simulation of combustion - Unibo
SIMULATION OF COMBUSTION
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Motivation FLAME KERNEL FORMATION IS A CRITICAL ISSUE IN ICE SINCE: ITS FEATURES AFFECT THE COMBUSTION DURATION CYCLE-TO-CYCLE VARIABILITY AFFECTS RIGHT EARLY BURNING RATE
THE 5%MFB TAKES 35-40% OF TOTAL COMBUSTION DURATION PHYSICAL PROCESS TO BE CONSIDERED PHYSICS OF SPARK DISCHARGE FLOW CONVECTIVE EFFECTS (ARC ELONGATION) TURBULENCE PHYSICAL CHARACTERISTICS OF THE MIXTURE (p, T, φ or pdf of φ)
Background CFD IGNITION MODELS ARE COMPLETELY RELIABLE ? NO IGNITION TIME AND LENGHT SCALES ARE TOO SMALL TO BE RESOLVED DURING PLASMA FORMATION ELECTRICAL CIRCUIT TOO COMPLEX TO BE MODELLED IN DETAIL COUPLING WITH MAIN COMBUSTION MODEL GRID DEPENDENCY
MANY 1D MODELS DECOUPLED FROM CFD SOLVER HAVE BEEN PRESENTED AND REFERENCED IN THE PAPER. THEY WOULD BE CONSIDERED ALL EULERIAN EXCEPT AKTIM AND DPKI.
Background LAGRANGIAN TRACKING REVIEW AKTIM MODEL - Duclos and Colin [COMODIA 2001] - The model includes a detailed description of the electrical system - Ignition kernels were modelled by a set of particles uniformly placed
DPIK - Fan et al. [SAE paper 1999-01-0175 ] - The flame kernel position is marked by particles
CURRENT MODEL EXPECTED CONTRIBUTION PROVIDE AN ALMOST GRID INDIPENDENT MODEL IMPROVE THE PHYSICAL GROUTH OF FLAME KERNEL EXPANSION RATE BASED ON MASS AND ENERGY CONSERVATION PROVIDE A DIRECT COUPLING METHOD WITH A FLAME SURFACE DENSITY MODEL
Spark Ignition Model ELECTRICAL SUB-MODEL FOR SPARK PLUG LUMP MODEL BASED ON THE MAIN AVAILABLE SPECIFICATIONS
LAGRANGIAN KERNEL SUBMODEL MASS AND ENERGY CONSERVATION SOLVED IN A VARIABLE CONTROL VOLUME DEFINED BY MEAN FLAME SURFACE COUPLING WITH MAIN SOLVER ENFORCED WITH PARTICULAR EMPHASIS ON FLAME SURFACE
Spark Ignition Model Lagrangian Ignition Model
Electrical submodel
LUMP/EASY MODELLING (NO WEAK POINT) PLASMA FORMATION NEGLECTED (ti (time and d llength th scales l ttoo short) h t)
Energy released during breakdown and glow phases:
Vbd2 Ebd = 2 Cbd ⋅ d ggapp
(Duclos and Colin, 2001)
E& glow = f ( Esp , t )
B Breakdown kd V Voltage lt evaluated l t d according di to t (Stone (St et. t Al, Al Sae S 2000): 2000)
P P + 324 Vbd = 4.3 + 13.6 d gap Tunb Tunb
Spark Ignition Model AFTER THE PLASMA PHASE: One flame kernel is deposited and initialized Flame Kernel is discretized by a set of triangular elements which expand radially
I-th cell
Each of these elements varies its area surface because of expansion and wrinkling by turbulence It contributes to reaction rate in its own reference fluid cells I-th
Spark Ignition Model Lagrangian Ignition Model
Thermodynamic model
Initial kernel conditions after plasma formation (Song and Sunwoo, Sunwoo 2000) :
⎡ ⎤ ⎢ ⎥ E − k 1 bd ⎥ ⋅ rk ,i = ⎢ ⎢ k ⎛ Tunb ⎞ ⎥ ⎟⎟π ⎥ p0 d gap ⎜⎜1 − ⎢ T ⎢⎣ i ⎠ ⎥ ⎝ ⎦
1/ 2
⎡ 1 ⎛ Tb ⎞ ⎤ ⎜ Ti = ⎢ ⎜ − 1⎟⎟ + 1⎥Tunb ⎠ ⎦ ⎣ k ⎝ Tunb
MASS CONSERVATION FOR A LAGRANGIAN SYSTEM
dm k = ρ unb ⋅ s lam , k ⋅ ( Ak ⋅ Ξ ) dt
Turbulence wrinkling
R Rearranged d -> >A An expression i for f th the mean kernel k l expansion i rate t
⎡ Vk drk ρ unb = slam ,k ⋅ Ξ − ⎢ dt ρk ⎣ Ak
⎛ 1 dTk 1 dp ⎞⎤ ⎜⎜ ⎟⎟⎥ − p dt ⎠⎦ ⎝ Tk dt
Spark Ignition Model Lagrangian Ignition Model
Thermodynamic model
If T≥3Tad heat conduction equation applies
⎛ ∂ 2Tpl 2 ∂Tpl ⎞ P − Q& w ⎟+ = α⎜ 2 + ⎜ ∂r ∂t r ∂r ⎠⎟ ρc pVk ⎝
∂Tpl
Energy Conservation if T Reasonable 2.00 R bl flow fl lenght l ht resolved l d in i RANS ((grid id size i 0.5 0 5 -> 1 mm))
Spark Ignition Model Lagrangian Ignition Model
Comparison with main Lagrangian models
Electrical Model AKTIM has a very sophisticated spark electrical model While in DPIK model is absent
Flame Kernel Deposition In present model, only one kernel is considered and its initial radius and temperature are evaluated depending on system characteristics and operating conditions. A “reasonble value” used in DPIK, while AKTIM adopts a different concept based on presumed multiple kernel ignition probability
Spark Ignition Model Lagrangian Ignition Model
Comparison with main Lagrangian models
Flame expansion velocity Derived from mass conservation according g to a lagrangian g g approach and accounting for wrinkling. In AKTIM each kernel is convected by gas flow. DPKI simply adds turbulence intensity to laminar flame velocity (questionable)
