct wall pressure distribution plots at high chamber pressures. For the highest two set point pressure ratios, the plotted data shows inflection points. This point may indicate the location of the center of the mixing region between the core flow and the surrounding subsonic secondary flow. The data from the traces at each vertical position were combined to create surface plots of the stagnation pressure in a quadrant of the duct exit. Figures 5.16 through 5.21 show the stagnation pressure surfaces for set point pressure ratios between 6.5 and 40.4. The total pressure across the quadrant shows a fairly uniform profile with some drop off near the sidewall and near the top wall due to boundary layer.
92 Set Point Pressure Ratio
Pressure Ratio (Poexit/Pb)
2.4
60.3 53.7 47.1 40.4 33.8 27.2 19.8 13.2 6.5
2.2 2.0 1.8 1.6 1.4 1.2 1.0 0
0.1
0.2
0.3
0.4
0.5
Position (x/wexit)
Figure 5.15 Single nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).
w) (x/ n o iti Pos 0.4 l a t zon i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
Duct Top Wall
2.5
Vertical Position (y/h)
0.0
Strut Centerline
0.2
0.4
Duct Side Wall
Pc/Pb = 6.5
Duct Centerline
Figure 5.16 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.5).
93 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 13.2
Figure 5.17 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.2).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 19.8
Figure 5.18 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.8).
94 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 27.2
Figure 5.19 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.2).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 33.8
Figure 5.20 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 33.8).
95 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 40.4
Figure 5.21 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 40.4).
Figures 5.22 through 5.24 show the stagnation pressure results for a quadrant at the duct exit for pressure set points of 47.1, 53.7 and 60.3, respectively. For these cases, the wall pressure ratio distribution plots (Figures 5.12, 5.13, and 5.14) indicated that the flow was not well mixed and a core flow existed throughout the duct. The stagnation pressure at the center of the exit is significantly higher than the pressure near the walls. The total pressure for the highest primary chamber pressure appears to show a sharper initial pressure gradient in the horizontal direction (towards the side wall) than in the vertical direction. This could be due to effects of the base of the strut. The large pressure gradients verify that the primary and secondary flows are not mixed at the exit, and a core flow is indeed present.
96 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 47.1
Figure 5.22 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 47.1).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 53.7
Figure 5.23 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 53.7).
97 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 60.3
Figure 5.24 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 60.3).
5.3
Dual Nozzle Strut
Experiments on the dual nozzle strut were conducted at chamber pressure set points of 3.5, 6.8, 10.2, 13.5, 16.9, 10.4, 24.0, 27.4, and 30.6. The primary mass flow for the dual nozzle strut at these pressure ratio set points corresponds to the same mass flow at a set point twice as high in the single nozzle strut. For example, the primary mass flow at a chamber pressure set point ratio of 3.4 in the dual nozzle strut is approximately equivalent to the primary mass flow at a chamber pressure set point ratio of 6.8 in the single nozzle strut. Data from ten separate tests at each chamber pressure were averaged for the mixing duct, mass flow, and Mach number results. As with the single nozzle strut, a single set of experiments is reported for the exit pressure profile plots.
98 5.3.1
Mass Flow Augmentation
Figure 5.25 shows the secondary and primary mass flow rates and the bypass ratio plotted against the set point ratio. The trends of this plot are similar to those for the single nozzle strut shown in Figure 5.1. The primary mass flow increases linearly with chamber pressure. The secondary mass flow increases with increasing chamber pressure until reaching a value of approximately 2.1 lbm/sec (0.91 kg/s) at a set point ratio of 20.4. As the ratio is increased above 20.4, the secondary mass flow remains fairly constant indicating that the secondary flow has choked.
Mass Flow (lbm/s)
Bypass Ratio (ms/mp)
3.5 3.0 2.5 Bypass Ratio Secondary Mass Flow
2.0 1.5
Primary Mass Flow
1.0 0.5 0.0 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc/Pb)
Figure 5.25 Dual nozzle strut secondary and primary mass flow.
The maximum calculated bypass ratio for this series of tests occurred for the lowest pressure ratio set point tested. As the pressure ratio is increased, the bypass ratio drops. Once the pressure ratio of 20.4 is reached, the secondary mass flow becomes
99 constant and the bypass ratio decreases only as a function of increasing primary mass flow.
5.3.2
Mach Numbers
The inlet and exit Mach numbers for the dual nozzle strut are presented in Figure 5.26. The inlet Mach number increased with increasing chamber pressure to a value of 0.29 around a set point pressure ratio of 20.4. As the pressure ratio is increased above 20.4, there is little variation in the inlet Mach number. The exit Mach number increases with increasing chamber pressure throughout the tests. Between set points of 24.4 and 27.4, the centerline exit flow becomes sonic. When the flow becomes sonic, there is an apparent change in slope. The highest Mach number determined at the exit was approximately 1.3. As noted for the single nozzle plots, the higher Mach numbers
1.6 1.4
Inlet
Mach Number
1.2
Exit
1.0 0.8 0.6 0.4 0.2 0.0 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc /Pb)
Figure 5.26 Dual nozzle inlet and exit centerline Mach numbers.
100 have a larger uncertainty, which is due to both the increased turbulent fluctuations and the methodology used to determine the uncertainty as described in Chapter 4.
5.3.3
Strut Gap Pressures
Figure 5.27 shows the pressure ratios in the strut gap region for each dual nozzle chamber pressure set point tested. Through the strut gap, the pressure ratio drops as the flow approaches the nozzle exit plane. For the dual nozzle strut, an instrumentation error prevented the use of one of the strut gap positions (2.53 hydraulic diameters upstream of the nozzle exit) that was available for the single nozzle strut. However, the trends in the strut gap for the dual nozzle strut are similar to those seen in the single nozzle, and the
Pc/Pb
Strut Gap Pressure Ratio (P/Pos)
1
3.5 6.8
0.9
10.2 13.5
0.8
16.9 20.4
0.7
24.0 27.4
0.6
30.6 Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.27 Dual nozzle strut gap pressure ratios.
101 additional pressure tap would not add significant insight. The minimum pressure ratio was located at the last pressure tap in the strut gap region. Thus if the choke in the strut gap is an aerodynamic choke, the pressure at the last strut gap position should reach the sonic pressure limit. Figure 5.28 shows an expanded plot of the strut gap region for these pressure ratios to more clearly show the flow behavior. Similar to the single nozzle strut gap pressure ratios, the dual nozzle strut gap pressure ratio decreases as the flow approaches the nozzle exit plane.
The lowest pressure ratio occurs at the last pressure tap,
0.843 hydraulic diameters upstream of the nozzle exit plane. A similar complex behavior can be seen at set points between 24.0 and 30.6, the set points where the secondary flow
Strut Gap Pressure Ratio (P/Pos)
0.7
Pc/Pb
0.65
20.4 24.0
0.6
27.4 30.6 Sonic Limit
0.55
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.28 Dual nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 20.4, 24.0, 27.4, and 30.6).
102 is choked for the dual nozzle strut. At set point pressure ratios of 24.0 and 27.4, the strutgap pressure ratios are nearly identical and are within uncertainty of the sonic limit. As the pressure ratio is increased above 27.4, the strut gap pressure ratios increase but remain within uncertainty of the sonic limit. Figure 5.29 shows the pressure ratio at the last strut gap position. As the set point pressure ratio is increased, the minimum strut gap pressure ratio decreases (approaching the sonic limit). When a set point pressure ratio of 24.0 is reached, the minimum pressure ratio is within uncertainty of the sonic limit. For the next highest set point pressure ratio (27.4), the strut gap pressure ratio is still within uncertainty of the sonic limit. As the chamber pressure is increased above 27.4, the minimum strut gap pressure ratio begins to increase moving away from the sonic limit, although at the highest set
Strut Gap Pressure Ratio (P/Pos)
1.0
0.9
0.8
0.7
0.6
0.5 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc /Pb)
Figure 5.29 Dual nozzle strut gap pressure ratios at last static pressure tap (0.843 hydraulic diameters upstream).
103 point the uncertainty band still reaches the sonic limit. Similar to the single nozzle strut, this indicates a change in behavior of the secondary flow.
The mass flow plot
(Figure 5.25) indicates a choke of the secondary flow, but the choke may be moving out of the strut gap region as the pressure ratio is increased above these set points.
5.3.4
Mixing Section Static Pressure Distribution
Figures 5.30 through 5.35 show the top and side wall pressure distributions for the dual nozzle strut at set point pressure ratios from 3.5 to 20.4. The trends in these plots follow the “low pressure” trend identified in the single nozzle strut pressure distributions. For all of these primary chamber pressures, the side wall pressure ratio drops in the strut gap. For set point pressure ratios of 16.9 and lower, the side wall pressure ratio begins to recover immediately after passing the strut nozzle exit plane.
The recovery region
continues until approximately 20 hydraulic diameters downstream. The top wall pressure ratio shows the same recirculation region in the first 0.6 hydraulic diameters downstream of the strut nozzle exit plane as indicated by a pressure ratio of one at the first two pressure taps. After the recirculation region, the top wall pressure ratio drops to a value comparable to the sidewall pressure ratio at the same location. The top wall pressure ratio then begins to recover and has fully recovered by 19.64 hydraulic diameters. For the pressure ratio set point of 20.5, the wall pressure ratio continues to drop in the mixing duct until 1.2 hydraulic diameters downstream then the pressure begins to recover. A similar trend was seen in the single nozzle pressure distributions for a set point pressure ratio of 40.5 (Figure 5.12).
Both the top and side wall pressure ratios recover by
104
1.2
Pressure Ratio Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 3.5
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.30 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 3.5).
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 6.8
0.0 -10
0
10
20 30 Position Position(x/D (x/Dh) h)
40
50
Figure 5.31 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 6.8).
105
1.2
Pressure Ratio (P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 10.2
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.32 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 10.2).
1.2
Pressure Ratio Ratio (P/Pos) (P/Pos) Pressure
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 13.5
0.0 -10
0
10
20 30 Position Position(x/D (x/Dh) h)
40
50
Figure 5.33 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 13.5).
106
1.2
PressureRatio Ratio(P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 16.9
0.0 -10
0
10
20
30
40
50
Position Position (x/D (x/Dh) h)
Figure 5.34 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 16.9).
1.2
Pressure Ratio Ratio (P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 20.5
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.35 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 20.5).
107 approximately 19.68 hydraulic diameters downstream of the strut nozzle exit plane. Thus, the primary chamber pressure seemed to have little influence on the mixing length. Figures 5.36 through 5.38 show the top and side wall pressure distributions for set point pressure ratios of 24.0, 27.4, and 30.7. These plots exhibit the “high pressure” trend. The set point pressure ratio of 24 is the primary chamber pressure at which the transition from the high to low pressure trends occurs. At this chamber pressure the pressure distribution plots showed characters of both trends.
For some tests, the pressure
distribution would follow the high pressure trend. In other tests the pressure distribution would initially show a low pressure trend, but midway through the test, the high pressure trend would develop. For this reason, the uncertainty associated with the average reading from multiple tests is very high.
1.2
Pressure Pressure Ratio Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 24.0
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.36 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 24.0).
108
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 27.4
0.0 -10
0
10
20 30 Position h) Position(x/D (x/Dh)
40
50
Figure 5.37 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 27.4).
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6 Side Wall Top Wall
0.4 0.2 Pc/Pb = 30.7
0.0 -10
0
10
20 30 Position h) Position(x/D (x/Dh)
40
50
Figure 5.38 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 30.7).
109 For higher set point pressure ratios (Pc/Pb =27.4 and 30.7), the high pressure trend was always present. There is still a side wall pressure ratio drop in the strut gap region. However, immediately past the nozzle exit plane, the pressure ratio continues to drop. In the single nozzle plots, the drop was to a fairly steady value of 0.3. However, for the dual nozzle plots, there is much more scatter in the data and the pressure ratio varies in the range of 0.3 to 0.6. A pressure recovery is clearly present after this region. For a set point pressure ratio of 27.4, it appears the wall pressure ratio almost recovers by the end of the duct. However, for a set point of 30.7, it does not appear that the pressure ratio recovers by the end of the duct. Thus a core flow was suspected to be present at the duct exit for both of the higher set point pressure ratios. Similar to the high pressure trends for the single nozzle pressure distribution plots, there were several areas of discontinuity which are believed to be due to shock structure in the duct.
5.3.5
Exit Pressure Profiles
Figure 5.39 shows total pressure traces across the horizontal centerline of the duct exit plane. The ratio of the total pressure divided by the back pressure is plotted against the horizontal location divided by the width of the duct. Traces at the three lowest chamber pressures show a uniform total pressure across the exit plane with some drop off in the side wall boundary layer. The next four set points show a small gradient across the exit plane but still indicate fairly complete mixing. At the highest set points (27.1 and 30.3), an obvious pressure gradient exists across the exit plane. These plots indicate the presence of a supersonic core flow (Po/P > 1.893). These two traces also have inflection points which would indicate the location of the center of the mixing region between the
110 core flow and the surrounding subsonic secondary flow.
These results verify the
presence of the supersonic core predicted by the duct wall pressure distributions.
Set Point Pressure Ratio
2.8
Pressure Ratio (Poexit/Pb)
2.6 2.4
30.3 27.1
2.2
23.8
2.0
19.9
1.8
16.7 13.3
1.6
10.1
1.4
6.9 3.5
1.2 1.0 0
0.1
0.2
0.3
0.4
0.5
Position (x/wexit)
Figure 5.39 Dual nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).
Figures 5.40 through 5.46 show the carpet plots of the exit total pressure for the dual nozzle strut set point ratios of 3.5 to 23.9. At these chamber pressures, the duct wall pressure distribution plots exhibited the low pressure trend. The sidewall and top wall duct pressure plots for set points from 3.5 to 16.9 indicated the flow was completely mixed within the first 17 hydraulic diameters of the duct downstream of the nozzle exit plane.
The exit profile plots for these chamber pressures verify that there is an
approximately uniform pressure distribution across a quadrant at the exit. Although at higher chamber pressures there is a slight pressure decrease near the sidewall and a slight
111 pressure variation across the exit plane, the total variation is relatively small. This verifies that the flow is well mixed at the exit. At Pc/Pb = 23.9, there is some pressure gradient across the quadrant with the center pressure being around 4 psi higher than the pressure near the walls. This chamber pressure is just below the chamber pressure at which the duct flow switches from the low pressure trend to the high pressure trend. Figures 5.47 and 5.48 show the stagnation pressure profiles at the exit for set point pressure ratios of 27.1 and 30.3. At these set points, the centerline traverse showed a larger pressure gradient across the exit. The centerline pressure was very high while the pressure near the walls dropped off significantly. The carpet plots verify this prediction.
/ n (x
w)
tio osi P 0.4 l nta o z i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio ( P
2.0
exit / P b)
Duct Top Wall
2.5
Vertical Position (y/h)
0.0
Strut Centerline
0.2
0.4
Duct Side Wall
Pc/Pb = 3.5
Duct Centerline
Figure 5.40 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 3.5).
112
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 6.9
Figure 5.41 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.9).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 10.1
Figure 5.42 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 10.1).
113
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 13.4
Figure 5.43 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.4).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 16.7
Figure 5.44 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 16.7).
114
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 19.9
Figure 5.45 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.9).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 23.9
Figure 5.46 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 23.9).
115
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 27.1
Figure 5.47 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.1).
/w) n (x o i t o si 0.4 al P t n rizo 0.2 o H
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 30.3
Figure 5.48 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 30.3).
CHAPTER 6
DISCUSSION OF RESULTS
6.1
Mass Flow and Bypass Ratio The primary and secondary mass flow rates for both struts were independently
plotted in Figures 5.1 and 5.25. For both struts, the primary mass flow rate is directly proportional to the chamber pressure. Figure 6.1 is a plot comparing the secondary mass flows for the single and dual nozzle struts at each set point pressure ratio. The maximum entrained (secondary) mass flows for both struts are equal (about 2.1 lbm/s) within uncertainty.
The maximum secondary mass flow for this study is limited by the
secondary flow minimum geometric area in the strut gap. Since this area is equal for both struts, the maximum secondary flow that can be induced should also be equal. For set point pressure ratios below the secondary flow choke point, the dual nozzle strut induces more secondary mass flow than the single nozzle strut. This can be explained by simple momentum principles. The total primary jet momentum, Jp, is approximately given by
J p = Ap Pp + m pV p ,
116
(6.1)
117 where Ap is the area of the nozzle exit, Pp is the pressure of the primary flow at the nozzle exit, m p is the mass flow through the nozzle and Vp is the velocity at the nozzle exit. At the same set point pressure ratio, the dual nozzle strut has twice the nozzle exit area as the single nozzle and twice the mass flow. The velocity and the pressure at the nozzle exit for both nozzles, however, will be approximately equal. Thus, at the same pressure set point, the total momentum of the dual nozzle primary flow will be twice that of the single nozzle strut. Since the momentum exchange is a primary driver for secondary flow entrainment, the dual nozzle strut has more momentum to exchange and thus can entrain more secondary flow. Once the secondary flow choke point is reached, the induced mass flow becomes constant and increases in chamber pressure do not increase the secondary mass flow.
2.5
Mass Flow (lb/s) Mass Flow (lbm/s)
2 1.5 1 Dual Nozzle Strut Single Nozzle Strut
0.5 0 0
10
20
30 40 50 Pressure Ratio Pressure Ratio(Pc/Pb) (Pc/Pb)
60
70
Figure 6.1 Secondary mass flow versus set point pressure ratio for single and dual nozzle struts.
118 Figure 6.2 shows the secondary mass flow in both struts plotted against the primary mass flow. By plotting the secondary mass flow against the primary mass flow rate, the loss in efficiency of the momentum exchange between the primary flow and secondary flow for the dual nozzle strut can be seen. For equivalent mass flow rates (Pcsingle = 2 Pcdual), the single nozzle strut induces a slightly higher mass flow rate for set point ratios below the secondary flow choke point. Because an equivalent mass flow rate in the dual nozzle strut occurs at a set point pressure ratio that is one half of the set point in the single nozzle, the nozzle exit pressure for the dual nozzle strut will be approximately one half of the nozzle exit pressure for the single nozzle strut. The first term on the right hand side of Equation (6.1) will be equal for the dual and single nozzle strut at equal mass flow rates. The velocity at the nozzle exit is a function of the area ratio and the chamber temperature. In both struts, the area ratio is the same and the
Secondary MassMass Flow Flow (lb/s) (lbm/s)
2.5
2
1.5
1
Dual Nozzle Strut Single Nozzle Strut
0.5
0 0
0.5
1
1.5 2 2.5 Primary Mass Flow (lb/sec) Primary Mass Flow (lbm/s)
3
Figure 6.2 Secondary mass flow comparison for both struts.
3.5
119 chamber temperature variation over the range of set points tested is negligible. Thus at equivalent mass flow rates, the momentum of the two jets is approximately equivalent. The difference in entrainment between the two struts may be due to a loss in the efficiency of the momentum exchange. This loss is attributed to the interaction of the two primary stream plumes with each other and the lower expansion angle of the primary flow plume leaving less surface area for interaction with the secondary flow stream. At set point pressure ratios above the choke point, there is an apparent change in the entrainment. The dual nozzle strut seems to entrain more secondary mass flow. Since the exit pressure for the single nozzle is double that of the dual nozzle for the same mass flow rate, the plume expansion for the single nozzle is greater. Thus the mimimum area the secondary flow sees (between the expanded primary flow and the wall) reduces quicker with increasing mass flow. The secondary mass flow induced with the single nozzle strut and the dual nozzle strut were compared with the results from previous studies at the UAH PRC [24, 25]. Although for some of the comparison plots no uncertainty level was available, the previous mass flow rates show very good agreement with the data from the current set of experiments. The maximum secondary mass flow was approximately the same and the primary nozzle chamber pressure which choked the flows was approximately the same. This agreement led to increased confidence in the results of the current experiment.
6.1.1
Mass Flow Calculations
Figure 6.1 indicated that the secondary flow becomes choked around set point pressure ratios 40.5 for the single nozzle strut and 24.0 for the dual nozzle strut. The strut
120 gap pressures (Figures 5.3 and 5.27) indicate that the pressure ratio in the strut gap region (P/Pos) approaches the sonic limit 0.528 at the same range of set point pressure ratios in each strut. For set point ratios 40.5 and 47.3 in the single nozzle strut, the pressure ratio in the strut gap region (Figure 5.3) is within uncertainty of the sonic limit. As the chamber pressure is increased further, the minimum pressure ratio in the strut gap increases away from the sonic limit. A similar trend was seen for the dual nozzle strut. At set point pressure ratios of 24.0 and 27.4, the minimum pressure ratio in the strut gap region was within uncertainty of the sonic limit. At a higher set point pressure ratio of 30.6, the pressure ratio had increased away from the sonic limit. However the strut gap pressure ratio still remained within uncertainty of the sonic limit. These data indicate that both ejectors are operating in all three Fabri regions over the range of pressure ratios examined (see Section 1.3). At low set points, the secondary flow does not reach the sonic limit, thus the ejector is operating in the mixed regime. At mid range set points, the secondary flow chokes and the pressure ratio in the minimum geometric area reaches the sonic limit, indicating an aerodynamic choke.
At these
operating conditions, the ejector is operating in the Fabri saturated supersonic regime. At high set points the choke moves downstream into the mixing duct and the pressure ratio in the mixing duct increases away from the sonic limit. At these operating conditions, the ejector is operating in the supersonic regime. For the saturated supersonic mode, the secondary flow is choked in the minimum geometric area and the mass flow can be calculated according to idealized flow equations using the entire cross section of the duct with no boundary layer reduction. The mass flow determined at the fairing, and plotted in Figure 6.2, must be equal to mass flow
121 through the strut gap. The theoretical maximum mass flow for air through an area equal to the strut gap area is 3.4 lbm/s (1.54 kg/s). This value is approximately 66% higher than the maximum secondary mass flow calculated from the experimental data. Furthermore, for isentropic choked flow in the strut gap, the inlet Mach number at the fairing would be 0.4 which is nearly twice as high as the calculated Mach number. Thus if the choke is an aerodynamic choke in the strut gap, then there are significant geometric effects in this region that have not been accounted for. The geometry of the duct would lead to significant boundary layers, particularly in the corners of the duct.
In the strut gap region, the boundary layer would be
compounded by four additional corners caused by the strut/wall intersections. Early studies of the PRC ejector system provided total pressure traces across the strut gap region [24]. The ratio of the measured stagnation pressure to atmospheric pressure in these figures indicated a fairly flat profile across the strut gap with some decrease in stagnation pressure near the walls. These data are indicative of a boundary layer buildup on the wall side of the strut gap region. The strut side boundary layer is smaller, but could still be significant. Thus, it is probable that the lower mass flow could be attributed to boundary layer growth. The traces from these plots were not taken near the top and side walls of the duct.
In the corner region, the boundary layer effect could be
intensified, reducing the stagnation pressure even further. The mass flow rates shown in Figure 6.2 are also idealized to some extent. Even when a simplified boundary layer thickness was accounted for, the mass flows calculated from the experimental data at the secondary flow inlet and through the nozzle do not equal the calculated mass flow at the mixing duct exit. The exit mass flow ranged from
122 8% to 28% greater than the sum of the inlet mass flow rates which violates the continuity equation. Through standard error propagation techniques, the measurement uncertainty was around 4% of the combined primary and secondary inlet mass flows. This leads to the conclusion that there are either additional losses in the duct not accounted for (such as leaks) or that the method used to calculate the mass flow has uncertainty which is greater than the measurement uncertainty. Although the incompressible flow assumption seems reasonable for the entrance region, there is an unknown velocity profile across the duct. The calculated secondary mass flow rate is based on the maximum centerline velocity and is thus somewhat larger than the true average value for the cross section. Thus some additional uncertainty in the mass flow calculation is believed to be attributed to the calculation methodology rather than the experimental uncertainty or additional losses in the system.
Despite the
uncertainty, the mass flow plots give an indication of the relative change in mass flow with increasing set point pressure ratio and the plots give a clear indication of a choking secondary flow.
6.1.2
Bypass Ratio
The plots of the bypass ratio plotted against the pressure ratio for each individual strut were shown in Figures 5.1 and 5.25. The two curves show similar trends; however, the dual nozzle strut initially shows a much sharper decrease in the bypass ratio with increasing pressure ratio. To directly compare the bypass ratio for the two struts, their bypass ratios are plotted against the primary mass flow rate in Figure 6.3. The largest bypass ratio occurred at the lowest mass flow rate for each struts. The average peak
123 bypass ratio was about 15% higher for the single nozzle strut than for the dual nozzle strut at the lowest pressure ratio. Similar to the trend for the secondary mass flow, for both struts at pressures below the secondary flow choke, the single nozzle strut has a slightly higher bypass ratio. The single nozzle strut appears to entrain more secondary air for a given primary mass flow rate. Once the choke is reached, the bypass ratio for each strut becomes approximately equal, and is strictly a function of the primary mass flow, independent of the number of nozzles in the strut.
3.5 3.0
Dual Nozzle Strut
Bypass Ratio
2.5
Single Nozzle Strut
2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Primary Mass Flow Rate (lbm/s)
Figure 6.3 Bypass ratio versus primary mass flow rate for single and dual nozzle struts.
The bypass ratio provides a measure of the effectiveness of the momentum exchange for the ejector in a propulsion application. As discussed in Chapter 1, the ideal operating condition from an entrainment stand point occurs when the peak bypass ratio
124 occurs at the same primary flow operating conditions as the secondary mass flow choke. For the chamber pressures examined in this study, the highest bypass ratio occurred for the lowest chamber pressure examined. Thus, the peak bypass ratio for each strut would occur at a chamber pressure lower than those tested in this study, and would be well below the chamber pressure for choked secondary flow. A single test of each strut was conducted to determine the suction ratio for lower pressure ratios. In this series of tests, the set point pressure ratio was decreased until a ratio of 2 was reached in each strut. This set point is the lowest operation point which maintains a choked primary flow. Figure 6.4 shows the bypass ratio versus the pressure ratio for the low pressure ratio tests for the dual and single nozzle struts. The highest
5
Bypass Ratio
4
3
2
1
0 0
5
10
15
20
25
30
Set Point Pressure Ratio Single Tests Dual Nozzle Low Pressures
Single Nozzle Low Pressures
Repeated Tests Dual Nozzle Repeated Values
Single Nozzle Repeated Values
Figure 6.4 Bypass ratio versus pressure ratio for the dual and single nozzle struts with low pressure test data.
125 bypass ratio determined from the low pressure tests occurred at the lowest set point. At these chamber pressures, the nozzle would be significantly over expanded and would be subject to separation and to shocks forming inside the nozzle which would decrease the efficiency of the rocket performance.
Increasing the duct cross-sectional area or
decreasing the nozzle exit area should move the peak towards the choke point; however, this would also change the characteristics of the duct, so the maximum mass flow would change.
6.2
Pressure Distribution
Figures 6.5 through 6.9 show plots of the wall pressure distributions for chamber pressures below the secondary flow choke point in the single and dual nozzle struts. Each plot shows the top and side wall pressure ratios for approximately equivalent primary mass flow rates. For the lowest set point pressure ratio in each strut (6.5 and 3.5), the wall pressure distributions appear to be almost identical. As the primary mass flow rate (e.g., set point pressure ratio is increased), the pressure distributions begin to separate. The pressure distribution in the strut gap region and in the first 15 inches of the mixing duct show similar trends; however, the pressure drop in this region is larger for the single nozzle strut than for the dual nozzle strut for approximately equal primary mass flow rates. This increased pressure drop also corresponds to a slightly larger secondary mass flow as was seen in the mass flow comparison plot (Figure 6.2).
126
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
6.5
Primary Mass Flow (lbm/s)
0.33
0.8
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
3.5
Primary Mass Flow (lbm/s)
0.36
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.5 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.3 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
13.2
0.8
Primary Mass Flow (lbm/s)
0.67
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
6.8
Primary Mass Flow (lbm/s)
0.70
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.6 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.7 lbm/s).
127
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
20.2
0.8
Primary Mass Flow (lbm/s)
1.03
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
10.2
Primary Mass Flow (lbm/s)
1.05
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.7 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.05 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
27.2
0.8
Primary Mass Flow (lbm/s)
1.39
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
13.5
Primary Mass Flow (lbm/s)
1.39
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.8 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.39 lbm/s).
128
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
33.8
0.8
Primary Mass Flow (lbm/s)
1.73
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
16.9
Primary Mass Flow (lbm/s)
1.74
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.9 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.74 lbm/s).
Figure 6.10 shows the mixing duct wall pressure distribution plots for the single and dual nozzle struts at set point pressure ratios of 40.5 (single nozzle) and 20.4 (dual nozzle). At these set points, the secondary flow has reached a choke in the strut gap region. The general trend for pressure recovery in this plot follows the low pressure trend. The wall pressure ratio drops through the strut gap region reaching the sonic limit (5.28) at the last pressure tap in the strut gap. The pressure ratio continues to drop just past the strut until it reaches some minimum value and then begins to recover. Both struts indicated a recirculation region at the top wall just downstream of the strut. The pressure ratio has completely recovered by 23 hydraulic diameters.
129
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
40.5
0.8
Primary Mass Flow (lbm/s)
2.07
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
20.4
Primary Mass Flow (lbm/s)
2.11
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.10 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.1 lbm/s).
Figures 6.11 through 6.13 show the pressure distribution for the single and dual nozzle duct at approximately equivalent primary mass flow rates for operating conditions at or above the secondary flow choke. These plots show a high pressure trend for the single nozzle strut. The dual nozzle strut wall pressure distribution in these plots was between the high and low pressure trends as described in Section 5.2.4. The plots of the highest two mass flows for each strut exhibit high pressure trends. For these two cases, the pressure recovery region occurs farther downstream for the single nozzle strut than it does for the dual nozzle strut. The pressure recovery curves have significantly different slopes. The dual nozzle recovery appears to be much steeper over the first portion of the recovery region, then begins to asymptotically approach a value of one. For the single
130
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
47.2
0.8
Primary Mass Flow (lbm/s)
2.41
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
24.0
Primary Mass Flow (lbm/s)
2.47
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.11 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.45 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
53.8
0.8
Primary Mass Flow (lbm/s)
2.74
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
27.4
Primary Mass Flow (lbm/s)
2.82
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.12 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.78 lbm/s).
131
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
60.5
0.8
Primary Mass Flow (lbm/s)
3.10
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
30.6
Primary Mass Flow (lbm/s)
3.16
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.13 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 3.13 lbm/s).
nozzle strut, the curve appears to have a lower slope which increases as the flow moves downstream. At equivalent mass flow rates, the pressure recovery for the dual nozzle strut is much better than that of the single. This is believed to be due to the pressure of the primary flow at the exit of the nozzle. From simple isentropic flow relations, it can be shown that the nozzle exit pressure for the dual nozzle strut is approximately half of the nozzle exit pressure for the equivalent mass flow in the single nozzle strut. This lower pressure seems to lead to a quicker pressure recovery.
6.3
Flow Visualization
As discussed in numerous literature sources [9, 10, 25, 42], the flow in an ejector mixing duct experiences a series of shock and expansion waves as the pressure attempts
132 to recover to the atmospheric value at the exit. Experiments were performed to capture shadowgraph images of the PRC ejector system to visualize any shock structures and correlate them to the experimental results [37]. It was found that pressure distribution trends in the mixing duct were a function of the primary mass flow rate rather than the nozzle exit pressure [43]. The shadowgraph images were taken while the pressure was ramped up, and while the tests were at quasi-steady state. The shadowgraphs were then compared to the spatial pressure data taken along the top and side walls of the duct. Figure 6.14 shows a series of four shadowgraphs at steady state conditions for four different chamber pressures. These images are representative of ramping up the chamber pressure to a set point pressure ratio of 47.2. Figure 6.14a shows a steady state image at a set point pressure ratio of 20.2. Barrel shocks can be seen emanating from the nozzle and terminating in a Mach disk at a location approximately 0.62 hydraulic diameters downstream of the nozzle exit. Figure 6.14b shows the steady state image at a pressure ratio of 33.8. In this figure, the barrel shocks have stretched and the Mach disk has widened and moved to a position approximately 2.4 hydraulic diameters downstream of the nozzle exit. In addition, weaker shock structures appear inside the barrel shocks. These weaker shocks are believed to emanate from the corners of the nozzle. Figure 6.14c shows the steady state image at a set point pressure ratio of 40.5. Here the barrel shocks have stretched even farther. The Mach disk does not appear as sharp in the image and has moved to a position approximately 3 hydraulic diameters downstream. Figure 6.14d shows the steady state image at a chamber pressure of 47.2. Here the barrel shocks have stretched even further, and intersect at a point approximately 4.8 hydraulic diameters downstream. The Mach disk has completely disappeared at this point.
133 The plume transition from to 40.5 to 47.2 has several interesting features. First, this transition is accompanied by a distinct change in pitch of the audible ejector “roar.” The mixing duct pressure distribution plots also show a change in trend.
The
shadowgraphs at higher chamber pressures did not reveal any new structure. The only changes in the shadowgraphs were additional stretching and widening of the barrel shock. The transition does not always occur at exactly the same set point pressure ratio. However, it is currently unknown to what extent other environmental factors such as temperature and humidity affect the flow transition.
Barrel Shock Mach Disk
a)
b) Nozzle Exit
c)
d)
Figure 6.14 Series of images depicting chamber pressure ramp up for single nozzle strut: (a) Pc/Pb = 13.3, (b) Pc/Pb = 33.8, (c) Pc/Pb = 40.5, and (d) Pc/Pb = 47.2.
The dual nozzle shadowgraphs revealed a more complex shock structure primarily due to the existence of an additional nozzle, as well as the lower pressures associated with the equivalent mass flow rates. Figure 6.15 shows four images of steady state shadowgraphs for the dual nozzle strut at four different chamber pressures. The four
134 images represent the ramp up process for the dual nozzle strut to a set point pressure ratio of 30.6. Figure 6.15a shows the steady state image for a set point pressure ratio of 19.6. Similar to the single nozzle images, barrel shocks emanate from the nozzles, and terminate in Mach disks approximately 1.8 hydraulic diameters downstream. Figure 6.15b shows the shadowgraph image at a steady state pressure ratio of 20.4. The barrel shocks in this image are more stretched out and still terminate in Mach disks. The barrel shocks for each of the dual nozzles are not symmetric. The inner sections of the shocks are being influenced by the shocks from the other nozzle. Figure 6.15c shows the shadowgraph image at a steady state pressure ratio of 24.0. The barrel shocks are stretched even farther, and the Mach disks have disappeared. For the dual nozzle strut, the transition from the low to high pressure trend occurs around this set point pressure ratio (24.0).
Figure 6.15d shows the shadowgraph image for the steady state
a)
b)
c)
d)
Figure 6.15 Series of images depicting chamber pressure ramp up for dual nozzle strut: (a) Pc/Pb = 16.8, (b) Pc/Pb = 20.4, (c) Pc/Pb = 24.0, and (d) Pc/Pb = 30.6.
135 pressure ratio of 30.6. This chamber pressure is above the transition pressure. In the figure, the outer portions of the barrel shocks have extended and intersect approximately 4.8 hydraulic diameters downstream of the strut. This is approximately the same location where the single nozzle shocks intersected for a set point pressure ratio of 47.2. Mixing duct pressure profiles for the dual nozzle strut were next overlaid on the shadowgraph images to correlate shock structures with the measured values. Once again, higher chamber pressures more insightful. Figure 6.16 shows a plot of the top wall pressure distribution plotted against the axial location for a set point pressure ratio of 30.7 (see Figure 5.38) overlaid on the shadowgraph image for that pressure. The high pressure trend is clearly visible. In this region of the duct, the pressure ratio is dropping to a constant value of approximately 0.3. At approximately 4.8 and 8.4 hydraulic diameters
1.1 Pressure R atio(P/P (P/Po Pressure Ratio b)
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0
2
4
6
8
Position in Duct (in)
Figure 6.16 Plot of top wall pressure distribution with shadowgraph image (dual nozzle strut Pc/Pb = 30.6).
136 downstream, there are discontinuities in the pressure ratio. At each of these locations, there is an increase in the pressure ratio consistent with crossing a shock. If the trailing edges of the barrel shocks are extended to the wall, they will hit the wall at approximately these locations. It is believed that the discontinuities are a result of these shocks. 6.4
Analytical Comparisons
A simplified classical axisymmetric model based on Fabri’s model (see Chapter 2) was created and used to estimate the bypass ratio for the non-axisymmetric ejector of this dissertation. An equivalent axisymmetric ejector was identified that had the same nozzle area ratio, the same mixing duct cross-sectional area relative to the nozzle exit area, and the same secondary flow inlet area relative to the duct area. Each model (supersonic, saturated supersonic, and mixed) was used to estimate the bypass ratio over the range of chamber pressures examined. Results for each model over the full range of pressures are presented, although at any pressure only one regime will exist. 6.4.1
Single Nozzle Strut
Figure 6.17 shows the bypass ratio versus the ratio of the stagnation pressure of the primary flow to that of the secondary flow for the single nozzle strut. All three models (mixed flow, saturated supersonic flow, and supersonic flow) are shown on the same plot. For a given pressure ratio, the regime which predicts the lowest bypass ratio is taken as the regime which will exist. Since the supersonic regime and the mixed regime are lower than the saturated supersonic regime for all pressure ratios examined, the model predicts that the flow will not enter the saturated supersonic regime.
137
8 7
Bypass Ratio
6
Mixed Flow Regime
5 4
Saturated Supersonic
3
Supersonic
2 1 0 0
20
40
60
80
PressureRatio Ratio(P (Pc/Pb) Pressure c/Pb)
Figure 6.17 One-dimensional model for axisymmetric ejector of equivalent geometry to single nozzle strut PRC ejector.
By taking the lowest bypass ratio predicted at any pressure ratio, a smooth curve for the ejector was created as shown in Figure 6.18. Experimental data from the single nozzle ejector is also shown in the figure. Qualitatively the predicted trends of the plots agree with the experimental data; however, as can be seen in the figure, the analytical models over predict the bypass ratio for a given pressure ratio. The theoretical values were from 25% to 53% higher than the experimental values. As mentioned earlier, the duct geometry can lead to a non-uniform velocity profile. Significant boundary layers will exist along the duct walls and in the duct corners. The maximum predicted bypass ratio for the set point pressure ratios of the experiment is around 4.75 and the ejector would be operating in the mixed regime for this pressure ratio. The model predicts a transition from the mixed regime to the supersonic regime will occur around a pressure
138 ratio of 50. Experimental evidence indicated that the transition from the mixed flow regime to the supersonic regime occurs around a pressure ratio of 34.
5
Bypass Ratio
4 3
Theory Experimental Data
2 1 0 0
20
40
60
80
Pressure Ratio (Pc(Pc/Pb) /Pb) Pressure Ratio
Figure 6.18 Comparison of theoretical symmetric ejector model with experimental data for non axisymmetric single nozzle ejector.
6.4.2
Dual Nozzle Strut
For the dual nozzle strut, an analytic model was created with a primary flow inlet area equal to the combined areas of the two nozzles. Figure 6.19 shows a plot of the predicted bypass ratio versus the pressure ratio for an axisymmetric ejector with equivalent geometry to the dual nozzle strut.
As with the single nozzle strut, the saturated
supersonic regime predicted higher bypass ratios than either the mixed flow model or the supersonic flow model. In general the models over predict the bypass ratio for a given pressure ratio. At very low set point pressure ratios, the mixed flow regime model predicted a peak bypass ratio and, as the pressure ratio is decreased below that point, the
139 bypass ratio drops. This does not agree with the experimental evidence. At these pressures, the ejector would be operating in the mixed flow with separation regime which was not modeled. The model predicts that the flow will transition from mixed flow to supersonic flow around a pressure ratio of 25. The experimentally determined mass flow rate clearly indicates a choke of the secondary flow which indicates the ejector is operating in the supersonic or saturated supersonic regime for pressure ratios above 20. According to the analytical models, the ejector would only operate in the supersonic and in the mixed regime. For this geometry the theoretical prediction is from 33% to 54% higher than the experimental data.
Bypass Ratio Pressure Ratio (Pc/Pb)
5 4 3
Theory Experimetnal Data
2 1 0 0
20
40
60
80
Pressure Ratio (Pc/Pb)
Figure 6.19 Comparison of Fabri models with dual nozzle strut data.
140 It is believed that there are two major factors which contribute to the poor predictions of the axisymmetric model for this strut ejector setup.
The first is the
geometry of the duct. Because of the rectangular cross section, the duct will have significant corner effects which will retard the flow and increase the boundary layer growth. This boundary layer will reduce the effective area through which the secondary flow will pass. The geometry will also cause a non-uniform velocity profile across the duct which invalidates one of the assumptions of Fabri’s models. The second major factor contributing to the discrepancy between the predicted value and the experimental value is the effect of the base area of the strut. In Fabri’s model, the base area was negligible because of its minimal size relative to other duct areas. In the PRC strut ejector setup, the base area is a significant size and, as was seen in the pressure distribution plots, causes a recirculation region. This region will result in losses in the flow, and induce turbulence. An approximate base pressure term was included in the analytical model, however, it did not compensate for all of the effects of the strut. Figure 6.20 shows a plot of the predicted bypass ratios for equivalent geometry axisymmetric ejectors for both the single and dual nozzle struts. The predicted trends agree with the experimental trends qualitatively. That is, for a given pressure ratio, the single nozzle strut induces more secondary mass flow. At a fixed mass flow (pressure ratio in the dual nozzle strut that is half the pressure ratio in the single nozzle strut), the dual nozzle strut induces more secondary mass flow.
141
5
Bypass Ratio
4 3
Single Nozzle Prediction
2
Dual Nozzle Prediction
1 0 0
20
40
60
80
Pressure Ratio (Pc/Pb) Figure 6.20 Theoretical bypass ratio for axisymmetric ejectors with geometry ratios equivalent to those in the single and dual nozzle PRC ejectors.
6.5
CFD Analysis
Since the simplified one-dimensional model predictions were not close to the experimental data, a CFD analysis of the ejector was performed. Several of the single nozzle experiments were simulated using the Fastran Computational Fluid Dynamics code by ESI. This work was done in a parallel study by Balasubramanyan [20, 44]. The studies analyzed the flow in the ejector in a piecewise fashion. The primary focus of the effort was to attempt to model the mixing duct behavior. The inlet section of the duct which consisted solely of secondary flow was modeled as a two-dimensional constant area duct, and the rocket nozzle in the strut was modeled in three dimensions to provide a picture of the primary flow stream entrance into the mixing duct. The results of the two efforts were then combined to perform a two-dimensional and a limited threedimensional evaluation of the mixing duct.
142 The ejector inlet was first modeled from the entrance of the constant area section of the duct (neglecting the contoured inlet) to the exit plane of the strut (the location where the secondary flow enters the mixing duct. The flow entering the straight section of the duct was assumed to be uniform and smooth. The model was given an inlet velocity, and a stagnation pressure equal to atmospheric pressure. Several turbulence models were evaluated. The pressure measurements in the strut gap region were used to evaluate the performance of the different models.
A two equation Menter-SST
turbulence model [44] was found to best fit the experimental data as can be seen in Figures 6.21 and 6.22.
0.64 Menter-SST
Pressure Ratio (P/Pos)
0.62
Experimental Strut Gap
0.60 0.58 0.56 0.54 0.52 -9
-8
-7
-6
-5
-4
-3
-2
-1
Distance from Exit Plane (x/D h)
Figure 6.21 Ejector strut gap sidewall pressure ratio (Pc/Pb = 40.4).
0
143
0.64 Experimental Data
Pressure Ratio (P/Pos)
0.62
Menter SST
0.60 0.58 0.56 0.54 0.52 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
Distance from Exit Plane (x/D h)
Figure 6.22 Ejector strut gap sidewall pressure ratio (Pc/Pb = 53.7) [44].
With fairly good agreement in the strut gap region, the embedded rocket nozzle was then modeled. Because of the complex geometry of the nozzle, a three-dimensional model was used for the nozzle. Figures 6.23 and 6.24 show the exit pressure and Mach numbers for the three-dimensional model of the nozzle. Results from the duct inlet and the rocket nozzle models were then combined and used as the inlet conditions to a two-dimensional mixing duct model. An extrapolated boundary condition was applied at the mixing duct exit. By using a two-dimensional model, the results of the top wall cannot be evaluated because of the complex flow phenomena around the strut.
However the sidewall pressures in the mixing duct
compared reasonably well with the experimental data as can be seen in Figures 6.25 and 6.26.
144
Figure 6.23 3-D strut rocket nozzle exit Mach contours.
Figure 6.24 3-D strut rocket nozzle exit pressure contours.
145
1.2
Pressure Ratio (P/Pos)
1.0 0.8 0.6
Experimental Sidewall
0.4
Spalart Allmaras K-Eplison
0.2
Baldwin Lomax Menter SST
0.0 0
10
20
30
40
50
Distance from Exit Plane (x/D h)
Figure 6.25 Sidewall pressures in ejector mixing duct (Pc/Pb = 40.4).
0.9 Experimental Data KE model Spalart Allamars Menter SST Baldwin Lomax
Pressure Ratio (P/Pos)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
10
20
30
40
Distance from Exit Plane (x/D h)
Figure 6.26 Sidewall pressures in ejector mixing duct (Pc/Pb = 53.7).
50
146 Multiple turbulence models were used for the analysis. For the low pressure case, the zero equation Baldwin Lomax and the Menter-SST models predicted the side wall pressures reasonably well throughout the duct. The Menter-SST model more closely predicted the recovery length than the Baldwin Lomax model. Both models predicted the exit pressure fairly accurately. For a pressure ratio set point of 53.7, the high pressure trend is evident in the CFD analysis. For this pressure, the Mentor-SST and the Spalart Albmaras models predicted the sidewall pressure better than the other models. The pressure drop at the entrance to the mixing duct was predicted more accurately using the Menter-SST model. A three-dimensional model of the mixing duct was also simulated at set point pressure ratio of 40.4. For this analysis, compressibility corrections were included in the models. The top wall pressures were compared to the results of the CFD analysis. Figure 6.27 shows the results of the three-dimensional analysis compared to the experimental data. It can be seen in the figure that the recirculation region downstream of the strut is captured by the models; however, the predicted size of the mixing region is not as large as the experimental data indicate. Additionally, the models do not capture the spreading of the mixing layer within the mixing zone very well and the pressure recovery prediction is not as good with the three-dimensional models as was shown for the two-dimensional case.
147
1.2
Pressure Ratio (P/Pos)
1.0 0.8 0.6 Experimental Data
0.4
3-D KE Model with Compressibility 3-D Menter-SST Refined Grid
0.2
3-D Baldwin Lomax Refined Grid
0.0 0
5
10
15
20
25
30
35
40
45
Distance from Exit Plane (x/D h)
Figure 6.27 3-D Pressure profiles at centerline of top-wall (Pc/Pb = 40.4).
50
CHAPTER 7
CONCLUSIONS
The primary focus of the current investigation was the characterization of a threedimensional non-axisymmetric ejector configuration. An experimental investigation of two strut based nozzle configurations provided insight into the pressure distribution, the mass flow entrainment, choking mechanisms, and flow structure in the ejector system. Classical ejector modes of operation were used to classify the ejector operating regimes. Results of the experiment were compared with simple one-dimensional analytical models and a limited CFD effort performed in a parallel study.
7.1
Flow Regimes In the current experiment, the primary nozzles were operated over a range of
chamber pressures which allowed the ejector to operate in both the mixed and the supersonic regimes. For low chamber pressure operating conditions (the mixed regime) the secondary flow remained unchoked in the strut gap as was shown in both the secondary mass flow and the strut gap pressure ratio plots. At high chamber pressures, the ejector was operating in the saturated supersonic regime. The secondary mass flow plot indicated that a choke of the secondary flow had occurred. As the primary mass
148
149 flow was increased, there was a slight decrease of the secondary mass flow. This decrease is indicative of a reduction in minimum area through which the secondary flow can pass. For this operating condition, the minimum area is between the plume of the primary flow and the wall of the duct.
This decrease is somewhat in contrast to
statements by Fabri and Addy who stated that the mass flow becomes invariant with respect to changes in the ratio of exit pressure to primary jet stagnation pressure once the supersonic regime is established. The range of pressures in which this ejector was operated was well above those studied by Fabri and Addy. As the primary flow total pressure increases, so too does the pressure at the exit of the strut nozzle. This would result in an increased deflection angle at the exit of the nozzle which in turn would lead to a smaller minimum area for the secondary flow at the choke location. This effect may also be a result of increased losses attributed to flow disturbances resulting from the nonaxisymmetric characteristics of the duct. At moderate chamber pressures, the secondary mass flow plots indicated a secondary flow choke; however, it is not clear if the choke is an aerodynamic choke in the strut gap or a mass choke in the mixing duct. The pressures in the strut gap region approach the sonic limit, and reach it within uncertainty. However, because of the uncertainty, it cannot be definitively declared an aerodynamic choke or a mass choke. Based on the idealized flow equations, the calculated secondary mass flow is well below the maximum secondary mass flow that could be achieved in the strut gap area for an atmospheric stagnation pressure. This would indicate that the type of choke is a mass addition choke and that an aerodynamic choke never occurs in the ejector. However the boundary layer approximation was based on a simple flat plate approximation on the
150 walls of the duct, and does not account for corner effects or for boundary layer buildup in the inlet, thus the estimate could be low. Because the pressure ratio increases away from the sonic limit as the primary chamber pressure increases, it is clear that at higher pressures, the secondary choke is not in the strut gap region. In a previous investigation, Smith concluded that choked secondary flow occurred around a set point pressure ratio of 33.8 and that this choke was a Fabri mass choke in the mixing duct based on the strut gap pressure ratios [25]. Smith further concluded that this choke moved from the mixing duct to the strut gap region around a set point of 44.2 for the single nozzle strut. Based on the current research, it appears that is not the case. The strut gap pressures begin to increase away from the sonic limit as the primary jet stagnation pressure is increased. It is more likely that the flow in the strutgap region was choking at a lower chamber pressure or the secondary flow was approaching the choked condition but was not fully choked until a set point pressure ratio of 44.2 was reached. In either case, the theory for a constant area ejector dictates that if the flow chokes in the strut gap, it must occur at a lower chamber pressure than a Fabri choke in the same duct.
7.2
Mixing Duct Pressure Distributions
The mixing duct pressure profiles showed two distinct trends for each strut. These trends were labeled the low pressure trend and the high pressure trend in a previous publication because of the apparent connection to the chamber pressure of the primary nozzle, although the development of each pattern in the mixing duct seems to be a function of the primary mass flow rate rather than the chamber pressure. The low pressure trend occurred when the ejector was operating in the mixed flow regime and
151 through a portion of the supersonic regime. The low pressure trend was characterized by a pressure drop in the strut gap region followed by either a pressure recovery starting at the entrance to the mixing duct and ending with a complete pressure equalization with the ambient static pressure by the end of the duct, or by a continued pressure drop in the mixing duct to some minimum pressure followed by a pressure recovery and ending with a complete pressure equalization with the ambient static pressure by the end of the duct. Exit profiles of the mixed flow total pressure indicated a constant, uniform, total pressure across a quadrant of the duct. The flow from the ejector was, therefore, fully mixed by the exit of the mixing duct. When the mixing duct pressure distribution shows the low pressure trend, the length of duct required for complete pressure recovery does not seem to vary much. Both the single and dual nozzle strut pressure distributions completely recovered by approximately 20 hydraulic diameters downstream of the exit plane. For the current ejector geometry, this length corresponds to approximately 17 in. (43 cm) downstream of the strut nozzle exit plane. This length agreed with the single nozzle study carried out by Smith [25], and with the PLIF study carried out by Parkensen, et al. [45]. Thus for both struts, the extra duct length would serve to add losses to the system, and would reduce the effectiveness of the ejector in a propulsion application. The high pressure trend was characterized by a pressure drop in the strut gap followed by a continued pressure drop at the entrance of the mixing duct to a minimum pressure ratio around a value of 0.3.
A pressure ratio between 0.3 and 0.6 was
maintained over a length of the mixing duct and then followed by a recovery region which had a more gradual slope than was seen in the low pressure plots. The length of
152 the region of this lower pressure ratio region was a function of the nozzle chamber pressure (and hence the mass flow rate of the primary fluid). For the high pressure trend, the pressure does not fully equalize with atmospheric pressure by the end of the instrumented duct. The exit total pressure profiles for this region indicate a total pressure gradient across a quadrant of the duct. This is evidence that for the high pressure trend, the flow does not mix completely by the end of the duct. Instead at the exit, a supersonic core flow is present surrounded by a lower velocity secondary flow. In the high pressure trend, pressure discontinuities were apparent in the mixing duct plots.
These
discontinuities were evidence of shock structure inside of the duct impinging on the duct walls. The change from the low pressure trend to the high pressure trend occurred around the same mass flow rate for both struts, emphasizing the dependence on primary mass flow rate. Overlaid plots of the single and dual nozzle strut wall pressure profiles for the same primary flow mass flow rate indicated that the magnitude of the chamber pressure had an apparent influence on the location of the start of the recovery region. The change in trend, from the low to high pressure trend, appears to be most strongly influenced by the primary mass flow rate. The location of the start of the recovery region for equivalent mass flow rates in the two struts was not equal. In the single nozzle strut, the location of the recovery region was much farther downstream than in the dual nozzle strut. This indicates that the recovery is influenced by the pressure of the primary fluid. As the chamber pressure increases, the recovery region moves downstream.
In propulsion
applications where complete mixing important, there may be advantages to operating with multiple lower pressure nozzles rather than a single higher pressure nozzle.
153 7.3
Mass Flow Entrainment
The induced mass flow and the bypass ratio showed strong dependencies on the primary mass flow rate of the ejector and weak dependencies on primary flow pressure at the entrance of the mixing duct. Overlaid plots of the secondary mass flow versus the primary mass flow showed that the two struts exhibited very similar behavior. Until the secondary flow chokes, the single nozzle strut induced slightly more secondary mass flow at an equivalent primary mass flow rate than the dual nozzle strut. A similar trend was seen for the bypass ratio. For an equivalent primary mass flow rate, the single nozzle strut had a slightly higher bypass ratio at primary mass flow rated below the secondary flow choke point. These results show the importance of the primary jet momentum in the entrainment of secondary air flow.
As discussed, an ejector acts as a momentum
exchange device. Momentum from the primary jet is imparted on the secondary fluid. For this setup, the velocity of the flow out of the nozzle is very high (around Mach 3). The momentum of the primary jet consists of a mass flux term and a pressure flux term. At the exit of the mixing duct, the mass flux term is an order of magnitude more than the pressure flux term. For the dual nozzle strut, the pressure flux term becomes even smaller because the pressure at the exit is half of the pressure for an equivalent mass flow in the single nozzle strut. Since the mass flux term is dominant, the dependence on the primary mass flow becomes apparent in the plots. The pressure flux term, however, is not negligible and is may account for differences in the mass flow entrainment and the bypass ratio at equivalent mass flow rates. As mentioned earlier, the recovery length for the high pressure trend plots was attributed to the primary flow exit pressure. Since the bypass ratio is an important efficiency parameter, fewer nozzles seem to be more
154 effective in exchanging momentum; however, once the secondary flow chokes, efficiency becomes less important than mixing length. Because the secondary flow chokes and begins to drop as the primary flow is increased, the momentum exchange between the primary and secondary flow does not improve once the choke point is reached. The two flows are assumed to remain distinct until the secondary flow choke point is reached somewhere in the mixing duct. After the choke, the majority of the mixing and the momentum exchange is assumed to occur. As the primary pressure is increased, the mixing between the two flow streams becomes less efficient and the duct is no longer long enough for complete mixing to occur.
7.4
Comparison to Analytical Models
Comparison of the experimental work with classical one-dimensional analysis techniques of Fabri and Addy showed that the performance trends of bypass ratio were similar to the trends for an axisymmetric case. The simplified one-dimensional models which were used to evaluate the current ejector system predicted trends similar to those seen in the experimental data. While one-dimensional models were fairly accurate for axisymmetric experimental cases, non-axisymmetric effects in the current system result in significant losses in the ejector which were not captured in these models. The bypass ratio was significantly overpredicted around 30% for both single and dual nozzle ejectors. The predicted transition point from mixed to supersonic flow was at a pressure ratio 32% lower than the predicted value for the single nozzle strut and 20% lower for the dual nozzle strut.
These differences are evidence of losses associated with the current
configuration. These losses are believed to be attributed to both the effect of flow
155 separation due to the significant base region of the strut, and to the geometry of both the mixing duct and the nozzle.
The non-axisymmetric characteristics of the current
geometry appear to add losses that speed up the onset of the supersonic flow regime. The trends of the classical models agreed with the trends of the current ejector system. It is believed that a geometry effect could be included in the models which would improve the performance predictions.
With corrections, similar models may
predict global characteristics well; however, without significant data from other ejector configuration, these terms would be specific to the current ejector setup and would not add much practical value to generalized modeling. A base area effect was added to the model for comparison to the PRC data. For Fabri’s ejector, the base area was negligible relative to the areas of the primary flow and secondary flow inlets; however, for both single and dual nozzle struts there is a significant portion of the strut which is unused. As the secondary flow and primary flow enter the mixing duct, a recirculation region is formed immediately downstream of the strut as was seen in the mixing duct pressure distribution plots. Pressure measurements on the downstream face of the strut indicated that the pressure in this region was approximately equal to the pressure at the strut gap region exit. So, an additional pressure term was added to the momentum equation to account for this effect.
7.5
CFD Analysis
Madhan modeled the single nozzle strut in a CFD code to evaluate turbulence models. The analysis was performed using a two-dimensional duct at set point pressure ratios of 20.2, 40.4 and 53.7. The secondary flow inlet was artificially adjusted until the
156 pressures in the strut gap region matched the data from the experiment. The strut rocket nozzle was modeled in a full 3-D mode. These two CFD results were then combined into a two-dimensional model with an extrapolated exit boundary condition. Mixing duct pressure data from the code was compared with the experimental data from these experiments. The analysis showed that the Spalart Allamart model showed reasonably good agreement with the experimental data in both the high pressure and low pressure trends. A three-dimensional model of the mixing duct was also analyzed for a set point pressure ratio of 40.4. The pressures in the mixing duct showed good agreement with the trends of the experimental result; however, the recirculation region just downstream of the strut was not adequately captured by the CFD model. A compressibility correction added to the model improved the agreement between the mixing duct pressures. A full set of the results from the experiments described in this dissertation are included in Appendix D.
7.6
Momentum Effects
The experiments revealed that the entrained mass flow for the ejector system is most strongly influenced by the total primary mass flow and hence by the primary jet momentum. The total momentum of the primary jet consists of two major terms, the mass flux (mass flow times the velocity) and the pressure flux (static pressure times the area). Because of the high velocity, the mass flux term will be the dominate term in this expression. In a series of experiments on a ducted rocket with a single nozzle of variable geometry, Djijkstra, et al. reported that the entrainment depended strongly on the configuration of the mixer, and that the nozzle exit pressure did not seem to affect the
157 entrainment significantly [2].
These results were similar to those found in this
experiment. However, a slightly higher secondary mass flow was achieved for the single nozzle than for the dual nozzle strut at the same mass flow rate. For the same mass flow rate, the stagnation pressure of the single nozzle strut is operated at double the chamber pressure of the dual nozzle strut as discussed earlier. Thus the pressure at the exit of the nozzle in the single nozzle strut will also be twice the pressure at the exit of the dual nozzle strut. When the exit pressure of the nozzle is greater than the ambient pressure in the duct, the nozzle becomes under expanded, and the plume begins to spread outward with two results: increased plume area giving a larger shear mixing region, and decreasing the area for the secondary flow. Based on the nozzle geometry and the strut gap pressure just before the mixing duct entrance, this expansion will occur at a set point pressure ratio between 20.4 and 24.0 for the dual nozzle strut and between 27.2 and 33.8 in the single nozzle strut. This is also the approximate location where the secondary mass flow levels off indicating a choke of the secondary flow as was seen in Figures 5.1 and 5.25. However the pressure for the dual nozzle strut will be much lower than the primary flow exit pressure for the single nozzle strut. Thus when the flow exits the dual nozzle, it will expand a greater degree providing a larger plume for a single nozzle. A direct comparison to Dijkstra’s experiments cannot be made because of the significant geometry differences. However, the trends from both experiments indicate that the primary mass flow rate is the most significant variable in determining the amount of entrained air. From the results of the experimental work, one advantage of multiple strut nozzles is that a higher total mass flow is achieved at a lower pressure, so for a given
158 chamber pressure, the bypass ratio is increased. However, because the mass flow is increased, the transition from the low pressure trend to the high pressure trend occurs at a lower primary operating pressure. Once this high pressure trend is established, the required mixing length for the duct increases significantly. It is believed that comparison of a single nozzle of the same area ratio with an exit area equal to the total primary flow exit area for the dual nozzle struts would not entrain as much secondary mass flow and would have an adverse effect on the mixing length.
7.7
Future Work There are several factors in an ejector design that affect operation. In the current
experiment, there were only two variables, the chamber pressure and the number of nozzles in the strut. Ejector optimization involves varying several other factors, such as the ratios of the inlet areas, the primary nozzle area ratio, the secondary flow stagnation pressure, the ratio of the secondary flow inlet area to the mixing duct area, and the composition of the operating fluids to name a few. The data presented in this dissertation could be used as a baseline for evaluating CFD models of the ejector. While the results of the experiment do not provide detailed three-dimensional flow field information, they do provide a baseline of data for a complex three-dimensional system. Such data can be used to benchmark CFD models which may be appropriate for more complicated ejector systems. Further experiments should be done modifying the geometry of the duct. If the strut gap cross-sectional area is reduced, the secondary flow can be forced to choke in the strut gap region, adding a definitive saturated supersonic regime. This in turn may result
159 in improved mixing at higher set point pressure ratios. Adding a third and fourth nozzle would allow for better comparison to some of the non-axisymmetric experimental work at other universities. With the strut base full of nozzles, the geometry more closely resembles a two-dimensional ejector system, simplifying the analysis considerably and making for a more direct comparison to other two-dimensional ejector configurations. Finally a wider mixing duct would allow for multiple struts to be installed in the duct. This type of system would allow investigations of the interaction between multiple primary and secondary flow stream streams. Such a case would more closely model a strut based RBCC engine. Three-dimensional CFD modeling of the current configuration (both single and dual nozzle struts) would make the variations between the dual and single nozzle strut more apparent. For the simple two-dimensional case, the CFD code was able to produce fairly good results for the centerline sidewall pressure measurements. However for the dual nozzle strut, this model will not be as accurate. The pressure measurements in the mixing duct were only taken along the centerline of the top and side walls. A more complete mapping of the pressure field in this region of the duct would be useful for full three-dimensional modeling of the ejector. The CFD model also focused on the mixing duct exclusively. The secondary flow inlet was artificially added by modifying inlet parameters until the strut gap pressures matched the experimental data. This code could not be used for other geometries unless experimental data was available. The current model could be improved to predict the strut gap pressures as well as the mixing duct pressure.
160 More imaging of the flow streams in both the mixing duct and in the inlet could provide additional insight into the flow behavior in these areas.
The rectangular
geometry of the duct is believed to significantly retard the flow in the corners. Use of a Particle Imaging Velocimeter to map the velocity fields in this region would improve the mass flow determination for this region, and would provide detailed flow field information for evaulating CFD models. In the mixing duct, the shadowgraph images revealed a complex shock structure exists in this region. Schlerien imaging in this region could reveal more detail of the shock train that occurs downstream of the primary jet. PIV imaging in this are could also provide a better evaluation of the completeness of the mixing between the flow streams. Seeding of the secondary flow with a flourescencing element and performing another PLIF study for the duct would also provide insight into the mixing phenomena. Ejectors have shown potential for use in advanced propulsion concepts. From a practical standpoint, the geometry of such vehicles will most likely have nonaxisymmetric characteristics. The current study shows that these effects influence the performance of the ejector. Before such engines can be developed and optimized, a better understanding of the fluid mechanics in the system is necessary. This research provides a baseline of data which can be used to evaluate a non-axisymmetric ejector configuration. A cold flow facility provides a relatively safe way to investigate the flow behavior. Experiments, such as those conducted here, can provide data for evaulating CFD codes for use with more complex geometries, and with more complicated flow phenomena.
APPENDICES
161
APPENDIX A
SYSTEMATIC UNCERTAINTY VALUES
162
psig
Strut Gap Pressure Tap 1 Strut Gap Pressure Tap 2 Strut Gap Pressure Tap 3 Strut Gap Pressure Tap 4 Strut Gap Pressure Tap 5 Strut Gap Pressure Tap 6 Strut Gap Pressure Tap 7 Strut Gap Pressure Tap 8 Strut Gap Pressure Tap 9 Strut Gap Pressure Tap 10 Secondary Flow Stagnation Pressure (at Fairing) Secondary Flow Static Pressure (at Fairing) Exit Stagnation Pressure (Pitot probe) Exit Static Pressure (Pitot probe) Exit Side Wall Pressure (Pitot probe) Strut Rocket Chamber Pressure Scani-Valve Top Wall Pressure Scani-Valve Side Wall Pressure Strut Rocket Chamber Temperature Secondary Flow Temperature (at inlet)
Pg1 Pg2 Pg3 Pg4 Pg5 Pg6 Pg7 Pg8 Pg9 Pg10 Pos Ps Poe2 Pe2 Pe Pc Ptw Psw Tc Tos
-14.7 to 30 psig
-14.7 to 30 psig
0 to 1000 psia
0 to 300 psig
-14.7 to 32 psig
0 to 300 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
Range
a
0
0
0.0006476
0.0005989
0.149
0.009034
0.008626
0.065
0.004655
0.005407
0.004904
0.005809
0.005593
0.005862
0.004563
0.008709
0.005427
0.003893
0.022
0.012
b
0
0
-0.002607
-0.000182
-0.736
-0.063
0.04
-0.135
-0.019
-0.023
-0.02
-0.026
-0.025
-0.025
-0.018
-0.041
-0.022
-0.015
-0.106
-0.058
* Systematic Unceratinty Constants: For Voltage Reading (V) the systematic uncertainty is given by: a*(V^2)+b*V+c
C
C
psig
psig
psig
psia
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
Units
Measured Quantity
c
1
1
0.03
0.007275
2.458
0.159
0.111
0.162
0.038
0.057
0.043
0.063
0.059
0.065
0.035
0.112
0.057
0.034
0.0309
0.163
Systematic Uncertainty Constants*
Table A.1 Systematic uncertainty constants for instrumentation.
163
APPENDIX B
REGRESSION UNCERTAINTY ANALYSIS FOR CALIBRATION
The following pages contain the Mathcad sheets used for calculating the transducer calibration constants and the equation for the systematic uncertainty of the transducers based on the voltages. All transducers were calibrated with either an air or water based dead weight tester.
164
165
166
167
168
169
APPENDIX C
MATHCAD CALCULATION SHEETS
The following pages contain the Mathcad worksheets used for the data analysis.of an individual test date. The data from tests at nine different setpoint pressure ratios on a given date are imported into the following sheet to produce the test average values for each set point. The six worksheets are 1. Data setup sheet. 2. Inlet Mach number Calculation sheet. 3. Exit Mach Number Calculation Sheet. 4. Strut Gap Pressure Ratio Calculation Sheet. 5. Mixing Duct Pressure Ratio Calculation Sheet. 6. Mass Flow and Suction ratio Calculation Sheet.
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
APPENDIX D
TEST RESULTS (AVERAGE VALUES)
215
216 Table D.1 Test averages for single nozzle strut Single Nozzle Test Data Averages (10 Tests) Nozzle Area Ratio = 4.66 Mixing Duct Cross Section : 4 in x 3.5 in Nozzle Hydraulic Diameter = 0.83 in Po2/Pb = 1 Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Secondary Flow Stagnation Pressure (psi)
Po1 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7
U_Po1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Secondary Flow Inlet Temperature (C) T1 21.4 20.1 19.3 18.8 18.2 18.2 18.1 18.0 17.7
U_T1 6.1 6.6 6.2 6.6 6.4 5.9 6.5 5.1 6.0
Secondary Flow Static Pressure At Fairing (psi)
P1 14.5 14.3 14.1 14.0 13.9 13.9 13.9 13.9 13.9
U_P1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Exit Stagnation Pressure (psi)
Exit wall Static Pressure (psi)
Poe 15.3 16.0 17.0 18.0 18.9 19.6 22.2 28.6 31.9
Pe 14.7 14.7 14.8 14.8 14.8 14.9 14.7 14.5 14.4
U_Poe 0.3 0.3 0.3 0.3 0.3 0.3 1.8 2.9 3.9
U_Pe 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.5
Exit Static Chamber Pressure Pitot Temperature (C) (psi) Pe2 U_Pe2 Tc U_Tc 14.7 0.2 16.6 7.5 14.7 0.2 9.7 8.2 14.7 0.2 7.3 7.2 14.8 0.2 6.4 7.2 14.8 0.2 5.7 7.6 14.8 0.2 5.9 6.6 14.8 0.2 6.2 7.9 14.7 0.2 6.3 6.1 14.7 0.2 6.7 6.7
Strut Gap Pressures (psi) Positon 1 P1 U_P1 13.9 0.1 12.9 0.1 11.7 0.1 10.5 0.1 9.5 0.1 9.0 0.1 9.1 0.1 9.2 0.1 9.3 0.1
Postion 2 P2 U_P2 13.9 0.1 12.9 0.2 11.7 0.2 10.5 0.1 9.5 0.1 8.9 0.1 9.0 0.1 9.1 0.1 9.3 0.1
Position 3 P3 U_P3 13.9 0.1 12.8 0.1 11.6 0.1 10.4 0.1 9.3 0.1 8.7 0.1 8.7 0.1 8.9 0.1 9.1 0.1
Position 4 P4 U_P4 13.9 0.1 12.8 0.1 11.5 0.1 10.3 0.1 9.2 0.1 8.5 0.1 8.5 0.1 8.7 0.1 8.9 0.1
Strut Gap Pressures (psi) Position 6 P6 U_P6 13.9 0.1 12.8 0.1 11.6 0.1 10.3 0.1 9.1 0.1 8.4 0.1 8.4 0.1 8.6 0.1 8.8 0.1
Position 7 P7 U_P7 13.9 0.1 12.7 0.1 11.5 0.1 10.1 0.1 8.9 0.1 8.0 0.1 8.0 0.1 8.2 0.1 8.5 0.1
Position 8 P8 U_P8 13.9 0.1 12.8 0.1 11.6 0.1 10.3 0.1 9.1 0.2 8.2 0.2 8.3 0.2 8.5 0.2 8.8 0.1
Position 9 P9 U_P9 13.9 0.1 12.8 0.1 11.5 0.1 10.2 0.1 9.0 0.1 8.1 0.1 8.1 0.1 8.3 0.1 8.6 0.1
Position 10 P10 U_P10 13.9 0.1 12.8 0.1 11.5 0.1 10.2 0.1 8.9 0.1 7.9 0.1 7.9 0.1 8.2 0.1 8.6 0.1
Position 5 P5 U_P5 13.9 0.1 12.8 0.1 11.5 0.1 10.3 0.1 9.1 0.1 8.4 0.1 8.4 0.1 8.6 0.1 8.8 0.1
217 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
6.5 Pr 0.946 0.950 0.955 0.958 0.960 0.961 0.962 0.963 0.965 0.965 0.966 0.966 0.968 0.968 0.968 0.969 0.971 0.970 0.971 0.971 0.975 0.972 0.973 0.975 0.978 0.981 0.985 0.988 0.990 0.992 0.994 0.995 0.996 0.997 0.997 0.999 0.998 0.999 0.999 1.000 1.000 1.000 1.000 0.999 1.001 1.000 1.000 1.001
0.5 U 0.004 0.004 0.004 0.003 0.004 0.004 0.004 0.003 0.003 0.003 0.004 0.003 0.003 0.003 0.004 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
13.2 Pr 0.876 0.885 0.896 0.904 0.911 0.915 0.918 0.921 0.925 0.925 0.926 0.928 0.931 0.930 0.932 0.933 0.938 0.936 0.938 0.939 0.949 0.947 0.954 0.961 0.969 0.976 0.983 0.987 0.993 0.996 0.999 1.000 1.000 1.001 1.000 1.003 1.002 1.002 1.003 1.005 1.003 1.004 1.001 1.000 1.004 1.002 1.002 1.004
0.7 U 0.006 0.006 0.005 0.005 0.005 0.005 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.005 0.005 0.006 0.006 0.005 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Sidewall Pressure Ratios (P/Patm) 20.2 0.9 27.2 1.0 Pr U Pr U 0.792 0.007 0.702 0.008 0.804 0.007 0.714 0.008 0.822 0.006 0.737 0.008 0.838 0.006 0.763 0.008 0.849 0.006 0.783 0.007 0.857 0.005 0.796 0.006 0.863 0.005 0.805 0.006 0.868 0.005 0.812 0.006 0.875 0.005 0.823 0.005 0.876 0.005 0.825 0.005 0.880 0.005 0.831 0.005 0.883 0.005 0.835 0.006 0.889 0.005 0.844 0.005 0.888 0.005 0.843 0.005 0.890 0.005 0.847 0.005 0.892 0.005 0.849 0.006 0.899 0.005 0.859 0.006 0.897 0.006 0.856 0.007 0.902 0.006 0.863 0.007 0.908 0.006 0.871 0.007 0.924 0.006 0.894 0.007 0.930 0.007 0.906 0.008 0.944 0.007 0.928 0.008 0.957 0.007 0.946 0.007 0.968 0.006 0.963 0.008 0.978 0.007 0.975 0.006 0.985 0.006 0.985 0.006 0.989 0.005 0.990 0.005 0.997 0.005 0.999 0.006 0.999 0.004 1.002 0.005 1.002 0.004 1.005 0.005 1.002 0.004 1.004 0.004 1.000 0.004 1.001 0.004 1.002 0.004 1.003 0.004 0.999 0.004 0.999 0.004 1.005 0.003 1.008 0.004 1.002 0.003 1.004 0.004 1.003 0.003 1.005 0.004 1.005 0.003 1.007 0.003 1.008 0.003 1.011 0.004 1.004 0.003 1.006 0.003 1.007 0.003 1.009 0.003 1.001 0.003 1.001 0.003 0.999 0.003 0.999 0.004 1.006 0.003 1.009 0.003 1.003 0.003 1.003 0.003 1.002 0.003 1.003 0.003 1.007 0.003 1.010 0.003
33.8 Pr 0.610 0.614 0.626 0.665 0.705 0.729 0.744 0.755 0.767 0.771 0.778 0.784 0.795 0.795 0.800 0.803 0.815 0.810 0.818 0.825 0.852 0.868 0.899 0.927 0.951 0.968 0.982 0.989 1.001 1.004 1.008 1.007 1.003 1.006 1.000 1.011 1.006 1.007 1.010 1.015 1.008 1.012 1.001 0.999 1.012 1.004 1.003 1.012
1.1 U 0.008 0.010 0.011 0.012 0.009 0.008 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.007 0.008 0.009 0.009 0.011 0.012 0.011 0.010 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.004 0.004 0.003 0.003 0.003 0.003
40.5 Pr 0.540 0.539 0.501 0.477 0.527 0.619 0.655 0.675 0.694 0.701 0.711 0.718 0.733 0.733 0.741 0.746 0.763 0.758 0.764 0.769 0.793 0.790 0.812 0.843 0.876 0.907 0.935 0.954 0.974 0.986 0.996 0.999 0.999 1.003 1.000 1.012 1.007 1.009 1.013 1.017 1.010 1.015 1.003 1.000 1.015 1.006 1.005 1.015
1.2 U 0.008 0.007 0.007 0.024 0.032 0.016 0.013 0.012 0.011 0.010 0.009 0.009 0.009 0.009 0.008 0.009 0.008 0.008 0.008 0.007 0.007 0.010 0.012 0.015 0.017 0.015 0.013 0.012 0.010 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003
218 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
6.5 Pr 1.002 1.003 0.949 0.957 0.965 0.960 0.961 0.962 0.964 0.964 0.966 0.967 0.977 0.970 0.972 0.973 0.977 0.975 0.977 0.978 0.980 0.980 0.981 0.982 0.992 0.986 0.988 0.991 0.993 0.995 0.996 0.996 0.997 0.998 0.999 1.000 1.000 1.000 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001
0.5 U 0.004 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
13.2 Pr 1.002 1.003 0.883 0.909 0.924 0.916 0.918 0.920 0.923 0.925 0.928 0.932 0.949 0.939 0.941 0.943 0.949 0.947 0.950 0.951 0.957 0.959 0.965 0.971 0.987 0.983 0.988 0.993 0.997 1.000 1.001 1.001 1.002 1.004 1.005 1.005 1.006 1.007 1.007 1.006 1.005 1.006 1.006 1.005 1.003 1.005 1.005 1.004
0.7 U 0.003 0.005 0.006 0.007 0.005 0.006 0.005 0.005 0.005 0.004 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.005 0.004 0.005 0.004 0.005 0.005 0.005 0.007 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Topwall Pressure Ratio (P/Patm) 20.2 0.9 27.2 1.0 Pr U Pr U 1.002 0.004 1.002 0.004 1.003 0.005 1.003 0.005 0.795 0.010 0.683 0.013 0.849 0.007 0.772 0.009 0.874 0.006 0.822 0.007 0.862 0.007 0.810 0.008 0.864 0.006 0.811 0.006 0.867 0.006 0.815 0.006 0.872 0.005 0.819 0.005 0.876 0.005 0.825 0.006 0.881 0.005 0.832 0.005 0.887 0.006 0.841 0.006 0.912 0.005 0.875 0.006 0.900 0.006 0.861 0.006 0.905 0.005 0.867 0.006 0.909 0.005 0.874 0.006 0.920 0.005 0.886 0.005 0.917 0.005 0.884 0.005 0.923 0.005 0.892 0.006 0.928 0.005 0.899 0.006 0.938 0.006 0.913 0.007 0.946 0.006 0.928 0.007 0.958 0.006 0.946 0.007 0.968 0.006 0.961 0.006 0.988 0.007 0.986 0.009 0.984 0.005 0.984 0.005 0.991 0.005 0.993 0.006 0.997 0.005 1.000 0.005 1.001 0.004 1.005 0.006 1.004 0.004 1.009 0.005 1.006 0.004 1.010 0.005 1.004 0.004 1.007 0.004 1.004 0.004 1.007 0.004 1.008 0.004 1.012 0.004 1.009 0.004 1.013 0.004 1.009 0.004 1.013 0.005 1.011 0.003 1.015 0.004 1.011 0.003 1.016 0.004 1.011 0.003 1.016 0.004 1.011 0.003 1.015 0.003 1.008 0.003 1.012 0.003 1.010 0.003 1.014 0.003 1.010 0.003 1.013 0.003 1.009 0.003 1.013 0.003 1.005 0.003 1.007 0.003 1.008 0.003 1.011 0.003 1.008 0.003 1.011 0.003 1.007 0.003 1.010 0.003
33.8 Pr 1.002 1.003 0.550 0.652 0.752 0.755 0.762 0.766 0.770 0.774 0.781 0.790 0.828 0.810 0.819 0.829 0.846 0.841 0.852 0.861 0.878 0.898 0.924 0.946 0.981 0.979 0.992 1.003 1.008 1.014 1.016 1.011 1.010 1.018 1.019 1.017 1.020 1.021 1.021 1.020 1.015 1.018 1.017 1.016 1.009 1.015 1.014 1.013
1.1 U 0.004 0.005 0.015 0.020 0.009 0.008 0.007 0.006 0.007 0.006 0.006 0.006 0.006 0.007 0.007 0.007 0.006 0.007 0.008 0.008 0.009 0.009 0.010 0.009 0.010 0.008 0.007 0.007 0.006 0.006 0.005 0.005 0.005 0.005 0.004 0.006 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
40.5 Pr 1.002 1.002 0.440 0.502 0.606 0.626 0.662 0.686 0.702 0.710 0.713 0.722 0.766 0.744 0.755 0.763 0.787 0.785 0.796 0.799 0.809 0.827 0.848 0.875 0.940 0.929 0.953 0.973 0.987 0.999 1.007 1.003 1.006 1.016 1.019 1.019 1.023 1.025 1.024 1.024 1.019 1.021 1.021 1.020 1.011 1.018 1.017 1.016
1.2 U 0.004 0.004 0.009 0.016 0.017 0.018 0.015 0.011 0.009 0.008 0.009 0.009 0.008 0.010 0.009 0.010 0.009 0.009 0.009 0.007 0.008 0.009 0.013 0.013 0.019 0.013 0.012 0.012 0.010 0.009 0.008 0.007 0.006 0.006 0.005 0.007 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003
219 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
47.2 Pr 0.545 0.545 0.508 0.465 0.427 0.354 0.301 0.296 0.303 0.286 0.274 0.258 0.383 0.374 0.342 0.320 0.346 0.258 0.296 0.294 0.364 0.340 0.303 0.294 0.295 0.315 0.326 0.308 0.311 0.310 0.335 0.369 0.389 0.417 0.472 0.512 0.545 0.588 0.636 0.687 0.764 0.780 0.816 0.852 0.886 0.907 0.925 0.946
Sidewall Pressure Ratios (P/Patm) 1.3 53.8 1.5 60.5 U Pr U Pr 0.008 0.569 0.006 0.597 0.006 0.569 0.006 0.594 0.005 0.535 0.006 0.561 0.016 0.485 0.010 0.512 0.015 0.446 0.020 0.466 0.008 0.389 0.007 0.411 0.007 0.327 0.007 0.354 0.007 0.317 0.007 0.336 0.009 0.315 0.009 0.326 0.009 0.296 0.009 0.305 0.007 0.284 0.008 0.293 0.007 0.267 0.008 0.277 0.020 0.326 0.034 0.292 0.007 0.386 0.011 0.368 0.009 0.371 0.008 0.388 0.012 0.341 0.008 0.363 0.011 0.355 0.009 0.370 0.009 0.269 0.009 0.278 0.011 0.306 0.010 0.312 0.011 0.299 0.011 0.303 0.014 0.368 0.012 0.371 0.009 0.324 0.022 0.295 0.008 0.322 0.007 0.343 0.014 0.302 0.009 0.317 0.017 0.301 0.010 0.306 0.027 0.305 0.015 0.300 0.035 0.319 0.010 0.317 0.052 0.304 0.010 0.309 0.059 0.307 0.010 0.311 0.073 0.303 0.011 0.303 0.087 0.300 0.010 0.310 0.098 0.307 0.026 0.297 0.118 0.342 0.015 0.309 0.141 0.337 0.009 0.347 0.112 0.351 0.034 0.378 0.122 0.362 0.011 0.387 0.113 0.301 0.016 0.301 0.114 0.292 0.032 0.265 0.112 0.332 0.023 0.323 0.102 0.334 0.032 0.339 0.079 0.411 0.036 0.408 0.073 0.346 0.060 0.329 0.059 0.395 0.092 0.318 0.051 0.483 0.085 0.373 0.041 0.567 0.064 0.429 0.033 0.619 0.067 0.404 0.025 0.678 0.063 0.510 0.022 0.744 0.047 0.568
1.8 U 0.005 0.005 0.006 0.007 0.017 0.012 0.006 0.006 0.009 0.009 0.008 0.008 0.011 0.020 0.009 0.008 0.009 0.012 0.008 0.011 0.010 0.020 0.011 0.008 0.009 0.015 0.017 0.008 0.011 0.012 0.012 0.009 0.031 0.016 0.034 0.013 0.010 0.015 0.021 0.011 0.011 0.018 0.025 0.049 0.018 0.066 0.071 0.036
47.2 Pr 1.002 1.001 0.437 0.491 0.550 0.487 0.432 0.384 0.348 0.313 0.282 0.257 0.365 0.366 0.432 0.386 0.373 0.332 0.314 0.296 0.329 0.299 0.310 0.391 0.535 0.296 0.298 0.298 0.365 0.382 0.334 0.316 0.438 0.414 0.406 0.560 0.633 0.616 0.637 0.752 0.791 0.813 0.840 0.877 0.939 0.921 0.938 0.953
Topwall Pressure Ratios (P/Patm) 1.3 53.8 1.5 60.5 U Pr U Pr 0.004 1.001 0.004 1.000 0.005 0.999 0.005 0.999 0.008 0.470 0.009 0.501 0.010 0.520 0.009 0.552 0.011 0.569 0.009 0.593 0.010 0.502 0.009 0.520 0.007 0.448 0.009 0.464 0.007 0.405 0.009 0.422 0.008 0.373 0.009 0.385 0.008 0.337 0.009 0.348 0.008 0.303 0.009 0.316 0.008 0.274 0.009 0.287 0.008 0.374 0.008 0.381 0.053 0.261 0.046 0.250 0.021 0.438 0.031 0.378 0.019 0.433 0.023 0.448 0.008 0.397 0.013 0.427 0.007 0.340 0.010 0.346 0.007 0.332 0.007 0.339 0.009 0.309 0.007 0.328 0.011 0.333 0.010 0.342 0.012 0.298 0.014 0.298 0.032 0.302 0.012 0.298 0.020 0.379 0.040 0.332 0.109 0.550 0.104 0.557 0.023 0.306 0.009 0.328 0.030 0.314 0.013 0.320 0.053 0.289 0.009 0.321 0.061 0.299 0.036 0.280 0.086 0.374 0.027 0.311 0.108 0.355 0.014 0.386 0.104 0.310 0.008 0.347 0.111 0.370 0.023 0.375 0.157 0.338 0.018 0.340 0.210 0.297 0.040 0.286 0.194 0.429 0.105 0.355 0.203 0.374 0.026 0.423 0.182 0.332 0.011 0.374 0.189 0.310 0.020 0.326 0.129 0.327 0.048 0.308 0.104 0.461 0.042 0.411 0.077 0.411 0.035 0.411 0.059 0.383 0.076 0.411 0.047 0.414 0.142 0.369 0.026 0.692 0.106 0.558 0.030 0.677 0.086 0.350 0.023 0.715 0.059 0.393 0.020 0.747 0.069 0.547
1.8 U 0.005 0.007 0.008 0.009 0.010 0.010 0.010 0.010 0.010 0.010 0.009 0.008 0.007 0.018 0.063 0.022 0.022 0.011 0.011 0.010 0.008 0.010 0.016 0.041 0.098 0.007 0.016 0.011 0.013 0.044 0.015 0.011 0.025 0.019 0.011 0.145 0.026 0.020 0.008 0.016 0.028 0.046 0.022 0.012 0.018 0.052 0.092 0.128
220
Table D.2 Test averages for dual nozzle strut. Dual Nozzle Test Data Averages (10 Tests) Nozzle Area Ratio = 4.66 Mixing Duct Cross Section : 4 in x 3.5 in Nozzle Hydraulic Diameter = 0.83 in Po2/Pb = 1 Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Secondary Flow Stagnation Pressure (psi)
Po1 14.7 14.8 14.7 14.7 14.7 14.7 14.7 14.7 14.7
U_Po1 0.5 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Secondary Flow Inlet Temperature (C) T1 287.0 287.0 287.0 287.0 286.0 285.0 286.0 285.0 286.0
U_T1 11.9 13.0 13.3 12.1 12.2 10.2 10.7 11.0 12.0
Secondary Flow Static Pressure At Fairing (psi)
P1 14.5 14.5 14.3 14.1 14.0 13.9 13.9 13.9 13.9
U_P1 0.5 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Exit Stagnation Pressure (psi)
Exit wall Static Pressure (psi)
Poe 15.3 16.0 16.8 18.0 19.2 20.6 22.3 29.3 39.1
Pe 14.7 14.8 14.8 14.8 14.8 14.8 14.9 14.6 14.0
U_Poe 0.8 0.6 0.7 0.6 0.6 0.6 1.0 4.7 5.4