Coupling with Flame surface Models In AKTIM and DPKI is based on the density surface of burning partcile representing the kernel. In the present model Flame surface density is computed according to a spherical kernel expansion which is sensitive to mixture charactetistics and flow conditions. Therefore the ECFM models is inizialized with current Σ value in i-th cells
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Combustion model FLAMELET COMBUSTION MODEL (ECFM, (ECFM Colins et Al. Al 2003) ⎛ Σ ∂ ⎜ μ⎞ ρ ∂Σ ∂u%i Σ ∂ ⎜ ⎛ μt + = + ⎜ ⎟⋅ ∂t ∂xi ∂xi ⎜ ⎝ Sct Sc ⎠ ∂xi ⎜ ⎝
⎞ ⎟ ⎟ + ( P1 + P2 + P3 ) ⋅ Σ − D ⎟ ⎟ ⎠
FRESH GAS ENTHALPY TRANSPORT EQUATION
∂ρ hu ∂ρ u%i hu ∂ ⎛ ⎛ μt μ ⎞ ∂hu + = + ⎟⋅ ⎜⎜ ∂t ∂xi ∂xi ⎜⎝ ⎝ Sct Sc ⎠ ∂xi
⎞ ρ ∂p ε ⎟⎟ + ⋅ + ρ ⋅ k ⎠ ρ o ∂t
Better accuracy in estimating the evolution of unburned gases thermodynamic conditions during the combustion process
KIVA MODELS Ignition model
Lagrangian Ignition Model
Main Combustion model
ECFM – Flamelet (Colin 2003)
Mono-component Fuel
Shell Fuel/Isooctane
Laminar flame speed
Metchalghi & Keck
Turbulence model
k-ε+wall function
Wall heat transfer
Corrected Han and Reitz
Flame front chemistry
1-step 1 step chemistry
Post-flame chemistry
Meintjes and Morgan
Knock model
AnB (Lafossas 2003)
Validation 1.2 liters, 4 Cylinders Gasoline Engine
Configurations Examined Engine Speed [rpm]
2400
3000
IMEP [bar]
48 4.8
92 9.2
AFR [ ]
13.2
14.6
24.4° to 32.4°
21.1° to 34°
Spark Advance Sweep
Validation VALIDATION OF CFD MODELS •Ignition •Combustion velocity •Wall heat flux 580mbar@2400rpm AFR=13 580mbar@2400rpm, AFR 13.2 2 35
30
Comb Vel
SA=24.4 KIVA EXPERIMENTAL b
Pressurre [bar]
25
20
15
WHF
10
c 5
0 -60 60
a
INIT -40 40
-20 20
0 20 c.a. [deg ATDC]
40
60
80
580mbar@2400rpm, AFR=13.2, SA24.4 200
580mbar@2400rpm, AFR=13.2, SA24.4
100 0
200 -5
0
5
10
200 100 0
-5 5
0
5
10
200
15 20 MFB5
25
15 20 MFB25
25
30
35
40 150
30
35
40
100 0 200 100 0
-5
-5
0
0
5
5
10
10
15 20 MFB50
25
15 20 MFB90
25
30
35
Engine cycles
Engine cycle es Engine cycles En ngine cycles Engin ne cycles
Reference cycle definition
100 50
40 0 15
30
35
20 25 Pressure[bar] @ 19.2 crank angle ATDC
30
40
The reference cycle is used for the sake of CFD results validation: it must represent the ‘typical’ combustion that can be attained for the given operating condition Th reference The f cycle l is i nott necessarily il the th mean pressure cycle l on the th crankshaft domain The relationship between the combustion progress (released heat) and the incylinder pressure is non-linear, non linear thus a normal distribution in terms of pressure could imply a non-normal distribution in terms of pressure
580mbar@2400rpm, AFR=13.2, SA24.4 200
580mbar@2400rpm, AFR=13.2,SA=24.4
100 0
30 -5
0
5
10
15 20 MFB5
25
30
35
40
-5 5
0
5
10
15 20 MFB25
25
30
35
40
-5
0
5
10
15 20 MFB50
25
30
35
40
200 100 0 200 100 0 200 100 0
-5
0
5
10
15 20 MFB90
25
30
35
25 Pres ssure [bar]
Engine cycle es Engine cycles En ngine cycles Engin ne cycles
Reference cycle definition
40
The selection of the representative cycles is accomplished by filtering the combustion with MFBxx near the mean values. The mean cycle in terms of pressure is then evaluated on the basis of the representative cycles. l
20 Representative cycles Mean cycle Average cycle
15
10 -5
0
5
10 15 20 c.a. [deg ATDC]
25
30
35
Validation Well tuned combustion models should h ld b be able bl t to reproduce d experimental behavior when modifying input engine parameter
Pres ssure [bar]
580mbar@2400rpm, AFR=13.2 35
SA=24.4 KIVA
30
SA=26.4 KIVA SA=27.4 KIVA
25
SA=28.4 KIVA
20
SA=30.4 KIVA SA=32.4 KIVA
15
EXPERIMENTAL
SA=29.4 KIVA
10 5
The ignition model plays a key role in the reconstruction of combustion evolution with different spark advance
0
-50
0 50 c.a. [deg ATDC] 900mbar@3000rpm, AFR=14.6
The simulation is able to describe the variation in combustion velocity as a p advance without function of spark tuning parameters
SA=21.1 KIVA SA 23.2 SA=23 2 KIVA SA=25.1 KIVA
50 Press sure [bar]
Two different conditions have been simulated: different loads and different air to fuel ratio.