U_Pe 0.5 0.1 0.4 0.4 0.4 0.4 0.5 0.7 1.4
Exit Static Chamber Pressure Pitot Temperature (C) (psi) Pe2 U_Pe2 Tc U_Tc 14.7 0.5 284.0 17.0 14.8 0.1 278.0 12.3 14.7 0.4 273.0 13.7 14.8 0.4 272.0 12.8 14.8 0.4 270.0 14.1 14.8 0.4 269.0 12.0 14.8 0.5 269.0 11.9 14.6 0.6 269.0 11.8 14.6 0.6 269.0 13.2
Strut Gap Pressures (psi) Positon 1 P1 U_P1 14.0 0.2 13.3 0.2 12.5 0.2 11.6 0.2 10.6 0.2 9.8 0.3 9.7 0.4 9.7 0.4 9.7 0.4
Postion 2 P2 U_P2 14.0 0.2 13.3 0.2 12.5 0.2 11.6 0.2 10.6 0.2 9.7 0.4 9.5 0.4 9.6 0.4 9.6 0.4
Position 3 P3 U_P3 14.0 0.2 13.3 0.2 12.4 0.2 11.4 0.2 10.3 0.2 9.4 0.3 9.2 0.3 9.2 0.3 9.3 0.3
Position 4 P4 U_P4 14.0 0.2 13.3 0.2 12.3 0.2 11.3 0.2 10.2 0.2 9.1 0.3 8.9 0.3 8.9 0.2 9.0 0.2
Strut Gap Pressures (psi) Position 6 P6 U_P6 14.0 0.2 13.3 0.2 12.4 0.2 11.3 0.2 10.2 0.2 9.1 0.3 8.9 0.3 8.9 0.3 9.0 0.2
Position 7 P7 U_P7 14.0 0.2 13.2 0.2 12.3 0.2 11.3 0.2 10.1 0.2 9.0 0.3 8.8 0.3 8.8 0.3 8.9 0.3
Position 8 P8 U_P8 13.9 0.2 13.1 0.2 12.0 0.3 10.6 0.4 9.0 0.7 7.2 0.8 6.9 0.7 6.9 0.7 7.0 0.7
Position 9 P9 U_P9 13.9 0.2 13.2 0.2 12.3 0.2 11.2 0.2 9.9 0.3 8.3 0.3 7.9 0.3 8.0 0.2 8.1 0.2
Position 10 P10 U_P10 13.9 0.2 13.2 0.2 12.3 0.2 11.2 0.2 9.8 0.3 8.2 0.4 7.7 0.3 7.7 0.2 7.9 0.2
Position 5 P5 U_P5 13.9 0.2 13.2 0.2 12.3 0.2 11.3 0.2 10.1 0.2 9.0 0.3 8.8 0.3 8.9 0.2 8.9 0.2
221 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb x/Dh 0.00 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
3.5 Pr 0.950 0.955 0.958 0.961 0.963 0.964 0.965 0.965 0.967 0.966 0.967 0.967 0.968 0.968 0.968 0.969 0.971 0.970 0.972 0.973 0.978 0.978 0.979 0.982 0.986 0.991 0.990 0.990 0.995 0.996 0.997 0.997 0.997 0.998 0.997 1.000 0.999 1.000 1.000 1.001 1.001 1.001 1.000 1.000 1.001 1.001 1.000 1.002
0.3 U 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.007 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
6.8 Pr 0.904 0.914 0.920 0.926 0.929 0.931 0.932 0.934 0.936 0.936 0.937 0.938 0.940 0.939 0.940 0.941 0.945 0.943 0.945 0.947 0.954 0.954 0.961 0.967 0.975 0.985 0.984 0.986 0.993 0.995 0.997 0.998 0.997 0.999 0.997 1.002 1.000 1.001 1.002 1.004 1.002 1.003 1.000 0.999 1.003 1.001 1.001 1.003
0.5 U 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.006 0.006 0.006 0.006 0.010 0.006 0.007 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Sidewall Pressure Ratios (P/Patm) 10.2 0.6 13.5 0.6 Pr U Pr U 0.844 0.004 0.772 0.007 0.859 0.004 0.793 0.006 0.870 0.004 0.811 0.006 0.880 0.004 0.825 0.005 0.886 0.004 0.835 0.005 0.891 0.004 0.842 0.005 0.894 0.004 0.847 0.005 0.897 0.004 0.852 0.004 0.901 0.004 0.858 0.005 0.901 0.004 0.859 0.005 0.903 0.004 0.862 0.005 0.905 0.004 0.864 0.005 0.909 0.004 0.870 0.005 0.908 0.004 0.869 0.005 0.910 0.004 0.872 0.005 0.911 0.004 0.876 0.005 0.918 0.004 0.886 0.005 0.915 0.004 0.883 0.005 0.920 0.004 0.894 0.006 0.924 0.004 0.901 0.007 0.935 0.005 0.917 0.006 0.938 0.005 0.922 0.007 0.947 0.005 0.930 0.006 0.956 0.005 0.943 0.006 0.965 0.005 0.957 0.007 0.979 0.013 0.974 0.016 0.979 0.005 0.972 0.007 0.981 0.004 0.972 0.005 0.989 0.004 0.985 0.006 0.992 0.004 0.987 0.005 0.995 0.004 0.991 0.005 0.996 0.004 0.991 0.005 0.996 0.004 0.990 0.004 0.998 0.004 0.993 0.004 0.996 0.004 0.989 0.004 1.002 0.003 0.999 0.004 1.000 0.003 0.996 0.004 1.000 0.003 0.997 0.004 1.002 0.003 1.001 0.004 1.005 0.003 1.005 0.004 1.002 0.003 1.002 0.003 1.004 0.003 1.004 0.003 1.000 0.003 0.997 0.003 0.999 0.003 0.996 0.003 1.005 0.003 1.005 0.003 1.001 0.003 1.001 0.003 1.001 0.003 1.000 0.003 1.005 0.003 1.007 0.003
16.9 Pr 0.683 0.710 0.734 0.758 0.773 0.783 0.790 0.797 0.805 0.807 0.811 0.815 0.823 0.822 0.827 0.833 0.847 0.841 0.857 0.867 0.886 0.894 0.903 0.919 0.938 0.960 0.956 0.954 0.974 0.975 0.981 0.981 0.978 0.984 0.978 0.993 0.988 0.991 0.996 1.003 1.000 1.003 0.992 0.991 1.005 0.999 0.998 1.008
0.7 U 0.014 0.012 0.012 0.011 0.010 0.009 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.007 0.008 0.009 0.008 0.007 0.006 0.006 0.006 0.024 0.005 0.006 0.005 0.005 0.005 0.005 0.005 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.004 0.004 0.003 0.003 0.003 0.003
20.4 Pr 0.565 0.594 0.611 0.653 0.690 0.709 0.719 0.727 0.737 0.741 0.753 0.763 0.778 0.770 0.783 0.790 0.812 0.761 0.826 0.845 0.863 0.868 0.867 0.888 0.914 0.941 0.933 0.931 0.953 0.956 0.962 0.964 0.962 0.968 0.963 0.979 0.974 0.980 0.986 0.996 0.995 0.997 0.981 0.984 1.004 0.994 0.997 1.008
0.9 U 0.020 0.019 0.024 0.021 0.016 0.013 0.012 0.012 0.012 0.011 0.010 0.011 0.012 0.011 0.012 0.012 0.013 0.019 0.015 0.017 0.014 0.016 0.010 0.011 0.012 0.036 0.010 0.008 0.009 0.008 0.007 0.006 0.006 0.006 0.007 0.006 0.009 0.007 0.007 0.005 0.004 0.005 0.010 0.006 0.006 0.006 0.009 0.005
222 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb x/Dh 0.28 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
3.5 Pr 1.001 1.001 0.955 0.966 0.972 0.967 0.966 0.967 0.967 0.968 0.968 0.969 0.973 0.970 0.971 0.972 0.975 0.973 0.974 0.979 0.977 0.978 0.981 0.983 0.991 0.989 0.992 0.994 0.996 0.997 0.998 0.999 1.000 1.001 1.001 1.001 1.002 1.002 1.002 1.002 1.001 1.002 1.002 1.002 1.001 1.002 1.002 1.002
0.3 U 0.004 0.009 0.004 0.004 0.004 0.004 0.003 0.004 0.004 0.003 0.003 0.003 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.006 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
6.8 Pr 1.000 1.003 0.910 0.928 0.942 0.936 0.938 0.941 0.944 0.945 0.946 0.947 0.953 0.949 0.949 0.950 0.956 0.953 0.955 0.961 0.960 0.962 0.968 0.973 0.985 0.983 0.987 0.992 0.995 0.998 0.999 1.001 1.002 1.004 1.004 1.003 1.005 1.005 1.005 1.004 1.004 1.005 1.005 1.004 1.003 1.004 1.004 1.004
0.5 U 0.004 0.007 0.006 0.006 0.005 0.004 0.005 0.006 0.006 0.006 0.006 0.006 0.008 0.005 0.005 0.005 0.005 0.005 0.005 0.007 0.005 0.005 0.006 0.007 0.008 0.006 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Topwall Pressure Ratio (P/Patm) 10.2 0.6 13.5 0.6 Pr U Pr U 1.000 0.004 0.999 0.004 1.002 0.006 1.001 0.006 0.860 0.007 0.799 0.008 0.891 0.006 0.843 0.007 0.907 0.005 0.863 0.007 0.898 0.005 0.857 0.007 0.900 0.006 0.868 0.007 0.905 0.005 0.884 0.006 0.910 0.005 0.891 0.005 0.913 0.005 0.888 0.004 0.915 0.004 0.883 0.004 0.917 0.004 0.883 0.004 0.924 0.008 0.893 0.010 0.919 0.004 0.886 0.004 0.920 0.004 0.887 0.004 0.922 0.004 0.891 0.004 0.930 0.004 0.903 0.004 0.927 0.004 0.900 0.005 0.931 0.004 0.907 0.005 0.941 0.008 0.921 0.010 0.941 0.004 0.922 0.005 0.947 0.004 0.931 0.006 0.956 0.005 0.943 0.006 0.964 0.005 0.953 0.006 0.980 0.009 0.972 0.011 0.978 0.004 0.970 0.006 0.984 0.005 0.977 0.007 0.989 0.004 0.984 0.006 0.993 0.004 0.989 0.006 0.996 0.004 0.993 0.006 0.999 0.004 0.996 0.005 1.000 0.004 0.997 0.005 1.002 0.004 0.999 0.005 1.004 0.004 1.003 0.004 1.005 0.004 1.004 0.004 1.004 0.004 1.004 0.004 1.007 0.004 1.007 0.004 1.007 0.004 1.008 0.004 1.008 0.004 1.008 0.004 1.006 0.004 1.007 0.004 1.006 0.003 1.007 0.004 1.007 0.003 1.008 0.004 1.007 0.003 1.009 0.004 1.007 0.003 1.008 0.003 1.005 0.004 1.007 0.004 1.006 0.003 1.008 0.003 1.006 0.003 1.007 0.003 1.006 0.003 1.008 0.003
16.9 Pr 0.999 1.000 0.712 0.780 0.806 0.797 0.811 0.836 0.854 0.851 0.841 0.841 0.853 0.842 0.844 0.851 0.865 0.862 0.872 0.890 0.891 0.903 0.918 0.931 0.957 0.953 0.963 0.972 0.978 0.983 0.987 0.989 0.993 0.997 0.999 1.002 1.004 1.006 1.007 1.006 1.007 1.008 1.009 1.009 1.007 1.009 1.008 1.009
0.7 U 0.004 0.006 0.017 0.012 0.010 0.009 0.009 0.008 0.007 0.006 0.008 0.007 0.014 0.006 0.007 0.007 0.006 0.006 0.006 0.013 0.006 0.006 0.006 0.006 0.014 0.005 0.005 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
20.4 Pr 0.999 0.999 0.541 0.682 0.738 0.731 0.747 0.775 0.801 0.811 0.797 0.792 0.796 0.788 0.801 0.809 0.825 0.820 0.837 0.863 0.863 0.875 0.894 0.908 0.940 0.931 0.943 0.952 0.959 0.966 0.971 0.973 0.979 0.984 0.987 0.993 0.995 0.998 1.000 1.002 1.002 1.003 1.005 1.006 1.005 1.007 1.007 1.008
0.9 U 0.004 0.005 0.036 0.022 0.013 0.012 0.011 0.009 0.011 0.010 0.008 0.011 0.020 0.017 0.009 0.009 0.008 0.010 0.014 0.016 0.011 0.015 0.012 0.014 0.018 0.011 0.011 0.010 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.007 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
223 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb Position 0.00 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
24.0 Pr 0.503 0.531 0.488 0.433 0.415 0.425 0.419 0.426 0.479 0.530 0.599 0.616 0.652 0.596 0.607 0.623 0.667 0.551 0.673 0.697 0.727 0.729 0.723 0.754 0.803 0.845 0.841 0.845 0.880 0.889 0.902 0.908 0.909 0.922 0.921 0.938 0.937 0.943 0.950 0.962 0.973 0.968 0.955 0.956 0.983 0.975 0.974 1.007
Sidewall Pressure Ratios (P/Patm) 0.9 27.4 0.9 30.6 U Pr U Pr 0.018 0.527 0.012 0.554 0.012 0.549 0.009 0.568 0.013 0.508 0.008 0.529 0.016 0.455 0.011 0.479 0.073 0.410 0.024 0.436 0.148 0.348 0.014 0.380 0.194 0.290 0.012 0.328 0.209 0.279 0.014 0.322 0.191 0.280 0.017 0.345 0.163 0.287 0.030 0.341 0.129 0.441 0.194 0.399 0.129 0.600 0.062 0.600 0.122 0.573 0.123 0.678 0.125 0.356 0.016 0.404 0.126 0.313 0.014 0.341 0.111 0.315 0.019 0.328 0.106 0.367 0.023 0.370 0.112 0.240 0.021 0.243 0.125 0.330 0.067 0.324 0.118 0.343 0.108 0.325 0.099 0.456 0.039 0.433 0.109 0.358 0.016 0.449 0.100 0.280 0.027 0.295 0.095 0.274 0.082 0.271 0.086 0.371 0.092 0.323 0.107 0.486 0.294 0.486 0.068 0.459 0.153 0.366 0.056 0.460 0.231 0.350 0.051 0.553 0.211 0.319 0.043 0.654 0.139 0.322 0.037 0.723 0.095 0.339 0.032 0.756 0.068 0.375 0.027 0.768 0.066 0.419 0.024 0.803 0.049 0.481 0.020 0.803 0.048 0.622 0.023 0.824 0.056 0.686 0.021 0.834 0.042 0.724 0.018 0.848 0.041 0.728 0.017 0.858 0.042 0.742 0.022 0.877 0.032 0.783 0.013 0.902 0.028 0.840 0.019 0.890 0.030 0.818 0.019 0.887 0.035 0.816 0.016 0.891 0.033 0.857 0.021 0.919 0.030 0.874 0.017 0.918 0.027 0.871 0.018 0.931 0.028 0.910 0.018 0.950 0.021 0.913
1.0 U 0.011 0.008 0.008 0.011 0.020 0.019 0.011 0.014 0.028 0.019 0.141 0.097 0.093 0.024 0.015 0.015 0.022 0.018 0.048 0.067 0.081 0.049 0.012 0.052 0.045 0.292 0.039 0.021 0.045 0.052 0.031 0.062 0.131 0.185 0.115 0.065 0.047 0.080 0.077 0.058 0.048 0.064 0.066 0.040 0.040 0.041 0.029 0.027
Pc/Pb x/Dh 0.28 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
24.0 Pr 0.998 0.997 0.379 0.499 0.540 0.502 0.513 0.552 0.588 0.562 0.528 0.569 0.694 0.750 0.676 0.552 0.611 0.737 0.743 0.712 0.691 0.759 0.770 0.791 0.851 0.829 0.852 0.871 0.885 0.899 0.912 0.919 0.932 0.941 0.948 0.964 0.963 0.970 0.975 0.986 0.987 0.987 0.990 0.994 0.996 0.998 1.000 1.002
Topwall Pressure Ratios (P/Patm) 0.9 27.4 0.9 30.6 U Pr U Pr 0.004 0.998 0.005 0.998 0.006 0.995 0.008 0.992 0.025 0.407 0.015 0.441 0.035 0.502 0.012 0.524 0.064 0.504 0.011 0.514 0.108 0.428 0.013 0.435 0.156 0.400 0.014 0.401 0.201 0.387 0.023 0.376 0.186 0.437 0.019 0.416 0.193 0.413 0.012 0.442 0.183 0.349 0.010 0.371 0.212 0.298 0.009 0.319 0.213 0.312 0.062 0.328 0.161 0.283 0.129 0.249 0.193 0.398 0.161 0.331 0.193 0.601 0.077 0.596 0.204 0.475 0.044 0.557 0.173 0.359 0.021 0.416 0.135 0.312 0.011 0.351 0.146 0.350 0.067 0.370 0.147 0.307 0.020 0.322 0.104 0.333 0.081 0.303 0.098 0.346 0.047 0.370 0.093 0.422 0.031 0.412 0.075 0.520 0.136 0.516 0.073 0.336 0.148 0.316 0.065 0.390 0.226 0.289 0.057 0.523 0.207 0.332 0.052 0.590 0.170 0.392 0.044 0.668 0.140 0.400 0.040 0.732 0.089 0.361 0.035 0.750 0.077 0.365 0.030 0.783 0.067 0.485 0.027 0.809 0.054 0.545 0.026 0.818 0.049 0.615 0.026 0.863 0.050 0.709 0.022 0.854 0.039 0.700 0.020 0.869 0.035 0.734 0.019 0.880 0.033 0.761 0.014 0.915 0.034 0.826 0.014 0.916 0.022 0.833 0.015 0.914 0.020 0.834 0.014 0.922 0.019 0.850 0.012 0.931 0.018 0.877 0.009 0.949 0.018 0.906 0.010 0.945 0.016 0.903 0.009 0.953 0.014 0.919 0.008 0.960 0.011 0.929
1.0 U 0.005 0.011 0.014 0.009 0.010 0.012 0.010 0.012 0.035 0.018 0.013 0.012 0.058 0.031 0.217 0.061 0.054 0.027 0.014 0.061 0.010 0.064 0.062 0.037 0.097 0.023 0.065 0.090 0.011 0.020 0.020 0.081 0.128 0.124 0.105 0.083 0.071 0.070 0.064 0.063 0.047 0.043 0.039 0.032 0.032 0.026 0.021 0.018
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by
DAVID M. LINEBERRY A DISSERTATION
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Mechanical and Aerospace Engineering to The School of Graduate Studies of The University of Alabama in Huntsville
HUNTSVILLE, ALABAMA 2007
UMI Number: 3272664
UMI Microform 3272664 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346
In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree from The University of Alabama in Huntsville, I agree that the Library of this University shall make it freely available for inspection. I further agree that permission for extensive copying for scholarly purposes may be granted by my advisor or, in his/her absence, by the Chair of the Department or the Dean of the School of Graduate Studies. It is also understood that due recognition shall be given to me and to The University of Alabama in Huntsville in any scholarly use which may be made of any material in this dissertation.
ii
DISSERTATION APPROVAL FORM Submitted by David M. Lineberry in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering and accepted on behalf of the Faculty of the School of Graduate Studies by the dissertation committee. We, the undersigned members of the Graduate Faculty of The University of Alabama in Huntsville, certify that we have advised and/or supervised the candidate on the work described in this dissertation. We further certify that we have reviewed the dissertation manuscript and approve it in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering.
iii
ABSTRACT The School of Graduate Studies The University of Alabama in Huntsville
Degree
Doctor of Philosophy
College/Dept. Engineering/Mechanical and Aerospace Engineering . Name of Candidate David M. Lineberry . Title Characterization of a Cold Flow Non-Axisymmetric Supersonic Ejector .
Experimental investigations of dual and single nozzle non-axisymmetric strut based supersonic ejectors were carried out. The strut nozzles transitioned from a round throat to a square exit with an expansion ratio of 4.6. The ejector system entrained secondary air from the lab and exhausted to the lab at atmospheric pressure. The ejectors were operated at equivalent mass flow rates at primary chamber pressure to back pressure ratios ranging from 6.8 to 61.2 for the single nozzle strut and 3.4 to 30.6 for the dual nozzle strut. Under these conditions both struts demonstrated operation in three distinct regimes: mixed, saturated supersonic and supersonic.
Secondary flow choking was
demonstrated for both struts at equivalent primary mass flow rates. The mixing length was determined by pressure recovery or equalization with the back pressure. This length remained relatively constant at approximately 20 nozzle hydraulic diameters for the primary mass flow rates in the mixed regime. At higher mass flow rates, the pressure recovery length increased and appeared to be strongly affected by the primary nozzle exit pressure. Surveys of duct exit stagnation pressure indicated poor mixing at high mass flow rates with a supersonic core existing through the mixing duct. Shadow graph images revealed a complex shock structure in the recovery region of the mixing duct. Classical analytical models for axisymmetric ejectors were used to investigate the effect
iv
of non-axisymmetric geometry.
Preliminary CFD simulations were performed to
investigate ejector mixing.
v
ACKNOWLEDGMENTS
The work documented in this dissertation would not have been possible without the assistance of several individuals. First I would like to thank Dr. Clark Hawk for his devotion to the students in the Propulsion Research Center. I would not be at this point in my life without his support. Second I would like to thank my dissertation advisor, Dr. Brian Landrum.
I would also like to acknowledge Dr. Marlow Moser for his
invaluable guidance in the experimental setup, and analysis of results. I would also like to thank Dr. Hugh Coleman, Dr. Kader Frendi, and Dr. C.P. Chen for their support of my research. In addition, a number of other individuals deserve mention for their assistance to my research. George Olden was a tremendous help in the lab in all aspects of the experiment from the beginning to the end of this work. A number of other individuals in the PRC should be recognized:
Balasubramanyam Madhanabharatam for the CFD
analysis, Tony Hall for his assistance with laboratory issues, Chris Linn and David Jackson for their help in the shadowgraph experiments, and finally Geri Gaeta for her assistance with the exit profile traces. I would also like to recognize the late Dr. Mark V. Bower. Dr. Bower was always available for consultation, and was supportive of me both in my academic pursuits and in my teaching endeavors at UAH. He will be greatly missed.
vi
TABLE OF CONTENTS
Page List of Figures .................................................................................................................... xi List of Tables ................................................................................................................... xvi List of Symbols ............................................................................................................... xvii Chapter 1.
INTRODUCTION....................................................................................................... 1 1.1
Introduction....................................................................................................... 1
1.2
Ejector Propulsion Applications ....................................................................... 1 1.2.1 Ducted Rockets....................................................................................... 2 1.2.2 Rocket Based Combined Cycle Engines ................................................ 3
2.
1.3
Principles of Ejector Operation......................................................................... 5
1.4
Ejector Flow Regimes....................................................................................... 8
1.5
Ejector Performance Characterization ............................................................ 10
1.6
Ejector Design Considerations........................................................................ 12
1.7
Ejector Analysis Techniques........................................................................... 14
1.8
Motivation....................................................................................................... 15
BACKGROUND....................................................................................................... 18 2.1
UAH Propulsion Research Center .................................................................. 18
2.2
Classical Ejector Research.............................................................................. 23 2.2.1 Fabri’s Ejector Model........................................................................... 23 2.2.2 Supersonic Regime............................................................................... 25 2.2.3 Saturated Supersonic Flow ................................................................... 28 2.2.4 Mixed Flow .......................................................................................... 28 2.2.5 Mixed Flow with Primary Separation .................................................. 31 2.2.6 Matching Fabri’s Models ..................................................................... 32 2.2.7 Addy’s Ejector Model .......................................................................... 34
vii
2.2.8 Supersonic Flow Regime Model .......................................................... 34 2.2.9 Mixed Flow Regime ............................................................................. 36 2.3
CFD Analysis.................................................................................................. 37
2.4
Current Experimental Work............................................................................ 39 2.4.1 Propulsion Engineering Research Center............................................. 39 2.4.2 Japan Aerospace Exploration Agency.................................................. 41 2.4.3 Aerojet .................................................................................................. 44 2.4.4 Small Scale Experimental Efforts ........................................................ 45
2.5 3.
Summary ......................................................................................................... 47
FACILITY AND EXPERIMENTAL SETUP .......................................................... 48 3.1
Facility ............................................................................................................ 48
3.2
Test Matrix...................................................................................................... 55 3.2.1 Mixing Duct Tests ................................................................................ 56 3.2.2 Exit Pressure Profiles ........................................................................... 58 3.2.3 Shadowgraph Visualizations ................................................................ 59
4.
UNCERTAINTY ANALYSIS AND DATA REDUCTION EQUATIONS ............ 62 4.1
Introduction..................................................................................................... 62
4.2
General Uncertainty ........................................................................................ 62 4.2.1 Single Variable Measurement Uncertainty .......................................... 63 4.2.2 Uncertainty for a Calculated Result ..................................................... 65 4.2.3 Uncertainty for a Collection of Results................................................ 66
4.3
Reducing Test Uncertainty Through Nominal Readings................................ 67
4.4
Pressure Transducers Calibration ................................................................... 68
4.5
Ejector Specific Uncertainty ........................................................................... 68 4.5.1 Mass Flow ............................................................................................ 69 4.5.2 Bypass Ratio......................................................................................... 71 4.5.3 Mach Number....................................................................................... 72 4.5.4 Pressure Ratios ..................................................................................... 73
viii
5.
EXPERIMENTAL RESULTS .................................................................................. 74 5.1
Introduction..................................................................................................... 74
5.2
Single Nozzle Strut ......................................................................................... 74 5.2.1 Mass Flow Augmentation .................................................................... 75 5.2.2 Mach Numbers ..................................................................................... 76 5.2.3 Strut Gap Pressures .............................................................................. 78 5.2.4 Mixing Section Static Pressure Distributions....................................... 82 5.2.5 Exit Pressure Profiles ........................................................................... 90
5.3
Dual Nozzle Strut............................................................................................ 97 5.3.1 Mass Flow Augmentation .................................................................... 98 5.3.2 Mach Numbers ..................................................................................... 99 5.3.3 Strut Gap Pressures ............................................................................ 100 5.3.4 Mixing Section Static Pressure Distribution ...................................... 103 5.3.5 Exit Pressure Profiles ......................................................................... 109
6.
DISCUSSION OF RESULTS ................................................................................. 116 6.1
Mass Flow and Bypass Ratio........................................................................ 116 6.1.1 Mass Flow Calculations ..................................................................... 119 6.1.2 Bypass Ratio....................................................................................... 122
6.2
Pressure Distribution..................................................................................... 125
6.3
Flow Visualization ........................................................................................ 131
6.4
Analytical Comparisons................................................................................ 136 6.4.1 Single Nozzle Strut............................................................................. 136 6.4.2 Dual Nozzle Strut ............................................................................... 138
6.5 7.
CFD Analysis................................................................................................ 141
CONCLUSIONS ..................................................................................................... 148 7.1
Flow Regimes ............................................................................................... 148
7.2
Mixing Duct Pressure Distributions.............................................................. 150
7.3
Mass Flow Entrainment ................................................................................ 153
7.4
Comparison to Analytical Models ................................................................ 154
7.5
CFD Analysis................................................................................................ 155 ix
7.6
Momentum Effects........................................................................................ 156
7.7
Future Work .................................................................................................. 158
APPENDIX A: Systematic Uncertainty Values ............................................................ 162 APPENDIX B: Regression Uncertainty Analysis for Calibration................................. 164 APPENDIX C: Mathcad Calculation Sheets ................................................................. 170 APPENDIX D: Test Results (Average Values)............................................................. 215 REFERENCES ............................................................................................................... 224
x
LIST OF FIGURES
Figure
Page
1.1 Schematic of a ducted rocket [2]. ................................................................................ 3 1.2 Schematic of the Aerojet StrutJet Concept [3]. ........................................................... 4 1.3 Specific impulse for RBCC operating modes [3]. ....................................................... 5 1.4 Axisymmetric ejector diagram..................................................................................... 6 1.5 Depiction of shear layer between a high speed primary jet and a low speed secondary flow. ....................................................................................................... 7 1.6 Mass Flow and Bypass ratio for a supersonic ejector [10]. ...................................... 11 2.1 Sketch of PRC ejector facility.................................................................................... 19 2.2 PLIF images of the mixing between the turbine exhaust and the two rocket plumes from the dual nozzle strut [23].............................................................................. 20 2.3 Probe locations for pressure traces in the PRC ejector [24]. ..................................... 21 2.4 Sketch of an axisymmetric ejector with Fabri’s notation. ......................................... 24 2.5 Sketch of an axisymmetric ejector with Fabri’s notation for mixed regime analysis.29 2.6 Comparison of recreated model with data from Fabri’s model. ................................ 32 2.7 Mixed regime comparison of current model with Fabri’s model. ............................. 33 2.8 Ejector configuration for Kitamura’s experiments [33]............................................. 42 2.9 Pressure recovery comparison in rectangular and circular cross section ejectors [33]........................................................................................................................ 42 2.10 Surface flow patterns for a circular duct (a) and a rectangular duct (b) ejector [33]........................................................................................................................ 43 3.1 Schematic of PRC cold flow ejector facility.............................................................. 48 3.2 Ejector test rig cross section. ..................................................................................... 49 3.3 Ejector test rig end view. ........................................................................................... 50
xi
3.4 Dual and single nozzle ejector struts. ........................................................................ 51 3.5 PRC ejector top wall static pressure tap locations. .................................................... 52 3.6 PRC ejector side wall pressure tap locations. ............................................................ 53 3.7 Secondary flow Pitot probe location in strut fairing.................................................. 54 3.8 Probe trace locations for stagnation pressure traces across the duct exit plane......... 58 3.9. Schematic of shadowgraph setup for ejector facility................................................ 59 3.10. Region of interest for shadowgraphy [37]. ............................................................. 60 5.1 Single nozzle strut primary and secondary mass flow comparison. .......................... 75 5.2 Secondary flow Mach number ahead of the strut and mixed flow Mach number at duct exit centerline (single nozzle strut). .............................................................. 77 5.3 Single nozzle strut gap pressure ratios....................................................................... 79 5.4 Single nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 40.5, 47.3, 53.9, and 60.6)...................................................................... 80 5.5 Single nozzle strut pressure ratio at last static pressure tap in the strut gap (0.843 hydraulic diameters upstream).............................................................................. 81 5.6 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 6.5)................. 83 5.7 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 13.2)............... 83 5.8 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 20.2)............... 84 5.9 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 27.2).............. 84 5.10 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 33.8)............ 85 5.11 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 40.5)............. 86 5.12 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 47.3). ............. 87 5.13 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 53.9). .............. 88 5.14 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 60.6). ............. 88 5.15 Single nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).................................................................................. 92 5.16 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.5). . 92
xii
5.17 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.2). 93 5.18 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.8). 93 5.19 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.2). 94 5.20 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 33.8). 94 5.21 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 40.4). 95 5.22 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 47.1). 96 5.23 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 53.7). 96 5.24 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 60.3). 97 5.25 Dual nozzle strut secondary and primary mass flow. .............................................. 98 5.26 Dual nozzle inlet and exit centerline Mach numbers............................................... 99 5.27 Dual nozzle strut gap pressure ratios. .................................................................... 100 5.28 Dual nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 20.4, 24.0, 27.4, and 30.6). .......................................................................................... 101 5.29 Dual nozzle strut gap pressure ratios at last static pressure tap (0.843 hydraulic diameters upstream). ........................................................................................... 102 5.30 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 3.5)................. 104 5.31 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 6.8).................. 104 5.32 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 10.2)............... 105 5.33 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 13.5)............... 105 5.34 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 16.9)............... 106 5.35 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 20.5)............... 106 5.36 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 24.0)............... 107 5.37 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 27.4)............... 108 5.38 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 30.7)............... 108 5.39 Dual nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A). ............................................................................................... 110
xiii
5.40 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 3.5).... 111 5.41 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.9).... 112 5.42 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 10.1).. 112 5.43 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.4).. 113 5.44 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 16.7).. 113 5.45 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.9).. 114 5.46 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 23.9).. 114 5.47 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.1).. 115 5.48 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 30.3).. 115 6.1 Secondary mass flow versus set point pressure ratio for single and dual nozzle struts.................................................................................................................... 117 6.2 Secondary mass flow comparison for both struts. ................................................... 118 6.3 Bypass ratio versus primary mass flow rate for single and dual nozzle struts. ....... 123 6.4: Bypass ratio versus pressure ratio for the dual and single nozzle struts with low pressure test data. ................................................................................................ 124 6.5: Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.3 lbm/s)........................................................................................ 126 6.6 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.7 lbm/s)........................................................................................ 126 6.7 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.05 lbm/s)...................................................................................... 127 6.8 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.39 lbm/s)...................................................................................... 127 6.9 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.74 lbm/s)...................................................................................... 128 6.10 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.1 lbm/s)........................................................................................ 129 6.11 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.45 lbm/s)...................................................................................... 130
xiv
6.12 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.78 lbm/s)...................................................................................... 130 6.13 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 3.13 lbm/s)...................................................................................... 131 6.14. Series of images depicting chamber pressure ramp up for single nozzle strut: (a) Pc/Pb = 13.3, (b) Pc/Pb = 33.8, (c) Pc/Pb = 40.5, and (d) Pc/Pb = 47.2................ 133 6.15 Series of images depicting chamber pressure ramp up for dual nozzle strut: (a) Pc/Pb = 16.8, (b) Pc/Pb = 20.4, (c) Pc/Pb = 24.0, and (d) Pc/Pb = 30.6. ....................... 134 6.16. Plot of top wall pressure distribution with shadowgraph image (dual nozzle strut Pc/Pb = 30.6). ...................................................................................................... 135 6.17 One-dimensional model for axisymmetric ejector of equivalent geometry to single nozzle strut PRC ejector...................................................................................... 137 6.18 Comparison of theoretical symmetric ejector model with experimental data for non axisymmetric single nozzle ejector..................................................................... 138 6.19 Comparison of Fabri models with dual nozzle strut data. ..................................... 139 6.20 Theoretical bypass ratio for axisymmetric ejectors with geometry ratios equivalent to those in the single and dual nozzle PRC ejectors. .......................................... 141 6.21 Ejector strut gap sidewall pressure ratio (Pc/Pb = 40.4)......................................... 142 6.22 Ejector strut gap sidewall pressure ratio (Pc/Pb = 53.7) [44]. ................................ 143 6.23 3-D strut rocket nozzle exit Mach contours............................................................ 144 6.24 3-D strut rocket nozzle exit pressure contours........................................................ 144 6.25 Sidewall pressures in ejector mixing duct (Pc/Pb = 40.4). ..................................... 145 6.26 Sidewall pressures in ejector mixing duct (Pc/Pb = 53.7). ..................................... 145 6.27 3-D Pressure profiles at centerline of top-wall (Pc/Pb = 40.4)............................... 147
xv
LIST OF TABLES
Table
Page
3.1
Ejector Test Matrix............................................................................................... 56
A.1
Systematic uncertainty constants for instrumentation........................................ 163
D.1
Test averages for single nozzle strut................................................................... 216
D.2
Test averages for dual nozzle strut...................................................................... 220
xvi
LIST OF SYMBOLS
a
speed of sound
a*
characteristic speed of sound
Aduct
mixing duct cross sectional area
Athroat
cross sectional area of the primary nozzle
B
systematic uncertainty
D
mixing duct diameter (Fabri’s model)
Dh
ejector rocket nozzle exit hydraulic diameter
f
skin friction factor
L
mixing duct length (Fabri’s model)
M
Mach number
M*
characteristic Mach number
m
mass flow
P
static pressure
Po
stagnation pressure
Rair
gas constant for air
S
sample standard deviation
S
standard deviation of the mean
T
temperature
To
stagnation temperature
U
total uncertainty
U
total uncertainty of the mean
w
width of ejector mixing duct
xvii
Greek δ*
boundary layer displacement thickness
γ
ratio of specific heats
λ
ratio of the mixing duct area to the primary nozzle exit area (Fabri’s model)
λ*
ratio of the throat area to the primary nozzle exit area (Fabri’s model)
λ’
ratio of the duct area at the secondary flow inlet to the primary nozzle exit area. (Fabri’s model)
μ
ratio of secondary flow stagnation pressure to the back pressure
ν
ratio of the primary jet plume width at maximum expansion to the primary nozzle exit area. (Fabri’s model)
ρ
density
σ
ratio of the diffuser exit area to the mixing duct exit area
ω
bypass ratio
ξ
ratio of the lateral surface area to that of the transverse area (Fabri’s model)
Subscripts 1
primary flow conditions
2
secondary flow conditions
3
mixed flow conditions
b
exit flow conditions
c
chamber conditions
p
primary flow conditions
s
secondary flow conditions
xviii
CHAPTER 1
INTRODUCTION
1.1
Introduction In the past several decades, the pursuit of a fully reusable launch vehicle has
driven interest in using airbreathing ejectors to provide thrust enhancement to traditional rocket propulsion devices.
Fundamentally, an ejector is a device which exchanges
momentum between a high velocity primary fluid stream and a low velocity secondary fluid stream. The momentum exchange occurs as a result of the viscous interaction between the two streams. As momentum is exchanged, the two streams mix until a single uniform mixture exists. The mixed stream will have a greater momentum than the initial primary stream and a higher pressure than the induced secondary fluid. Although the principles behind ejector operation are relatively simple, the fluid mechanics in even a simple ejector are not well understood.
1.2
Ejector Propulsion Applications Ejector-rocket devices have been studied in various forms over the past five
decades [1]. Concepts such as ducted rockets, ram-rocket, air-augment rockets, and rocket ejector nozzle engines, ejector ramjets, ejector scramjets and rocket based
1
2 combined cycle engines utilize the ejector effect. The augmented thrust comes from the entrainment of secondary flow from the atmosphere which can either add momentum to a primary flow exhaust or be combusted with a fuel to increase the total energy of the exhaust gases. By increasing the thrust without additional onboard propellant, a higher overall specific impulse for the vehicle is achieved. Although the devices mentioned have different performance considerations, they all operate under the same principles, a secondary air flow entrained by a primary flow stream. The simplest of these devices is the ducted rocket and the most complex is the rocket based combined cycle engine. The complexity comes from incorporation of many modes of operation, but the ejector physics in all of these systems is essentially the same.
1.2.1
Ducted Rockets Figure 1.1 shows a schematic of a ducted rocket. Here the rocket engine is
exhausted into a mixing duct with an open inlet and an open exit.
Air from the
surrounding atmosphere is ingested through the ejector action, mixes with the rocket exhaust, and can be used in a downstream combustion process. By utilizing the oxygen in the ingested air, the total onboard oxidizer required for the engine is reduced. In most ducted rocket concepts either the primary rocket is fuel rich or additional fuel is injected into the mixed flow stream for downstream combustion. Even without the downstream combustion, ducted rockets can offer a thrust increase over conventional rockets at low flight speeds.
In addition to increasing thrust, the ingested air for combustion can
significantly improve the specific impulse of the vehicle. At low Mach numbers, the specific impulse increase can be in the range of 10 to 20% even without combustion [2].
3 With the addition of combustion, the specific impulse can be augmented in the range of 200% [2]. Since the flow path for the engine is relatively simple, the thrust augmentation comes at a low design cost.
Fuel Injection
Primary Rocket
Air
Mixer
Combustor
Nozzle
Figure 1.1 Schematic of a ducted rocket [2].
1.2.2
Rocket Based Combined Cycle Engines Many organizations have studied reusable launch vehicles that use a Rocket
Based Combined Cycle, RBCC, engine as an alternative to carrying all the oxidizer onboard [3-6]. Generally an RBCC vehicle incorporates four modes of engine operation into a single duct or flow path. Figure 1.2 shows a diagram of the Aerojet StrutJet RBCC engine concept [3].
The ejector rocket mode is used for take off and the initial
acceleration to around Mach 2. As the vehicle passes Mach 2, the ejector rockets are no longer used, and the engine transitions to the ramjet operation mode. As the vehicle velocity passes approximately Mach 5, the engine transitions to scramjet operation. This mode is used until the vehicle ascends to the upper atmosphere where air breathing
4 engine operation is no longer viable. The engine transitions to a pure rocket mode to accelerate into space.
Figure 1.2 Schematic of the Aerojet StrutJet Concept [3].
By using four different modes of operation, the vehicle can operate in the mode which provides the highest specific impulse (ISP) for that flight regime. By utilizing atmospheric air as an oxidizer in the first three airbreathing modes, the propellant weight is significantly reduced. In theory, an RBCC vehicle can achieve overall mission ISP values which are significantly higher than those of a conventional pure rocket launch vehicle [3]. Figure 1.3 shows the potential ISP improvement of the operating modes of an RBCC vehicle over that of a chemical rocket propulsion system. The concept of an RBCC engine is relatively straightforward; however, development of such an engine is a complex task. The desired engine geometry for each
5 operational mode differs, so the transition from one mode to the next would also involve physical changes to as duct area, fuel injection location, and ignition location. The physical changes would also be accompanied by operational changes in the engine fuel and oxidizer flow rates, cooling flow rates, etc. Although there are many enabling technologies which must be developed to build and test an RBCC engine, the potential benefits of such an engine make it an attractive alternative to traditional propulsion methods.
7000 TURBOJETS
HYDROGEN FUEL
6000
5000 SPECIFIC IMPULSE (SECONDS)
RAMJETS
4000
3000
SCRAMJETS
Ducted Rockets
2000
ACCERERATION MODES (MANY CANDIDATES)
1000
0
2
4
6
8
ROCKETS
10
12
14
16
MACH NUMBER
Figure 1.3 Specific impulse for RBCC operating modes [3].
1.3
Principles of Ejector Operation As stated previously, an ejector is a momentum exchange device which is
designed to transfer momentum from a driven primary flow to an ingested secondary
6 fluid. The interaction along the boundary between the two jets transfers momentum from the primary jet to the secondary fluid by means of viscous effects and pressure interaction. The result of this interaction is a loss of momentum in the primary jet, lowering the jet velocity and pressure, and an increase of momentum to the ingested secondary fluid, increasing the secondary flow velocity and pressure. These two initially separate flow streams mix as the momentum is transferred and result in a fully mixed stream with a momentum that is higher than the momentum of the initial driven primary flow.
If the primary flow stream is supersonic, then the configuration is deemed a
supersonic ejector. A sketch of a typical axisymmetric supersonic ejector is shown in Figure 1.4. The primary stream is typically accelerated through a nozzle and exhausted into an openended duct. Upon leaving the nozzle, the primary stream is either turned inward through shock compression, exhausts parallel to the wall, or is turned outward through a free expansion. These modes are denoted as over expanded, ideally expanded, or under
Minimum Geometric Area (Aerodynamic Choke Location)
Mixing Duct
Secondary Flow Mixed Flow Primary Flow
Ejector Nozzle
Mass Addition Choke Location
Primary Jet Boundary
Figure 1.4 Axisymmetric ejector diagram.
Ejector Exit
7 expanded and refer to the exit pressure of the nozzle relative to the surrounding pressure. After the primary flow leaves the nozzle, viscous effects across the boundary between the primary flow and the secondary fluid cause the surrounding pressure to drop as the secondary fluid is “dragged” by the primary flow. This pressure reaches some minimum value once the steady state operation has been reached. The resultant lower pressure in the duct aids in the developing and maintaining the flow of the secondary fluid. The boundary between two flow streams of different velocities, as in the case of the secondary and primary flow streams in an ejector, is known as a free jet boundary. A continuous static pressure is maintained across this boundary. Between the two streams, a shear layer is established from the point where the two flows first contact. This layer becomes thicker as it progresses downstream. The shear layer acts to accelerate the secondary flow and impede the primary flow as shown in Figure 1.5. In addition to the velocity changes across this shear layer, mixing between the primary and secondary streams occurs across this layer.
Initial Stream Profiles
Subsequent Stream Profiles
US
US Shear Layer Boundary Dividing Streamline Shear Layer Boundary UP
UP
Figure 1.5 Depiction of shear layer between a high speed primary jet and a low speed secondary flow.
8 1.4
Ejector Flow Regimes In some of the earliest comprehensive studies of ejectors, Fabri established two
main regimes of ejector operation, the mixed regime and the supersonic regime [7, 8]. Although there are other subsets of these regimes, this classification has been used as a standard throughout ejector literature. These regimes are categorized by whether or not the secondary flow reaches a choke before significant mixing with the primary flow has occurred. For a given geometry and a fixed secondary flow stagnation pressure, the ejector operating regime is dependant primarily on the ratio of the stagnation pressure of the primary flow to the back pressure at the exit of the ejector (Pop/Pb). For low values of Pop/Pb the ejector operates in the mixed regime. The secondary flow remains subsonic throughout the ejector until it mixes with the primary stream. At these operating conditions the primary flow is typically over expanded and the flow is turned inward (towards the centerline of the ejector) through a series of shocks at the exit of the primary nozzle. In this regime, changes to Pop/Pb affect the amount of secondary mass flow ingested through the duct. As the pressure ratio decreases, the secondary mass flow will decrease until the limiting case of zero entrained mass flow is reached. Mixing between the primary and secondary streams begins immediately upon entering the mixing duct. The secondary flow pressure will be at a minimum value where the two flows converge and then begin to recover (increase) as the flow proceeds down the mixing duct. If the pressure at the nozzle exit reaches a critical pressure, the primary flow may separate from the nozzle wall. If separation occurs, the performance of the ejector is significantly reduced. This condition represents a special case of the mixed operating
9 regime. For most supersonic ejector propulsion applications, this critical pressure is lower than typical operating conditions. At high Pop/Pb values the ejector operates in the supersonic regime and the secondary flow chokes prior to mixing with the primary flow. The limiting case for this flow regime is the saturated supersonic regime where the secondary flow chokes at the minimum geometric area through which it flows. This type of choking mechanism is known as a traditional aerodynamic choke. In an ejector, this minimum area is typically the area of the duct between the primary nozzle and the duct wall (upstream of the mixing duct) as shown in Figure 1.4. The saturated supersonic regime can occur for pressure ratios at which the primary flow is either over expanded or ideally expanded. When the ejector is operating in this flow regime, the maximum amount of secondary mass flow that can be induced by the primary flow stream is entrained. Mixing between the two flow streams begins at the entrance to the mixing duct and there is an almost immediate pressure recovery. At Pop/Pb values above saturated supersonic flow regime values, the ejector enters the pure supersonic regime.
In this regime the secondary flow choke point moves
downstream from the minimum geometric area to the point of maximum expansion of the primary flow stream. This location is identified as the mass addition choke location in Figure 1.4. The primary flow plume acts as a physical restriction to the secondary flow and creates a minimum area smaller than the minimum geometric area in the strut gap region. This type of choke is known as a mass addition or Fabri choke. Between the primary nozzle exit plane and the mass addition choke point, the mixing between the two flow streams is minimal. The mass flow in the minimum
10 geometric area will be slightly less than that for the saturated supersonic regime flow conditions. Once the flow enters the supersonic regime, the secondary mass flow cannot be increased by changes to Pop/Pb [7, 8]. However, the secondary mass flow can be reduced if the primary flow stream stagnation pressure is increased or if the back pressure is reduced. Such variation would result in a greater expansion of the primary plume and thus a smaller minimum area for the mass addition choke. Downstream of the mass addition choke, the two flow streams mix and begin the recompression and pressure recovery process. Once the supersonic regime is reached, pressure ratio increases (which increases in the energy of the primary flow) serve to pump the mixed flow to a higher pressure rather than increase the entrained mass flow [9].
1.5
Ejector Performance Characterization In most ejector applications the performance is characterized by the secondary
mass flow entrainment per mass flow of primary fluid (the bypass ratio) and the pressure increase of the secondary fluid through the ejector (the compression ratio). Figure 1.6 shows a plot of the mass flow rates of the primary ( m 1 ) and secondary fluids ( m 2 ) and the bypass ratio plotted against the ratio of the stagnation pressures of the primary fluid (Pop) to that of the secondary fluid (Pos). The figure is from a constant area supersonic ejector study conducted by Bartosiewicz [10].
In the study, the primary chamber
pressure was varied while the secondary flow stagnation pressure remained constant. The bypass ratio and mass flows were measured over a range of ejector operational modes. Because the nozzle geometry is fixed, the primary mass flow for this ejector is
11 m2 /m1
m2, m1
Peak Bypass Ratio
0.016
24 0.011 19 14
0.006 Secondary Flow Choke
9 0.001
m1/m2 m 2 /m1 m1 m1
4
m m22
-1 3
5
7
9
11
Mass Flow (kg/s)
Bypass Ratio (m2/m1 (%))
29
-0.004 13
Stagnation Pressure Ratio (Pop /Pos)
Figure 1.6 Mass Flow and Bypass ratio for a supersonic ejector [10].
proportional to the primary chamber pressure, and increases linearly as Pop/Pos increases. The secondary mass flow (initially negative indicating zero induced mass flow) increases until it chokes. Once this choke point is reached, the ejector is in the supersonic regime. The bypass ratio, initially at zero (the limiting case for the mixed flow regime), increases to a peak value as the primary mass flow is increased. The bypass ratio then drops as the primary mass flow is increased. As can be seen in the figure, this choke represents the maximum amount of secondary flow which can be induced for a given set of operating conditions and further increases in the primary mass flow rate do not increase the secondary mass flow rate. For this data the choke pressure ratio is the same as the peak
12 bypass ratio. However, this is not the case for all supersonic ejectors and is dependent on the geometry of the ejector. Once the secondary mass flow chokes, the bypass ratio becomes inversely proportional to the primary mass flow (and hence the primary total pressure). For most ejector applications, maximizing the bypass ratio is desirable as this condition represents a high level of efficiency in the momentum exchange between the two fluids. Additionally if the peak bypass ratio occurs near the choke point for the secondary flow, as shown in Figure 1.6, then the ejector is operating not only at a maximum efficiency from a momentum exchange standpoint, but it is also inducing the maximum amount of secondary mass flow. However, the peak bypass ratio generally occurs at low pressure ratios. To achieve the necessary thrust for many propulsion applications, a higher primary chamber pressure must be used and the bypass ratio that is available for the operating chamber pressure can offer some enhancement to the engine performance.
1.6
Ejector Design Considerations Performance of an ejector is dependant on a number of thermodynamic and
geometric factors.
Figure 1.1 depicted an axisymmetric ejector, which is the most
commonly used in experimental studies because its simple geometry can be analytically modeled. The flow through an axisymmetric cross section is quasi-one-dimensional in nature with approximately uniform flow properties that vary only in the axial direction. Non-axisymmetric geometry introduces significant complexities to the flow field. In either the axisymmetric or non-axisymmetric case, the areas of the primary flow nozzle
13 exit, the secondary flow minimum geometric area, and the duct exit area influence the regime of ejector operation and hence influence the entrainment and the compression ratio. The primary nozzle area ratio influences the mass flow rate and the exit Mach number and pressure of the primary flow thus influencing the entrainment and the compression ratio for the ejector. The length of the mixing duct affects the flow mixing as well as the recompression process for the mixed flow.
In a propulsion application, this length is
important especially if the mixture is then to be combusted to provide additional thrust. The duct must be long enough for complete mixing, but not too long so that additional losses will drain energy from the mixed flow. The mixing duct is also where the pressure recovery must occur if there is no diffuser. A longer duct will allow for better pressure recovery and more complete mixing, but can also result in increased system frictional losses reducing the compression ratio and the momentum of the exit stream. This duct mixing length will have an impact on the overall vehicle design and thus an efficient mixing process will result in a shorter flow path and reduced overall vehicle size and weight. Thermodynamic properties of the gas influence the behavior of the ejector as well. The pressures at the exit of the duct as well as the stagnation pressures of the primary and secondary flow influence the ejector operation regime. The bypass ratio is strongly influenced by the pressures as well as the composition of the gasses (molecular weight) in the ejector and the stagnation temperatures of the flows. One of the difficulties with using ejectors in a propulsive application is that the geometry which simplifies analysis is not always the most practical for the overall launch
14 vehicle design. Many of the rocket based combined cycle vehicle concepts that use ejectors utilize non-axisymmetric geometries [3, 4, 11]. These geometries make for a simpler design from a packaging stand point. At best these geometries can be simplified to two-dimensional analysis, but more often a full three-dimensional analysis of the complex flow is required. In addition, there can be irreversibilities (shock structures, separation, viscous dissipation) in the flow, combustion effects, heat transfer effects, and turbulence effects which can be enhanced by the three-dimensional characteristics.
1.7
Ejector Analysis Techniques A number of analytical approaches have been taken to model propulsion ejector
operation. Models vary in complexity from a very simple balance of the governing equations for axisymmetric geometry and inviscid flow, to very complex computational fluid mechanics analysis for specific three-dimensional ejector configurations with downstream combustion. In general most of the simple analytical models rely on satisfying the three governing equations of continuity, momentum and energy. The model is generally closed by assuming symmetry, ideal gases, isentropic flow, and a viscous mixing model as needed. One of the complications in dealing with modeling an ejector is that depending on the operating regime (mixed or supersonic), the assumptions used to close the model differ slightly.
Almost all of the models rely on either
simultaneous solution of the governing equations or on an iterative solution. Several papers have been published with methods for determining operation of simple axisymmetric ejectors [7, 9, 10, 12-15].
Many of these models have shown good
agreement with experimental data for axisymmetric geometries. The most significant
15 problems with these models in terms of propulsive applications is their reliance on the one-dimensional forms of the governing equations and not adequately capturing the viscous effects in the duct. As the geometry of the flow becomes more complex, these models break down. A detailed discussion of classical one-dimensional modeling of ejectors is provided in Chapter 2. As an alternative to one-dimensional analytical modeling, computational fluid dynamics (CFD) simulation is becoming a viable alternative to experimental variation of ejector geometries. Several published works have focused on CFD analysis of ejector operation [10, 16-22]. These CFD models have typically focused on the one- or twodimensional ejector systems. While these simulations have provided some insight into flow behavior, there is a need to extend CFD models to three-dimensional ejectors to capture more complex flow phenomena. For this approach to be successful, meaningful experimental data from complex three-dimensional geometries must be readily available to validate the computer models.
1.8
Motivation Although ejector phenomena have been studied extensively from both an
experimental and analytical standpoint, the fundamental fluid mechanics of even simple ejector systems are not well understood. The interactions between the flow streams in an ejector occur at very high velocities and in turbulent regimes. The primary jet can undergo a complex shock train which recompresses the fluid, and the secondary flow can either be subsonic or supersonic. If sonic, the secondary flow choking mechanism may
16 either be geometric due to a minimum physical area or a mass addition choke due to the interaction with the primary jet. Ejector operation is dependent on several different parameters such as the composition of the fluids, the geometry of the nozzle and the mixing duct, operating pressures of the fluids, and the diffuser duct characteristics. Most experimental studies focus on only a few different variations of these parameters. Most of the analytical work performed on ejectors relies on either relatively simple one-dimensional models or on a full computational fluid dynamics approach. The simple one-dimensional approach can provide reasonable results for axisymmetric cases, but when the geometry is threedimensional, this model does not predict three-dimensional ejector performance characteristics well. CFD approaches can produce relatively good global results but do not reproduce the detailed fluid phenomena because of a lack of detailed experimental data for comparison.
To improve the modeling, a more extensive database of
experimental data is required. This dissertation presents an experimental investigation of a three-dimensional, non-axisymmetric, supersonic ejector, representative of what could be used in a rocket based combined cycle propulsion system. The experiment was carried out over multiple operating regimes and for two different non-axisymmetric nozzle configurations.
The
ejector was operated over a wide range of primary flow stagnation pressures. A rigorous analysis was performed to assess the experimental uncertainty associated with the measurements. The experimental results were then evaluated to determine the operating regimes, the choking mechanisms, the mass flow entrainment, and the mixing characteristics for the two system configurations.
17 Two analysis techniques were evaluated for application to the more complex three-dimensional geometry of this study. The theoretical results were compared to the experimental results to determine additional considerations that would improve the model. The experimental results were also compared with some simple two-dimensional CFD simulations performed in a parallel study to evaluate CFD turbulence modeling techniques for use in these complex flow systems. Finally, the experimental effort provides a benchmark of experimental data with uncertainty that can be used to further evaluate detailed three-dimensional CFD codes for use in ejector systems.
CHAPTER 2
BACKGROUND
2.1
UAH Propulsion Research Center The Propulsion Research Center (PRC) at the University of Alabama in
Huntsville has an ongoing research project dedicated to studying the fluid mechanics in ejector systems. The facility was developed in 1996 as part of a cooperative research effort with NASA and Aerojet. The ejector configuration was based on the AeroJet StrutJet concept [3].
The StrutJet utilized a non-axisymmetric design based on a
rectangular engine mounted underneath the vehicle body. The PRC test rig consisted of a 1/6th scale strut model mounted in a rectangular duct 4.0 inches tall by 3.5 inches wide. Figure 2.1 shows a sketch of the PRC test rig. In one of the first sets of experiments in the PRC cold flow facility, the mixing between a flow stream from a turbine exhaust slit and the primary flow streams from the main rocket nozzles in a dual nozzle strut was examined [23]. The ratio of the chamber pressure to the stagnation pressure of the turbine exhaust was varied for the experiments. The turbine exhaust slot was operated at a stagnation pressure of 275 psi for all tests and the pressure ratio was operated at set point ratios of 1, 1.5, and 2. The primary flow was
18
19
Figure 2.1 Sketch of PRC ejector facility.
also heated up to a temperature of 750 ºR so that the convective Mach number between the turbine exhaust and the rocket nozzles would match full scale conditions. The flow from the turbine exhaust slot was seeded with acetone and a Planar Laser Induced Fluorescence (PLIF) diagnostic method was used to observe mixing between the gases. Figure 2.2 shows images taken at various distances from the exit plane. The study showed that the mixing zone reached from the exit plane of the strut to a distance of about 20.45 hydraulic diameters (of the rocket nozzle exit) downstream. As the pressure ratio increased, the mixing between the streams was delayed but the overall mixing length did not vary significantly. Thus at higher chamber pressures, the mixing occurred slowly at first but became more rapid as the flow moved downstream. This study
20 provided a qualitative view of the mixing between streams in the duct, but little
Pressure Ratio (Pc /Poturbine)
quantitative information on the detailed flow field was recorded.
2.0
1.5
1.0 0.00 0.57
1.14 1.70 2.27
7.95
11.65
20.45
Distance from Exit Plane (L/Dh)
Figure 2.2 PLIF images of the mixing between the turbine exhaust and the two rocket plumes from the dual nozzle strut [23].
Additional studies with the ejector facility investigated pressure traces across the duct at various downstream locations to provide more insight into the pressure field [24]. Stagnation pressure traces were taken in the strut gap region at locations 3.88 in. (9.84 cm) and 3.0 in. (7.62 cm) upstream of the nozzle exit plane, at the nozzle exit plane, and 4.25 in. (10.8 cm) downstream of the nozzle exit plane in the mixing duct. Three probes were used in the pressure traces. Each probe was connected to a 300 psi
21 (2.07 MPa) pressure transducer and their vertical positions relative to the strut nozzles are shown in Figure 2.3.
Rocket Nozzle Turbine Nozzle Probe 1 Probe 2
2,58 in 2,0 in Probe 3
0.5 in
Figure 2.3 Probe locations for pressure traces in the PRC ejector [24].
For all tests the back pressure was equal to atmospheric pressure (approximately 14.7 psi 0.1 MPa). By varying the chamber pressure in the strut rockets, the ratio of the rocket chamber pressure to the back pressure was varied. Tests were conducted at pressure ratios of 13.6, 18.7, 24.9 and 37.4. The data showed the total pressure is very uniform across the center of the region but that there is a slight drop off of total pressure as the probes approached the side wall. Due to the geometry of the probes, the traces could only be moved within about 0.25 inches (6.35 cm) of the side wall, but were able to move very close to the strut. No uncertainty estimates were given for this data and the resolution of the pressure transducer was too low for the data recorded. However, these
22 plots indicate a boundary layer developing along the side wall of the duct. Although the data from these plots could not be used to reliably estimate the boundary layer thickness, they did indicate that the boundary layer thickness is significant and must be considered when determining the mass flow through this region. Pressure traces in the mixing duct showed the spreading of the primary jet plume and indicated the presence of a core flow at 4.25 inches downstream of the duct. Smith [25] upgraded the data acquisition capability of the PRC facility and performed a comprehensive study of the single nozzle strut. For this series of tests, the ratio of the chamber pressure to the back pressure was varied from 6.8 to 44.2. The duct was instrumented with pressure taps along the centerline of the top and side walls of the mixing duct to measure the wall pressure distributions. This study focused on the fluid mechanics of the ejector system specifically examining the choking mechanism, mass flow entrainment, and the mixing duct pressure distributions. A secondary mass choke was identified to occur at a pressure ratio (Pc/Pb) of 34, and Smith concluded that the choke persisted for pressure ratios between 34 and 40.8. He stated that the choke transitioned to an aerodynamic choke at a pressure ratio of 44.2. The bypass ratio was found to be highest at the lowest chamber pressure and decreased sharply with increasing chamber pressure until the choke point was reached. Once the secondary flow choked, the bypass ratio was inversely proportional to the chamber pressure.
The pressure
distribution indicated complex flow patterns in the first 10 inches (25.4 cm) of the mixing duct and it was concluded that the flow became fully mixed within a distance of 15 in. (38.1 cm) of the primary nozzle exit plane. Smith concluded that the asymmetric effects led to enhanced mixing effects.
23 2.2
Classical Ejector Research Many of the early works on ejectors focused on modeling axisymmetric ejector
systems using simple analytical approaches. As noted in Chapter 1 these approaches generally rely on balancing continuity, momentum, and energy equations, coupled with a wall friction and or a mixing model. Steady quasi-one-dimensional flow is generally assumed to simplify the governing equations. This type of analysis has generally showed very good agreement for global parameters such as the bypass ratio for axisymmetric ejectors.
2.2.1
Fabri’s Ejector Model One of the early works published on supersonic ejectors was by Fabri and
Siestrunk [8]. A simple one-dimensional axisymmetric ejector model was presented and the predicted results were compared with experimental data. Fabri outlined four flow patterns or regimes of operation for a supersonic ejector: mixed with separation, mixed, saturated supersonic, and supersonic. Each of these regimes was modeled separately depending on the significant flow features. Ejector performance was characterized by the bypass ratio, ω, and the ratio of the secondary flow stagnation pressure to the back pressure, μ.
Fabri listed the following major geometric influences on ejector
performance: mixing tube length, diffuser design, cross-sectional areas of the mixing duct, nozzle throat, nozzle exit, and the secondary flow mixing duct inlet area, and the geometric shape of primary nozzle.
In addition to these parameters, the ejector is
influenced by the thermodynamic state of the primary and secondary fluids, and the back
24 pressure on the ejector. Fabri’s model was able to accurately predict the effect that varying these parameters had on performance. Figure 2.4 shows a schematic of an ejector with Fabri’s geometric notation. The primary and secondary flows are represented by a prime (′) or a double prime (″) respectively. The area of the primary jet is taken as a unit area, S, and all other areas are referenced relative to this area. The dimensions given in Figure 2.4 are the ratios of the local area to the primary jet area. Thus the total area of the mixing duct is λS. In his analytical models, Fabri assumed quasi-one-dimensional flow, an axisymmetric primary nozzle with uniform supersonic flow at the exit, a cylindrical constant area mixing duct, a secondary flow entrance which establishes the minimum geometric area at the entrance to the mixing duct, uniform secondary flow at the entrance to the mixing duct, the primary and secondary fluids have the same composition (air), both streams act as perfect gases,
Secondary Flow Choke Location Supersonic Regime Secondary Flow
Primary Flow
λ’-υ
λ’-1
υ
1
λ/λ*
1
Nozzle Base Area
λ
e Jet Boundary
Figure 2.4 Sketch of an axisymmetric ejector with Fabri’s notation.
25 and both flows have the same stagnation temperatures. For individual models of the separate flow regimes, additional assumptions were added.
2.2.2
Supersonic Regime In the supersonic regime, the secondary flow achieves a choke in the mixing duct
at the location of maximum expansion of the primary flow, location e in Figure 2.4. Fabri modeled the primary and secondary flow as separate streams and neglected interaction between them until the point where the secondary flow chokes (location e). When the ejector is operating in this regime, the back pressure has no effect on the bypass ratio because the choked condition defines the mass flow for each stream. Each stream was modeled as one-dimensional isentropic flow between the inlet to the mixing duct, location 1, and the point where the secondary flow chokes, location e. Fabri’s model produced results which were very close to experimental data with one exception, as he noted, this model does not enforce equal pressure across the jet boundary. A second limitation to this model is that the effects of the base of the primary nozzle are not included except as a reduced area for the secondary flow. However, this did not cause significant deviation from the experimental data for Fabri’s experiment because the base area of the primary nozzle was small relative to the other inlet areas and to the mixing tube area. Fabri’s model for the supersonic regime consisted of five equations. The first two equations were mass balance equations for each of the two flow streams. When recast in terms of the characteristic Mach number (M*), these equations become
26
ν=
(M ) (M ) * p,e
( (
⎛m - M ⎜ 2 ⎜ m2 - M * p,e ⎝
2 * p,1
2
) )
⎞ ⎟ 2 ⎟ ⎠
2 * p,1
1 γ-1
,
(2.1)
and
( (
) )
( (
⎛ m2 - M * s,1 ⎜ 2 ⎜ m2 - M * s,e ⎝
* 2 s,1
M λ′ - ν = λ′ - 1 M *s,e
) )
1
⎞ γ-1 ⎟ . 2 ⎟ ⎠
2
(2.2)
Here the variable m is given by
m=
γ +1 , γ -1
(2.3)
where γ is the ratio of specific heats for the gas. Since both flows are assumed to be isentropic between the mixing duct inlet and the choke location, the pressures at these two points can be related using isentropic flow equations. In terms of the characteristic Mach number, these equations become
( (
) )
( (
) )
2 * Pp,e ⎛⎜ m - M p,e = Pp,1 ⎜ m 2 - M * p,1 ⎝
2 2
γ
⎞ γ-1 ⎟ , ⎟ ⎠
(2.4)
and * ⎛ 2 Ps,e ⎜ m - M s,e = Ps,1 ⎜ m 2 - M * s,1 ⎝
2 2
γ
⎞ γ-1 ⎟ . ⎟ ⎠
(2.5)
The fifth equation required for Fabri’s supersonic regime model is a momentum balance between the inlet section and the downstream choke point. For steady, inviscid flow with negligible body forces the momentum equation becomes
27
Pp,1
( ) + ( λ′ - 1) P 1+ ( M ) = - (M ) m - (M ) 1+ ( M ) νP + ( λ′ - ν ) P m -(M )
1+ M *p,1 m2
2
* 2 s,1
s,1
2 * p,1
* 2 s,1
2
2 * p,e
p,e
2
s,e
2
* p,e
( ) - (M )
1+ M m2
* 2 s,e
.
(2.6)
* 2 s,e
If the secondary flow at location e is assumed to be sonic, the local characteristic Mach number will be equal to one. With known conditions for the primary flow at the inlet, and a known geometry, Equations (2.1) through (2.6) represent 5 equations with 6 unknown quantities (ν, M *p,e , M *s,e , Ps,1 , Pp,e , Ps,e ). Thus, for every value of Ps,1 the remaining unknown variables can be determined by simultaneously solving these equations. Once the pressures and Mach numbers are known, the bypass ratio, ω, and the ratio of the secondary flow stagnation pressure to the back pressure, μ, can be determined according to
Po M v = ( λ′ - 1 ) s Po p M
* s,1 * p,1
( (
⎛ m2 - M * s,1 ⎜ ⎜ m2 - M * p,1 ⎝
) )
1
1
⎞ γ-1 To 2 ⎟ ⎛ p⎞ , 2 ⎟ ⎜⎝ Tos ⎟⎠ ⎠
2
(2.7)
and ⎛ Ps,1 ⎜ m2 μ= Pb ⎜ m 2 - M * s,1 ⎝
(
1
)
⎞ γ-1 ⎟ . 2 ⎟ ⎠
(2.8)
Here the stagnation pressure for either the secondary or primary flow is related to the static pressure according to γ
Po ⎛ m 2 ⎞ γ-1 =⎜ ⎟ . P ⎝ m 2 - M *2 ⎠
(2.9)
28 2.2.3
Saturated Supersonic Flow In the saturated supersonic flow regime, the secondary flow chokes in the
minimum geometric area of the duct between the primary nozzle and the duct walls at Section 1. The bypass ratio is strictly a function of the stagnation conditions of the flow. The back pressure has no influence on the bypass ratio if the ejector is operating in this regime. The secondary induced flow is independent of the primary mass flow rate. The performance of the ejector is thus strictly a function of the stagnation pressures and stagnation temperatures of the two flow streams, the primary flow Mach number at the nozzle exit, and the geometry of the duct. The bypass ratio in this regime is given by
P μ = v ( λ′ - 1 ) b Po p
(
⎛ 1 ⎜ m2 - 1 2 M *p,1 ⎜⎝ m 2 - M *p,1
)
(
1
)
1
⎞ γ-1 To 2 ⎟ ⎛ p⎞ . 2 ⎟ ⎜⎝ Tos ⎟⎠ ⎠
(2.10)
For given nozzle conditions (Pop, Mp), the primary mass flow can be calculated through isentropic equations and the secondary mass flow can be calculated from Equation (2.7). The remaining flow properties can be determined assuming isentropic flow with a given mass flow and area.
2.2.4
Mixed Flow In the mixed flow regime, the secondary flow remains subsonic throughout the
ejector. Unlike the supersonic regime, the entrained mass flow and thus the bypass ratio are dependent on the back pressure. Figure 2.5 shows a sketch of the ejector for the analysis of flow in this regime. The two flow streams begin mixing at the entrance to the mixing duct (Location 1). Since the back pressure influences the performance of the
29 ejector, the property changes through the diffuser, a mixing model, and a model for frictional losses in the duct must also be included
λ’-1 Secondary Flow Primary Flow
Mixing Duct
λ/λ*
Diffuser
λ
1
1
2
λσ
3
Figure 2.5 Sketch of an axisymmetric ejector with Fabri’s notation for mixed regime analysis.
The analysis of the flow in the mixed regime relies on some method of estimating the effects of the viscous interaction between the walls of the duct and the flow stream. Fabri modeled the associated pressure drop using
(a ) (M ) f×ρ * 2
δP = ∫
* 2
2
dξ ,
(2.11)
where f is the coefficient of friction, M* represents a mean value of the characteristic Mach number at any intermediate section, and ξ is the ratio of the area of the lateral surfaces to that of the transverse section. This ratio is given by
ξ=
4L , D
where L is the length of the mixing duct and D is the diameter of the mixing duct.
(2.12)
30 At the entrance to the diffuser, Location 2 in Figure 2.5, the two flow streams are completely mixed. Since the mixed flow is subsonic, the pressure at this point must be greater than or equal to the back pressure at the exit of the duct (Section 3). Thus, the back pressure limits the amount of secondary mass flow that can be entrained. Fabri’s mixed flow model consisted of five equations. The flow was broken into two sections, the mixing duct section and the diffuser section. The governing equations for the mixing duct are
Pp,1
(
M *p,1
a*p m 2 - M *p,12
Pp,1
)
+ ( λ′ - 1) Ps,1
a*p M *p,1 m 2 - M *p,1
(
* M s,1
* 2 a*s m 2 - M s,1
+ ( λ′ - 1) Ps,1 2
)
= λP2
a*m
(
M 2* , m 2 - M 2* 2
)
* * a*s M s,1 a*m M m,2 , = λP 2 * 2 m 2 - M *s,12 m 2 - M m,2
(2.13)
(2.14)
and
(
(
Pp,1 1+ M *p,1
(
m 2 - M *p,1
)
) 2
2
)+P
( ) ( )
2 ⎡ ⎤ 1+ M *s,1 λ - λ′ ⎥ ⎢ ( λ′ - 1 ) + 2 = s,1 2 2 * ⎢ m ⎥ m M p,1 ⎣ ⎦
⎛ fξ m 2 +1 ⎞ * 1+ ⎜ 1+ ⎟ M2 2 m2 ⎠ ⎝ λP2 2 m 2 - M 2*
( )
2
.
(2.15)
( )
The pressure and Mach number at the exit of the mixing duct (Region 2) are related to the pressure and Mach number at the end of the diffuser (Region 3) by
σ=
( P M (m 3
and
( )) , - (M ) )
P2 M 2* m 2 - M 2* * 3
2
2
* 2 3
(2.16)
31
(m
2
)( ) - (M )
+1 M *
m2
* 2
2
(
( ) ( )
2
m 2 1- M * f ⋅ dξ dσ = 2 2 σ m2 - M *
) dM
*
M*
,
(2.17)
where σ is the ratio of the exit area to the area at the end of the mixing duct. With no diffuser, σ is equal to 1 and dσ is equal to 0. For this case the expression simplifies to
( ) ( )
1- M 2* m2 +1 f ξ = ( d) m2 2 2 M 2*
2
2
( ) 2(M ) 1- M 3*
2
* 2 3
⎛ M* +ln ⎜ 2* ⎝ M3
⎞ ⎟, ⎠
(2.18)
where ξd is the ratio of the diffuser lateral area to the transverse cross-sectional area. Because the two flow streams are assumed to have the same composition and have equal stagnation temperatures, the energy equation is not needed for this model. For a chosen value of M 3* and known values of the primary jet and the back pressure, the equations can be solved for the pressure and Mach number in Section 2 and at the secondary flow mixing duct inlet (Section 1). The bypass ratio is then calculated according to Equation (2.10).
2.2.5
Mixed Flow with Primary Separation In this regime the primary pressure is low enough that the primary flow separates
from the nozzle wall prior to Section 1. The primary flow leaves this part of the nozzle parallel to the mixing duct walls and does not reattach within the nozzle. The portion of the nozzle which is not filled with the primary flow is assumed to be at the subsonic secondary pressure at Section 1. The equations for mixed flow in the previous section still generally hold, but they must be slightly modified to account for new effective areas at the inlet of the mixing duct. Fabri used an approximation for the point of separation in the nozzle. He assumed the flow separated when the ratio of the nozzle pressure to the
32 surrounding pressure ( Ps,2 ) was less than or equal to 2.5. The results for primary flow with separation were not as close to Fabri’s experimental results because of this assumption.
2.2.6
Matching Fabri’s Models The equations for the supersonic, saturated supersonic, and the mixed regime
were used to recreate Fabri’s ejector predictions for use in the current study. Figure 2.6 shows a comparison of the results for the supersonic and saturated supersonic model calculations compared with selected points extrapolated from Fabri’s original paper [8]. The model assumes a primary flow characteristic Mach number of 1.78, a primary nozzle exit area of 0.45 cm2, a mixing duct cross-sectional area of 0.95 cm2, and a exit to primary flow stagnation pressure ratio of 3.5. The current model calculations reasonably
Supersonic Regime 0.6
Saturated Supersonic Regime
Bypass Ratio
0.5 Fabri's Experimental Data
0.4
Supersonic Model
0.3
Saturated Supersonic Model
0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Pos/Pb
Figure 2.6 Comparison of recreated model with data from Fabri’s model.
33 match the points extracted from Fabri’s paper. It is believed that the slight discrepancies can be attributed to the extraction process as well as to the fact that Fabri’s work was performed in the 1950’s without the use of computers for computation and plotting. There could be some errors in Fabri’s computations due to rounding errors which grow through the analysis. Despite the discrepancies in the plotted data, the redeveloped model tracks the original model very well. Figure 2.7 shows a plot of the mixed regime flow model predictions, against mixed flow data predicted for Fabri’s ejector. For these predictions, a primary nozzle exit area of 0.45 cm2, a mixing duct exit to primary nozzle exit area ratio of 2.37, and pressure ratios of 4.5 and 3.5 were used. As can be seen in Figure 2.7, the recreated model once again tracks the extrapolated data very well but slightly over predicts the bypass ratio for a given bypass ratio. The slight discrepancies between the recreated
0.8
Fabri's Experimental Results (Pc/Pb = 4.5)
Bypass Ratio
0.7
Mixed Regime Model (Pc/Pb = 4.5)
0.6 0.5
Saturated Supersonic Regime Model (Pc/Pb = 4.5) Fabri's Experimental Results (Pc/Pb = 3.5)
0.4 0.3 0.2
Mixed Regime Model (Pc/Pb = 3.5)
0.1 0.0 0.0
0.2
0.4
0.6
0.8
1.0
Pos/Pb
Figure 2.7 Mixed regime comparison of current model with Fabri’s model.
34 model and the original data are believed to be to Fabri’s calculation accuracy and to the data extrapolation process.
2.2.7
Addy’s Ejector Model Similar to Fabri, Addy performed another set of experiments on axisymmetric
ejectors with a constant area mixing duct [26]. Addy developed models for both the mixed regime and the supersonic regime. As described in the following sections, the models were based on the same general assumptions as Fabri but with a couple of additional conditions for the specific regime models.
2.2.8
Supersonic Flow Regime Model In the saturated supersonic flow regime, Addy’s model was identical to Fabri’s,
although Addy’s model was recast to use different parameters. Addy’s bypass ratio was based on the maximum flow through the strut gap and through the primary nozzle. In this regime, the secondary flow is aerodynamically choked in the gap between the nozzle and the diffuser duct. For this condition, the bypass ratio is given by
ms A Pos , = s m p Ap Po p
(2.19)
where the ms is the secondary mass flow rate, mp is the primary mass flow rate, As is the inlet area to the mixing duct for the secondary fluid, Ap is the inlet area to the mixing duct for the primary flow, Pos is the secondary flow stagnation pressure, and Pop is the primary flow stagnation pressure. For the supersonic flow regime, Addy determined the flow between the inlet to the diffuser and the choke point by assuming an inviscid secondary and primary flow,
35 and then superimposing mixing along the boundary into the flow field. This mixing results in a higher secondary mass flow rate over that given by the inviscid interaction. For the inviscid two stream model, the secondary flow is considered to be onedimensional in nature, and the primary flow retains two-dimensional (axisymmetric) characteristics. The secondary stream is treated by conventional one-dimensional gas dynamic methods and the primary stream is solved using a method of characteristics for steady irrotational supersonic flow. The governing equations are simultaneously solved subject to the condition that the pressure along the boundary is continuous (a condition neglected by Fabri). The solution starts from a given flow geometry and primary Mach number. The ratio of the secondary static pressure to the primary stagnation pressure is selected such that the nozzle is under expanded. A finite subsonic secondary flow Mach number at the inlet to the mixing duct is selected. The flow field corresponding to the selected values of the pressure ratio and the trial Mach number is then calculated. Once the flow field has been established through the method described above, the viscous mixing along the boundary is determined. A plane two-dimensional flow model for turbulent constant pressure mixing of two uniform parallel streams is used. The mixing region is superimposed upon the inviscid two stream boundary under the assumption that for the case of over expanded primary flow, the mixing will not significantly influence the inviscid flow field because the secondary mass flow will be small. In the mixing model, Addy determines a displacement thickness for the boundary layer between the jets which results in a decrease in the available flow area for the secondary flow according to
ΔA = -2πR2 δ* ,
(2.20)
36 where ΔA is the area decrease, R2 is the radius of the secondary flow, and δ* is the displacement thickness. The corresponding increase in the mass flow ratio as a result of the mixing is given by Δms Po R δ* = -2 s *2 * , mp Po p R p R p
(2.21)
where R*p is the radius of the primary flow plume at the point of choking. The mixing displacement thickness is determined using the momentum and continuity equations on a control volume between undeflected streamlines of both the primary and secondary flow streams. The corrected bypass ratio is then given by
⎛ ms ⎜⎜ ⎝ mp
⎞ ⎛m ⎞ ⎛ Δms =⎜ s ⎟ +⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎠corrected ⎝ m p ⎠inviscid ⎝ m p
⎞ . ⎟⎟ ⎠ mixing
(2.22)
One of the significant limitations of Addy’s analysis is the assumption that the mixing effects do not significantly alter the inviscid flow field. If the secondary mass entrained due to mixing is of the same order of magnitude as the inviscid secondary mass flow, the assumption breaks down.
2.2.9
Mixed Flow Regime In the mixed flow regime Addy used a one-dimensional analysis technique similar
to Fabri’s model including frictional losses along the diffuser duct wall. For uniform inlet flow, the momentum and continuity equations were applied between the entrance section and the point downstream where the two flows are uniformly mixed and subsonic. Because the stagnation temperatures of the primary and secondary flows are equal, the energy equation was not required for Addy’s model.
37 The continuity and momentum equations were recast in terms of pressure ratios; the ratio of the secondary flow static pressure at the inlet to the primary flow stagnation pressure and the secondary flow Mach number are independent variables. For a selected pressure ratio, the subsonic exit Mach number and the static pressure at the entrance to the mixed region can be determined as functions of the secondary flow inlet Mach number. For long diffuser tubes, frictional effects were accounted for from the inlet to the mixed region to the exit of the duct using standard compressible Fanno flow relations with a coefficient of friction equal to 0.005. The final condition was matching the exit pressure to the ambient pressure using adiabatic flow relations (isentropic flow relations between Po, P and Mach number) recognizing that Po at the exit will be different from Po at point 2 due to friction effects. The value of Ms,1 can be determined from the specified Ps,1/Pop and Pb/Pop for a given ejector geometry. The secondary mass flow can then be established with P, T, and Ms,1. Addy compared the results of his model to that of Fabri. The two models showed good agreement for higher values of the secondary Mach number at the inlet to the mixing duct. For low values of the secondary flow Mach number (the mixed flow regime), Addy’s results which include viscous effects were much closer to the experimental data than Fabri’s model.