SA=27.3 KIVA
40
SA=29.2 KIVA SA=33.1 KIVA SA=34.0 KIVA
30
EXPERIMENTAL
20 10 0 -50
0 c.a. [deg ATDC]
50
Validation 580mbar@2400, AFR=13.2 35 MFB05 EXP MFB25 EXP
30
The first Law oh Thermodynamics is used to extract combustion information from experimental data and from simulation
MFB50 EXP MFB90 EXP
25
MFB05 KIVA MFB25 KIVA
Combustion angles
20
γ
dV 1 dP + ROHR = P γ − 1 dϑc γ − 1 dϑc
MFB50 KIVA MFB90 KIVA
15 10 5 0 -5 -10 -15 24
25
26
27
28 29 Spark Advance
30
31
32
33
850mbar@3000rpm, AFR=13.2 40 30 Combust ion angles
The model is able to well represent all the main combustion angles with different operating conditions
20 10 0 -10 20
22
24
26 28 Spark Advance
30
32
34
Validation 580mbar@2400rpm, AFR=13.2
900mbar@3000rpm, AFR=14.6
30
50 0-5% MFB EXP
0-5% MFB EXP
5-90% MFB EXP 0-5% MFB KIVA
5-90% MFB EXP 0-5% MFB KIVA
45
5-90% MFB KIVA
5-90% MFB KIVA
25
Combustion duratio ons
Combustion duratiions
40
20
35
30
25
20
15 22
23
24
25
26
27 28 29 Spark Advance
30
31
32
33
15 20
22
24
26 28 Spark Advance
30
32
34
Combustion durations The start of combustion is well represented (MFB5 – SI): the high SA cause an increase in the early stages of combustion because of the different thermodynamics at ignition.
Ignition model - Conclusion A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: •Spark main electrical characteristics (Lump model) •Mixture Mi t thermophysical th h i l properties ti (thermodynamic (th d i lagrangian l i model) d l) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against g experimental p data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Knock Model CHEMKIN Solution of several chemical equilibrium reactions
Time consuming
REDUCED KINETICS Shell Model
No tuning parameters
EMPIRICAL MODEL AnB (autoignition)
Imposition autoignition delay Based on experimental evidence
AnB KNOCK MODEL (Lafossas et Al, 2002, IFP) The model uses a two step chemistry for the simulation of auto-ignition auto ignition In the first step a precursor of the auto-ignition is calculated and then, when it reaches a critical concentration, the knock combustion is forced. AUTO-IGNITION DELAY
⎛ IO ⎞ θ = A⎜ ⎟ 100 ⎝ ⎠
3.4017
B −n T
P e
A, n, B tuning parameters
FUEL CONSUMPTION RATE
dYFu = YFu Ak with Ak = 104 e dt
3500 Tg
AnB KNOCK MODEL (Lafossas et Al, 2002, IFP)
The chemical kinetics during auto-ignition delay are not linear
dYp dt
YP
= YTFu F (θ )
Yp = YTFu
∫ϑ
=1
= Precursor
where
δ θ + 4(1 − δθ ) 2
F (θ ) = KNOCKING CRITERIA
dt
2
θ
Yp YTFu
REFERENCE KNOCK INTENSITY DEFINITION
Similar considerations for the reference mean combustion cycle y can be applied to define the ‘typical’ knocking cycle, for the given operating condition. The same procedure described before leads to the definition of a representative cycle, but the high-frequency components are filtered out by averaging different engine cycles. cycles MAPO (Maximum Amplitude of Pressure Oscillations) and KO (K (Knock k Onset) O t) parameters t can be b used d to t validate lid t th the highhi h frequency content of the pressure signal
(
MAPO = max Php
TDC + 70° TDC
)
KO = ϑc ( Php > thresholds )
REFERENCE KNOCK INTENSITY DEFINITION
Due to the non-normal distribution, the average MAPO is not the most likely value: the validation is carried out by means of the median MAPO MAPO distribution, distribution 900mbar@4500 rpm rpm, AFR=13 AFR=13.2, 2 SA=37 SA=37.5 5° 35 30
Measured Distribution (MFB5 and MFB50 selection) Median Value (MFB5 and MFB50 selection) Mean Value (MFB5 and MFB50 selection)
Engine C Cycles
25 20 15 10 5 0 0
5
10 MAPO [bar]
15
20
Validation of knock model The local evolution of pressure at sensor location has been compared to experimental p signals g 80 Experimental Simulated
70
In-Cylinder In-Cylinder Pressure Pressure [[[bar] bar]
60 50 40 30 20
10 0 -100
0.1
-80
-60
-40 -20 0 20 40 60 Crankshaft Angle [°] 950 mbar@4500 rpm, AFR=13.2, SA=37.5°
80
100
Simulated Experimental
0.09 0.08
FFT FFT Amplit Amplittude ude [bar] [bar]
0.07 0.06 0 05 0.05 0.04 0.03 0.02 0.01 0 0.5
1
1.5 Frequency [Hz]
2 4
x 10
Knock model Knock causes high in-homogeneities in the chamber Exhaust side
Spark plug
Intakeside
Knock model Knock causes high in-homogeneities in the chamber Exhaust side MAPO 7.9 bar
Spark plug MAPO 9 9.4 4b bar Intake side MAPO 5.8 5 8 bar
In the reference case knock induces high velocities (charge motion) in the chamber, raising the convective fluxes
Knock model EVALUATION OF KNOCK SEVERITY PARAMETERS Autoignition delay has been artificially perturbed in order to cause different severity of knocking condition with a fix Spark Advance
The amount of fuel mass involved in autoignition varies form 9% to 15% The aim of the analysis is to find knock severity indexes based on damage risk The indexes must base on information available by analyzing local pressure trace
Knock model COMBUSTION VELOCITY EVALUATION Fuel consumption rate [g/s]
Local fuel consumption rate [g/(s*cm^3)]
Knocking g combustion involves small volumes with high g specific p combustion rates
Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX
In case of severe knocking condition the maximum heat flux at the wall is five times higher than that referring to normal combustions •Increase in combustion rate Increase in convective fluxes •Increase
Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX
The difference between the integral value at EVO in case of non-knocking combustion and that of the knocking one can be used as a damage related parameter for knock detection purpose Reference case (blue line) has an integral wall heat flux out of trend with respect to the amount of fuel involved i knock in k k
Knock model During knock the heat losses increase, the net heat release should decrease, being evaluated neglecting the heat exchanges
CHRNET
dPlp ⎞ ⎛ γ dV 1 Plp V = ∫⎜ + ⎟ γ − 1 d ϑ γ − 1 d ϑ c c ⎠ ⎝ KIVA simulation@4500rpm, AFR13.2, SA 41.5
700
The CHRnet is not sensitive to sensor p position: a heat flux sensitive knock index can then be based on the evaluation of CHR