2.3
CFD Analysis Although the one-dimensional analytical models can reasonably predict global
parameters such as the bypass ratio, they do not provide a description of the flow field within the ejector duct or accurately capture the mixing between the flow streams. For
38 this more detailed information computational fluid dynamics (CFD) must be employed. Several efforts over the years have been made to validate CFD modeling techniques using experimental data and to use these CFD codes to evaluate the influence of various parameters in the ejector [1, 10, 16, 18, 19, 21, 27, 28]. The majority of the CFD studies have focused on one-dimensional or twodimensional ejector systems. The axisymmetric nature allows the geometry to be created in one or two dimensions and produces relatively fast model convergence. Like the lower-order analytical models, CFD models produce good results for global variables such as the mass flow entrainment and the compression ratio, but still do not predict the flow field details well [21]. As the distance from the primary nozzle increases, the unsteadiness of the flow increases and the predictions can deviate significantly from the actual flow behavior. Although many CFD models have been used to predict and validate fluid mechanics experimental work, there is not a consistent modeling approach for all ejector systems. Velazques presented a comprehensive survey of various CFD approaches which have been used to model ejector rockets [27]. He once again pointed out that the global quantities of engineering interest are reasonably predicted on the simple geometries; however, even on these geometries, the local flow details cannot be studied due to the large computational cost. A parametric study of a rocket based combined cycle engine in all rocket mode was carried out by Steffen, et al. [28]. The study evaluated the effect of four geometric and two flow field variables set at three levels each. Variations of the inlet areas of the primary and secondary flow, the mixing duct area and length, and the stagnation
39 properties of the primary and secondary flow were evaluated to determine the influence of these parameters on the predicted flow field and on the global performance of an axisymmetric ejector. Many of the CFD simulations have been used to predict hot fire experimental performance. However as noted earlier, there is no global modeling technique for even simple cold flow ejectors. The addition of an injected fuel with mixing and combustion further complicates the simulations. As with the cold flow cases, these models have been able to reasonably predict global parameters, but cannot predict local flow field details very accurately. Often the CFD studies can provide insight into characteristic flow behavior but cannot reproduce the experimental data.
2.4
Current Experimental Work Several universities and companies have performed experimental work on
ejectors and Rocket Based Combined Cycle vehicle concepts. Research in this area has varied from simple cold flow axisymmetric ejector systems to hot fire RBCC engine concepts. This section describes some of the research work that has been released in the open literature.
2.4.1
Propulsion Engineering Research Center The Propulsion Engineering Research Center (PERC) at The Pennsylvania State
University has conducted a series of experimental and analytical research efforts on a Rocket Based Combined Cycle system operating in ejector mode [19, 29, 30]. The PERC facility consists of a two-dimensional duct with slit type strut nozzles.
40 Experiments have been conducted in both a single and a twin thruster configuration. The facility utilizes a direct connect mode in which the inlet of the duct is connected to a blow down facility. Thus the mass flow rate and the stagnation pressure of the secondary (entrained) air can be controlled. The PERC facility is a hot fire facility which means the primary exhaust gases are products of combustion from the rocket chamber. The exhaust products are combusted with entrained air, and in some cases injected fuel in a downstream portion of the duct, and the products from this combustion are accelerated through a converging nozzle. The PERC research has focused on the mixing and combustion in the downstream region of the duct utilizing Raman Spectroscopy to determine species concentration at various locations. The nozzles for the dual and twin thruster configuration are half of the size of the single nozzle configuration so that the same primary mass flow rate is produced for the same chamber pressure. The cross-sectional area of the PERC duct is 15 in2 (96.8 cm2) and the total blockage area by the strut/s is 4.55 in2 (29.4 cm2). The area ratio of the strut nozzles is 3.3. For equivalent primary mass flow rates of the single and twin thruster configurations, the twin thruster configuration entrained more secondary mass flow than the single thruster. The average secondary mass flow rate was approximately 15% greater for the twin thruster configuration. As a result of increased shear area in the twin thruster configuration, the mixing between the flow streams was improved. The single thruster configuration required approximately twice as much duct for complete mixing. In addition, the overall static pressure in the duct was significantly higher for the twin thruster configuration [30].
41 2.4.2
Japan Aerospace Exploration Agency Aoki, Lee, Masuya, Kanda and Kudo performed a series of analyses and
experimental studies on a two-dimensional ejector for application in a single stage to orbit vehicle [4, 31, 32].
The ejector apparatus consisted of a two-dimensional
rectangular primary entrance and a rectangular secondary flow entrance. The secondary flow inlet area could be varied, and the primary flow inlet Mach number varied from 2.4 to 3.4. Additionally an area choke was located downstream of the mixing section to simulate the effects of thermal choking of the flow. The area of the secondary throat could also be varied. The experiment used air as the primary fluid and nitrogen as the secondary fluid. The total pressures of both the primary and secondary fluid were varied. Both one- and two-dimensional analytical models were developed. All of the models neglected friction drag, heat transfer to the walls, and base pressure effects. Additionally, the calculations assumed complete mixing in the test section and choking at a downstream throat. The models were able to predict the pressure recovery and the secondary mass flow fairly accurately. Working in conjunction with JAXA, Kitamura, et al. investigated the pressure recovery of rectangular and circular mixing ducts of ejector-ramjets [33]. Figure 2.8 shows a schematic of the ejector configurations for this study.
Three different
axisymmetrc primary nozzles were investigated in the experiment and these were operated over a chamber pressure range of 2.5 MPa to 5.5 MPa. The ingested air was controlled with venturi orifices. To simulate pressure increase due to combustion, plugs were used to modify the exit area. Figure 2.9 shows a plot of the pressure along the wall
42
Figure 2.8 Ejector configuration for Kitamura’s experiments [33].
Figure 2.9 Pressure recovery comparison in rectangular and circular cross section ejectors [33].
43 of both the circular and rectangular ducts for an operating pressure of 2.8 MPa and a bypass ratio of 0.33. As can be seen in the figure, the pressure recovery began in approximately the same downstream location; however, the total pressure recovery was about 5% lower for the rectangular duct. The recovery length for the rectangular duct was significantly longer than the length required for the circular duct. Flow fields in the ducts were visualized using a silicon oil and a fluorescent powder. After a test run, the ejector duct was disassembled and examined. Figure 2.10 shows a comparison of the flow patterns in the circular and rectangular ducts. The rectangular duct flow pattern appeared asymmetric with recirculating flow and separation. Kitamura concluded that the flow field was a result of the corner effects and flow separation in the duct.
Figure 2.10 Surface flow patterns for a circular duct (a) and a rectangular duct (b) ejector [33].
44 2.4.3
Aerojet The Aerojet Strutjet concept was originally developed for a reusable launch
vehicle to replace the current shuttle system. The Strutjet engine incorporates an ejector mode for take off and initial acceleration to ramjet speeds (around Mach 2.5). Figure 1.2 showed a diagram of the Strutjet engine concept. The research at Aerojet has made significant achievements towards a demonstratable vehicle concept [34], but several technologies must be matured before even ground test of flight configurations engines are possible. The Strutjet engine concept uses multiple struts with embedded rocket engines mounted in the engine duct. The ejector action of the exhausting rocket plumes entrains secondary air from the atmosphere through the gaps between the struts. The ejector pumping is complete much faster with the multiple struts than without struts utilizing a two-dimensional flow path [34]. The ducted rocket mode of the Strutjet provides some added specific impulse over an all-rocket engine up to Mach 2.5 where the ramjet mode would take over. In addition to engine performance studies, Aerojet has investigated the performance of a single stage to orbit concept powered by the Strutjet including multiple vehicle body configurations and sizes [3, 34]. The studies showed that the Strutjet concept has the potential to provide improved design margins over conventional rocket launch systems. The margins can be used to reduce operating costs through reduced maintenance activities of the highly reusable systems and the reduction in engine replacement cost possible through a significantly smaller vehicle and horizontal takeoff. The horizontal takeoff and landing concept vehicle offers gross takeoff mass that is
45 about 44% less than the all rocket design and the dry mass that is about 68% less than the all rocket design.
2.4.4
Small Scale Experimental Efforts On a smaller scale, many research efforts have focused on cold flow
experimentation on one-dimensional geometry ejectors [14, 15, 35, 36]. Young and Idem performed a series of cold flow experiments for air-air sonic and supersonic ejectors [35]. The study investigated the influence of the separation distance between the primary nozzle exit and the mixing tube radius.
Two primary nozzle configurations were
examined: a converging nozzle and a converging-diverging nozzle.
The distance
between the primary nozzle exit and the constant area mixing tube entrance was systematically varied. Equal stagnation temperatures for the primary and secondary flow were maintained and the mixing duct exit pressure was maintained at atmospheric pressure. The study showed for all cases that the bypass ratio decreased with increasing primary to secondary flow stagnation pressure ratios.
As the distance between the
primary nozzle exit and the mixing duct entrance was increased, the bypass ratio increased until a separation distance of 0.512 times the radius of the mixing tube was reached. As the separation distance was increased beyond this value, the bypass ratio was constant for a given stagnation pressure ratio. The study also showed that the mixing length was independent of the separation distance, but was dependent on the primary nozzle Mach number. As Mach number increased, the mixing length increased. Dutton, et al. performed an investigation of an axisymmetric supersonicsupersonic ejector configuration focusing on the compression ratio of the secondary
46 flow [14]. A one-dimensional model of the ejector similar to Fabri’s was developed to predict the performance. An overall control volume around the mixing duct was used and uniform velocity and pressure distributions were assumed at the entrance to the mixing duct with a fully mixed and uniform stream at the exit of the mixing duct. Both supersonic and saturated supersonic models were employed depending on the ejector operation regime. Comparison of the theoretical predictions with the experimental work showed that the predicted maximum ejector compression ratios were 15% to 22% higher than the measured values and that the ejector was susceptible to separation of the secondary stream at the point of confluence of the primary and secondary streams. A parametric study was performed for eight model parameters to determine their influence on the compression ratio. The eight parameters were the primary stream Mach number, the secondary stream Mach number, the specific heat ratios of the primary and secondary stream, the ratio of the stagnation temperatures of the primary and secondary streams, the ratio of the molecular weights of the primary and secondary flow streams, the ratio of the areas of the primary and secondary flow stream, and the ratio of the stagnation pressures of the primary and secondary flow streams. The most effective means for improving the ejector pressure recovery was to compress the secondary stream towards sonic conditions, either upstream of the ejector or in the mixing tube, and to operate near the matched static pressure point with a high Mach number, high stagnation temperature, low molecular weight primary gas [14]. If the pressure of the primary flow at the entrance to the mixing duct was higher than the secondary pressure at the same point, then separation of the secondary flow occurred, which degrades the ejector performance.
47 2.5
Summary Numerous other experimental studies and computational analyses of ejector
systems have been performed. Generally, these efforts focus on axisymmetric or twodimensional configurations at best.
These types of configurations may indicate
performance trends of non-axisymmetric geometries; however, the geometry will impart significant losses in the system. No simple analytical method has been found which accurately captures the global performance parameters for complex geometries like the current PRC test configuration. CFD results can predict global parameters reasonably well for relatively simple geometries and can provide insight into flow phenomena, but they cannot predict detailed flow field information. While a propulsion engine utilizing an ejector would have a portion of the flow field influenced by hot fire effects, a well established cold flow model which reasonably predicts detailed flow field information is needed to evaluate the majority of the ejector behavior which is not combustion related.
CHAPTER 3
FACILITY AND EXPERIMENTAL SETUP
3.1
Facility The PRC cold flow ejector facility is shown schematically in Figure 3.1. The
facility consists of an air supply system, the ejector test apparatus, and the data acquisition instrumentation. The air supply systems consist of a 500 ft3 (14.16 m3) air storage tank located outside of the facility and a 24 ft3 (0.68 m3) surge tank located in the test bay.
Both tanks were hydrostatically tested to 3500 psi (24.13 MPa).
Air is
compressed by a four stage piston compressor to a storage pressure of 2500 psi (17.24 MPa). The compressor has a purification system which cleans and dries the air
Flow Control Valve Air Tanks (524 ft3) Compressor
Ejector Duct
Figure 3.1 Schematic of PRC cold flow ejector facility.
48
49 before storage. The supply lines connecting the storage tank to the duct consist of seamless stainless steel tubing rated for high pressure applications.
The minimum
diameter of the lines connecting the tank to the ejector rig is 1.25 in (3.18 cm). A side view of the ejector duct is shown in Figure 3.2 and an end view is shown in Figure 3.3. The ejector consists of a constant area rectangular duct with a contoured inlet. The duct has 0.75 in. (1.91 cm) thick aluminum top and bottom walls, and 0.75 in. (1.91 cm) thick Plexiglas side walls. The constant area section of the duct is 3.5 in. (8.89 cm.) by 4.0 in. (10.16 cm.) tall. The contoured inlet is constructed of sheet metal and has a constant width of 3.5 in. (8.89 cm.). The inlet is elliptically contoured from 48 in. (121.92 cm.) tall at the entrance to 4.0 in. (10.16 cm.) tall where it attaches to the duct over a 5 ft. (1.524 m) length.
The inlet was designed to produce a uniform
secondary flow velocity profile into the constant area section of the duct.
17.0 in. 60.0 60.0”in.
45.5” 45.5 in.
17.0”
Contoured Inlet
Mixing Duct
Flow Direction
Fairing
Strut
Figure 3.2 Ejector test rig cross section.
50
Strut Primary Nozzles
4.0” 4.0 in.
3.5”
3.5 in.
Figure 3.3 Ejector test rig end view.
The primary flow for the ejector is driven through converging diverging nozzles which are embedded in a strut mounted approximately 45.5 in (115.57 cm.) upstream of the duct exit. Figure 3.4 depicts the two ejector struts used for this investigation. The struts are machined from carbon steel and have identical external dimensions. One strut has a single embedded nozzle and the other has two embedded nozzle.
The single
embedded nozzle exit is centered on the downstream face of the strut.
The two
embedded nozzles are located 1 in. apart and evenly spaced around the center of the downstream face of the strut. In addition, the dual nozzle strut has a vertical slit 0.1 in (0.254 cm). wide by 0.25 in (0.635 cm) high. This slit was designed to simulate exhaust from a turbine on the Aerojet Strutjet engine used in previous mixing studies [23]. For the current experiment, the slit was plugged with filler material, and sanded until the surface was smooth. The nozzles in both struts have the same geometry. The nozzles transition from a circular throat to a rectangular exit with an expansion ratio of 4.6 and a throat diameter of 0.46 in. (1.1684 cm).
Thus when operated at the same chamber
pressure, the dual nozzle strut will pass twice the mass flow of the single nozzle.
51 Pressure Tap
Thermocouple Location
Primary Feed
Primary Feed
Pressure Tap
Primary Feed
Thermocouple Location
Figure 3.4 Dual and single nozzle ejector struts.
The struts are designed to be installed in the duct assembly. An aerodynamic fairing is mounted on the upstream side of the strut.
The fairing was machined from
aluminum stock with a 0.5 in (1.27 cm) radiused leading edge and is 1.0 in (2.54 cm) wide by 5.0 in. (12.7 cm) long. This fairing provides a smooth transition from the inlet portion of the duct to the strut gap region. Air flow from the storage tanks to the strut is regulated by a pneumatically operated proportional-integral-derivative, PID, controller.
A pressure transducer
connected to the chamber in the embedded nozzles provides the feedback signal for the PID controller. In previous tests, the voltage for the chamber pressure set point was regulated by a manual control variable resistance potentiometer [25]. For the current set of experiments, this was replaced with software driven digital control. A desired pressure is set from the control software and the corresponding set point voltage is sent through the data acquisition card to the PID. The PID valve adjusts until the voltage signal from the pressure transducer in the strut chamber matches the set point voltage of the controlling software. Through this setup, the chamber pressure can be maintained within the desired pressure set point plus or minus 5 psi (34.5 kPa). A consistent chamber
52 pressure is thus maintained for equivalent runs, thus improving the repeatability of the experiment. Figure 3.5 shows a top view of the mixing duct identifying static pressure tap locations. Taps are mounted along the top wall and side wall of the mixing region of the duct (the region between the nozzle exit plane and the duct exit) and in the strut gap region (the region between the strut and the side wall). Forty-eight pressure taps are mounted along the centerline of the top wall. The first tap is located 0.25 in. (0.635 cm) downstream of the strut nozzle exit plane. The second tap is located 0.5 in. (1.27 cm) downstream of the nozzle exit plane. The next 20 taps are mounted on 0.5 in. (1.27 cm) centers starting from the second tap. The remaining 27 taps are mounted on 1 inch (2.54 cm) centers starting 1 inch (2.54 cm) downstream of the 21st tap and ending 7.0 in. (17.78 cm) upstream of the exit plane.
Nozzle Exit Plane Strut Gap Region
0.25 in. spacing 2 times
Mixing Duct Region
0.50 in. spacing 18 times
1.00 in. spacing 28 times
Figure 3.5 PRC ejector top wall static pressure tap locations.
Figure 3.6 shows a side view of the duct with static tap locations. Forty-eight pressure taps are mounted along the centerline of the sidewall of the duct in the mixing
53 region. The first tap is mounted in the same plane as the nozzle exit. The next 20 taps are mounted on 0.5 inch (1.27 cm) centers downstream of the first tap. The remaining 27 side wall pressure taps are mounted on 1 inch (2.54 cm) centers starting from the 21st pressure tap.
Nozzle Exit Plane Strut Gap Region
0.70 in. spacing 10 times
Mixing Duct Region
0.50 in. spacing 20 times
1.00 in. spacing 27 times
0.50 in.
Figure 3.6 PRC ejector side wall pressure tap locations.
With the exception of the first taps, the pressure taps on the top and side walls of the duct are mounted at the same distance downstream of the nozzle exit plane. These static pressure taps are read using a mechanical Scani-Valve pressure reader. The ScaniValve has two pressure transducers: one for the top wall pressure taps and one for the sidewall pressure taps. One additional pressure tap is mounted on the sidewall centerline 0.5 inches upstream of the duct exit plane. This tap measures the static pressure of the flow exiting the duct and is measured with an independent transducer. The static pressure taps in the strut gap region of the duct can be seen in Figure 3.6. The strut gap is the portion of the duct upstream of the nozzle exit plane, and
54 downstream of the aerodynamic fairing. Ten pressure taps are mounted on one sidewall in the strut gap region. It is assumed that the pressure distribution on the opposite side of the duct will be identical. The ten taps are evenly spaced over 7 inches (17.78 cm) starting 0.7 inches (1.78 cm) upstream of the nozzle exit plane. Two Pitot-static probes are used to measure the total pressure and static pressure of the secondary flow and of the exit flow.
The first Probe is mounted in the
aerodynamic fairing and protrudes approximately 1 inch upstream into the secondary flow. Figure 3.7 shows a drawing of this probe location. The second probe is mounted at the exit of the duct on a traversing mechanism so that the tip of the probe is just inside the exit plane. The traversing mechanism allows the probe to be moved across the duct in the horizontal plane.
Aerodynamic Fairing
Strut
Fairing Pitot Probe
Figure 3.7 Secondary flow Pitot probe location in strut fairing.
Two thermocouples are mounted in the duct. The first is located inside the strut nozzle chamber (see Figure 3.4). This thermocouple measures the total pressure of the
55 primary flow. The second thermocouple is mounted at the inlet of the constant section of the duct. This thermocouple measures the temperature of the secondary flow. The experiment is controlled using LabView® software. The code was developed for the experiments carried out by Smith [25] and was modified for the current set of experiments. A given set point chamber pressure and the lab atmospheric pressure are entered into the code. The code converts the set point pressure into a voltage and sends a signal to the PID controller valve. The PID controller valve then adjusts the size of the valve opening until the voltage from the strut nozzle chamber pressure transducer matches the desired set point. Once the chamber pressure reaches the desired set point pressure, the code begins to record data from the instrumentation through out the duct.
3.2
Test Matrix Numerous tests were carried out to investigate different performance
characteristics of the ejector. The set of experimental results presented in this dissertation is primarily from three specific types of tests and are summarized in Table 3.1. Each of the test types had a different focus and, because runtime was limited by the available stored air, not all of the regions of interest were examined in each test.
The
instrumentation for the tests was categorized into four groups: the rocket chamber, the mixing duct, the exit Pitot, and the entrance and strut gap.
The rocket chamber
measurement locations consist of the static tap in the rocket chamber and the thermocouple in the rocket chamber. Since chamber pressure was the control variable, this set of measurements was recorded for all tests. The mixing duct measurement group consists of the 48 top wall and 48 sidewall static pressure taps.
The exit Pitot
56 measurement group consists of the exit Pitot-static probe and the centerline sidewall exit pressure tap. The entrance and strut gap measurement group consists of the ten centerline sidewall strut gap pressure taps in the strut gap region as well as the fairing pitot static probe and the entrance thermocouple.
Table 3.1 Ejector Test Matrix Measurement Locations Entrance Number of Chamber Rocket Mixing Experiment Complete Exit Pitot and Strut Pressures (psi) Chamber Duct Focus Gap Tests
3.2.1
Single Nozzle Strut 100, 200, 300, 400, 500, 600, X 700, 800, 900
Mixing Duct Tests
10
Exit Profiles
1
100, 200, 300, 400, 500, 600, 700, 800, 900
Low Pressures
1
20, 25, 30, 35, 40, 45, 50, 55
X
X
X
X
X
X
X
X
X
X
Dual Nozzle Strut 50, 100, 150, 200, 250, 300, X 350, 400, 450
X
Mixing Duct Tests
10
Exit Profiles
1
50, 100, 150, 200, 250, 300, 350, 400, 450
X
X
X
Low Pressures
1
20, 30, 40, 50, 70
X
X
X
X
Mixing Duct Tests The first series of tests focused on the pressure distributions in the mixing duct.
As noted earlier, these taps are connected to a mechanically actuated Scani-Valve. To get
57 a complete set of readings for a single test, the Scani-Valve must step through each pressure tap, let the pressure equalize, record the voltage, then step to the next tap. The Scani-Valve steps through each of the 48 ports sequentially. For each port both a top and a side wall pressure measurement are taken. The controlling software reads the pressure at a given port then commands the Scani-Valve to step to the next port for each transducer. When the pressure is read at the 48th port, the Scani-Valve returns to the first port and begins the sequence again. At each port, the software waits approximately 0.1 sec. for the pressure to adjust before reading the transducer voltage.
Through
experimental analysis, it was determined that this delay was sufficient to allow the pressure to adjust and equalize from the last reading. Tests focusing on the mixing duct pressures require more runtime than tests focusing on other areas. For this series of tests, the ejector was brought up to steady state operation for each desired set point pressure ratio. Once the set point had been reached the stagnation and static pressure at the aerodynamic fairing, static and stagnation pressures at the duct exit, exit centerline sidewall pressure, the inlet temperature, the ejector rocket chamber temperature, the ejector rocket chamber pressure, and the static pressures for the first top wall and first sidewall static pressure taps were recorded. The Scani-Valve was then commanded to step to the second top wall and side wall positions and the aforementioned set of measurements was recorded again. The test was continued until the pressure at each of the 48 side wall and 48 top wall pressure taps was measured ten times.
58 3.2.2
Exit Pressure Profiles The second series of tests focused on the total pressure distribution at the exit of
the duct. Stagnation and static pressure measurements were made through out a quadrant at the exit of the duct using a Pitot-static probe mounted on a traversing mechanism. Symmetry was assumed across the horizontal and vertical centerline planes. Traces were taken at the five vertically distributed locations shown in Figure 3.8. Traces were taken starting at the center of the duct exit and traversing towards the wall and then returning to the center of the duct. The probe was then moved upward (towards the top wall) and a new set of pressure measurements was taken. For each trace, measurements were made at eleven locations across the horizontal line of motion.
At each location,
15 measurements of the exit stagnation and static pressures, exit centerline sidewall static pressure, rocket chamber pressure and temperature, strut gap pressures, inlet stagnation
h = 4.00 in.
w = 3.50 in.
Figure 3.8 Probe trace locations for stagnation pressure traces across the duct exit plane.
59 and static pressures, and inlet temperature were made over a 2 second time span as the probe paused. This gave a total of 22 measurements for each parameter at each of the eleven locations.
3.2.3
Shadowgraph Visualizations A third series of experiments was performed to capture shadowgraph images of
the PRC ejector system to visualize any shock structures and correlate them to the experimental results [37]. Reference [38] discusses various shadowgraph and Schlieren techniques and was the primary source of information for the shadowgraph setup used in this project.
For ease of construction, the simplest method, known as direct
shadowgraphy, was chosen. Figure 3.9 shows a diagram of the setup for the direct shadowgraph method. The only requirements for this system are a point light source, the flow region of interest, and a flat screen onto which the shadow is projected. Figure 3.10 shows the general region in the mixing duct that was imaged.
Light Source
Box to Reduce Light
Ejector Duct Screen
Observation Position
Figure 3.9 Schematic of shadowgraph setup for ejector facility.
60
Strut Ejector
Region of Shadowgraphy
Mixing Duct
≈ 10 in
Flow Direction
Figure 3.10 Region of interest for shadowgraphy [37].
Shadowgraphy was performed for both the single and dual nozzle struts. For the single nozzle strut, the set point pressure ratio (Pc/Pb) was varied from 6.8 to 60.5. For the dual nozzle strut, the set point pressure ratios were varied from 3.4 to 30.6. These chamber pressures provide approximately equivalent primary mass flow rates, i.e., a set point of 3.4 in the dual nozzle has an equivalent primary mass flow as a set point of 6.8 in the single nozzle strut. For these tests, only the rocket chamber measurement group parameters were recorded. The majority of the data presented in this dissertation is from the mixing duct tests.
For these tests, the set chamber pressure was achieved as described in the
preceding section. Once the steady state chamber pressure was reached, the pressure at each of the forty-eight side wall and top wall pressure taps was measured ten times. The pressures at other locations in the duct were measured 480 times during the same test. This test was repeated ten times with each test occurring on a different day.
61 The exit profile tests were used to determine the total pressure variation across a quadrant of the exit. Only one complete set of data from this test was collected. The Pitot-static probe was allowed to traverse across the exit of the duct recording the total pressure and static pressure at 10 different locations, then moved back towards the top wall stopping at the same locations to take ten more readings. When the probe returned to the center position, the test was stopped. The probe was then moved vertically closer to the top wall, and the test was conducted again traversing the probe toward the sidewall stopping at the same locations for readings. A total of 5 different locations was used from the center of the exit to the top wall. The low pressure tests were conducted to determine the maximum bypass ratio that could be achieved for this ejector. These tests were used for comparison purposes only. The tests were conducted in short runs, and 100 measurements were made from the rocket chamber, exit Pitot and entrance and strut gap measurement locations for a set chamber pressure. Since only one test was conducted at each chamber pressure the repeatability in these data points is not included. In addition to the tests listed in Table 3.1, a number of additional tests was used to test components of the facility setup. Tests were run to examine the repeatability of the digital chamber pressure control, to establish the minimum time for pressure equalization in the static pressure tap tubing, and single tests were run to obtain shadowgraph images.
CHAPTER 4
UNCERTAINTY ANALYSIS AND DATA REDUCTION EQUATIONS
4.1
Introduction This chapter presents a general discussion of uncertainty followed by specific
approaches used in the ejector experiments. The data reduction equations used for analysis will be presented. The uncertainty analysis methods outlined in Coleman and Steele [39] were used for this analysis.
The systematic uncertainty constants for
measured parameters are presented in Appendix A. An example of an analysis for the calculated quantity of secondary mass flow is presented at the end of the chapter.
4.2
General Uncertainty Measurement errors are divided into two categories, random errors and systematic
errors. A random error is one that contributes to scatter in the measured values, and thus can have a different magnitude for measurements of the same variable at steady state. A systematic error is one that is common to all of the measurements of the same variable, and thus has the same magnitude for all measurements of the same value at a steady state. The total error associated with a measured variable is the sum of the systematic error and random error components.
62
63 For the experiments presented in this dissertation, multiple measurements of the same variable were made at a presumed steady state. Because this experiments deals with high speed flow which can be turbulent, the measurement variation is associated with the turbulent fluctuations as well as the random measurement error.
Because
multiple tests at the same set point produced consistent average results, it is assumed that the measurements are statistically steady in time throughout the duct. The average measurements from multiple tests at the same set point are presented in this work. The variation of the test averages for the same set point composes the random uncertainty for the average result. The systematic uncertainties associated with the measurements were determined through an end to end calibration of the data acquisition system. That is, a known pressure was applied to the transducer, and values were recorded using the same data acquisition card and the same computer that were used for the experiment. Thus the calibration uncertainty combines systematic uncertainties of the transducer, the uncertainty in the “known” applied pressure, the data acquisition card, as well as other uncertainties associated with the setup of the system. The data from the calibration was applied to a regression uncertainty analysis to determine the scale and offset of the transducer and to determine the uncertainty associated with the reading. A sample of the regression uncertainty analysis is included in Appendix B.
4.2.1
Single Variable Measurement Uncertainty
For a sample containing N repeated measurements of a single variable (X). The sample standard deviation, SX, is given by
64
⎛ 1 SX = ⎜ ∑ Xi - X ⎝ N - 1 i=1 N
(
1 N
N
)
2
1 2
⎞ ⎟ , ⎠
(4.1)
where the average, X , is calculated as X=
∑X
i
,
(4.2)
i=1
and the standard deviation of the mean, S X , is given by SX =
SX . N
(4.3)
The random uncertainty is given by t ⋅ SX ,
(4.4)
and the random uncertainty of the mean is given by t ⋅ SX ,
(4.5)
where the factor t is a coverage factor and is obtained from the t-distribution [39]. The value of t depends on the combined number of degrees of freedom in the estimates of both systematic and random uncertainties. In all of the cases analyzed in this study, the combined number of degrees of freedom is greater than 9, so for 95% confidence uncertainty estimates, t is taken equal to 2.0 [39]. The total uncertainty, UX, for a single value is given by U X = 2 ⋅ S X 2 + BX 2 ,
(4.6)
and the total uncertainty of the mean, U X , is given by U X = 2 ⋅ S X 2 + BX 2 .
(4.7)
65 4.2.2
Uncertainty for a Calculated Result
Often a result is determined from several measured variables by using a data reduction equation (DRE). In general form, a DRE can be written as r = r ( X 1 , X 2 ,...X J ) ,
(4.8)
where r is the desired result, and X1 through XJ are the measured values from an experiment.
An uncertainty propagation equation can be used to determine the
systematic uncertainty in the result due to the uncertainties in the measured variables. For the general form of the DRE, the systematic uncertainty of the calculated result r is 2
2
2
⎛ ∂r ⎞ ⎛ ∂r ⎞ ⎛ ∂r ⎞ 2 2 2 Br 2 = ⎜ ⎟ BX J + ... ⎟ BX 1 + ⎜ ⎟ BX 2 + ... + ⎜ ∂ ∂ ∂ X X X ⎝ 1⎠ ⎝ 2⎠ ⎝ J⎠ , ⎛ ∂r ⎞ ⎛ ∂r ⎞ +2 ⎜ ⎟⎜ ⎟ BX i X k ⎝ ∂X i ⎠ ⎝ ∂X k ⎠
(4.9)
where the BX terms are the systematic uncertainties associated with the X variables and there is a correlated systematic uncertainty term (BXiXk) for each pair of variables that share a common error source [39]. The random uncertainty may be calculated using a similar error propagation equation; however, the correlated terms of the equation can be difficult to quantify in an experiment. These correlated errors can have a significant influence on the total random uncertainty [40]. Thus, the random uncertainty may be better estimated by computing a result for each set of measured variables at a single point in time. This produces a set of results for each set of measured values. The variation in the set of results may then be determined using Equation (4.1). By calculating the random uncertainty in this manner, the correlated effects are automatically captured. The random uncertainty of the result is then given by
66 2 ⋅ Sr ,
(4.10)
and the random uncertainty of the mean for the set of results is given by 2 ⋅ Sr .
(4.11)
U r = 2 ⋅ Sr 2 + Br 2 ,
(4.12)
In such a case, the total uncertainty in r is
and the uncertainty of the mean from the sample of results is calculated as 2
U r = 2 ⋅ S r + Br 2 .
4.2.3
(4.13)
Uncertainty for a Collection of Results
In the present experiment, multiple tests were taken at the same steady state set point. The desired results were calculated from each test and the associated uncertainties were determined. An average value of the result for each set point was determined from the test averages. This value is the reported result for that set point. To calculate the uncertainty of the collection of results, each test average value is treated as a single measurement value and the total uncertainty determined for a specific test is treated as the systematic uncertainty for a single data point value. That is, for test 1 at a set point of 100 psi chamber pressure, the secondary mass flow was determined to be 0.183 lbm/s and the total uncertainty was (Ums) ± 0.001 lbm/s. When all tests are examined and the average of the secondary mass flows at 100 psi chamber pressure is taken, The value of secondary mass flow from test 1 becomes data point one in the collection and the total uncertainty from test 1 (Ums)test1, becomes the systematic uncertainty associated with data point one in the set of secondary mass flow values (Bms)test1. The random uncertainty for
67 the collection of tests is determined by calculating the standard deviation of the data set using Equation (4.1), and then multiplying the standard deviation by a coverage factor using Equation (4.4) or (4.5).
4.3
Reducing Test Uncertainty Through Nominal Readings
A set of readings was taken at atmospheric conditions with no flow through the facility for all pressure transducers prior to and after each test run. An average pressure value was determined from the readings for each transducer. This value represents the nominal reading of the transducer. When a gauge pressure transducer is used to measure atmospheric pressure, the reading from the transducer should produce a pressure value of zero. However, as is often the case, the transducer can produce a value slightly more or slightly less than the zero value.
This slight deviation represents a portion of the
systematic uncertainty in the transducer. By subtracting the nominal transducer reading from the value measured during the test, some of this uncertainty can be eliminated from the experiment. Since the calibration of the transducer produced a scale and an offset, by subtracting the reading from a nominal reading, the offsets will cancel out. Thus the nominal reading becomes the offset. Thus in reality only the slope from the calibration is used. Additionally, since the same transducer measures both the nominal reading and the test reading, the readings share the systematic uncertainty of that transducer. As discussed earlier, when two readings share a common error source they are said to be correlated.
Because the nominal reading is subtracted from the test reading, the
derivatives of the data reduction equation with respect to the measured variable and the
68 nominal value of the measured variable will have opposite signs. This will result in a negative term in Equation (4.9), lowering the total systematic uncertainty.
4.4
Pressure Transducers Calibration
As stated earlier, an “end-to-end” calibration was preformed to estimate the systematic uncertainty associated with each of the pressure transducers. Each transducer was calibrated in place using either an air or a water based dead weight tester. For the calibration, the transducer is connected to the dead weight tester and the signal is read through the same data acquisition card using the same computer that is used for the actual test. By calibrating in this manner, the total systematic uncertainty determined from calibration will include uncertainties from both the calibration standard and the data acquisition system. Each transducer was calibrated in the positive range of pressure and a calibration curve extrapolated for the negative gauge pressures.
A regression
uncertainty analysis [39] was performed to determine the systematic uncertainty associated with the calibration. This type of analysis produces a second order curve of pressure uncertainty as a function of the voltage reading from the transducer. The uncertainty from the center of the pressure range is lower than the uncertainty at the end of the range. A sample of the regression uncertainty methodology, and the uncertainty expressions for each of the transducers is included in Appendix B.
4.5
Ejector Specific Uncertainty
The following section describes the specific data reduction equations and the specific uncertainty methods used for in the current experimental investigation. The
69 uncertainty for these equations was determined using the methods outlined in the previous sections. Sample calculation sheets are provided in Appendix C.
4.5.1
Mass Flow
The mass flow rates of the primary and secondary streams are determined from pressure and temperature measurements at various locations in the facility described in Chapter 3. The secondary mass flow rate is calculated from the centerline static and total pressure measurement at the aerodynamic fairing and the temperature measurement at the duct entrance. The secondary mass flow is calculated as γ-1 ⎡ ⎤ γ ⎢⎛ Po ⎞ γ ⎥, m = Aduct ⋅ P ⋅ 1 ⋅ ⎥ RairT γ - 1 ⎢⎜⎝ P ⎟⎠ ⎣ ⎦
2
(4.14)
where P is the static pressure, Rair is the specific gas constant for air (1716 ft-lbf/slug R), T is the temperature of the flow, γ is the ratio of specific heat for air (1.4), and Po is the
stagnation pressure of the flow. Aduct is the cross-sectional area of the duct at the location of the measurements. Because of the geometry of the duct, it was assumed that there could be significant boundary layer build up at the probe location. The area of the duct was corrected to account for the boundary layer using a simple flat plate boundary layer approach. The displacement thickness of the boundary layer was calculated using
⎡ ⎤ 1 .16 ⎥ ⎢ δ = ⋅x⋅ , 1 ⎥ ⎢ 8 7 ⎣⎢ Rex ⎦⎥ *
(4.15)
70 where δ* is the displacement thickness, x is the distance from the entrance of the duct constant area section, and Rex is the Reynolds number based on x. With the displacement thickness, the area of the duct at the probe location was calculated as Aduct = (l - 2 ⋅ δ* )(w - 2 ⋅ δ* ) ,
(4.16)
where h is the height of the duct and w is the width of the duct. The height and width are each reduced by 2 times δ* to account for boundary layers on both top and bottom, and the 2 side walls. The centerline velocity at the fairing was used along with the calculated density to calculate the Reynolds number. The mass flow calculation of Equation (4.14) assumes a uniform velocity profile across the duct with a boundary layer near the walls. For real flows, there will be some maximum centerline velocity. Thus these calculations are subject to some additional uncertainty because of the assumptions used for the calculation.
This uncertainty has not been quantified for this dissertation.
The
uncertainty presented with the results is associated with the measurements only. Since nominal pressures were used to lower the uncertainty, the full data reduction must include the nominal pressures. By subtracting the nominal reading from the test reading, all of the pressure values become gauge readings, so the atmospheric pressure must also be added to the pressure term in the data reduction equations. Thus the pressure terms must be replaced in all data reduction equations by P = Preading - Pnominal + Patmospheric .
(4.17)
In all of the equations presented in this analysis, the nominal and atmospheric pressure terms will not be shown in the equations, but it should be noted that the actual equation will included additional terms for each pressure value.
71 The primary mass flow is calculated assuming choked isentropic flow through the nozzle. The chamber pressure is assumed to be the stagnation pressure for the flow, and the chamber temperature is assumed to be the stagnation temperature. The mass flow is calculated according to γ+1
mp =
Pc Tc
Athroat
γ Rair
⎛ 2 ⎞ γ-1 ⎜ ⎟ , ⎝ γ +1 ⎠
(4.18)
where Pc is the stagnation pressure, Tc is the chamber temperature, and Athroat is the area of the nozzle throat (0.466 in2).
4.5.2
Bypass Ratio
The ratio of secondary mass flow rate to primary mass flow rate is known as the bypass ratio or the bypass ratio. This is a key parameter for RBCC applications as it can be used to determine the required onboard oxidizer. Combining Equations (4.17) and (4.18) yields the total data reduction equation for the bypass ratio, ω.
ω=
γ-1 ⎡ ⎤ 2 γ ⎢⎛ Pos ⎞ γ ⎥ Aduct × Ps × × ⎜ ⎟ - 1⎥ RairTs γ - 1 ⎢⎝ Ps ⎠ ⎢⎣ ⎥⎦
Pop Top
Athroat
γ Rair
⎛ 2 ⎞ ⎜ γ +1 ⎟ ⎝ ⎠
γ+1 γ-1
,
(4.19)
where the subscript s refers to secondary flow stream conditions, and the subscript p refers to primary flow stream conditions.
72 4.5.3
Mach Number
Mach numbers were calculated at two locations in the flow, ahead of the strut at the aerodynamic fairing, and at the exit of the duct. At the aerodynamic fairing, the flow was always subsonic allowing a straight forward calculation and uncertainty analysis to be performed. At the exit of the duct, the Mach number could either be supersonic or subsonic depending on the flow conditions. When the flow is supersonic, the Mach number calculation and the uncertainty analysis become increasingly complicated. When the flow is subsonic, the Mach number can be determined by γ-1 ⎛ ⎞ 2 ⎜ ⎛ Po ⎞ γ ⎟, M= 1 ⎜ ⎟ ⎟ γ -1⎜⎝ P ⎠ ⎝ ⎠
(4.20)
where Po and P are the stagnation and static pressures measured from the Pitot-static probe at the duct exit. The derivatives required for the systematic uncertainty equation can be calculated directly and applied to Equation (4.9). When the flow is supersonic, a Pitot probe inserted in the flow induces a shock wave to form on the nose of the probe. The measurement from the Pitot probe reflects the pressure on the downstream (subsonic) side of the shock wave [41]. The Mach number is determined by a process of iteration on the downstream Mach number using γ
⎡ γ - 1 2 ⎞ ⎤ γ-1 ⎛ 1+ M 1 ⎟⎥ ⎢ ⎜ ⎡ ⎤ Po2 2γ γ -1 2 = ⎢1+ M 12 - 1 ⎥ ⋅ ⎢1+ ⎜ ⎟⎥ , P1 2 ⎜ γ× M 2 - γ - 1 ⎟ ⎥ ⎣ γ +1 ⎦ ⎢ 1 ⎢⎣ ⎝ 2 ⎠ ⎥⎦
(
)
(4.21)
where Po2 is the stagnation pressure of the shocked flow measured by the Pitot-static probe, and P1 is the static pressure measured just upstream of the Pitot probe by a wall tap.
73 Because this is an iterative process, Equation (4.9) cannot be directly used to determine the systematic uncertainties for the result.
Therefore, a Monte Carlo
simulation was performed for each test in which supersonic flow was determined. Using measured values of Po2 and P1 with appropriate systematic uncertainties randomly generated, 10000 values of Mach number were calculated. The total uncertainty was determined using Equation (2.12). The drawback to this approach was that correlated errors were not accounted for in the simulation. The resulting uncertainties are therefore conservative, since in this case the correlated errors would have reduced the overall uncertainty.
4.5.4
Pressure Ratios
Many of the presented results are pressure ratios or functions of a pressure ratio. The pressure ratio is the absolute pressure divided by either the stagnation pressure of the secondary flow or the back pressure. For these experiments, both of these pressures are equal to the atmospheric pressure. As was noted earlier, nominal readings from the instrumentation at no-flow conditions were used to zero the measurement.
So the
pressures shown in the equations are actually the values given by Equation (4.17). The uncertainty calculation for the pressure ratio is straightforward, and will not be given further treatment.