600
CHRnet [JJ]
500
Sensor spark location - knock Sensor exhaust side - knock Sensor intake side - knock Sensor spark location No Knock
400
300
200
100
0 -60
-40
-20
0
20 40 60 Crankshaft Angle [°]
80
100
120
14
Knock model The CHRNET, however, depends on other factors (e.g., combustion phasing, synthesized by MFB50): only cycles with a given value of MFB50 must be taken into account. MAPO values are randomly distributed in non-knocking conditions; as knock happens the correlation between MAPO MAPO-CHR CHRNET becomes high high. For a given SA only the cycles with average MFB50 are considered (cycles filt i ) filtering)
The correlation between MAPO and CHRNET is then introduced:
KNOCK SEVERITY INDEX
Knock model KNOCK SEVERITY INDEX The Cumulative Heat Release based index is sensitive to knock severity (increases with SA, after knock takes place) and is almost linearly related to the simulated heat losses
Conclusion - knock model A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: •Spark main electrical characteristics (Lump model) •Mixture Mi t thermophysical th h i l properties ti (thermodynamic (th d i lagrangian l i model) d l) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against g experimental p data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA
Conclusion - knock model The choice of knock model has been driven by the needs of the research: a deeper insight in knocking combustion for better understanding experimental pressure signal The AnB empirical model has been developed and tuned against experimental data. The reconstruction of pressure evolution at spark location is good good. The analysis of results has allowed to create a knock severity index based on the Cumulative Net Heat Release in the chamber chamber. The index is based on both on the high and low frequency content of pressure signals and proved to be position in-sensitive.
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Cycle by Cycle Variation Reduction of consumption Î Leaner CombustionÎ Cyclic Variability Cycle by Cycle Variation defined as the non-repeatability of the combustion process on a cycle p y resolved basis CAUSES AND INFLUENCING FACTORS MIXTURE COMPOSITION CYLINDER CHARGING IGNITION FACTORS IN CYLINDER FLOW FACTORS
MIXTURE COMPOSITION
•Air to fuel ratio •Mixture non-homogeneity •Fuel type •Residual gas fraction
Evaluation Of Cyclic Variation Configurations Examined Regime
FIXED > 15000rpm
Spark Advance
Fixed
Load
WOT
Mean Lambda
> Lambda of Maximum Laminar Flame Speed
Chain Measurement Encoder Indicating System
AVL 365, 360 pulses per revolution AVL Indimodul 621 (14 bit max 800kHz) bit,
Pressure Sensor
Kistler
Charge g amplifier p
Kistler
Analog Filter
Bessel, 6 poles
The pressure traces of 200 consecutive cycles have been recorded end filtered with a lowpass analog filter The methodology for the measurement of cyclic variability of an internal combustion engine g strongly influences its evaluation
Pressure Related Parameters
Pmax and ϑPmax ⎛ ∂P ⎞ and ϑ⎛ ∂P ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ∂ϑ ⎠max ⎝ ∂ϑ ⎠max IMEP
Coefficient Of Variation of IMEP COVIMEP
Std ( IMEP) = ×100 × 100 mean( IMEP)
IMEP ↓ ⇔ COV(IMEP) ↑ λREF
+0.04
+0.08 +0.10
Work output variations strongly influence engine driveability and performance and it has been demonstrated that they are well related to combustion instability
pdf
pdf
Frequency distribution of IMEP
IMEP
IMEP
pd df
pd df
Asymmetric
IMEP
IMEP
Care must be taken when using the COV of IMEP for the identification of the variability y of an engine, g because samples for leaner combustions are not compatible with a gaussian distribution
Analysis of exp. pressure traces The higher differences in pressure variability occur during the expansion phase where the positive phase, work output is generated. This well correlates with the differences in the variability of IMEP
Inlet Valve Closing Noise
Combustion Start
Analysis y of heat release Minimum in COV(P) on a crank angle b i can b basis be used d as th the ““starting t ti point of combustion”
Heat Release extracted from pressure by using the First Law of Thermodynamics HYPOTHESES: •No heat transfer to wall (adiabatic chamber) •Fixed Fixed Specific Heat Capacity Ratio k=1 k=1.3 3 •Theoretical (Rigid) Piston Displacement
Combustion angles g of MFB •Moving towards leaner mixture, the combustion durations increase affecting g all the combustion angles •Differences are mainly formed in the early stages of combustion (0-5%) and are not sensitively incremented for later angles •The laminar flame speed’s dependence on air to fuel ratio cannot justify this tendency because it should have been amplified p the different trends •Increase in the variability of combustion duration as the mixture air index is increased •This variability maintains nearly constant during the evolution of the first half of combustion
The A/F ratio influences the combustion duration and cyclic variability of the early stages of combustion b ti
Experimental analysis: conclusion The statistical investigation of the experimental in-cylinder pressure d t recorded data d d for f the th different diff t mean lambda l bd shows h that: th t •The cycle-by-cycle variation increases when leaner mixture are considered with respect to the optimum value for the highest flame speed •The reduction of IMEP well correlates with the increase of COV of IMEP •The The variability of work output is closely related to the instability of the early stages of combustion •The The IMEP distribution can not be described in terms of a gaussian function when the COV increases with leaner conbustion •The statistical analysis of combustion angles shows that the cyclic variation affects mainly the initial flame development i.e, 0-5% MFB duration thus suggesting that the cyclic variation is closely related to mixture tu e qua quality ty a around ou d spark spa