CHAPTER 5
EXPERIMENTAL RESULTS
5.1
Introduction Cold flow experiments were carried out on both dual and single nozzle struts.
Aside from the number of strut nozzles, chamber pressure was the only control variable for the tests. The duct entrains air and exhausts air from the lab. Therefore the back pressure and the stagnation pressure of the secondary flow are equal to atmospheric pressure. For each chamber pressure set point, data points were determined as averages of ten tests conducted on separate days. A summary of the results with associated uncertainties is provided in Appendix D.
5.2
Single Nozzle Strut Experiments on the single nozzle strut were conducted at chamber pressure set
points of 6.5, 13.2, 20.2, 27.2, 33.8, 40.5, 47.3, 53.9, and 60.6. For mixing duct focused experiments, ten tests were conducted on separate days at each chamber pressure. For the exit profile experiments, a single series of tests at approximately the same chamber pressure set points was conducted.
74
75 5.2.1
Mass Flow Augmentation
Figure 5.1 shows the primary and secondary mass flow rates and the bypass ratio plotted against the set point pressure ratio (Pc/Pb). The primary mass flow is directly proportional to the chamber pressure. The secondary mass flow increase begins to level off around a value of 2.1 lbm/sec (0.95 kg/s) at a pressure ratio of 41. This corresponds to a primary mass flow of approximately equal mass flow, 2.1 lbm/sec (0.95 kg/s). The leveling off of the secondary mass flow trace is indication that the flow has become choked. The secondary mass flow can only be increased from this point by changing the stagnation conditions of the secondary flow. Thus the maximum amount of secondary flow that can be induced at standard atmospheric conditions is 2.1 lbm/sec (0.95 kg/s). The uncertainty bars in the plot account for both measurement uncertainty and the uncertainty associated with test-to-test set point variation.
Additionally, slight
Mass Flow (lbm/s)
Bypass Ratio (ms/mp)
3.5 3.0 2.5 Bypass Ratio Secondary Mass Flow
2.0 1.5
Primary Mass Flow
1.0 0.5 0.0 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.1 Single nozzle strut primary and secondary mass flow comparison.
76 differences in the measured values could be due to different atmospheric conditions at the time of each test. This uncertainty is also included in the bars indicated. The maximum measured bypass ratio occurs at the lowest chamber pressure set point. At a primary mass flow of approximately 2.1 lbm/sec (0.95 kg/s) and a pressure ratio of approximately 41, the secondary mass flow becomes constant. As the chamber pressure increases further, the bypass ratio becomes inversely proportional to the chamber pressure and there is no added mass benefit. For this ejector the peak bypass ratio did not occur at the same set point pressure ratio as the secondary flow choke. As noted in Section 1.4 an ejector is operating at a maximum efficiency when the peak bypass ratio and the choke point occur at the same set point.
The bypass ratio shown is not the peak bypass ratio for this ejector
configuration, rather it is the largest bypass ratio value measured for this series of tests. The maximum bypass ratio would occur at a lower set point then tested here. The bypass ratio is influenced by the duct geometry and the nozzle configuration. For this ejector configuration, changes to the geometry should shift the bypass ratio. However, these geometry changes would also affect the maximum secondary mass flow and in a propulsion engine application affect the overall size of the vehicle.
5.2.2
Mach Numbers
Figure 5.2 shows the Mach numbers of the secondary flow at the fairing and of the mixed flow at the center of the duct exit for each of the chamber pressures studied. The secondary flow Mach number was calculated using Equation (4.20). The secondary flow Mach number ahead of the strut peaked around a value of 0.29 at a primary pressure
77 ratio of approximately 41 and remained subsonic for all tests. As expected this is consistent with the secondary mass flow choking indicated in Figure 5.1. The exit Mach number was both subsonic and supersonic depending on the rocket chamber pressure. When the flow was subsonic, Equation (4.20) was used to calculate the Mach number. When the flow was supersonic, Equation (4.21) was used to calculate the Mach number. For supersonic flow, pressure fluctuations increased significantly which in turn increased the random uncertainty in the calculation. In addition, a Monte Carlo approach was used to determine the total uncertainty. The increased random uncertainty and the uncertainty analysis approach combine to significantly increase the uncertainty associated with the calculated Mach number. This behavior is illustrated by
1.4
Mach Number
1.2
Inlet Exit
1.0 0.8 0.6 0.4 0.2 0.0 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.2 Secondary flow Mach number ahead of the strut and mixed flow Mach number at duct exit centerline (single nozzle strut).
78 the large uncertainty bars on the exit Mach number data at high pressure ratios in Figure 5.2. The Mach number at the duct exit continued to increase with increasing chamber pressure.
Around a pressure ratio of 47, the rate of increase changed
dramatically. Above this chamber pressure, the primary and secondary flows will fully mix by the exit of the duct. This will be shown more clearly in the exit pressure profile plots. For the highest pressure ratio in this dataset, the exit pressure measurements indicated that the centerline exit flow was supersonic with a Mach number of approximately 1.11.
5.2.3
Strut Gap Pressures
While the plots of Figures 5.1 and 5.2 indicate that the secondary flow becomes choked, these plots do not indicate the type of choke that occurs. In order to determine the choking mechanism, the secondary flow static pressures in the strut gap were examined. If the choke is an aerodynamic choke, it will occur in this region of the duct. Figure 5.3 shows the ratio of the wall static pressure to the secondary flow stagnation pressure at each of the ten pressure tap locations in the strut gap. All of the chamber pressure set points for the single nozzle strut are shown in the figure. The location of the pressure taps are shown as the ratio of the distance from the nozzle exit plane divided by the hydraulic diameter of the nozzle exit area. The dashed line in Figure 5.3 shows the sonic limit (Ps/Pos = 0.528 for γ = 1.4). A pressure ratio at or below this point would indicate the presence of an aerodynamic choke.
79 Pc/Pb
Strut Gap Pressure Ratio (P/Pos)
1
6.5 0.9
13.2 20.2
0.8
27.2 33.8 40.5
0.7
47.3 53.9
0.6
60.6 Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.3 Single nozzle strut gap pressure ratios.
Figure 5.3 shows consistent trends through the strut gap at any set point. The pressure ratio decreases as the flow approaches the nozzle exit plane. This trend is consistent with pressure loss due to a growing boundary layer in the gap. The lowest pressure ratio occurs at the last pressure tap, 0.843 hydraulic diameters upstream of the nozzle exit plane. A complex behavior can be seen at set points between 40.5 and 60.6, the set points where the secondary flow is choked. At set point pressure ratios of 40.5 and 47.3, the strutgap pressure ratios are nearly identical and are within uncertainty of the sonic limit. As the pressure ratio is increased above 47.3, the strut gap pressure ratios increase (away from the sonic limit). Figure 5.4 is an expanded plot of the strut gap region for these pressure ratios to more clearly show the flow behavior.
80
Strut Gap Pressure Ratio (P/Pos)
0.65
Pc/Pb 0.6
40.5 47.3 53.9 60.6
0.55
Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.4 Single nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 40.5, 47.3, 53.9, and 60.6).
The change in behavior in the strut gap region can be more clearly seen by examining the pressure ratios at the last strut gap position only. Figure 5.5 is a plot of the strut gap pressure ratio at the final strut gap position versus the set point pressure ratio. As the set point increases, the strut gap pressure ratio decreases and approaches the sonic limit. Between set point pressure ratios of 40.8 and 47.6, the strut gap pressure ratios are within uncertainty of the sonic limit. When the set point pressure ratio increases above 47.3, the behavior as the pressure ratio begins to increase. The plot of secondary mass flow indicated an apparent choke of the secondary flow around a set point pressure ratio of 33.8. The strut gap pressure ratio for this set point has not yet reached the sonic limit. This indicates that if a choke has occurred it is a mass choke of the secondary flow in the mixing duct. As the set point is increased above 33.8, the minimum strut gap pressure
81 ratio continues to decrease. If a choke had occurred in the strut gap, the pressure ratio could not decrease any further. For the next two highest chamber pressure set points examined (40.5 and 47.3), the pressure ratio at strut gap position 10 appears to be within uncertainty of the sonic limit. This indicates that the secondary flow chokes in the strut gap for this range of set points. For set point pressure ratios higher than 47.3, the pressure ratio in the strut gap increases away from the sonic limit indicating the flow is no longer choked in the strut gap. The mass flow plot indicated that the flow remained choked at these higher set points, thus the choke location has moved downstream of the strut gap into the mixing duct.
Strut Gap Pressure Ratio (P/Pos)
1.0 0.9 0.8 0.7
Sonic Limit
0.6 0.5 0
10
20
30
40
50
60
70
Set Point Pressure Ratio (Pc /Pb)
Figure 5.5 Single nozzle strut pressure ratio at last static pressure tap in the strut gap (0.843 hydraulic diameters upstream).
82 5.2.4
Mixing Section Static Pressure Distributions
Static pressure measurements along the centerlines of the top and side walls of the duct are used to evaluate mixing of the primary and secondary flow streams. Figures 5.6 through 5.11 show plots of the top and sidewall pressures for chamber pressure set points varying from 6.5 to 33.8. The wall pressures in the figures have been normalized by the secondary flow total pressure measured at the fairing upstream of the strut (the lab atmospheric pressure). A pressure ratio of 1 indicates the primary and secondary flow have fully mixed at that point. The strut gap pressure ratios have been included with the sidewall pressures distribution. At the top of the plots is a cross section of the duct for positional reference. For chamber pressure ratio set points between 6.5 and 33.8, the pressure distribution plots indicate that the sidewall pressure ratio drops through the strut gap and then begins to recover in the mixing duct. As seen in Figures 5.1 and 5.2, secondary flow did not reach a choke for set point pressure ratios of 33.8 and lower. Thus for these plots the ejector is operating in the mixed regime. The lowest sidewall pressure ratio is found at the last position in the strut gap region. The first side wall pressure tap in the mixing duct region shows a value approximately equal to the last strut gap pressure ratio. The pressure ratio begins to recover from this point and has completely recovered to a pressure ratio of 1.0 by 20 hydraulic diameters. The top wall pressure taps show a similar trend to the sidewall taps. The first two taps are located immediately downstream of the strut. In this region, the flow separates and recirculates as the secondary flow tries to turn around the strut base. This results in a
83
1.2
Pressure Pressure Ratio Ratio (P/Po (P/Pos) s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2
Pc/Pb = 6.5
0.0 -10
0
10
20
30
40
50
Position Position(x/Dh) (x/Dh)
Figure 5.6 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 6.5).
1.2
Pressure Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 13.2
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.7 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 13.2).
84
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 20.2
0.0 -10
0
10
20 30 Position (x/D ) h Position (x/Dh)
40
50
Figure 2.8 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 20.2).
Pressure Ratio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 27.2
0.0 -10
0
10
20 30 Position (x/D ) Position (x/Dh)h
40
50
Figure 2.9 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 27.2).
85
1.2
(P/Pos) Pressure Ratio (P/Po s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 33.8
0.0 -10
0
10
20
30
40
50
Position (x/Dh) Position (x/Dh)
Figure 5.10 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 33.8).
pressure ratio of 1 at the first two top wall pressure tap locations. At approximately 1.2 hydraulic diameters downstream, the lowest top wall pressure ratio is found. The pressure ratio begins to recover from this position, and has fully recovered by 20 hydraulic diameters downstream of the strut nozzle exit plane.
This pressure
equalization is an indication that the two flows have mixed. For these pressure ratio set points, the chamber pressure had little influence on the length of duct required for pressure recovery and mixing. Figure 5.11 shows the top and side wall pressure distribution for a set point pressure ratio of 40.5. The side wall pressure ratio distribution slightly deviates from the other lower pressure distributions. The pressure ratio dropped in the strut gap region. However, the pressure ratio continued to drop once the flow passed the strut nozzle exit
86 plane.
The lowest pressure ratio was found approximately 1.2 hydraulic diameters
downstream of the strut nozzle exit plane. The sidewall pressure begins to recover from this point and has fully recovered by 22.9 hydraulic diameters downstream of the nozzle exit plane. The top wall pressure ratio distribution for this set point followed the same trend as the lower pressures. For this set point, the secondary flow has reached a choke in the strut gap region of the duct. As flow expands from the choke into the mixing duct, the flow experiences an acceleration which accounts for the pressure drop.
Pressure PressureRatio Ratio(P/Pos) (P/Pos)
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc = 40.5 psi
0.0 -10
0
10
20 30 Position(x/Dh) (x/Dh) Position
40
50
Figure 5.11 Single nozzle strut top and side wall pressure distributions (Pc/Pb = 40.5).
The pattern of an initial pressure ratio drop to a low value, followed by a recovery region to pressure equalization, is identified as the “low pressure” trend. This trend will again be seen with the dual nozzle struts at low set point pressure ratios. It should be
87 noted that the trend appears to be mass flow driven as opposed to pressure driven. That is, the same trends are seen in the dual nozzle strut at the equivalent mass flow rates rather than the equivalent chamber pressures. However, the lower mass flow rates are results of lower chamber pressures in the strut rockets. This point will be discussed in more detail in a later section. Figures 5.12 through 5.14 show plots of the top and side wall pressure distributions for set point pressure ratios of 47.3, 53.9, and 60.6. The trends seen in these plots are significantly different from the “low pressure” trends observed in Figures 5.6 through 5.11. As seen in Figures 5.1 and 5.2, the secondary mass flow is choked at these set point pressure ratios. For these set points, there is a sharp drop in sidewall pressure ratios which begins at the strut nozzle exit plane and drops to a pressure ratio of
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 Side Wall
1.0
Top Wall 0.8 0.6 0.4 0.2 Pc/Pb = 47.3
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.12 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 47.3).
88
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0
Side Wall Top Wall
0.8 0.6 0.4 0.2 Pc/Pb = 53.9
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.13 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 53.9).
Pressure PressureRatio Ratio(P/Pos) (P/Pos)
1.2 1.0 Side Wall Top Wall
0.8 0.6 0.4 0.2 Pc/Pb = 60.6
0.0 -10
0
10
20
30
40
50
Position(x/Dh) (x/Dh) Position
Figure 5.14 Single nozzle strut top and side wall pressure distribution (Pc/Pb = 60.6).
89 approximately 0.25 at 5.4 hydraulic diameters downstream of the nozzle exit plane. There is an apparent pressure ratio discontinuity at this location as the pressure ratio increases, then begins to drop to a value of 0.3. The pressure ratio appears relatively steady at this value until some point downstream where the flow begins to recover. The distance from the nozzle exit plane to this pressure recovery point increases with the setpoint pressure ratio. The side wall pressure ratio does not appear to completely recover to a value of 1 by the last pressure tap (44.6 hydraulic diameters downstream of the nozzle exit plane). This is an indication that the secondary and primary flows are not well mixed for these chamber pressures. The pressure ratio measurement uncertainty in the recovery region of Figures 5.12 through 5.14 is relatively large. This uncertainty is a reflection of the flow unsteadiness rather than instrumentation uncertainty. Each point is averaged from ten measurements from ten tests. The average values of the pressure ratios from each test were very close. However, the standard deviation of the ten measurements was very large because of pressure fluctuations due to the turbulent nature of the flow. The top wall pressure ratios in Figure 5.12 exhibit a slightly different trend from the side wall pressure ratios. The region of separation within the first half inch of duct downstream of the strut is still visible in the first two measurements of the top wall pressure trace. At 1.2 hydraulic diameters downstream, the top wall pressure ratio drops to an intermediate value between 0.4 and 0.5 depending on the set point pressure ratio. The pressure ratio then rises to a value of 0.55 and 0.66 around 3.6 hydraulic diameters downstream. The pressure ratio then steadily drops to a minimum value around 0.25 at 6.6 hydraulic diameters downstream.
Between 7.8 and 8.4 hydraulic diameters
90 downstream there is a sharp discontinuity in the pressure ratio which increases to a value around 0.45. The pressure ratio then drops again and continues to go through a series of steady decreases followed by discontinuous rises until the pressure ratio begins a steady recovery to atmospheric pressure. The recovery location for the top wall pressure ratio is the same as that of the side wall. As with the side wall, the recovery location appears to be dependent on the set point pressure and does not fully recover by the end of the instrumented duct (42 hydraulic diameters downstream of the exit plane). Because the embedded rocket nozzle is designed for optimum expansion at a chamber pressure around a pressure ratio set point of 44.2, the trend change of the pressure ratio distribution was originally theorized to be due to the transition in plume behavior from overexpanded to ideal and then underexpanded. However, tests of a dual nozzle strut indicate the trend is more likely due to primary mass flow addition. The sharp discontinuities found in the higher pressure ratio plots are caused by shock structure in the duct. The presence of the shocks was verified through shadowgraph flow visualization which will be presented in a later section.
5.2.5
Exit Pressure Profiles
Based on the wall profile plots (Figures 5.12 through 5.14), it was believed that at high chamber pressures the flow does not have time to mix within the length of the duct. Thus a high pressure core flow would exist at the exit. Figure 5.15 shows the results of one set of duct traces across the centerline horizontal plane (trace location A in Figure 3.8). The average stagnation pressure measurement with uncertainty for each position in the duct exit is given. When the secondary and primary flows are completely
91 mixed, the stagnation pressure should be constant across the duct exit plane. The data in Figure 5.15 indicate that the flow appears to be well mixed for set point pressure ratios up to 40.8. For these set points there is a slight drop off near the side wall (x/wexit = 0) which is believed to be attributed to a thickening boundary layer. This drop off becomes more pronounced as the set point pressure ratio is increased. At higher pressure ratio set points of 47.1, 53.7, and 54.4, a clear variation of the stagnation pressure exists across the exit plane. At the center of the duct, the stagnation pressure is at a maximum and drops as the side wall is approached. These data verify the presence of a high velocity core flow surrounded by a lower velocity secondary flow, and also show that complete mixing does not occur at these pressures. This agrees with trends in the corresponding top wall and side wall pressure data (Figure 5.10 and Figures 5.12 through 5.14). The stagnation pressure measurements at the high primary chamber pressures exhibited large variations in the measured steady state values which is indicative of turbulent flow. This was also noted for the mixing duct wall pressure distribution plots at high chamber pressures. For the highest two set point pressure ratios, the plotted data shows inflection points. This point may indicate the location of the center of the mixing region between the core flow and the surrounding subsonic secondary flow. The data from the traces at each vertical position were combined to create surface plots of the stagnation pressure in a quadrant of the duct exit. Figures 5.16 through 5.21 show the stagnation pressure surfaces for set point pressure ratios between 6.5 and 40.4. The total pressure across the quadrant shows a fairly uniform profile with some drop off near the sidewall and near the top wall due to boundary layer.
92 Set Point Pressure Ratio
Pressure Ratio (Poexit/Pb)
2.4
60.3 53.7 47.1 40.4 33.8 27.2 19.8 13.2 6.5
2.2 2.0 1.8 1.6 1.4 1.2 1.0 0
0.1
0.2
0.3
0.4
0.5
Position (x/wexit)
Figure 5.15 Single nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).
w) (x/ n o iti Pos 0.4 l a t zon i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
Duct Top Wall
2.5
Vertical Position (y/h)
0.0
Strut Centerline
0.2
0.4
Duct Side Wall
Pc/Pb = 6.5
Duct Centerline
Figure 5.16 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.5).
93 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 13.2
Figure 5.17 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.2).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 19.8
Figure 5.18 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.8).
94 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 27.2
Figure 5.19 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.2).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 33.8
Figure 5.20 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 33.8).
95 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 40.4
Figure 5.21 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 40.4).
Figures 5.22 through 5.24 show the stagnation pressure results for a quadrant at the duct exit for pressure set points of 47.1, 53.7 and 60.3, respectively. For these cases, the wall pressure ratio distribution plots (Figures 5.12, 5.13, and 5.14) indicated that the flow was not well mixed and a core flow existed throughout the duct. The stagnation pressure at the center of the exit is significantly higher than the pressure near the walls. The total pressure for the highest primary chamber pressure appears to show a sharper initial pressure gradient in the horizontal direction (towards the side wall) than in the vertical direction. This could be due to effects of the base of the strut. The large pressure gradients verify that the primary and secondary flows are not mixed at the exit, and a core flow is indeed present.
96 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 47.1
Figure 5.22 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 47.1).
w) (x/ n itio Pos 0.4 l a nt rizo 0.2 o H
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 53.7
Figure 5.23 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 53.7).
97 w) (x/ n o siti 0.4 l Po a t on z i r 0.2 Ho
Press ur
1.0
e Ra t io ( P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 60.3
Figure 5.24 Single nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 60.3).
5.3
Dual Nozzle Strut
Experiments on the dual nozzle strut were conducted at chamber pressure set points of 3.5, 6.8, 10.2, 13.5, 16.9, 10.4, 24.0, 27.4, and 30.6. The primary mass flow for the dual nozzle strut at these pressure ratio set points corresponds to the same mass flow at a set point twice as high in the single nozzle strut. For example, the primary mass flow at a chamber pressure set point ratio of 3.4 in the dual nozzle strut is approximately equivalent to the primary mass flow at a chamber pressure set point ratio of 6.8 in the single nozzle strut. Data from ten separate tests at each chamber pressure were averaged for the mixing duct, mass flow, and Mach number results. As with the single nozzle strut, a single set of experiments is reported for the exit pressure profile plots.
98 5.3.1
Mass Flow Augmentation
Figure 5.25 shows the secondary and primary mass flow rates and the bypass ratio plotted against the set point ratio. The trends of this plot are similar to those for the single nozzle strut shown in Figure 5.1. The primary mass flow increases linearly with chamber pressure. The secondary mass flow increases with increasing chamber pressure until reaching a value of approximately 2.1 lbm/sec (0.91 kg/s) at a set point ratio of 20.4. As the ratio is increased above 20.4, the secondary mass flow remains fairly constant indicating that the secondary flow has choked.
Mass Flow (lbm/s)
Bypass Ratio (ms/mp)
3.5 3.0 2.5 Bypass Ratio Secondary Mass Flow
2.0 1.5
Primary Mass Flow
1.0 0.5 0.0 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc/Pb)
Figure 5.25 Dual nozzle strut secondary and primary mass flow.
The maximum calculated bypass ratio for this series of tests occurred for the lowest pressure ratio set point tested. As the pressure ratio is increased, the bypass ratio drops. Once the pressure ratio of 20.4 is reached, the secondary mass flow becomes
99 constant and the bypass ratio decreases only as a function of increasing primary mass flow.
5.3.2
Mach Numbers
The inlet and exit Mach numbers for the dual nozzle strut are presented in Figure 5.26. The inlet Mach number increased with increasing chamber pressure to a value of 0.29 around a set point pressure ratio of 20.4. As the pressure ratio is increased above 20.4, there is little variation in the inlet Mach number. The exit Mach number increases with increasing chamber pressure throughout the tests. Between set points of 24.4 and 27.4, the centerline exit flow becomes sonic. When the flow becomes sonic, there is an apparent change in slope. The highest Mach number determined at the exit was approximately 1.3. As noted for the single nozzle plots, the higher Mach numbers
1.6 1.4
Inlet
Mach Number
1.2
Exit
1.0 0.8 0.6 0.4 0.2 0.0 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc /Pb)
Figure 5.26 Dual nozzle inlet and exit centerline Mach numbers.
100 have a larger uncertainty, which is due to both the increased turbulent fluctuations and the methodology used to determine the uncertainty as described in Chapter 4.
5.3.3
Strut Gap Pressures
Figure 5.27 shows the pressure ratios in the strut gap region for each dual nozzle chamber pressure set point tested. Through the strut gap, the pressure ratio drops as the flow approaches the nozzle exit plane. For the dual nozzle strut, an instrumentation error prevented the use of one of the strut gap positions (2.53 hydraulic diameters upstream of the nozzle exit) that was available for the single nozzle strut. However, the trends in the strut gap for the dual nozzle strut are similar to those seen in the single nozzle, and the
Pc/Pb
Strut Gap Pressure Ratio (P/Pos)
1
3.5 6.8
0.9
10.2 13.5
0.8
16.9 20.4
0.7
24.0 27.4
0.6
30.6 Sonic Limit
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.27 Dual nozzle strut gap pressure ratios.
101 additional pressure tap would not add significant insight. The minimum pressure ratio was located at the last pressure tap in the strut gap region. Thus if the choke in the strut gap is an aerodynamic choke, the pressure at the last strut gap position should reach the sonic pressure limit. Figure 5.28 shows an expanded plot of the strut gap region for these pressure ratios to more clearly show the flow behavior. Similar to the single nozzle strut gap pressure ratios, the dual nozzle strut gap pressure ratio decreases as the flow approaches the nozzle exit plane.
The lowest pressure ratio occurs at the last pressure tap,
0.843 hydraulic diameters upstream of the nozzle exit plane. A similar complex behavior can be seen at set points between 24.0 and 30.6, the set points where the secondary flow
Strut Gap Pressure Ratio (P/Pos)
0.7
Pc/Pb
0.65
20.4 24.0
0.6
27.4 30.6 Sonic Limit
0.55
0.5 -9
-7
-5
-3
-1
Distance from Nozzle Exit Plane (x/D h)
Figure 5.28 Dual nozzle strut gap pressure ratios for high set point pressure ratios (Pc/Pb = 20.4, 24.0, 27.4, and 30.6).
102 is choked for the dual nozzle strut. At set point pressure ratios of 24.0 and 27.4, the strutgap pressure ratios are nearly identical and are within uncertainty of the sonic limit. As the pressure ratio is increased above 27.4, the strut gap pressure ratios increase but remain within uncertainty of the sonic limit. Figure 5.29 shows the pressure ratio at the last strut gap position. As the set point pressure ratio is increased, the minimum strut gap pressure ratio decreases (approaching the sonic limit). When a set point pressure ratio of 24.0 is reached, the minimum pressure ratio is within uncertainty of the sonic limit. For the next highest set point pressure ratio (27.4), the strut gap pressure ratio is still within uncertainty of the sonic limit. As the chamber pressure is increased above 27.4, the minimum strut gap pressure ratio begins to increase moving away from the sonic limit, although at the highest set
Strut Gap Pressure Ratio (P/Pos)
1.0
0.9
0.8
0.7
0.6
0.5 0
5
10
15
20
25
30
35
Set Point Pressure Ratio (Pc /Pb)
Figure 5.29 Dual nozzle strut gap pressure ratios at last static pressure tap (0.843 hydraulic diameters upstream).
103 point the uncertainty band still reaches the sonic limit. Similar to the single nozzle strut, this indicates a change in behavior of the secondary flow.
The mass flow plot
(Figure 5.25) indicates a choke of the secondary flow, but the choke may be moving out of the strut gap region as the pressure ratio is increased above these set points.
5.3.4
Mixing Section Static Pressure Distribution
Figures 5.30 through 5.35 show the top and side wall pressure distributions for the dual nozzle strut at set point pressure ratios from 3.5 to 20.4. The trends in these plots follow the “low pressure” trend identified in the single nozzle strut pressure distributions. For all of these primary chamber pressures, the side wall pressure ratio drops in the strut gap. For set point pressure ratios of 16.9 and lower, the side wall pressure ratio begins to recover immediately after passing the strut nozzle exit plane.
The recovery region
continues until approximately 20 hydraulic diameters downstream. The top wall pressure ratio shows the same recirculation region in the first 0.6 hydraulic diameters downstream of the strut nozzle exit plane as indicated by a pressure ratio of one at the first two pressure taps. After the recirculation region, the top wall pressure ratio drops to a value comparable to the sidewall pressure ratio at the same location. The top wall pressure ratio then begins to recover and has fully recovered by 19.64 hydraulic diameters. For the pressure ratio set point of 20.5, the wall pressure ratio continues to drop in the mixing duct until 1.2 hydraulic diameters downstream then the pressure begins to recover. A similar trend was seen in the single nozzle pressure distributions for a set point pressure ratio of 40.5 (Figure 5.12).
Both the top and side wall pressure ratios recover by
104
1.2
Pressure Ratio Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 3.5
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.30 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 3.5).
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 6.8
0.0 -10
0
10
20 30 Position Position(x/D (x/Dh) h)
40
50
Figure 5.31 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 6.8).
105
1.2
Pressure Ratio (P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 10.2
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.32 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 10.2).
1.2
Pressure Ratio Ratio (P/Pos) (P/Pos) Pressure
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 13.5
0.0 -10
0
10
20 30 Position Position(x/D (x/Dh) h)
40
50
Figure 5.33 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 13.5).
106
1.2
PressureRatio Ratio(P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 16.9
0.0 -10
0
10
20
30
40
50
Position Position (x/D (x/Dh) h)
Figure 5.34 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 16.9).
1.2
Pressure Ratio Ratio (P/Po (P/Pos) Pressure s)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 20.5
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.35 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 20.5).
107 approximately 19.68 hydraulic diameters downstream of the strut nozzle exit plane. Thus, the primary chamber pressure seemed to have little influence on the mixing length. Figures 5.36 through 5.38 show the top and side wall pressure distributions for set point pressure ratios of 24.0, 27.4, and 30.7. These plots exhibit the “high pressure” trend. The set point pressure ratio of 24 is the primary chamber pressure at which the transition from the high to low pressure trends occurs. At this chamber pressure the pressure distribution plots showed characters of both trends.
For some tests, the pressure
distribution would follow the high pressure trend. In other tests the pressure distribution would initially show a low pressure trend, but midway through the test, the high pressure trend would develop. For this reason, the uncertainty associated with the average reading from multiple tests is very high.
1.2
Pressure Pressure Ratio Ratio (P/Pos) (P/Pos)
1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 24.0
0.0 -10
0
10
20
30
40
50
Position Position(x/D (x/Dh) h)
Figure 5.36 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 24.0).
108
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6
Side Wall Top Wall
0.4 0.2 Pc/Pb = 27.4
0.0 -10
0
10
20 30 Position h) Position(x/D (x/Dh)
40
50
Figure 5.37 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 27.4).
PressureRatio Ratio(P/Pos) (P/Pos) Pressure
1.2 1.0 0.8 0.6 Side Wall Top Wall
0.4 0.2 Pc/Pb = 30.7
0.0 -10
0
10
20 30 Position h) Position(x/D (x/Dh)
40
50
Figure 5.38 Dual nozzle strut top and side wall pressure distribution (Pc/Pb = 30.7).
109 For higher set point pressure ratios (Pc/Pb =27.4 and 30.7), the high pressure trend was always present. There is still a side wall pressure ratio drop in the strut gap region. However, immediately past the nozzle exit plane, the pressure ratio continues to drop. In the single nozzle plots, the drop was to a fairly steady value of 0.3. However, for the dual nozzle plots, there is much more scatter in the data and the pressure ratio varies in the range of 0.3 to 0.6. A pressure recovery is clearly present after this region. For a set point pressure ratio of 27.4, it appears the wall pressure ratio almost recovers by the end of the duct. However, for a set point of 30.7, it does not appear that the pressure ratio recovers by the end of the duct. Thus a core flow was suspected to be present at the duct exit for both of the higher set point pressure ratios. Similar to the high pressure trends for the single nozzle pressure distribution plots, there were several areas of discontinuity which are believed to be due to shock structure in the duct.
5.3.5
Exit Pressure Profiles
Figure 5.39 shows total pressure traces across the horizontal centerline of the duct exit plane. The ratio of the total pressure divided by the back pressure is plotted against the horizontal location divided by the width of the duct. Traces at the three lowest chamber pressures show a uniform total pressure across the exit plane with some drop off in the side wall boundary layer. The next four set points show a small gradient across the exit plane but still indicate fairly complete mixing. At the highest set points (27.1 and 30.3), an obvious pressure gradient exists across the exit plane. These plots indicate the presence of a supersonic core flow (Po/P > 1.893). These two traces also have inflection points which would indicate the location of the center of the mixing region between the
110 core flow and the surrounding subsonic secondary flow.
These results verify the
presence of the supersonic core predicted by the duct wall pressure distributions.
Set Point Pressure Ratio
2.8
Pressure Ratio (Poexit/Pb)
2.6 2.4
30.3 27.1
2.2
23.8
2.0
19.9
1.8
16.7 13.3
1.6
10.1
1.4
6.9 3.5
1.2 1.0 0
0.1
0.2
0.3
0.4
0.5
Position (x/wexit)
Figure 5.39 Dual nozzle exit stagnation pressure measurements across the horizontal centerline (trace location A).
Figures 5.40 through 5.46 show the carpet plots of the exit total pressure for the dual nozzle strut set point ratios of 3.5 to 23.9. At these chamber pressures, the duct wall pressure distribution plots exhibited the low pressure trend. The sidewall and top wall duct pressure plots for set points from 3.5 to 16.9 indicated the flow was completely mixed within the first 17 hydraulic diameters of the duct downstream of the nozzle exit plane.
The exit profile plots for these chamber pressures verify that there is an
approximately uniform pressure distribution across a quadrant at the exit. Although at higher chamber pressures there is a slight pressure decrease near the sidewall and a slight
111 pressure variation across the exit plane, the total variation is relatively small. This verifies that the flow is well mixed at the exit. At Pc/Pb = 23.9, there is some pressure gradient across the quadrant with the center pressure being around 4 psi higher than the pressure near the walls. This chamber pressure is just below the chamber pressure at which the duct flow switches from the low pressure trend to the high pressure trend. Figures 5.47 and 5.48 show the stagnation pressure profiles at the exit for set point pressure ratios of 27.1 and 30.3. At these set points, the centerline traverse showed a larger pressure gradient across the exit. The centerline pressure was very high while the pressure near the walls dropped off significantly. The carpet plots verify this prediction.
/ n (x
w)
tio osi P 0.4 l nta o z i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio ( P
2.0
exit / P b)
Duct Top Wall
2.5
Vertical Position (y/h)
0.0
Strut Centerline
0.2
0.4
Duct Side Wall
Pc/Pb = 3.5
Duct Centerline
Figure 5.40 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 3.5).
112
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 6.9
Figure 5.41 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 6.9).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 10.1
Figure 5.42 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 10.1).
113
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 13.4
Figure 5.43 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 13.4).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 16.7
Figure 5.44 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 16.7).
114
w) (x/ n itio Pos 0.4 l a nt ri z o 0.2 o H
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 19.9
Figure 5.45 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 19.9).
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press ur
1.0
e Ra t io (P
1.5
2.0
exit / P ) b
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 23.9
Figure 5.46 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 23.9).
115
w) (x/ n o siti 0.4 l Po a t n o z i r 0.2 Ho
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 27.1
Figure 5.47 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 27.1).
/w) n (x o i t o si 0.4 al P t n rizo 0.2 o H
Press u
1.0
r e Ra
1.5
tio (P
2.0
exit / P b)
2.5
Vertical Position (y/h)
0.0
0.2
0.4
Pc/Pb = 30.3
Figure 5.48 Dual nozzle strut total pressure profile across duct exit quadrant (Pc/Pb = 30.3).
CHAPTER 6
DISCUSSION OF RESULTS
6.1
Mass Flow and Bypass Ratio The primary and secondary mass flow rates for both struts were independently
plotted in Figures 5.1 and 5.25. For both struts, the primary mass flow rate is directly proportional to the chamber pressure. Figure 6.1 is a plot comparing the secondary mass flows for the single and dual nozzle struts at each set point pressure ratio. The maximum entrained (secondary) mass flows for both struts are equal (about 2.1 lbm/s) within uncertainty.
The maximum secondary mass flow for this study is limited by the
secondary flow minimum geometric area in the strut gap. Since this area is equal for both struts, the maximum secondary flow that can be induced should also be equal. For set point pressure ratios below the secondary flow choke point, the dual nozzle strut induces more secondary mass flow than the single nozzle strut. This can be explained by simple momentum principles. The total primary jet momentum, Jp, is approximately given by
J p = Ap Pp + m pV p ,
116
(6.1)
117 where Ap is the area of the nozzle exit, Pp is the pressure of the primary flow at the nozzle exit, m p is the mass flow through the nozzle and Vp is the velocity at the nozzle exit. At the same set point pressure ratio, the dual nozzle strut has twice the nozzle exit area as the single nozzle and twice the mass flow. The velocity and the pressure at the nozzle exit for both nozzles, however, will be approximately equal. Thus, at the same pressure set point, the total momentum of the dual nozzle primary flow will be twice that of the single nozzle strut. Since the momentum exchange is a primary driver for secondary flow entrainment, the dual nozzle strut has more momentum to exchange and thus can entrain more secondary flow. Once the secondary flow choke point is reached, the induced mass flow becomes constant and increases in chamber pressure do not increase the secondary mass flow.
2.5
Mass Flow (lb/s) Mass Flow (lbm/s)
2 1.5 1 Dual Nozzle Strut Single Nozzle Strut
0.5 0 0
10
20
30 40 50 Pressure Ratio Pressure Ratio(Pc/Pb) (Pc/Pb)
60
70
Figure 6.1 Secondary mass flow versus set point pressure ratio for single and dual nozzle struts.
118 Figure 6.2 shows the secondary mass flow in both struts plotted against the primary mass flow. By plotting the secondary mass flow against the primary mass flow rate, the loss in efficiency of the momentum exchange between the primary flow and secondary flow for the dual nozzle strut can be seen. For equivalent mass flow rates (Pcsingle = 2 Pcdual), the single nozzle strut induces a slightly higher mass flow rate for set point ratios below the secondary flow choke point. Because an equivalent mass flow rate in the dual nozzle strut occurs at a set point pressure ratio that is one half of the set point in the single nozzle, the nozzle exit pressure for the dual nozzle strut will be approximately one half of the nozzle exit pressure for the single nozzle strut. The first term on the right hand side of Equation (6.1) will be equal for the dual and single nozzle strut at equal mass flow rates. The velocity at the nozzle exit is a function of the area ratio and the chamber temperature. In both struts, the area ratio is the same and the
Secondary MassMass Flow Flow (lb/s) (lbm/s)
2.5
2
1.5
1
Dual Nozzle Strut Single Nozzle Strut
0.5
0 0
0.5
1
1.5 2 2.5 Primary Mass Flow (lb/sec) Primary Mass Flow (lbm/s)
3
Figure 6.2 Secondary mass flow comparison for both struts.
3.5
119 chamber temperature variation over the range of set points tested is negligible. Thus at equivalent mass flow rates, the momentum of the two jets is approximately equivalent. The difference in entrainment between the two struts may be due to a loss in the efficiency of the momentum exchange. This loss is attributed to the interaction of the two primary stream plumes with each other and the lower expansion angle of the primary flow plume leaving less surface area for interaction with the secondary flow stream. At set point pressure ratios above the choke point, there is an apparent change in the entrainment. The dual nozzle strut seems to entrain more secondary mass flow. Since the exit pressure for the single nozzle is double that of the dual nozzle for the same mass flow rate, the plume expansion for the single nozzle is greater. Thus the mimimum area the secondary flow sees (between the expanded primary flow and the wall) reduces quicker with increasing mass flow. The secondary mass flow induced with the single nozzle strut and the dual nozzle strut were compared with the results from previous studies at the UAH PRC [24, 25]. Although for some of the comparison plots no uncertainty level was available, the previous mass flow rates show very good agreement with the data from the current set of experiments. The maximum secondary mass flow was approximately the same and the primary nozzle chamber pressure which choked the flows was approximately the same. This agreement led to increased confidence in the results of the current experiment.
6.1.1
Mass Flow Calculations
Figure 6.1 indicated that the secondary flow becomes choked around set point pressure ratios 40.5 for the single nozzle strut and 24.0 for the dual nozzle strut. The strut
120 gap pressures (Figures 5.3 and 5.27) indicate that the pressure ratio in the strut gap region (P/Pos) approaches the sonic limit 0.528 at the same range of set point pressure ratios in each strut. For set point ratios 40.5 and 47.3 in the single nozzle strut, the pressure ratio in the strut gap region (Figure 5.3) is within uncertainty of the sonic limit. As the chamber pressure is increased further, the minimum pressure ratio in the strut gap increases away from the sonic limit. A similar trend was seen for the dual nozzle strut. At set point pressure ratios of 24.0 and 27.4, the minimum pressure ratio in the strut gap region was within uncertainty of the sonic limit. At a higher set point pressure ratio of 30.6, the pressure ratio had increased away from the sonic limit. However the strut gap pressure ratio still remained within uncertainty of the sonic limit. These data indicate that both ejectors are operating in all three Fabri regions over the range of pressure ratios examined (see Section 1.3). At low set points, the secondary flow does not reach the sonic limit, thus the ejector is operating in the mixed regime. At mid range set points, the secondary flow chokes and the pressure ratio in the minimum geometric area reaches the sonic limit, indicating an aerodynamic choke.
At these
operating conditions, the ejector is operating in the Fabri saturated supersonic regime. At high set points the choke moves downstream into the mixing duct and the pressure ratio in the mixing duct increases away from the sonic limit. At these operating conditions, the ejector is operating in the supersonic regime. For the saturated supersonic mode, the secondary flow is choked in the minimum geometric area and the mass flow can be calculated according to idealized flow equations using the entire cross section of the duct with no boundary layer reduction. The mass flow determined at the fairing, and plotted in Figure 6.2, must be equal to mass flow
121 through the strut gap. The theoretical maximum mass flow for air through an area equal to the strut gap area is 3.4 lbm/s (1.54 kg/s). This value is approximately 66% higher than the maximum secondary mass flow calculated from the experimental data. Furthermore, for isentropic choked flow in the strut gap, the inlet Mach number at the fairing would be 0.4 which is nearly twice as high as the calculated Mach number. Thus if the choke is an aerodynamic choke in the strut gap, then there are significant geometric effects in this region that have not been accounted for. The geometry of the duct would lead to significant boundary layers, particularly in the corners of the duct.
In the strut gap region, the boundary layer would be
compounded by four additional corners caused by the strut/wall intersections. Early studies of the PRC ejector system provided total pressure traces across the strut gap region [24]. The ratio of the measured stagnation pressure to atmospheric pressure in these figures indicated a fairly flat profile across the strut gap with some decrease in stagnation pressure near the walls. These data are indicative of a boundary layer buildup on the wall side of the strut gap region. The strut side boundary layer is smaller, but could still be significant. Thus, it is probable that the lower mass flow could be attributed to boundary layer growth. The traces from these plots were not taken near the top and side walls of the duct.