Simulation of combustion: λ uniform Initial Flow condition mapped from results of the simulation of intake process (AVL (AVLFIRE v8.4)
KIVA
Good reconstruction of the mean pressure curve tendencies t d i No information on Cyclic Variation
Slam = f ( λ , P, T ) Laminar Flame Speed Velocità Laminare 0.6
EXP
0.55 0.5 04 0.45 0.4 0.35 0.7 0.75 0.8 0.85 0.9 0.95 0.7
1
1.05 1.1 1.15 1.2
LambdaX
1.2
Mixture quality at ignition The analysis of the experimental pressure traces clearly indicated the early l stages t off combustion b ti as th the kkey processes iin th the onsett off cycle l by cycle variation. It is necessary to characterize the local mixture quality at the ignition with respect to: 1. The local cycle by cycle variability of the mixture composition 2 The fuel distribution at the spark plug location and its 2. homogeneity in the combustion chamber Any attempt A tt t to t reconstruct t t the th combustion b ti iinstability t bilit trends t d with ith leaner l mixture composition must concern with the imposition of these two information: a RANS methodology is presented for a preliminary parametric assessment of cycle by cycle variation in SI engine
Local A/F variability and mixture homogeneity
Local Lambda variability, (Baritaud et Al., Combustion And Diagnostics 2006)
Mixture homogeneity Length Scale
∫
λ ( s )ds
Sphere ( Lu )
4π L
2 u
= λmean
Lu
Description of RANS methodlogy λmean = REF Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
The variability of the local value of lambda at ignition is forced in the simulations of combustion The combustion process is initialized by forcing a local lambda different from the mean one one. As the flame kernel grows up, the chemical and physical proprieties tend to those of the mean mixture with a linear interpolation based on the ratio between the flame radius and Lu.
Description of RANS methodlogy λmean = REF Laminar Velocità Flame LaminareSpeed
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.04 Laminar Velocità Flame LaminareSpeed
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.08 Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.10 Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Statistical analysis y of results Velocità Laminare
The stochastic variability of the local lambda at the ignition is represented by four different perturbations from the mean value 0.7 0.7
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
A statistical analysis of the results of the RANS simulations is possible by imposing the cumulative probability of each sample as a weighting factor
Pressure variation analysis y EXP
The numerical methodology gy p performance in predicting the influence of the AFR on cyclic variability are aligned to experimental evidence The mixture non homogeneity together with the variation on the local value of lambda cause higher variation of pressure traces with leaner combustion
KIVA
This variation is located in the expansion phase, where the IMEP is mainly created
Variation of MFB angles g EXP
KIVA
Variation of IMEP
IM MEP
IMEP
STD L Locall L Lambda bd 0 0.02 02 STD Local Lambda 0.08 STD Local Lambda 0.12
Mean Lambda
COV of IMEP STD Local Lambda 0.02
COV V of IMEP
The combustion simulations clearly reveal a decrease in IMEP when increasing Air to Fuel ratio
STD Local Lambda 0.08 STD Local Lambda 0.12
Mean Lambda
The imposition of the variability of local lambda at the ignition has resulted in the identification of an increase in the variation of IMEP for leaner mixture An increase A i i the in th variability i bilit off the th initial local lambda causes not only an increase of COV of IMEP, but also a decrease of IMEP, IMEP because of the non-symmetrically distribution of IMEP over the mean value
STD ⇒ PMI
Variation of IMEP – lambda REF+0.1
The numerical methodology has well reconstructed the predominant non-symmetric behaviour of the system, though excite with a symmetric one
CCV - Conclusion A combined experimental and numerical methodology for the evaluation of the dependence of Cycle by Cycle Variation on mixture composition has been presented The estimation of the cyclic variation was based on the evaluation of the COV of IMEP, but for leanest combustion it has been demonstrated that the distribution of the IMEP is far from being well represented by a gauss-distribution The analysis of pressure data for different air to fuel ratios has revealed the close relation between the early stages of combustion and the cyclic variability A numerical methodology has been developed to analyze the influence of the air to fuel composition on the combustion process. The non-homogeneity of the mixture proved to influence much more the leaner combustions. The cyclic variability has been described by means of RANS simulation, by imposing a given local lambda variability on the combustion models. The results well reconstruct the increase in the cyclic variability of the leaner combustion in terms of IMEP statistic distributions and allow a better understanding of the root causes of cyclic variability of internal combustion engines
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OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Motivation FLAME KERNEL FORMATION IS A CRITICAL ISSUE IN ICE SINCE: ITS FEATURES AFFECT THE COMBUSTION DURATION CYCLE-TO-CYCLE VARIABILITY AFFECTS RIGHT EARLY BURNING RATE
THE 5%MFB TAKES 35-40% OF TOTAL COMBUSTION DURATION PHYSICAL PROCESS TO BE CONSIDERED PHYSICS OF SPARK DISCHARGE FLOW CONVECTIVE EFFECTS (ARC ELONGATION) TURBULENCE PHYSICAL CHARACTERISTICS OF THE MIXTURE (p, T, φ or pdf of φ)
Background CFD IGNITION MODELS ARE COMPLETELY RELIABLE ? NO IGNITION TIME AND LENGHT SCALES ARE TOO SMALL TO BE RESOLVED DURING PLASMA FORMATION ELECTRICAL CIRCUIT TOO COMPLEX TO BE MODELLED IN DETAIL COUPLING WITH MAIN COMBUSTION MODEL GRID DEPENDENCY
MANY 1D MODELS DECOUPLED FROM CFD SOLVER HAVE BEEN PRESENTED AND REFERENCED IN THE PAPER. THEY WOULD BE CONSIDERED ALL EULERIAN EXCEPT AKTIM AND DPKI.
Background LAGRANGIAN TRACKING REVIEW AKTIM MODEL - Duclos and Colin [COMODIA 2001] - The model includes a detailed description of the electrical system - Ignition kernels were modelled by a set of particles uniformly placed
DPIK - Fan et al. [SAE paper 1999-01-0175 ] - The flame kernel position is marked by particles
CURRENT MODEL EXPECTED CONTRIBUTION PROVIDE AN ALMOST GRID INDIPENDENT MODEL IMPROVE THE PHYSICAL GROUTH OF FLAME KERNEL EXPANSION RATE BASED ON MASS AND ENERGY CONSERVATION PROVIDE A DIRECT COUPLING METHOD WITH A FLAME SURFACE DENSITY MODEL
Spark Ignition Model ELECTRICAL SUB-MODEL FOR SPARK PLUG LUMP MODEL BASED ON THE MAIN AVAILABLE SPECIFICATIONS
LAGRANGIAN KERNEL SUBMODEL MASS AND ENERGY CONSERVATION SOLVED IN A VARIABLE CONTROL VOLUME DEFINED BY MEAN FLAME SURFACE COUPLING WITH MAIN SOLVER ENFORCED WITH PARTICULAR EMPHASIS ON FLAME SURFACE
Spark Ignition Model Lagrangian Ignition Model
Electrical submodel
LUMP/EASY MODELLING (NO WEAK POINT) PLASMA FORMATION NEGLECTED (ti (time and d llength th scales l ttoo short) h t)
Energy released during breakdown and glow phases:
Vbd2 Ebd = 2 Cbd ⋅ d ggapp
(Duclos and Colin, 2001)
E& glow = f ( Esp , t )
B Breakdown kd V Voltage lt evaluated l t d according di to t (Stone (St et. t Al, Al Sae S 2000): 2000)
P P + 324 Vbd = 4.3 + 13.6 d gap Tunb Tunb
Spark Ignition Model AFTER THE PLASMA PHASE: One flame kernel is deposited and initialized Flame Kernel is discretized by a set of triangular elements which expand radially
I-th cell
Each of these elements varies its area surface because of expansion and wrinkling by turbulence It contributes to reaction rate in its own reference fluid cells I-th
Spark Ignition Model Lagrangian Ignition Model
Thermodynamic model
Initial kernel conditions after plasma formation (Song and Sunwoo, Sunwoo 2000) :
⎡ ⎤ ⎢ ⎥ E − k 1 bd ⎥ ⋅ rk ,i = ⎢ ⎢ k ⎛ Tunb ⎞ ⎥ ⎟⎟π ⎥ p0 d gap ⎜⎜1 − ⎢ T ⎢⎣ i ⎠ ⎥ ⎝ ⎦
1/ 2
⎡ 1 ⎛ Tb ⎞ ⎤ ⎜ Ti = ⎢ ⎜ − 1⎟⎟ + 1⎥Tunb ⎠ ⎦ ⎣ k ⎝ Tunb
MASS CONSERVATION FOR A LAGRANGIAN SYSTEM
dm k = ρ unb ⋅ s lam , k ⋅ ( Ak ⋅ Ξ ) dt
Turbulence wrinkling
R Rearranged d -> >A An expression i for f th the mean kernel k l expansion i rate t
⎡ Vk drk ρ unb = slam ,k ⋅ Ξ − ⎢ dt ρk ⎣ Ak
⎛ 1 dTk 1 dp ⎞⎤ ⎜⎜ ⎟⎟⎥ − p dt ⎠⎦ ⎝ Tk dt
Spark Ignition Model Lagrangian Ignition Model
Thermodynamic model
If T≥3Tad heat conduction equation applies
⎛ ∂ 2Tpl 2 ∂Tpl ⎞ P − Q& w ⎟+ = α⎜ 2 + ⎜ ∂r ∂t r ∂r ⎠⎟ ρc pVk ⎝
∂Tpl
Energy Conservation if T Reasonable 2.00 R bl flow fl lenght l ht resolved l d in i RANS ((grid id size i 0.5 0 5 -> 1 mm))
Spark Ignition Model Lagrangian Ignition Model
Comparison with main Lagrangian models
Electrical Model AKTIM has a very sophisticated spark electrical model While in DPIK model is absent
Flame Kernel Deposition In present model, only one kernel is considered and its initial radius and temperature are evaluated depending on system characteristics and operating conditions. A “reasonble value” used in DPIK, while AKTIM adopts a different concept based on presumed multiple kernel ignition probability
Spark Ignition Model Lagrangian Ignition Model
Comparison with main Lagrangian models
Flame expansion velocity Derived from mass conservation according g to a lagrangian g g approach and accounting for wrinkling. In AKTIM each kernel is convected by gas flow. DPKI simply adds turbulence intensity to laminar flame velocity (questionable)
Coupling with Flame surface Models In AKTIM and DPKI is based on the density surface of burning partcile representing the kernel. In the present model Flame surface density is computed according to a spherical kernel expansion which is sensitive to mixture charactetistics and flow conditions. Therefore the ECFM models is inizialized with current Σ value in i-th cells
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Combustion model FLAMELET COMBUSTION MODEL (ECFM, (ECFM Colins et Al. Al 2003) ⎛ Σ ∂ ⎜ μ⎞ ρ ∂Σ ∂u%i Σ ∂ ⎜ ⎛ μt + = + ⎜ ⎟⋅ ∂t ∂xi ∂xi ⎜ ⎝ Sct Sc ⎠ ∂xi ⎜ ⎝
⎞ ⎟ ⎟ + ( P1 + P2 + P3 ) ⋅ Σ − D ⎟ ⎟ ⎠
FRESH GAS ENTHALPY TRANSPORT EQUATION
∂ρ hu ∂ρ u%i hu ∂ ⎛ ⎛ μt μ ⎞ ∂hu + = + ⎟⋅ ⎜⎜ ∂t ∂xi ∂xi ⎜⎝ ⎝ Sct Sc ⎠ ∂xi
⎞ ρ ∂p ε ⎟⎟ + ⋅ + ρ ⋅ k ⎠ ρ o ∂t
Better accuracy in estimating the evolution of unburned gases thermodynamic conditions during the combustion process
KIVA MODELS Ignition model
Lagrangian Ignition Model
Main Combustion model