In the corner region, the boundary layer effect could be
intensified, reducing the stagnation pressure even further. The mass flow rates shown in Figure 6.2 are also idealized to some extent. Even when a simplified boundary layer thickness was accounted for, the mass flows calculated from the experimental data at the secondary flow inlet and through the nozzle do not equal the calculated mass flow at the mixing duct exit. The exit mass flow ranged from
122 8% to 28% greater than the sum of the inlet mass flow rates which violates the continuity equation. Through standard error propagation techniques, the measurement uncertainty was around 4% of the combined primary and secondary inlet mass flows. This leads to the conclusion that there are either additional losses in the duct not accounted for (such as leaks) or that the method used to calculate the mass flow has uncertainty which is greater than the measurement uncertainty. Although the incompressible flow assumption seems reasonable for the entrance region, there is an unknown velocity profile across the duct. The calculated secondary mass flow rate is based on the maximum centerline velocity and is thus somewhat larger than the true average value for the cross section. Thus some additional uncertainty in the mass flow calculation is believed to be attributed to the calculation methodology rather than the experimental uncertainty or additional losses in the system.
Despite the
uncertainty, the mass flow plots give an indication of the relative change in mass flow with increasing set point pressure ratio and the plots give a clear indication of a choking secondary flow.
6.1.2
Bypass Ratio
The plots of the bypass ratio plotted against the pressure ratio for each individual strut were shown in Figures 5.1 and 5.25. The two curves show similar trends; however, the dual nozzle strut initially shows a much sharper decrease in the bypass ratio with increasing pressure ratio. To directly compare the bypass ratio for the two struts, their bypass ratios are plotted against the primary mass flow rate in Figure 6.3. The largest bypass ratio occurred at the lowest mass flow rate for each struts. The average peak
123 bypass ratio was about 15% higher for the single nozzle strut than for the dual nozzle strut at the lowest pressure ratio. Similar to the trend for the secondary mass flow, for both struts at pressures below the secondary flow choke, the single nozzle strut has a slightly higher bypass ratio. The single nozzle strut appears to entrain more secondary air for a given primary mass flow rate. Once the choke is reached, the bypass ratio for each strut becomes approximately equal, and is strictly a function of the primary mass flow, independent of the number of nozzles in the strut.
3.5 3.0
Dual Nozzle Strut
Bypass Ratio
2.5
Single Nozzle Strut
2.0 1.5 1.0 0.5 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Primary Mass Flow Rate (lbm/s)
Figure 6.3 Bypass ratio versus primary mass flow rate for single and dual nozzle struts.
The bypass ratio provides a measure of the effectiveness of the momentum exchange for the ejector in a propulsion application. As discussed in Chapter 1, the ideal operating condition from an entrainment stand point occurs when the peak bypass ratio
124 occurs at the same primary flow operating conditions as the secondary mass flow choke. For the chamber pressures examined in this study, the highest bypass ratio occurred for the lowest chamber pressure examined. Thus, the peak bypass ratio for each strut would occur at a chamber pressure lower than those tested in this study, and would be well below the chamber pressure for choked secondary flow. A single test of each strut was conducted to determine the suction ratio for lower pressure ratios. In this series of tests, the set point pressure ratio was decreased until a ratio of 2 was reached in each strut. This set point is the lowest operation point which maintains a choked primary flow. Figure 6.4 shows the bypass ratio versus the pressure ratio for the low pressure ratio tests for the dual and single nozzle struts. The highest
5
Bypass Ratio
4
3
2
1
0 0
5
10
15
20
25
30
Set Point Pressure Ratio Single Tests Dual Nozzle Low Pressures
Single Nozzle Low Pressures
Repeated Tests Dual Nozzle Repeated Values
Single Nozzle Repeated Values
Figure 6.4 Bypass ratio versus pressure ratio for the dual and single nozzle struts with low pressure test data.
125 bypass ratio determined from the low pressure tests occurred at the lowest set point. At these chamber pressures, the nozzle would be significantly over expanded and would be subject to separation and to shocks forming inside the nozzle which would decrease the efficiency of the rocket performance.
Increasing the duct cross-sectional area or
decreasing the nozzle exit area should move the peak towards the choke point; however, this would also change the characteristics of the duct, so the maximum mass flow would change.
6.2
Pressure Distribution
Figures 6.5 through 6.9 show plots of the wall pressure distributions for chamber pressures below the secondary flow choke point in the single and dual nozzle struts. Each plot shows the top and side wall pressure ratios for approximately equivalent primary mass flow rates. For the lowest set point pressure ratio in each strut (6.5 and 3.5), the wall pressure distributions appear to be almost identical. As the primary mass flow rate (e.g., set point pressure ratio is increased), the pressure distributions begin to separate. The pressure distribution in the strut gap region and in the first 15 inches of the mixing duct show similar trends; however, the pressure drop in this region is larger for the single nozzle strut than for the dual nozzle strut for approximately equal primary mass flow rates. This increased pressure drop also corresponds to a slightly larger secondary mass flow as was seen in the mass flow comparison plot (Figure 6.2).
126
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
6.5
Primary Mass Flow (lbm/s)
0.33
0.8
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
3.5
Primary Mass Flow (lbm/s)
0.36
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.5 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.3 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
13.2
0.8
Primary Mass Flow (lbm/s)
0.67
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
6.8
Primary Mass Flow (lbm/s)
0.70
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.6 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 0.7 lbm/s).
127
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
20.2
0.8
Primary Mass Flow (lbm/s)
1.03
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
10.2
Primary Mass Flow (lbm/s)
1.05
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.7 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.05 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
27.2
0.8
Primary Mass Flow (lbm/s)
1.39
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
13.5
Primary Mass Flow (lbm/s)
1.39
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.8 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.39 lbm/s).
128
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
33.8
0.8
Primary Mass Flow (lbm/s)
1.73
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
16.9
Primary Mass Flow (lbm/s)
1.74
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.9 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 1.74 lbm/s).
Figure 6.10 shows the mixing duct wall pressure distribution plots for the single and dual nozzle struts at set point pressure ratios of 40.5 (single nozzle) and 20.4 (dual nozzle). At these set points, the secondary flow has reached a choke in the strut gap region. The general trend for pressure recovery in this plot follows the low pressure trend. The wall pressure ratio drops through the strut gap region reaching the sonic limit (5.28) at the last pressure tap in the strut gap. The pressure ratio continues to drop just past the strut until it reaches some minimum value and then begins to recover. Both struts indicated a recirculation region at the top wall just downstream of the strut. The pressure ratio has completely recovered by 23 hydraulic diameters.
129
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
40.5
0.8
Primary Mass Flow (lbm/s)
2.07
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single
Top Wall Single
Side Wall Dual
Top Wall Dual
Set Point (Pc/Pb)
20.4
Primary Mass Flow (lbm/s)
2.11
0.0 -10
0
10
20
30
40
50
Position (x/Dh)
Figure 6.10 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.1 lbm/s).
Figures 6.11 through 6.13 show the pressure distribution for the single and dual nozzle duct at approximately equivalent primary mass flow rates for operating conditions at or above the secondary flow choke. These plots show a high pressure trend for the single nozzle strut. The dual nozzle strut wall pressure distribution in these plots was between the high and low pressure trends as described in Section 5.2.4. The plots of the highest two mass flows for each strut exhibit high pressure trends. For these two cases, the pressure recovery region occurs farther downstream for the single nozzle strut than it does for the dual nozzle strut. The pressure recovery curves have significantly different slopes. The dual nozzle recovery appears to be much steeper over the first portion of the recovery region, then begins to asymptotically approach a value of one. For the single
130
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
47.2
0.8
Primary Mass Flow (lbm/s)
2.41
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
24.0
Primary Mass Flow (lbm/s)
2.47
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.11 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.45 lbm/s).
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
53.8
0.8
Primary Mass Flow (lbm/s)
2.74
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
27.4
Primary Mass Flow (lbm/s)
2.82
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.12 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 2.78 lbm/s).
131
Pressure Ratio (P/Pos)
1.2
Single Nozzle Strut
1.0
Set Point (Pc/Pb)
60.5
0.8
Primary Mass Flow (lbm/s)
3.10
Dual Nozzle Strut
0.6 0.4 0.2
Side Wall Single Side Wall Dual
0.0 -10
0
10
20
30
Set Point (Pc/Pb)
30.6
Primary Mass Flow (lbm/s)
3.16
Top Wall Single Top Wall Dual 40
50
Position (x/Dh)
Figure 6.13 Pressure distribution comparison between single and dual nozzle struts (primary mass flow = 3.13 lbm/s).
nozzle strut, the curve appears to have a lower slope which increases as the flow moves downstream. At equivalent mass flow rates, the pressure recovery for the dual nozzle strut is much better than that of the single. This is believed to be due to the pressure of the primary flow at the exit of the nozzle. From simple isentropic flow relations, it can be shown that the nozzle exit pressure for the dual nozzle strut is approximately half of the nozzle exit pressure for the equivalent mass flow in the single nozzle strut. This lower pressure seems to lead to a quicker pressure recovery.
6.3
Flow Visualization
As discussed in numerous literature sources [9, 10, 25, 42], the flow in an ejector mixing duct experiences a series of shock and expansion waves as the pressure attempts
132 to recover to the atmospheric value at the exit. Experiments were performed to capture shadowgraph images of the PRC ejector system to visualize any shock structures and correlate them to the experimental results [37]. It was found that pressure distribution trends in the mixing duct were a function of the primary mass flow rate rather than the nozzle exit pressure [43]. The shadowgraph images were taken while the pressure was ramped up, and while the tests were at quasi-steady state. The shadowgraphs were then compared to the spatial pressure data taken along the top and side walls of the duct. Figure 6.14 shows a series of four shadowgraphs at steady state conditions for four different chamber pressures. These images are representative of ramping up the chamber pressure to a set point pressure ratio of 47.2. Figure 6.14a shows a steady state image at a set point pressure ratio of 20.2. Barrel shocks can be seen emanating from the nozzle and terminating in a Mach disk at a location approximately 0.62 hydraulic diameters downstream of the nozzle exit. Figure 6.14b shows the steady state image at a pressure ratio of 33.8. In this figure, the barrel shocks have stretched and the Mach disk has widened and moved to a position approximately 2.4 hydraulic diameters downstream of the nozzle exit. In addition, weaker shock structures appear inside the barrel shocks. These weaker shocks are believed to emanate from the corners of the nozzle. Figure 6.14c shows the steady state image at a set point pressure ratio of 40.5. Here the barrel shocks have stretched even farther. The Mach disk does not appear as sharp in the image and has moved to a position approximately 3 hydraulic diameters downstream. Figure 6.14d shows the steady state image at a chamber pressure of 47.2. Here the barrel shocks have stretched even further, and intersect at a point approximately 4.8 hydraulic diameters downstream. The Mach disk has completely disappeared at this point.
133 The plume transition from to 40.5 to 47.2 has several interesting features. First, this transition is accompanied by a distinct change in pitch of the audible ejector “roar.” The mixing duct pressure distribution plots also show a change in trend.
The
shadowgraphs at higher chamber pressures did not reveal any new structure. The only changes in the shadowgraphs were additional stretching and widening of the barrel shock. The transition does not always occur at exactly the same set point pressure ratio. However, it is currently unknown to what extent other environmental factors such as temperature and humidity affect the flow transition.
Barrel Shock Mach Disk
a)
b) Nozzle Exit
c)
d)
Figure 6.14 Series of images depicting chamber pressure ramp up for single nozzle strut: (a) Pc/Pb = 13.3, (b) Pc/Pb = 33.8, (c) Pc/Pb = 40.5, and (d) Pc/Pb = 47.2.
The dual nozzle shadowgraphs revealed a more complex shock structure primarily due to the existence of an additional nozzle, as well as the lower pressures associated with the equivalent mass flow rates. Figure 6.15 shows four images of steady state shadowgraphs for the dual nozzle strut at four different chamber pressures. The four
134 images represent the ramp up process for the dual nozzle strut to a set point pressure ratio of 30.6. Figure 6.15a shows the steady state image for a set point pressure ratio of 19.6. Similar to the single nozzle images, barrel shocks emanate from the nozzles, and terminate in Mach disks approximately 1.8 hydraulic diameters downstream. Figure 6.15b shows the shadowgraph image at a steady state pressure ratio of 20.4. The barrel shocks in this image are more stretched out and still terminate in Mach disks. The barrel shocks for each of the dual nozzles are not symmetric. The inner sections of the shocks are being influenced by the shocks from the other nozzle. Figure 6.15c shows the shadowgraph image at a steady state pressure ratio of 24.0. The barrel shocks are stretched even farther, and the Mach disks have disappeared. For the dual nozzle strut, the transition from the low to high pressure trend occurs around this set point pressure ratio (24.0).
Figure 6.15d shows the shadowgraph image for the steady state
a)
b)
c)
d)
Figure 6.15 Series of images depicting chamber pressure ramp up for dual nozzle strut: (a) Pc/Pb = 16.8, (b) Pc/Pb = 20.4, (c) Pc/Pb = 24.0, and (d) Pc/Pb = 30.6.
135 pressure ratio of 30.6. This chamber pressure is above the transition pressure. In the figure, the outer portions of the barrel shocks have extended and intersect approximately 4.8 hydraulic diameters downstream of the strut. This is approximately the same location where the single nozzle shocks intersected for a set point pressure ratio of 47.2. Mixing duct pressure profiles for the dual nozzle strut were next overlaid on the shadowgraph images to correlate shock structures with the measured values. Once again, higher chamber pressures more insightful. Figure 6.16 shows a plot of the top wall pressure distribution plotted against the axial location for a set point pressure ratio of 30.7 (see Figure 5.38) overlaid on the shadowgraph image for that pressure. The high pressure trend is clearly visible. In this region of the duct, the pressure ratio is dropping to a constant value of approximately 0.3. At approximately 4.8 and 8.4 hydraulic diameters
1.1 Pressure R atio(P/P (P/Po Pressure Ratio b)
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0
2
4
6
8
Position in Duct (in)
Figure 6.16 Plot of top wall pressure distribution with shadowgraph image (dual nozzle strut Pc/Pb = 30.6).
136 downstream, there are discontinuities in the pressure ratio. At each of these locations, there is an increase in the pressure ratio consistent with crossing a shock. If the trailing edges of the barrel shocks are extended to the wall, they will hit the wall at approximately these locations. It is believed that the discontinuities are a result of these shocks. 6.4
Analytical Comparisons
A simplified classical axisymmetric model based on Fabri’s model (see Chapter 2) was created and used to estimate the bypass ratio for the non-axisymmetric ejector of this dissertation. An equivalent axisymmetric ejector was identified that had the same nozzle area ratio, the same mixing duct cross-sectional area relative to the nozzle exit area, and the same secondary flow inlet area relative to the duct area. Each model (supersonic, saturated supersonic, and mixed) was used to estimate the bypass ratio over the range of chamber pressures examined. Results for each model over the full range of pressures are presented, although at any pressure only one regime will exist. 6.4.1
Single Nozzle Strut
Figure 6.17 shows the bypass ratio versus the ratio of the stagnation pressure of the primary flow to that of the secondary flow for the single nozzle strut. All three models (mixed flow, saturated supersonic flow, and supersonic flow) are shown on the same plot. For a given pressure ratio, the regime which predicts the lowest bypass ratio is taken as the regime which will exist. Since the supersonic regime and the mixed regime are lower than the saturated supersonic regime for all pressure ratios examined, the model predicts that the flow will not enter the saturated supersonic regime.
137
8 7
Bypass Ratio
6
Mixed Flow Regime
5 4
Saturated Supersonic
3
Supersonic
2 1 0 0
20
40
60
80
PressureRatio Ratio(P (Pc/Pb) Pressure c/Pb)
Figure 6.17 One-dimensional model for axisymmetric ejector of equivalent geometry to single nozzle strut PRC ejector.
By taking the lowest bypass ratio predicted at any pressure ratio, a smooth curve for the ejector was created as shown in Figure 6.18. Experimental data from the single nozzle ejector is also shown in the figure. Qualitatively the predicted trends of the plots agree with the experimental data; however, as can be seen in the figure, the analytical models over predict the bypass ratio for a given pressure ratio. The theoretical values were from 25% to 53% higher than the experimental values. As mentioned earlier, the duct geometry can lead to a non-uniform velocity profile. Significant boundary layers will exist along the duct walls and in the duct corners. The maximum predicted bypass ratio for the set point pressure ratios of the experiment is around 4.75 and the ejector would be operating in the mixed regime for this pressure ratio. The model predicts a transition from the mixed regime to the supersonic regime will occur around a pressure
138 ratio of 50. Experimental evidence indicated that the transition from the mixed flow regime to the supersonic regime occurs around a pressure ratio of 34.
5
Bypass Ratio
4 3
Theory Experimental Data
2 1 0 0
20
40
60
80
Pressure Ratio (Pc(Pc/Pb) /Pb) Pressure Ratio
Figure 6.18 Comparison of theoretical symmetric ejector model with experimental data for non axisymmetric single nozzle ejector.
6.4.2
Dual Nozzle Strut
For the dual nozzle strut, an analytic model was created with a primary flow inlet area equal to the combined areas of the two nozzles. Figure 6.19 shows a plot of the predicted bypass ratio versus the pressure ratio for an axisymmetric ejector with equivalent geometry to the dual nozzle strut.
As with the single nozzle strut, the saturated
supersonic regime predicted higher bypass ratios than either the mixed flow model or the supersonic flow model. In general the models over predict the bypass ratio for a given pressure ratio. At very low set point pressure ratios, the mixed flow regime model predicted a peak bypass ratio and, as the pressure ratio is decreased below that point, the
139 bypass ratio drops. This does not agree with the experimental evidence. At these pressures, the ejector would be operating in the mixed flow with separation regime which was not modeled. The model predicts that the flow will transition from mixed flow to supersonic flow around a pressure ratio of 25. The experimentally determined mass flow rate clearly indicates a choke of the secondary flow which indicates the ejector is operating in the supersonic or saturated supersonic regime for pressure ratios above 20. According to the analytical models, the ejector would only operate in the supersonic and in the mixed regime. For this geometry the theoretical prediction is from 33% to 54% higher than the experimental data.
Bypass Ratio Pressure Ratio (Pc/Pb)
5 4 3
Theory Experimetnal Data
2 1 0 0
20
40
60
80
Pressure Ratio (Pc/Pb)
Figure 6.19 Comparison of Fabri models with dual nozzle strut data.
140 It is believed that there are two major factors which contribute to the poor predictions of the axisymmetric model for this strut ejector setup.
The first is the
geometry of the duct. Because of the rectangular cross section, the duct will have significant corner effects which will retard the flow and increase the boundary layer growth. This boundary layer will reduce the effective area through which the secondary flow will pass. The geometry will also cause a non-uniform velocity profile across the duct which invalidates one of the assumptions of Fabri’s models. The second major factor contributing to the discrepancy between the predicted value and the experimental value is the effect of the base area of the strut. In Fabri’s model, the base area was negligible because of its minimal size relative to other duct areas. In the PRC strut ejector setup, the base area is a significant size and, as was seen in the pressure distribution plots, causes a recirculation region. This region will result in losses in the flow, and induce turbulence. An approximate base pressure term was included in the analytical model, however, it did not compensate for all of the effects of the strut. Figure 6.20 shows a plot of the predicted bypass ratios for equivalent geometry axisymmetric ejectors for both the single and dual nozzle struts. The predicted trends agree with the experimental trends qualitatively. That is, for a given pressure ratio, the single nozzle strut induces more secondary mass flow. At a fixed mass flow (pressure ratio in the dual nozzle strut that is half the pressure ratio in the single nozzle strut), the dual nozzle strut induces more secondary mass flow.
141
5
Bypass Ratio
4 3
Single Nozzle Prediction
2
Dual Nozzle Prediction
1 0 0
20
40
60
80
Pressure Ratio (Pc/Pb) Figure 6.20 Theoretical bypass ratio for axisymmetric ejectors with geometry ratios equivalent to those in the single and dual nozzle PRC ejectors.
6.5
CFD Analysis
Since the simplified one-dimensional model predictions were not close to the experimental data, a CFD analysis of the ejector was performed. Several of the single nozzle experiments were simulated using the Fastran Computational Fluid Dynamics code by ESI. This work was done in a parallel study by Balasubramanyan [20, 44]. The studies analyzed the flow in the ejector in a piecewise fashion. The primary focus of the effort was to attempt to model the mixing duct behavior. The inlet section of the duct which consisted solely of secondary flow was modeled as a two-dimensional constant area duct, and the rocket nozzle in the strut was modeled in three dimensions to provide a picture of the primary flow stream entrance into the mixing duct. The results of the two efforts were then combined to perform a two-dimensional and a limited threedimensional evaluation of the mixing duct.
142 The ejector inlet was first modeled from the entrance of the constant area section of the duct (neglecting the contoured inlet) to the exit plane of the strut (the location where the secondary flow enters the mixing duct. The flow entering the straight section of the duct was assumed to be uniform and smooth. The model was given an inlet velocity, and a stagnation pressure equal to atmospheric pressure. Several turbulence models were evaluated. The pressure measurements in the strut gap region were used to evaluate the performance of the different models.
A two equation Menter-SST
turbulence model [44] was found to best fit the experimental data as can be seen in Figures 6.21 and 6.22.
0.64 Menter-SST
Pressure Ratio (P/Pos)
0.62
Experimental Strut Gap
0.60 0.58 0.56 0.54 0.52 -9
-8
-7
-6
-5
-4
-3
-2
-1
Distance from Exit Plane (x/D h)
Figure 6.21 Ejector strut gap sidewall pressure ratio (Pc/Pb = 40.4).
0
143
0.64 Experimental Data
Pressure Ratio (P/Pos)
0.62
Menter SST
0.60 0.58 0.56 0.54 0.52 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
Distance from Exit Plane (x/D h)
Figure 6.22 Ejector strut gap sidewall pressure ratio (Pc/Pb = 53.7) [44].
With fairly good agreement in the strut gap region, the embedded rocket nozzle was then modeled. Because of the complex geometry of the nozzle, a three-dimensional model was used for the nozzle. Figures 6.23 and 6.24 show the exit pressure and Mach numbers for the three-dimensional model of the nozzle. Results from the duct inlet and the rocket nozzle models were then combined and used as the inlet conditions to a two-dimensional mixing duct model. An extrapolated boundary condition was applied at the mixing duct exit. By using a two-dimensional model, the results of the top wall cannot be evaluated because of the complex flow phenomena around the strut.
However the sidewall pressures in the mixing duct
compared reasonably well with the experimental data as can be seen in Figures 6.25 and 6.26.
144
Figure 6.23 3-D strut rocket nozzle exit Mach contours.
Figure 6.24 3-D strut rocket nozzle exit pressure contours.
145
1.2
Pressure Ratio (P/Pos)
1.0 0.8 0.6
Experimental Sidewall
0.4
Spalart Allmaras K-Eplison
0.2
Baldwin Lomax Menter SST
0.0 0
10
20
30
40
50
Distance from Exit Plane (x/D h)
Figure 6.25 Sidewall pressures in ejector mixing duct (Pc/Pb = 40.4).
0.9 Experimental Data KE model Spalart Allamars Menter SST Baldwin Lomax
Pressure Ratio (P/Pos)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
10
20
30
40
Distance from Exit Plane (x/D h)
Figure 6.26 Sidewall pressures in ejector mixing duct (Pc/Pb = 53.7).
50
146 Multiple turbulence models were used for the analysis. For the low pressure case, the zero equation Baldwin Lomax and the Menter-SST models predicted the side wall pressures reasonably well throughout the duct. The Menter-SST model more closely predicted the recovery length than the Baldwin Lomax model. Both models predicted the exit pressure fairly accurately. For a pressure ratio set point of 53.7, the high pressure trend is evident in the CFD analysis. For this pressure, the Mentor-SST and the Spalart Albmaras models predicted the sidewall pressure better than the other models. The pressure drop at the entrance to the mixing duct was predicted more accurately using the Menter-SST model. A three-dimensional model of the mixing duct was also simulated at set point pressure ratio of 40.4. For this analysis, compressibility corrections were included in the models. The top wall pressures were compared to the results of the CFD analysis. Figure 6.27 shows the results of the three-dimensional analysis compared to the experimental data. It can be seen in the figure that the recirculation region downstream of the strut is captured by the models; however, the predicted size of the mixing region is not as large as the experimental data indicate. Additionally, the models do not capture the spreading of the mixing layer within the mixing zone very well and the pressure recovery prediction is not as good with the three-dimensional models as was shown for the two-dimensional case.
147
1.2
Pressure Ratio (P/Pos)
1.0 0.8 0.6 Experimental Data
0.4
3-D KE Model with Compressibility 3-D Menter-SST Refined Grid
0.2
3-D Baldwin Lomax Refined Grid
0.0 0
5
10
15
20
25
30
35
40
45
Distance from Exit Plane (x/D h)
Figure 6.27 3-D Pressure profiles at centerline of top-wall (Pc/Pb = 40.4).
50
CHAPTER 7
CONCLUSIONS
The primary focus of the current investigation was the characterization of a threedimensional non-axisymmetric ejector configuration. An experimental investigation of two strut based nozzle configurations provided insight into the pressure distribution, the mass flow entrainment, choking mechanisms, and flow structure in the ejector system. Classical ejector modes of operation were used to classify the ejector operating regimes. Results of the experiment were compared with simple one-dimensional analytical models and a limited CFD effort performed in a parallel study.
7.1
Flow Regimes In the current experiment, the primary nozzles were operated over a range of
chamber pressures which allowed the ejector to operate in both the mixed and the supersonic regimes. For low chamber pressure operating conditions (the mixed regime) the secondary flow remained unchoked in the strut gap as was shown in both the secondary mass flow and the strut gap pressure ratio plots. At high chamber pressures, the ejector was operating in the saturated supersonic regime. The secondary mass flow plot indicated that a choke of the secondary flow had occurred. As the primary mass
148
149 flow was increased, there was a slight decrease of the secondary mass flow. This decrease is indicative of a reduction in minimum area through which the secondary flow can pass. For this operating condition, the minimum area is between the plume of the primary flow and the wall of the duct.
This decrease is somewhat in contrast to
statements by Fabri and Addy who stated that the mass flow becomes invariant with respect to changes in the ratio of exit pressure to primary jet stagnation pressure once the supersonic regime is established. The range of pressures in which this ejector was operated was well above those studied by Fabri and Addy. As the primary flow total pressure increases, so too does the pressure at the exit of the strut nozzle. This would result in an increased deflection angle at the exit of the nozzle which in turn would lead to a smaller minimum area for the secondary flow at the choke location. This effect may also be a result of increased losses attributed to flow disturbances resulting from the nonaxisymmetric characteristics of the duct. At moderate chamber pressures, the secondary mass flow plots indicated a secondary flow choke; however, it is not clear if the choke is an aerodynamic choke in the strut gap or a mass choke in the mixing duct. The pressures in the strut gap region approach the sonic limit, and reach it within uncertainty. However, because of the uncertainty, it cannot be definitively declared an aerodynamic choke or a mass choke. Based on the idealized flow equations, the calculated secondary mass flow is well below the maximum secondary mass flow that could be achieved in the strut gap area for an atmospheric stagnation pressure. This would indicate that the type of choke is a mass addition choke and that an aerodynamic choke never occurs in the ejector. However the boundary layer approximation was based on a simple flat plate approximation on the
150 walls of the duct, and does not account for corner effects or for boundary layer buildup in the inlet, thus the estimate could be low. Because the pressure ratio increases away from the sonic limit as the primary chamber pressure increases, it is clear that at higher pressures, the secondary choke is not in the strut gap region. In a previous investigation, Smith concluded that choked secondary flow occurred around a set point pressure ratio of 33.8 and that this choke was a Fabri mass choke in the mixing duct based on the strut gap pressure ratios [25]. Smith further concluded that this choke moved from the mixing duct to the strut gap region around a set point of 44.2 for the single nozzle strut. Based on the current research, it appears that is not the case. The strut gap pressures begin to increase away from the sonic limit as the primary jet stagnation pressure is increased. It is more likely that the flow in the strutgap region was choking at a lower chamber pressure or the secondary flow was approaching the choked condition but was not fully choked until a set point pressure ratio of 44.2 was reached. In either case, the theory for a constant area ejector dictates that if the flow chokes in the strut gap, it must occur at a lower chamber pressure than a Fabri choke in the same duct.
7.2
Mixing Duct Pressure Distributions
The mixing duct pressure profiles showed two distinct trends for each strut. These trends were labeled the low pressure trend and the high pressure trend in a previous publication because of the apparent connection to the chamber pressure of the primary nozzle, although the development of each pattern in the mixing duct seems to be a function of the primary mass flow rate rather than the chamber pressure. The low pressure trend occurred when the ejector was operating in the mixed flow regime and
151 through a portion of the supersonic regime. The low pressure trend was characterized by a pressure drop in the strut gap region followed by either a pressure recovery starting at the entrance to the mixing duct and ending with a complete pressure equalization with the ambient static pressure by the end of the duct, or by a continued pressure drop in the mixing duct to some minimum pressure followed by a pressure recovery and ending with a complete pressure equalization with the ambient static pressure by the end of the duct. Exit profiles of the mixed flow total pressure indicated a constant, uniform, total pressure across a quadrant of the duct. The flow from the ejector was, therefore, fully mixed by the exit of the mixing duct. When the mixing duct pressure distribution shows the low pressure trend, the length of duct required for complete pressure recovery does not seem to vary much. Both the single and dual nozzle strut pressure distributions completely recovered by approximately 20 hydraulic diameters downstream of the exit plane. For the current ejector geometry, this length corresponds to approximately 17 in. (43 cm) downstream of the strut nozzle exit plane. This length agreed with the single nozzle study carried out by Smith [25], and with the PLIF study carried out by Parkensen, et al. [45]. Thus for both struts, the extra duct length would serve to add losses to the system, and would reduce the effectiveness of the ejector in a propulsion application. The high pressure trend was characterized by a pressure drop in the strut gap followed by a continued pressure drop at the entrance of the mixing duct to a minimum pressure ratio around a value of 0.3.
A pressure ratio between 0.3 and 0.6 was
maintained over a length of the mixing duct and then followed by a recovery region which had a more gradual slope than was seen in the low pressure plots. The length of
152 the region of this lower pressure ratio region was a function of the nozzle chamber pressure (and hence the mass flow rate of the primary fluid). For the high pressure trend, the pressure does not fully equalize with atmospheric pressure by the end of the instrumented duct. The exit total pressure profiles for this region indicate a total pressure gradient across a quadrant of the duct. This is evidence that for the high pressure trend, the flow does not mix completely by the end of the duct. Instead at the exit, a supersonic core flow is present surrounded by a lower velocity secondary flow. In the high pressure trend, pressure discontinuities were apparent in the mixing duct plots.
These
discontinuities were evidence of shock structure inside of the duct impinging on the duct walls. The change from the low pressure trend to the high pressure trend occurred around the same mass flow rate for both struts, emphasizing the dependence on primary mass flow rate. Overlaid plots of the single and dual nozzle strut wall pressure profiles for the same primary flow mass flow rate indicated that the magnitude of the chamber pressure had an apparent influence on the location of the start of the recovery region. The change in trend, from the low to high pressure trend, appears to be most strongly influenced by the primary mass flow rate. The location of the start of the recovery region for equivalent mass flow rates in the two struts was not equal. In the single nozzle strut, the location of the recovery region was much farther downstream than in the dual nozzle strut. This indicates that the recovery is influenced by the pressure of the primary fluid. As the chamber pressure increases, the recovery region moves downstream.
In propulsion
applications where complete mixing important, there may be advantages to operating with multiple lower pressure nozzles rather than a single higher pressure nozzle.
153 7.3
Mass Flow Entrainment
The induced mass flow and the bypass ratio showed strong dependencies on the primary mass flow rate of the ejector and weak dependencies on primary flow pressure at the entrance of the mixing duct. Overlaid plots of the secondary mass flow versus the primary mass flow showed that the two struts exhibited very similar behavior. Until the secondary flow chokes, the single nozzle strut induced slightly more secondary mass flow at an equivalent primary mass flow rate than the dual nozzle strut. A similar trend was seen for the bypass ratio. For an equivalent primary mass flow rate, the single nozzle strut had a slightly higher bypass ratio at primary mass flow rated below the secondary flow choke point. These results show the importance of the primary jet momentum in the entrainment of secondary air flow.
As discussed, an ejector acts as a momentum
exchange device. Momentum from the primary jet is imparted on the secondary fluid. For this setup, the velocity of the flow out of the nozzle is very high (around Mach 3). The momentum of the primary jet consists of a mass flux term and a pressure flux term. At the exit of the mixing duct, the mass flux term is an order of magnitude more than the pressure flux term. For the dual nozzle strut, the pressure flux term becomes even smaller because the pressure at the exit is half of the pressure for an equivalent mass flow in the single nozzle strut. Since the mass flux term is dominant, the dependence on the primary mass flow becomes apparent in the plots. The pressure flux term, however, is not negligible and is may account for differences in the mass flow entrainment and the bypass ratio at equivalent mass flow rates. As mentioned earlier, the recovery length for the high pressure trend plots was attributed to the primary flow exit pressure. Since the bypass ratio is an important efficiency parameter, fewer nozzles seem to be more
154 effective in exchanging momentum; however, once the secondary flow chokes, efficiency becomes less important than mixing length. Because the secondary flow chokes and begins to drop as the primary flow is increased, the momentum exchange between the primary and secondary flow does not improve once the choke point is reached. The two flows are assumed to remain distinct until the secondary flow choke point is reached somewhere in the mixing duct. After the choke, the majority of the mixing and the momentum exchange is assumed to occur. As the primary pressure is increased, the mixing between the two flow streams becomes less efficient and the duct is no longer long enough for complete mixing to occur.
7.4
Comparison to Analytical Models
Comparison of the experimental work with classical one-dimensional analysis techniques of Fabri and Addy showed that the performance trends of bypass ratio were similar to the trends for an axisymmetric case. The simplified one-dimensional models which were used to evaluate the current ejector system predicted trends similar to those seen in the experimental data. While one-dimensional models were fairly accurate for axisymmetric experimental cases, non-axisymmetric effects in the current system result in significant losses in the ejector which were not captured in these models. The bypass ratio was significantly overpredicted around 30% for both single and dual nozzle ejectors. The predicted transition point from mixed to supersonic flow was at a pressure ratio 32% lower than the predicted value for the single nozzle strut and 20% lower for the dual nozzle strut.
These differences are evidence of losses associated with the current
configuration. These losses are believed to be attributed to both the effect of flow
155 separation due to the significant base region of the strut, and to the geometry of both the mixing duct and the nozzle.
The non-axisymmetric characteristics of the current
geometry appear to add losses that speed up the onset of the supersonic flow regime. The trends of the classical models agreed with the trends of the current ejector system. It is believed that a geometry effect could be included in the models which would improve the performance predictions.
With corrections, similar models may
predict global characteristics well; however, without significant data from other ejector configuration, these terms would be specific to the current ejector setup and would not add much practical value to generalized modeling. A base area effect was added to the model for comparison to the PRC data. For Fabri’s ejector, the base area was negligible relative to the areas of the primary flow and secondary flow inlets; however, for both single and dual nozzle struts there is a significant portion of the strut which is unused. As the secondary flow and primary flow enter the mixing duct, a recirculation region is formed immediately downstream of the strut as was seen in the mixing duct pressure distribution plots. Pressure measurements on the downstream face of the strut indicated that the pressure in this region was approximately equal to the pressure at the strut gap region exit. So, an additional pressure term was added to the momentum equation to account for this effect.
7.5
CFD Analysis
Madhan modeled the single nozzle strut in a CFD code to evaluate turbulence models. The analysis was performed using a two-dimensional duct at set point pressure ratios of 20.2, 40.4 and 53.7. The secondary flow inlet was artificially adjusted until the
156 pressures in the strut gap region matched the data from the experiment. The strut rocket nozzle was modeled in a full 3-D mode. These two CFD results were then combined into a two-dimensional model with an extrapolated exit boundary condition. Mixing duct pressure data from the code was compared with the experimental data from these experiments. The analysis showed that the Spalart Allamart model showed reasonably good agreement with the experimental data in both the high pressure and low pressure trends. A three-dimensional model of the mixing duct was also analyzed for a set point pressure ratio of 40.4. The pressures in the mixing duct showed good agreement with the trends of the experimental result; however, the recirculation region just downstream of the strut was not adequately captured by the CFD model. A compressibility correction added to the model improved the agreement between the mixing duct pressures. A full set of the results from the experiments described in this dissertation are included in Appendix D.
7.6
Momentum Effects
The experiments revealed that the entrained mass flow for the ejector system is most strongly influenced by the total primary mass flow and hence by the primary jet momentum. The total momentum of the primary jet consists of two major terms, the mass flux (mass flow times the velocity) and the pressure flux (static pressure times the area). Because of the high velocity, the mass flux term will be the dominate term in this expression. In a series of experiments on a ducted rocket with a single nozzle of variable geometry, Djijkstra, et al. reported that the entrainment depended strongly on the configuration of the mixer, and that the nozzle exit pressure did not seem to affect the
157 entrainment significantly [2].
These results were similar to those found in this
experiment. However, a slightly higher secondary mass flow was achieved for the single nozzle than for the dual nozzle strut at the same mass flow rate. For the same mass flow rate, the stagnation pressure of the single nozzle strut is operated at double the chamber pressure of the dual nozzle strut as discussed earlier. Thus the pressure at the exit of the nozzle in the single nozzle strut will also be twice the pressure at the exit of the dual nozzle strut. When the exit pressure of the nozzle is greater than the ambient pressure in the duct, the nozzle becomes under expanded, and the plume begins to spread outward with two results: increased plume area giving a larger shear mixing region, and decreasing the area for the secondary flow. Based on the nozzle geometry and the strut gap pressure just before the mixing duct entrance, this expansion will occur at a set point pressure ratio between 20.4 and 24.0 for the dual nozzle strut and between 27.2 and 33.8 in the single nozzle strut. This is also the approximate location where the secondary mass flow levels off indicating a choke of the secondary flow as was seen in Figures 5.1 and 5.25. However the pressure for the dual nozzle strut will be much lower than the primary flow exit pressure for the single nozzle strut. Thus when the flow exits the dual nozzle, it will expand a greater degree providing a larger plume for a single nozzle. A direct comparison to Dijkstra’s experiments cannot be made because of the significant geometry differences. However, the trends from both experiments indicate that the primary mass flow rate is the most significant variable in determining the amount of entrained air. From the results of the experimental work, one advantage of multiple strut nozzles is that a higher total mass flow is achieved at a lower pressure, so for a given
158 chamber pressure, the bypass ratio is increased. However, because the mass flow is increased, the transition from the low pressure trend to the high pressure trend occurs at a lower primary operating pressure. Once this high pressure trend is established, the required mixing length for the duct increases significantly. It is believed that comparison of a single nozzle of the same area ratio with an exit area equal to the total primary flow exit area for the dual nozzle struts would not entrain as much secondary mass flow and would have an adverse effect on the mixing length.
7.7
Future Work There are several factors in an ejector design that affect operation. In the current
experiment, there were only two variables, the chamber pressure and the number of nozzles in the strut. Ejector optimization involves varying several other factors, such as the ratios of the inlet areas, the primary nozzle area ratio, the secondary flow stagnation pressure, the ratio of the secondary flow inlet area to the mixing duct area, and the composition of the operating fluids to name a few. The data presented in this dissertation could be used as a baseline for evaluating CFD models of the ejector. While the results of the experiment do not provide detailed three-dimensional flow field information, they do provide a baseline of data for a complex three-dimensional system. Such data can be used to benchmark CFD models which may be appropriate for more complicated ejector systems. Further experiments should be done modifying the geometry of the duct. If the strut gap cross-sectional area is reduced, the secondary flow can be forced to choke in the strut gap region, adding a definitive saturated supersonic regime. This in turn may result
159 in improved mixing at higher set point pressure ratios. Adding a third and fourth nozzle would allow for better comparison to some of the non-axisymmetric experimental work at other universities. With the strut base full of nozzles, the geometry more closely resembles a two-dimensional ejector system, simplifying the analysis considerably and making for a more direct comparison to other two-dimensional ejector configurations. Finally a wider mixing duct would allow for multiple struts to be installed in the duct. This type of system would allow investigations of the interaction between multiple primary and secondary flow stream streams. Such a case would more closely model a strut based RBCC engine. Three-dimensional CFD modeling of the current configuration (both single and dual nozzle struts) would make the variations between the dual and single nozzle strut more apparent. For the simple two-dimensional case, the CFD code was able to produce fairly good results for the centerline sidewall pressure measurements. However for the dual nozzle strut, this model will not be as accurate. The pressure measurements in the mixing duct were only taken along the centerline of the top and side walls. A more complete mapping of the pressure field in this region of the duct would be useful for full three-dimensional modeling of the ejector. The CFD model also focused on the mixing duct exclusively. The secondary flow inlet was artificially added by modifying inlet parameters until the strut gap pressures matched the experimental data. This code could not be used for other geometries unless experimental data was available. The current model could be improved to predict the strut gap pressures as well as the mixing duct pressure.
160 More imaging of the flow streams in both the mixing duct and in the inlet could provide additional insight into the flow behavior in these areas.
The rectangular
geometry of the duct is believed to significantly retard the flow in the corners. Use of a Particle Imaging Velocimeter to map the velocity fields in this region would improve the mass flow determination for this region, and would provide detailed flow field information for evaulating CFD models. In the mixing duct, the shadowgraph images revealed a complex shock structure exists in this region. Schlerien imaging in this region could reveal more detail of the shock train that occurs downstream of the primary jet. PIV imaging in this are could also provide a better evaluation of the completeness of the mixing between the flow streams. Seeding of the secondary flow with a flourescencing element and performing another PLIF study for the duct would also provide insight into the mixing phenomena. Ejectors have shown potential for use in advanced propulsion concepts. From a practical standpoint, the geometry of such vehicles will most likely have nonaxisymmetric characteristics. The current study shows that these effects influence the performance of the ejector. Before such engines can be developed and optimized, a better understanding of the fluid mechanics in the system is necessary. This research provides a baseline of data which can be used to evaluate a non-axisymmetric ejector configuration. A cold flow facility provides a relatively safe way to investigate the flow behavior. Experiments, such as those conducted here, can provide data for evaulating CFD codes for use with more complex geometries, and with more complicated flow phenomena.