ECFM – Flamelet (Colin 2003)
Mono-component Fuel
Shell Fuel/Isooctane
Laminar flame speed
Metchalghi & Keck
Turbulence model
k-ε+wall function
Wall heat transfer
Corrected Han and Reitz
Flame front chemistry
1-step 1 step chemistry
Post-flame chemistry
Meintjes and Morgan
Knock model
AnB (Lafossas 2003)
Validation 1.2 liters, 4 Cylinders Gasoline Engine
Configurations Examined Engine Speed [rpm]
2400
3000
IMEP [bar]
48 4.8
92 9.2
AFR [ ]
13.2
14.6
24.4° to 32.4°
21.1° to 34°
Spark Advance Sweep
Validation VALIDATION OF CFD MODELS •Ignition •Combustion velocity •Wall heat flux 580mbar@2400rpm AFR=13 580mbar@2400rpm, AFR 13.2 2 35
30
Comb Vel
SA=24.4 KIVA EXPERIMENTAL b
Pressurre [bar]
25
20
15
WHF
10
c 5
0 -60 60
a
INIT -40 40
-20 20
0 20 c.a. [deg ATDC]
40
60
80
580mbar@2400rpm, AFR=13.2, SA24.4 200
580mbar@2400rpm, AFR=13.2, SA24.4
100 0
200 -5
0
5
10
200 100 0
-5 5
0
5
10
200
15 20 MFB5
25
15 20 MFB25
25
30
35
40 150
30
35
40
100 0 200 100 0
-5
-5
0
0
5
5
10
10
15 20 MFB50
25
15 20 MFB90
25
30
35
Engine cycles
Engine cycle es Engine cycles En ngine cycles Engin ne cycles
Reference cycle definition
100 50
40 0 15
30
35
20 25 Pressure[bar] @ 19.2 crank angle ATDC
30
40
The reference cycle is used for the sake of CFD results validation: it must represent the ‘typical’ combustion that can be attained for the given operating condition Th reference The f cycle l is i nott necessarily il the th mean pressure cycle l on the th crankshaft domain The relationship between the combustion progress (released heat) and the incylinder pressure is non-linear, non linear thus a normal distribution in terms of pressure could imply a non-normal distribution in terms of pressure
580mbar@2400rpm, AFR=13.2, SA24.4 200
580mbar@2400rpm, AFR=13.2,SA=24.4
100 0
30 -5
0
5
10
15 20 MFB5
25
30
35
40
-5 5
0
5
10
15 20 MFB25
25
30
35
40
-5
0
5
10
15 20 MFB50
25
30
35
40
200 100 0 200 100 0 200 100 0
-5
0
5
10
15 20 MFB90
25
30
35
25 Pres ssure [bar]
Engine cycle es Engine cycles En ngine cycles Engin ne cycles
Reference cycle definition
40
The selection of the representative cycles is accomplished by filtering the combustion with MFBxx near the mean values. The mean cycle in terms of pressure is then evaluated on the basis of the representative cycles. l
20 Representative cycles Mean cycle Average cycle
15
10 -5
0
5
10 15 20 c.a. [deg ATDC]
25
30
35
Validation Well tuned combustion models should h ld b be able bl t to reproduce d experimental behavior when modifying input engine parameter
Pres ssure [bar]
580mbar@2400rpm, AFR=13.2 35
SA=24.4 KIVA
30
SA=26.4 KIVA SA=27.4 KIVA
25
SA=28.4 KIVA
20
SA=30.4 KIVA SA=32.4 KIVA
15
EXPERIMENTAL
SA=29.4 KIVA
10 5
The ignition model plays a key role in the reconstruction of combustion evolution with different spark advance
0
-50
0 50 c.a. [deg ATDC] 900mbar@3000rpm, AFR=14.6
The simulation is able to describe the variation in combustion velocity as a p advance without function of spark tuning parameters
SA=21.1 KIVA SA 23.2 SA=23 2 KIVA SA=25.1 KIVA
50 Press sure [bar]
Two different conditions have been simulated: different loads and different air to fuel ratio.
SA=27.3 KIVA
40
SA=29.2 KIVA SA=33.1 KIVA SA=34.0 KIVA
30
EXPERIMENTAL
20 10 0 -50
0 c.a. [deg ATDC]
50
Validation 580mbar@2400, AFR=13.2 35 MFB05 EXP MFB25 EXP
30
The first Law oh Thermodynamics is used to extract combustion information from experimental data and from simulation
MFB50 EXP MFB90 EXP
25
MFB05 KIVA MFB25 KIVA
Combustion angles
20
γ
dV 1 dP + ROHR = P γ − 1 dϑc γ − 1 dϑc
MFB50 KIVA MFB90 KIVA
15 10 5 0 -5 -10 -15 24
25
26
27
28 29 Spark Advance
30
31
32
33
850mbar@3000rpm, AFR=13.2 40 30 Combust ion angles
The model is able to well represent all the main combustion angles with different operating conditions
20 10 0 -10 20
22
24
26 28 Spark Advance
30
32
34
Validation 580mbar@2400rpm, AFR=13.2
900mbar@3000rpm, AFR=14.6
30
50 0-5% MFB EXP
0-5% MFB EXP
5-90% MFB EXP 0-5% MFB KIVA
5-90% MFB EXP 0-5% MFB KIVA
45
5-90% MFB KIVA
5-90% MFB KIVA
25
Combustion duratio ons
Combustion duratiions
40
20
35
30
25
20
15 22
23
24
25
26
27 28 29 Spark Advance
30
31
32
33
15 20
22
24
26 28 Spark Advance
30
32
34
Combustion durations The start of combustion is well represented (MFB5 – SI): the high SA cause an increase in the early stages of combustion because of the different thermodynamics at ignition.