APPENDICES
161
APPENDIX A
SYSTEMATIC UNCERTAINTY VALUES
162
psig
Strut Gap Pressure Tap 1 Strut Gap Pressure Tap 2 Strut Gap Pressure Tap 3 Strut Gap Pressure Tap 4 Strut Gap Pressure Tap 5 Strut Gap Pressure Tap 6 Strut Gap Pressure Tap 7 Strut Gap Pressure Tap 8 Strut Gap Pressure Tap 9 Strut Gap Pressure Tap 10 Secondary Flow Stagnation Pressure (at Fairing) Secondary Flow Static Pressure (at Fairing) Exit Stagnation Pressure (Pitot probe) Exit Static Pressure (Pitot probe) Exit Side Wall Pressure (Pitot probe) Strut Rocket Chamber Pressure Scani-Valve Top Wall Pressure Scani-Valve Side Wall Pressure Strut Rocket Chamber Temperature Secondary Flow Temperature (at inlet)
Pg1 Pg2 Pg3 Pg4 Pg5 Pg6 Pg7 Pg8 Pg9 Pg10 Pos Ps Poe2 Pe2 Pe Pc Ptw Psw Tc Tos
-14.7 to 30 psig
-14.7 to 30 psig
0 to 1000 psia
0 to 300 psig
-14.7 to 32 psig
0 to 300 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
-14.7 to 32 psig
Range
a
0
0
0.0006476
0.0005989
0.149
0.009034
0.008626
0.065
0.004655
0.005407
0.004904
0.005809
0.005593
0.005862
0.004563
0.008709
0.005427
0.003893
0.022
0.012
b
0
0
-0.002607
-0.000182
-0.736
-0.063
0.04
-0.135
-0.019
-0.023
-0.02
-0.026
-0.025
-0.025
-0.018
-0.041
-0.022
-0.015
-0.106
-0.058
* Systematic Unceratinty Constants: For Voltage Reading (V) the systematic uncertainty is given by: a*(V^2)+b*V+c
C
C
psig
psig
psig
psia
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
psig
Units
Measured Quantity
c
1
1
0.03
0.007275
2.458
0.159
0.111
0.162
0.038
0.057
0.043
0.063
0.059
0.065
0.035
0.112
0.057
0.034
0.0309
0.163
Systematic Uncertainty Constants*
Table A.1 Systematic uncertainty constants for instrumentation.
163
APPENDIX B
REGRESSION UNCERTAINTY ANALYSIS FOR CALIBRATION
The following pages contain the Mathcad sheets used for calculating the transducer calibration constants and the equation for the systematic uncertainty of the transducers based on the voltages. All transducers were calibrated with either an air or water based dead weight tester.
164
165
166
167
168
169
APPENDIX C
MATHCAD CALCULATION SHEETS
The following pages contain the Mathcad worksheets used for the data analysis.of an individual test date. The data from tests at nine different setpoint pressure ratios on a given date are imported into the following sheet to produce the test average values for each set point. The six worksheets are 1. Data setup sheet. 2. Inlet Mach number Calculation sheet. 3. Exit Mach Number Calculation Sheet. 4. Strut Gap Pressure Ratio Calculation Sheet. 5. Mixing Duct Pressure Ratio Calculation Sheet. 6. Mass Flow and Suction ratio Calculation Sheet.
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
APPENDIX D
TEST RESULTS (AVERAGE VALUES)
215
216 Table D.1 Test averages for single nozzle strut Single Nozzle Test Data Averages (10 Tests) Nozzle Area Ratio = 4.66 Mixing Duct Cross Section : 4 in x 3.5 in Nozzle Hydraulic Diameter = 0.83 in Po2/Pb = 1 Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 6.5 13.2 20.2 27.2 33.8 40.5 47.2 53.8 60.5
U 0.5 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.8
Secondary Flow Stagnation Pressure (psi)
Po1 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7
U_Po1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Secondary Flow Inlet Temperature (C) T1 21.4 20.1 19.3 18.8 18.2 18.2 18.1 18.0 17.7
U_T1 6.1 6.6 6.2 6.6 6.4 5.9 6.5 5.1 6.0
Secondary Flow Static Pressure At Fairing (psi)
P1 14.5 14.3 14.1 14.0 13.9 13.9 13.9 13.9 13.9
U_P1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Exit Stagnation Pressure (psi)
Exit wall Static Pressure (psi)
Poe 15.3 16.0 17.0 18.0 18.9 19.6 22.2 28.6 31.9
Pe 14.7 14.7 14.8 14.8 14.8 14.9 14.7 14.5 14.4
U_Poe 0.3 0.3 0.3 0.3 0.3 0.3 1.8 2.9 3.9
U_Pe 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.5
Exit Static Chamber Pressure Pitot Temperature (C) (psi) Pe2 U_Pe2 Tc U_Tc 14.7 0.2 16.6 7.5 14.7 0.2 9.7 8.2 14.7 0.2 7.3 7.2 14.8 0.2 6.4 7.2 14.8 0.2 5.7 7.6 14.8 0.2 5.9 6.6 14.8 0.2 6.2 7.9 14.7 0.2 6.3 6.1 14.7 0.2 6.7 6.7
Strut Gap Pressures (psi) Positon 1 P1 U_P1 13.9 0.1 12.9 0.1 11.7 0.1 10.5 0.1 9.5 0.1 9.0 0.1 9.1 0.1 9.2 0.1 9.3 0.1
Postion 2 P2 U_P2 13.9 0.1 12.9 0.2 11.7 0.2 10.5 0.1 9.5 0.1 8.9 0.1 9.0 0.1 9.1 0.1 9.3 0.1
Position 3 P3 U_P3 13.9 0.1 12.8 0.1 11.6 0.1 10.4 0.1 9.3 0.1 8.7 0.1 8.7 0.1 8.9 0.1 9.1 0.1
Position 4 P4 U_P4 13.9 0.1 12.8 0.1 11.5 0.1 10.3 0.1 9.2 0.1 8.5 0.1 8.5 0.1 8.7 0.1 8.9 0.1
Strut Gap Pressures (psi) Position 6 P6 U_P6 13.9 0.1 12.8 0.1 11.6 0.1 10.3 0.1 9.1 0.1 8.4 0.1 8.4 0.1 8.6 0.1 8.8 0.1
Position 7 P7 U_P7 13.9 0.1 12.7 0.1 11.5 0.1 10.1 0.1 8.9 0.1 8.0 0.1 8.0 0.1 8.2 0.1 8.5 0.1
Position 8 P8 U_P8 13.9 0.1 12.8 0.1 11.6 0.1 10.3 0.1 9.1 0.2 8.2 0.2 8.3 0.2 8.5 0.2 8.8 0.1
Position 9 P9 U_P9 13.9 0.1 12.8 0.1 11.5 0.1 10.2 0.1 9.0 0.1 8.1 0.1 8.1 0.1 8.3 0.1 8.6 0.1
Position 10 P10 U_P10 13.9 0.1 12.8 0.1 11.5 0.1 10.2 0.1 8.9 0.1 7.9 0.1 7.9 0.1 8.2 0.1 8.6 0.1
Position 5 P5 U_P5 13.9 0.1 12.8 0.1 11.5 0.1 10.3 0.1 9.1 0.1 8.4 0.1 8.4 0.1 8.6 0.1 8.8 0.1
217 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
6.5 Pr 0.946 0.950 0.955 0.958 0.960 0.961 0.962 0.963 0.965 0.965 0.966 0.966 0.968 0.968 0.968 0.969 0.971 0.970 0.971 0.971 0.975 0.972 0.973 0.975 0.978 0.981 0.985 0.988 0.990 0.992 0.994 0.995 0.996 0.997 0.997 0.999 0.998 0.999 0.999 1.000 1.000 1.000 1.000 0.999 1.001 1.000 1.000 1.001
0.5 U 0.004 0.004 0.004 0.003 0.004 0.004 0.004 0.003 0.003 0.003 0.004 0.003 0.003 0.003 0.004 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
13.2 Pr 0.876 0.885 0.896 0.904 0.911 0.915 0.918 0.921 0.925 0.925 0.926 0.928 0.931 0.930 0.932 0.933 0.938 0.936 0.938 0.939 0.949 0.947 0.954 0.961 0.969 0.976 0.983 0.987 0.993 0.996 0.999 1.000 1.000 1.001 1.000 1.003 1.002 1.002 1.003 1.005 1.003 1.004 1.001 1.000 1.004 1.002 1.002 1.004
0.7 U 0.006 0.006 0.005 0.005 0.005 0.005 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.005 0.005 0.006 0.006 0.005 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Sidewall Pressure Ratios (P/Patm) 20.2 0.9 27.2 1.0 Pr U Pr U 0.792 0.007 0.702 0.008 0.804 0.007 0.714 0.008 0.822 0.006 0.737 0.008 0.838 0.006 0.763 0.008 0.849 0.006 0.783 0.007 0.857 0.005 0.796 0.006 0.863 0.005 0.805 0.006 0.868 0.005 0.812 0.006 0.875 0.005 0.823 0.005 0.876 0.005 0.825 0.005 0.880 0.005 0.831 0.005 0.883 0.005 0.835 0.006 0.889 0.005 0.844 0.005 0.888 0.005 0.843 0.005 0.890 0.005 0.847 0.005 0.892 0.005 0.849 0.006 0.899 0.005 0.859 0.006 0.897 0.006 0.856 0.007 0.902 0.006 0.863 0.007 0.908 0.006 0.871 0.007 0.924 0.006 0.894 0.007 0.930 0.007 0.906 0.008 0.944 0.007 0.928 0.008 0.957 0.007 0.946 0.007 0.968 0.006 0.963 0.008 0.978 0.007 0.975 0.006 0.985 0.006 0.985 0.006 0.989 0.005 0.990 0.005 0.997 0.005 0.999 0.006 0.999 0.004 1.002 0.005 1.002 0.004 1.005 0.005 1.002 0.004 1.004 0.004 1.000 0.004 1.001 0.004 1.002 0.004 1.003 0.004 0.999 0.004 0.999 0.004 1.005 0.003 1.008 0.004 1.002 0.003 1.004 0.004 1.003 0.003 1.005 0.004 1.005 0.003 1.007 0.003 1.008 0.003 1.011 0.004 1.004 0.003 1.006 0.003 1.007 0.003 1.009 0.003 1.001 0.003 1.001 0.003 0.999 0.003 0.999 0.004 1.006 0.003 1.009 0.003 1.003 0.003 1.003 0.003 1.002 0.003 1.003 0.003 1.007 0.003 1.010 0.003
33.8 Pr 0.610 0.614 0.626 0.665 0.705 0.729 0.744 0.755 0.767 0.771 0.778 0.784 0.795 0.795 0.800 0.803 0.815 0.810 0.818 0.825 0.852 0.868 0.899 0.927 0.951 0.968 0.982 0.989 1.001 1.004 1.008 1.007 1.003 1.006 1.000 1.011 1.006 1.007 1.010 1.015 1.008 1.012 1.001 0.999 1.012 1.004 1.003 1.012
1.1 U 0.008 0.010 0.011 0.012 0.009 0.008 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.007 0.008 0.009 0.009 0.011 0.012 0.011 0.010 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.004 0.004 0.003 0.003 0.003 0.003
40.5 Pr 0.540 0.539 0.501 0.477 0.527 0.619 0.655 0.675 0.694 0.701 0.711 0.718 0.733 0.733 0.741 0.746 0.763 0.758 0.764 0.769 0.793 0.790 0.812 0.843 0.876 0.907 0.935 0.954 0.974 0.986 0.996 0.999 0.999 1.003 1.000 1.012 1.007 1.009 1.013 1.017 1.010 1.015 1.003 1.000 1.015 1.006 1.005 1.015
1.2 U 0.008 0.007 0.007 0.024 0.032 0.016 0.013 0.012 0.011 0.010 0.009 0.009 0.009 0.009 0.008 0.009 0.008 0.008 0.008 0.007 0.007 0.010 0.012 0.015 0.017 0.015 0.013 0.012 0.010 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003
218 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
6.5 Pr 1.002 1.003 0.949 0.957 0.965 0.960 0.961 0.962 0.964 0.964 0.966 0.967 0.977 0.970 0.972 0.973 0.977 0.975 0.977 0.978 0.980 0.980 0.981 0.982 0.992 0.986 0.988 0.991 0.993 0.995 0.996 0.996 0.997 0.998 0.999 1.000 1.000 1.000 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001
0.5 U 0.004 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
13.2 Pr 1.002 1.003 0.883 0.909 0.924 0.916 0.918 0.920 0.923 0.925 0.928 0.932 0.949 0.939 0.941 0.943 0.949 0.947 0.950 0.951 0.957 0.959 0.965 0.971 0.987 0.983 0.988 0.993 0.997 1.000 1.001 1.001 1.002 1.004 1.005 1.005 1.006 1.007 1.007 1.006 1.005 1.006 1.006 1.005 1.003 1.005 1.005 1.004
0.7 U 0.003 0.005 0.006 0.007 0.005 0.006 0.005 0.005 0.005 0.004 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.005 0.004 0.005 0.004 0.005 0.005 0.005 0.007 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Topwall Pressure Ratio (P/Patm) 20.2 0.9 27.2 1.0 Pr U Pr U 1.002 0.004 1.002 0.004 1.003 0.005 1.003 0.005 0.795 0.010 0.683 0.013 0.849 0.007 0.772 0.009 0.874 0.006 0.822 0.007 0.862 0.007 0.810 0.008 0.864 0.006 0.811 0.006 0.867 0.006 0.815 0.006 0.872 0.005 0.819 0.005 0.876 0.005 0.825 0.006 0.881 0.005 0.832 0.005 0.887 0.006 0.841 0.006 0.912 0.005 0.875 0.006 0.900 0.006 0.861 0.006 0.905 0.005 0.867 0.006 0.909 0.005 0.874 0.006 0.920 0.005 0.886 0.005 0.917 0.005 0.884 0.005 0.923 0.005 0.892 0.006 0.928 0.005 0.899 0.006 0.938 0.006 0.913 0.007 0.946 0.006 0.928 0.007 0.958 0.006 0.946 0.007 0.968 0.006 0.961 0.006 0.988 0.007 0.986 0.009 0.984 0.005 0.984 0.005 0.991 0.005 0.993 0.006 0.997 0.005 1.000 0.005 1.001 0.004 1.005 0.006 1.004 0.004 1.009 0.005 1.006 0.004 1.010 0.005 1.004 0.004 1.007 0.004 1.004 0.004 1.007 0.004 1.008 0.004 1.012 0.004 1.009 0.004 1.013 0.004 1.009 0.004 1.013 0.005 1.011 0.003 1.015 0.004 1.011 0.003 1.016 0.004 1.011 0.003 1.016 0.004 1.011 0.003 1.015 0.003 1.008 0.003 1.012 0.003 1.010 0.003 1.014 0.003 1.010 0.003 1.013 0.003 1.009 0.003 1.013 0.003 1.005 0.003 1.007 0.003 1.008 0.003 1.011 0.003 1.008 0.003 1.011 0.003 1.007 0.003 1.010 0.003
33.8 Pr 1.002 1.003 0.550 0.652 0.752 0.755 0.762 0.766 0.770 0.774 0.781 0.790 0.828 0.810 0.819 0.829 0.846 0.841 0.852 0.861 0.878 0.898 0.924 0.946 0.981 0.979 0.992 1.003 1.008 1.014 1.016 1.011 1.010 1.018 1.019 1.017 1.020 1.021 1.021 1.020 1.015 1.018 1.017 1.016 1.009 1.015 1.014 1.013
1.1 U 0.004 0.005 0.015 0.020 0.009 0.008 0.007 0.006 0.007 0.006 0.006 0.006 0.006 0.007 0.007 0.007 0.006 0.007 0.008 0.008 0.009 0.009 0.010 0.009 0.010 0.008 0.007 0.007 0.006 0.006 0.005 0.005 0.005 0.005 0.004 0.006 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
40.5 Pr 1.002 1.002 0.440 0.502 0.606 0.626 0.662 0.686 0.702 0.710 0.713 0.722 0.766 0.744 0.755 0.763 0.787 0.785 0.796 0.799 0.809 0.827 0.848 0.875 0.940 0.929 0.953 0.973 0.987 0.999 1.007 1.003 1.006 1.016 1.019 1.019 1.023 1.025 1.024 1.024 1.019 1.021 1.021 1.020 1.011 1.018 1.017 1.016
1.2 U 0.004 0.004 0.009 0.016 0.017 0.018 0.015 0.011 0.009 0.008 0.009 0.009 0.008 0.010 0.009 0.010 0.009 0.009 0.009 0.007 0.008 0.009 0.013 0.013 0.019 0.013 0.012 0.012 0.010 0.009 0.008 0.007 0.006 0.006 0.005 0.007 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003
219 Table D.1 Test averages for single nozzle strut. (cont.) Pc/Pb Position 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
47.2 Pr 0.545 0.545 0.508 0.465 0.427 0.354 0.301 0.296 0.303 0.286 0.274 0.258 0.383 0.374 0.342 0.320 0.346 0.258 0.296 0.294 0.364 0.340 0.303 0.294 0.295 0.315 0.326 0.308 0.311 0.310 0.335 0.369 0.389 0.417 0.472 0.512 0.545 0.588 0.636 0.687 0.764 0.780 0.816 0.852 0.886 0.907 0.925 0.946
Sidewall Pressure Ratios (P/Patm) 1.3 53.8 1.5 60.5 U Pr U Pr 0.008 0.569 0.006 0.597 0.006 0.569 0.006 0.594 0.005 0.535 0.006 0.561 0.016 0.485 0.010 0.512 0.015 0.446 0.020 0.466 0.008 0.389 0.007 0.411 0.007 0.327 0.007 0.354 0.007 0.317 0.007 0.336 0.009 0.315 0.009 0.326 0.009 0.296 0.009 0.305 0.007 0.284 0.008 0.293 0.007 0.267 0.008 0.277 0.020 0.326 0.034 0.292 0.007 0.386 0.011 0.368 0.009 0.371 0.008 0.388 0.012 0.341 0.008 0.363 0.011 0.355 0.009 0.370 0.009 0.269 0.009 0.278 0.011 0.306 0.010 0.312 0.011 0.299 0.011 0.303 0.014 0.368 0.012 0.371 0.009 0.324 0.022 0.295 0.008 0.322 0.007 0.343 0.014 0.302 0.009 0.317 0.017 0.301 0.010 0.306 0.027 0.305 0.015 0.300 0.035 0.319 0.010 0.317 0.052 0.304 0.010 0.309 0.059 0.307 0.010 0.311 0.073 0.303 0.011 0.303 0.087 0.300 0.010 0.310 0.098 0.307 0.026 0.297 0.118 0.342 0.015 0.309 0.141 0.337 0.009 0.347 0.112 0.351 0.034 0.378 0.122 0.362 0.011 0.387 0.113 0.301 0.016 0.301 0.114 0.292 0.032 0.265 0.112 0.332 0.023 0.323 0.102 0.334 0.032 0.339 0.079 0.411 0.036 0.408 0.073 0.346 0.060 0.329 0.059 0.395 0.092 0.318 0.051 0.483 0.085 0.373 0.041 0.567 0.064 0.429 0.033 0.619 0.067 0.404 0.025 0.678 0.063 0.510 0.022 0.744 0.047 0.568
1.8 U 0.005 0.005 0.006 0.007 0.017 0.012 0.006 0.006 0.009 0.009 0.008 0.008 0.011 0.020 0.009 0.008 0.009 0.012 0.008 0.011 0.010 0.020 0.011 0.008 0.009 0.015 0.017 0.008 0.011 0.012 0.012 0.009 0.031 0.016 0.034 0.013 0.010 0.015 0.021 0.011 0.011 0.018 0.025 0.049 0.018 0.066 0.071 0.036
47.2 Pr 1.002 1.001 0.437 0.491 0.550 0.487 0.432 0.384 0.348 0.313 0.282 0.257 0.365 0.366 0.432 0.386 0.373 0.332 0.314 0.296 0.329 0.299 0.310 0.391 0.535 0.296 0.298 0.298 0.365 0.382 0.334 0.316 0.438 0.414 0.406 0.560 0.633 0.616 0.637 0.752 0.791 0.813 0.840 0.877 0.939 0.921 0.938 0.953
Topwall Pressure Ratios (P/Patm) 1.3 53.8 1.5 60.5 U Pr U Pr 0.004 1.001 0.004 1.000 0.005 0.999 0.005 0.999 0.008 0.470 0.009 0.501 0.010 0.520 0.009 0.552 0.011 0.569 0.009 0.593 0.010 0.502 0.009 0.520 0.007 0.448 0.009 0.464 0.007 0.405 0.009 0.422 0.008 0.373 0.009 0.385 0.008 0.337 0.009 0.348 0.008 0.303 0.009 0.316 0.008 0.274 0.009 0.287 0.008 0.374 0.008 0.381 0.053 0.261 0.046 0.250 0.021 0.438 0.031 0.378 0.019 0.433 0.023 0.448 0.008 0.397 0.013 0.427 0.007 0.340 0.010 0.346 0.007 0.332 0.007 0.339 0.009 0.309 0.007 0.328 0.011 0.333 0.010 0.342 0.012 0.298 0.014 0.298 0.032 0.302 0.012 0.298 0.020 0.379 0.040 0.332 0.109 0.550 0.104 0.557 0.023 0.306 0.009 0.328 0.030 0.314 0.013 0.320 0.053 0.289 0.009 0.321 0.061 0.299 0.036 0.280 0.086 0.374 0.027 0.311 0.108 0.355 0.014 0.386 0.104 0.310 0.008 0.347 0.111 0.370 0.023 0.375 0.157 0.338 0.018 0.340 0.210 0.297 0.040 0.286 0.194 0.429 0.105 0.355 0.203 0.374 0.026 0.423 0.182 0.332 0.011 0.374 0.189 0.310 0.020 0.326 0.129 0.327 0.048 0.308 0.104 0.461 0.042 0.411 0.077 0.411 0.035 0.411 0.059 0.383 0.076 0.411 0.047 0.414 0.142 0.369 0.026 0.692 0.106 0.558 0.030 0.677 0.086 0.350 0.023 0.715 0.059 0.393 0.020 0.747 0.069 0.547
1.8 U 0.005 0.007 0.008 0.009 0.010 0.010 0.010 0.010 0.010 0.010 0.009 0.008 0.007 0.018 0.063 0.022 0.022 0.011 0.011 0.010 0.008 0.010 0.016 0.041 0.098 0.007 0.016 0.011 0.013 0.044 0.015 0.011 0.025 0.019 0.011 0.145 0.026 0.020 0.008 0.016 0.028 0.046 0.022 0.012 0.018 0.052 0.092 0.128
220
Table D.2 Test averages for dual nozzle strut. Dual Nozzle Test Data Averages (10 Tests) Nozzle Area Ratio = 4.66 Mixing Duct Cross Section : 4 in x 3.5 in Nozzle Hydraulic Diameter = 0.83 in Po2/Pb = 1 Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Set Point Pressure Ratio (Pc/Pb)
Pc/Pb 3.5 6.8 10.2 13.5 16.9 20.4 24.0 27.4 30.6
U 0.3 0.5 0.6 0.6 0.7 0.9 0.9 0.9 1.0
Secondary Flow Stagnation Pressure (psi)
Po1 14.7 14.8 14.7 14.7 14.7 14.7 14.7 14.7 14.7
U_Po1 0.5 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Secondary Flow Inlet Temperature (C) T1 287.0 287.0 287.0 287.0 286.0 285.0 286.0 285.0 286.0
U_T1 11.9 13.0 13.3 12.1 12.2 10.2 10.7 11.0 12.0
Secondary Flow Static Pressure At Fairing (psi)
P1 14.5 14.5 14.3 14.1 14.0 13.9 13.9 13.9 13.9
U_P1 0.5 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Exit Stagnation Pressure (psi)
Exit wall Static Pressure (psi)
Poe 15.3 16.0 16.8 18.0 19.2 20.6 22.3 29.3 39.1
Pe 14.7 14.8 14.8 14.8 14.8 14.8 14.9 14.6 14.0
U_Poe 0.8 0.6 0.7 0.6 0.6 0.6 1.0 4.7 5.4
U_Pe 0.5 0.1 0.4 0.4 0.4 0.4 0.5 0.7 1.4
Exit Static Chamber Pressure Pitot Temperature (C) (psi) Pe2 U_Pe2 Tc U_Tc 14.7 0.5 284.0 17.0 14.8 0.1 278.0 12.3 14.7 0.4 273.0 13.7 14.8 0.4 272.0 12.8 14.8 0.4 270.0 14.1 14.8 0.4 269.0 12.0 14.8 0.5 269.0 11.9 14.6 0.6 269.0 11.8 14.6 0.6 269.0 13.2
Strut Gap Pressures (psi) Positon 1 P1 U_P1 14.0 0.2 13.3 0.2 12.5 0.2 11.6 0.2 10.6 0.2 9.8 0.3 9.7 0.4 9.7 0.4 9.7 0.4
Postion 2 P2 U_P2 14.0 0.2 13.3 0.2 12.5 0.2 11.6 0.2 10.6 0.2 9.7 0.4 9.5 0.4 9.6 0.4 9.6 0.4
Position 3 P3 U_P3 14.0 0.2 13.3 0.2 12.4 0.2 11.4 0.2 10.3 0.2 9.4 0.3 9.2 0.3 9.2 0.3 9.3 0.3
Position 4 P4 U_P4 14.0 0.2 13.3 0.2 12.3 0.2 11.3 0.2 10.2 0.2 9.1 0.3 8.9 0.3 8.9 0.2 9.0 0.2
Strut Gap Pressures (psi) Position 6 P6 U_P6 14.0 0.2 13.3 0.2 12.4 0.2 11.3 0.2 10.2 0.2 9.1 0.3 8.9 0.3 8.9 0.3 9.0 0.2
Position 7 P7 U_P7 14.0 0.2 13.2 0.2 12.3 0.2 11.3 0.2 10.1 0.2 9.0 0.3 8.8 0.3 8.8 0.3 8.9 0.3
Position 8 P8 U_P8 13.9 0.2 13.1 0.2 12.0 0.3 10.6 0.4 9.0 0.7 7.2 0.8 6.9 0.7 6.9 0.7 7.0 0.7
Position 9 P9 U_P9 13.9 0.2 13.2 0.2 12.3 0.2 11.2 0.2 9.9 0.3 8.3 0.3 7.9 0.3 8.0 0.2 8.1 0.2
Position 10 P10 U_P10 13.9 0.2 13.2 0.2 12.3 0.2 11.2 0.2 9.8 0.3 8.2 0.4 7.7 0.3 7.7 0.2 7.9 0.2
Position 5 P5 U_P5 13.9 0.2 13.2 0.2 12.3 0.2 11.3 0.2 10.1 0.2 9.0 0.3 8.8 0.3 8.9 0.2 8.9 0.2
221 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb x/Dh 0.00 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
3.5 Pr 0.950 0.955 0.958 0.961 0.963 0.964 0.965 0.965 0.967 0.966 0.967 0.967 0.968 0.968 0.968 0.969 0.971 0.970 0.972 0.973 0.978 0.978 0.979 0.982 0.986 0.991 0.990 0.990 0.995 0.996 0.997 0.997 0.997 0.998 0.997 1.000 0.999 1.000 1.000 1.001 1.001 1.001 1.000 1.000 1.001 1.001 1.000 1.002
0.3 U 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.007 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
6.8 Pr 0.904 0.914 0.920 0.926 0.929 0.931 0.932 0.934 0.936 0.936 0.937 0.938 0.940 0.939 0.940 0.941 0.945 0.943 0.945 0.947 0.954 0.954 0.961 0.967 0.975 0.985 0.984 0.986 0.993 0.995 0.997 0.998 0.997 0.999 0.997 1.002 1.000 1.001 1.002 1.004 1.002 1.003 1.000 0.999 1.003 1.001 1.001 1.003
0.5 U 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.006 0.006 0.006 0.006 0.010 0.006 0.007 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Sidewall Pressure Ratios (P/Patm) 10.2 0.6 13.5 0.6 Pr U Pr U 0.844 0.004 0.772 0.007 0.859 0.004 0.793 0.006 0.870 0.004 0.811 0.006 0.880 0.004 0.825 0.005 0.886 0.004 0.835 0.005 0.891 0.004 0.842 0.005 0.894 0.004 0.847 0.005 0.897 0.004 0.852 0.004 0.901 0.004 0.858 0.005 0.901 0.004 0.859 0.005 0.903 0.004 0.862 0.005 0.905 0.004 0.864 0.005 0.909 0.004 0.870 0.005 0.908 0.004 0.869 0.005 0.910 0.004 0.872 0.005 0.911 0.004 0.876 0.005 0.918 0.004 0.886 0.005 0.915 0.004 0.883 0.005 0.920 0.004 0.894 0.006 0.924 0.004 0.901 0.007 0.935 0.005 0.917 0.006 0.938 0.005 0.922 0.007 0.947 0.005 0.930 0.006 0.956 0.005 0.943 0.006 0.965 0.005 0.957 0.007 0.979 0.013 0.974 0.016 0.979 0.005 0.972 0.007 0.981 0.004 0.972 0.005 0.989 0.004 0.985 0.006 0.992 0.004 0.987 0.005 0.995 0.004 0.991 0.005 0.996 0.004 0.991 0.005 0.996 0.004 0.990 0.004 0.998 0.004 0.993 0.004 0.996 0.004 0.989 0.004 1.002 0.003 0.999 0.004 1.000 0.003 0.996 0.004 1.000 0.003 0.997 0.004 1.002 0.003 1.001 0.004 1.005 0.003 1.005 0.004 1.002 0.003 1.002 0.003 1.004 0.003 1.004 0.003 1.000 0.003 0.997 0.003 0.999 0.003 0.996 0.003 1.005 0.003 1.005 0.003 1.001 0.003 1.001 0.003 1.001 0.003 1.000 0.003 1.005 0.003 1.007 0.003
16.9 Pr 0.683 0.710 0.734 0.758 0.773 0.783 0.790 0.797 0.805 0.807 0.811 0.815 0.823 0.822 0.827 0.833 0.847 0.841 0.857 0.867 0.886 0.894 0.903 0.919 0.938 0.960 0.956 0.954 0.974 0.975 0.981 0.981 0.978 0.984 0.978 0.993 0.988 0.991 0.996 1.003 1.000 1.003 0.992 0.991 1.005 0.999 0.998 1.008
0.7 U 0.014 0.012 0.012 0.011 0.010 0.009 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.007 0.008 0.009 0.008 0.007 0.006 0.006 0.006 0.024 0.005 0.006 0.005 0.005 0.005 0.005 0.005 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.004 0.004 0.004 0.003 0.003 0.003 0.003
20.4 Pr 0.565 0.594 0.611 0.653 0.690 0.709 0.719 0.727 0.737 0.741 0.753 0.763 0.778 0.770 0.783 0.790 0.812 0.761 0.826 0.845 0.863 0.868 0.867 0.888 0.914 0.941 0.933 0.931 0.953 0.956 0.962 0.964 0.962 0.968 0.963 0.979 0.974 0.980 0.986 0.996 0.995 0.997 0.981 0.984 1.004 0.994 0.997 1.008
0.9 U 0.020 0.019 0.024 0.021 0.016 0.013 0.012 0.012 0.012 0.011 0.010 0.011 0.012 0.011 0.012 0.012 0.013 0.019 0.015 0.017 0.014 0.016 0.010 0.011 0.012 0.036 0.010 0.008 0.009 0.008 0.007 0.006 0.006 0.006 0.007 0.006 0.009 0.007 0.007 0.005 0.004 0.005 0.010 0.006 0.006 0.006 0.009 0.005
222 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb x/Dh 0.28 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
3.5 Pr 1.001 1.001 0.955 0.966 0.972 0.967 0.966 0.967 0.967 0.968 0.968 0.969 0.973 0.970 0.971 0.972 0.975 0.973 0.974 0.979 0.977 0.978 0.981 0.983 0.991 0.989 0.992 0.994 0.996 0.997 0.998 0.999 1.000 1.001 1.001 1.001 1.002 1.002 1.002 1.002 1.001 1.002 1.002 1.002 1.001 1.002 1.002 1.002
0.3 U 0.004 0.009 0.004 0.004 0.004 0.004 0.003 0.004 0.004 0.003 0.003 0.003 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.006 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
6.8 Pr 1.000 1.003 0.910 0.928 0.942 0.936 0.938 0.941 0.944 0.945 0.946 0.947 0.953 0.949 0.949 0.950 0.956 0.953 0.955 0.961 0.960 0.962 0.968 0.973 0.985 0.983 0.987 0.992 0.995 0.998 0.999 1.001 1.002 1.004 1.004 1.003 1.005 1.005 1.005 1.004 1.004 1.005 1.005 1.004 1.003 1.004 1.004 1.004
0.5 U 0.004 0.007 0.006 0.006 0.005 0.004 0.005 0.006 0.006 0.006 0.006 0.006 0.008 0.005 0.005 0.005 0.005 0.005 0.005 0.007 0.005 0.005 0.006 0.007 0.008 0.006 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
Topwall Pressure Ratio (P/Patm) 10.2 0.6 13.5 0.6 Pr U Pr U 1.000 0.004 0.999 0.004 1.002 0.006 1.001 0.006 0.860 0.007 0.799 0.008 0.891 0.006 0.843 0.007 0.907 0.005 0.863 0.007 0.898 0.005 0.857 0.007 0.900 0.006 0.868 0.007 0.905 0.005 0.884 0.006 0.910 0.005 0.891 0.005 0.913 0.005 0.888 0.004 0.915 0.004 0.883 0.004 0.917 0.004 0.883 0.004 0.924 0.008 0.893 0.010 0.919 0.004 0.886 0.004 0.920 0.004 0.887 0.004 0.922 0.004 0.891 0.004 0.930 0.004 0.903 0.004 0.927 0.004 0.900 0.005 0.931 0.004 0.907 0.005 0.941 0.008 0.921 0.010 0.941 0.004 0.922 0.005 0.947 0.004 0.931 0.006 0.956 0.005 0.943 0.006 0.964 0.005 0.953 0.006 0.980 0.009 0.972 0.011 0.978 0.004 0.970 0.006 0.984 0.005 0.977 0.007 0.989 0.004 0.984 0.006 0.993 0.004 0.989 0.006 0.996 0.004 0.993 0.006 0.999 0.004 0.996 0.005 1.000 0.004 0.997 0.005 1.002 0.004 0.999 0.005 1.004 0.004 1.003 0.004 1.005 0.004 1.004 0.004 1.004 0.004 1.004 0.004 1.007 0.004 1.007 0.004 1.007 0.004 1.008 0.004 1.008 0.004 1.008 0.004 1.006 0.004 1.007 0.004 1.006 0.003 1.007 0.004 1.007 0.003 1.008 0.004 1.007 0.003 1.009 0.004 1.007 0.003 1.008 0.003 1.005 0.004 1.007 0.004 1.006 0.003 1.008 0.003 1.006 0.003 1.007 0.003 1.006 0.003 1.008 0.003
16.9 Pr 0.999 1.000 0.712 0.780 0.806 0.797 0.811 0.836 0.854 0.851 0.841 0.841 0.853 0.842 0.844 0.851 0.865 0.862 0.872 0.890 0.891 0.903 0.918 0.931 0.957 0.953 0.963 0.972 0.978 0.983 0.987 0.989 0.993 0.997 0.999 1.002 1.004 1.006 1.007 1.006 1.007 1.008 1.009 1.009 1.007 1.009 1.008 1.009
0.7 U 0.004 0.006 0.017 0.012 0.010 0.009 0.009 0.008 0.007 0.006 0.008 0.007 0.014 0.006 0.007 0.007 0.006 0.006 0.006 0.013 0.006 0.006 0.006 0.006 0.014 0.005 0.005 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
20.4 Pr 0.999 0.999 0.541 0.682 0.738 0.731 0.747 0.775 0.801 0.811 0.797 0.792 0.796 0.788 0.801 0.809 0.825 0.820 0.837 0.863 0.863 0.875 0.894 0.908 0.940 0.931 0.943 0.952 0.959 0.966 0.971 0.973 0.979 0.984 0.987 0.993 0.995 0.998 1.000 1.002 1.002 1.003 1.005 1.006 1.005 1.007 1.007 1.008
0.9 U 0.004 0.005 0.036 0.022 0.013 0.012 0.011 0.009 0.011 0.010 0.008 0.011 0.020 0.017 0.009 0.009 0.008 0.010 0.014 0.016 0.011 0.015 0.012 0.014 0.018 0.011 0.011 0.010 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.007 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
223 Table D.2 Test averages for dual nozzle strut. (cont.) Pc/Pb Position 0.00 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
24.0 Pr 0.503 0.531 0.488 0.433 0.415 0.425 0.419 0.426 0.479 0.530 0.599 0.616 0.652 0.596 0.607 0.623 0.667 0.551 0.673 0.697 0.727 0.729 0.723 0.754 0.803 0.845 0.841 0.845 0.880 0.889 0.902 0.908 0.909 0.922 0.921 0.938 0.937 0.943 0.950 0.962 0.973 0.968 0.955 0.956 0.983 0.975 0.974 1.007
Sidewall Pressure Ratios (P/Patm) 0.9 27.4 0.9 30.6 U Pr U Pr 0.018 0.527 0.012 0.554 0.012 0.549 0.009 0.568 0.013 0.508 0.008 0.529 0.016 0.455 0.011 0.479 0.073 0.410 0.024 0.436 0.148 0.348 0.014 0.380 0.194 0.290 0.012 0.328 0.209 0.279 0.014 0.322 0.191 0.280 0.017 0.345 0.163 0.287 0.030 0.341 0.129 0.441 0.194 0.399 0.129 0.600 0.062 0.600 0.122 0.573 0.123 0.678 0.125 0.356 0.016 0.404 0.126 0.313 0.014 0.341 0.111 0.315 0.019 0.328 0.106 0.367 0.023 0.370 0.112 0.240 0.021 0.243 0.125 0.330 0.067 0.324 0.118 0.343 0.108 0.325 0.099 0.456 0.039 0.433 0.109 0.358 0.016 0.449 0.100 0.280 0.027 0.295 0.095 0.274 0.082 0.271 0.086 0.371 0.092 0.323 0.107 0.486 0.294 0.486 0.068 0.459 0.153 0.366 0.056 0.460 0.231 0.350 0.051 0.553 0.211 0.319 0.043 0.654 0.139 0.322 0.037 0.723 0.095 0.339 0.032 0.756 0.068 0.375 0.027 0.768 0.066 0.419 0.024 0.803 0.049 0.481 0.020 0.803 0.048 0.622 0.023 0.824 0.056 0.686 0.021 0.834 0.042 0.724 0.018 0.848 0.041 0.728 0.017 0.858 0.042 0.742 0.022 0.877 0.032 0.783 0.013 0.902 0.028 0.840 0.019 0.890 0.030 0.818 0.019 0.887 0.035 0.816 0.016 0.891 0.033 0.857 0.021 0.919 0.030 0.874 0.017 0.918 0.027 0.871 0.018 0.931 0.028 0.910 0.018 0.950 0.021 0.913
1.0 U 0.011 0.008 0.008 0.011 0.020 0.019 0.011 0.014 0.028 0.019 0.141 0.097 0.093 0.024 0.015 0.015 0.022 0.018 0.048 0.067 0.081 0.049 0.012 0.052 0.045 0.292 0.039 0.021 0.045 0.052 0.031 0.062 0.131 0.185 0.115 0.065 0.047 0.080 0.077 0.058 0.048 0.064 0.066 0.040 0.040 0.041 0.029 0.027
Pc/Pb x/Dh 0.28 0.57 1.14 1.70 2.27 2.84 3.41 3.98 4.55 5.11 5.68 6.25 6.82 7.39 7.95 8.52 9.09 9.66 10.23 10.80 11.36 12.50 13.64 14.77 15.91 17.05 18.18 19.32 20.45 21.59 22.73 23.86 25.00 26.14 27.27 28.41 29.55 30.68 31.82 32.95 34.09 35.23 36.36 37.50 38.64 39.77 40.91 42.05
24.0 Pr 0.998 0.997 0.379 0.499 0.540 0.502 0.513 0.552 0.588 0.562 0.528 0.569 0.694 0.750 0.676 0.552 0.611 0.737 0.743 0.712 0.691 0.759 0.770 0.791 0.851 0.829 0.852 0.871 0.885 0.899 0.912 0.919 0.932 0.941 0.948 0.964 0.963 0.970 0.975 0.986 0.987 0.987 0.990 0.994 0.996 0.998 1.000 1.002
Topwall Pressure Ratios (P/Patm) 0.9 27.4 0.9 30.6 U Pr U Pr 0.004 0.998 0.005 0.998 0.006 0.995 0.008 0.992 0.025 0.407 0.015 0.441 0.035 0.502 0.012 0.524 0.064 0.504 0.011 0.514 0.108 0.428 0.013 0.435 0.156 0.400 0.014 0.401 0.201 0.387 0.023 0.376 0.186 0.437 0.019 0.416 0.193 0.413 0.012 0.442 0.183 0.349 0.010 0.371 0.212 0.298 0.009 0.319 0.213 0.312 0.062 0.328 0.161 0.283 0.129 0.249 0.193 0.398 0.161 0.331 0.193 0.601 0.077 0.596 0.204 0.475 0.044 0.557 0.173 0.359 0.021 0.416 0.135 0.312 0.011 0.351 0.146 0.350 0.067 0.370 0.147 0.307 0.020 0.322 0.104 0.333 0.081 0.303 0.098 0.346 0.047 0.370 0.093 0.422 0.031 0.412 0.075 0.520 0.136 0.516 0.073 0.336 0.148 0.316 0.065 0.390 0.226 0.289 0.057 0.523 0.207 0.332 0.052 0.590 0.170 0.392 0.044 0.668 0.140 0.400 0.040 0.732 0.089 0.361 0.035 0.750 0.077 0.365 0.030 0.783 0.067 0.485 0.027 0.809 0.054 0.545 0.026 0.818 0.049 0.615 0.026 0.863 0.050 0.709 0.022 0.854 0.039 0.700 0.020 0.869 0.035 0.734 0.019 0.880 0.033 0.761 0.014 0.915 0.034 0.826 0.014 0.916 0.022 0.833 0.015 0.914 0.020 0.834 0.014 0.922 0.019 0.850 0.012 0.931 0.018 0.877 0.009 0.949 0.018 0.906 0.010 0.945 0.016 0.903 0.009 0.953 0.014 0.919 0.008 0.960 0.011 0.929
1.0 U 0.005 0.011 0.014 0.009 0.010 0.012 0.010 0.012 0.035 0.018 0.013 0.012 0.058 0.031 0.217 0.061 0.054 0.027 0.014 0.061 0.010 0.064 0.062 0.037 0.097 0.023 0.065 0.090 0.011 0.020 0.020 0.081 0.128 0.124 0.105 0.083 0.071 0.070 0.064 0.063 0.047 0.043 0.039 0.032 0.032 0.026 0.021 0.018
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