Ignition model - Conclusion A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: •Spark main electrical characteristics (Lump model) •Mixture Mi t thermophysical th h i l properties ti (thermodynamic (th d i lagrangian l i model) d l) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against g experimental p data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Knock Model CHEMKIN Solution of several chemical equilibrium reactions
Time consuming
REDUCED KINETICS Shell Model
No tuning parameters
EMPIRICAL MODEL AnB (autoignition)
Imposition autoignition delay Based on experimental evidence
AnB KNOCK MODEL (Lafossas et Al, 2002, IFP) The model uses a two step chemistry for the simulation of auto-ignition auto ignition In the first step a precursor of the auto-ignition is calculated and then, when it reaches a critical concentration, the knock combustion is forced. AUTO-IGNITION DELAY
⎛ IO ⎞ θ = A⎜ ⎟ 100 ⎝ ⎠
3.4017
B −n T
P e
A, n, B tuning parameters
FUEL CONSUMPTION RATE
dYFu = YFu Ak with Ak = 104 e dt
3500 Tg
AnB KNOCK MODEL (Lafossas et Al, 2002, IFP)
The chemical kinetics during auto-ignition delay are not linear
dYp dt
YP
= YTFu F (θ )
Yp = YTFu
∫ϑ
=1
= Precursor
where
δ θ + 4(1 − δθ ) 2
F (θ ) = KNOCKING CRITERIA
dt
2
θ
Yp YTFu
REFERENCE KNOCK INTENSITY DEFINITION
Similar considerations for the reference mean combustion cycle y can be applied to define the ‘typical’ knocking cycle, for the given operating condition. The same procedure described before leads to the definition of a representative cycle, but the high-frequency components are filtered out by averaging different engine cycles. cycles MAPO (Maximum Amplitude of Pressure Oscillations) and KO (K (Knock k Onset) O t) parameters t can be b used d to t validate lid t th the highhi h frequency content of the pressure signal
(
MAPO = max Php
TDC + 70° TDC
)
KO = ϑc ( Php > thresholds )
REFERENCE KNOCK INTENSITY DEFINITION
Due to the non-normal distribution, the average MAPO is not the most likely value: the validation is carried out by means of the median MAPO MAPO distribution, distribution 900mbar@4500 rpm rpm, AFR=13 AFR=13.2, 2 SA=37 SA=37.5 5° 35 30
Measured Distribution (MFB5 and MFB50 selection) Median Value (MFB5 and MFB50 selection) Mean Value (MFB5 and MFB50 selection)
Engine C Cycles
25 20 15 10 5 0 0
5
10 MAPO [bar]
15
20
Validation of knock model The local evolution of pressure at sensor location has been compared to experimental p signals g 80 Experimental Simulated
70
In-Cylinder In-Cylinder Pressure Pressure [[[bar] bar]
60 50 40 30 20
10 0 -100
0.1
-80
-60
-40 -20 0 20 40 60 Crankshaft Angle [°] 950 mbar@4500 rpm, AFR=13.2, SA=37.5°
80
100
Simulated Experimental
0.09 0.08
FFT FFT Amplit Amplittude ude [bar] [bar]
0.07 0.06 0 05 0.05 0.04 0.03 0.02 0.01 0 0.5
1
1.5 Frequency [Hz]
2 4
x 10
Knock model Knock causes high in-homogeneities in the chamber Exhaust side
Spark plug
Intakeside
Knock model Knock causes high in-homogeneities in the chamber Exhaust side MAPO 7.9 bar
Spark plug MAPO 9 9.4 4b bar Intake side MAPO 5.8 5 8 bar
In the reference case knock induces high velocities (charge motion) in the chamber, raising the convective fluxes
Knock model EVALUATION OF KNOCK SEVERITY PARAMETERS Autoignition delay has been artificially perturbed in order to cause different severity of knocking condition with a fix Spark Advance
The amount of fuel mass involved in autoignition varies form 9% to 15% The aim of the analysis is to find knock severity indexes based on damage risk The indexes must base on information available by analyzing local pressure trace
Knock model COMBUSTION VELOCITY EVALUATION Fuel consumption rate [g/s]
Local fuel consumption rate [g/(s*cm^3)]
Knocking g combustion involves small volumes with high g specific p combustion rates
Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX
In case of severe knocking condition the maximum heat flux at the wall is five times higher than that referring to normal combustions •Increase in combustion rate Increase in convective fluxes •Increase
Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX
The difference between the integral value at EVO in case of non-knocking combustion and that of the knocking one can be used as a damage related parameter for knock detection purpose Reference case (blue line) has an integral wall heat flux out of trend with respect to the amount of fuel involved i knock in k k
Knock model During knock the heat losses increase, the net heat release should decrease, being evaluated neglecting the heat exchanges
CHRNET
dPlp ⎞ ⎛ γ dV 1 Plp V = ∫⎜ + ⎟ γ − 1 d ϑ γ − 1 d ϑ c c ⎠ ⎝ KIVA simulation@4500rpm, AFR13.2, SA 41.5
700
The CHRnet is not sensitive to sensor p position: a heat flux sensitive knock index can then be based on the evaluation of CHR
600
CHRnet [JJ]
500
Sensor spark location - knock Sensor exhaust side - knock Sensor intake side - knock Sensor spark location No Knock
400
300
200
100
0 -60
-40
-20
0
20 40 60 Crankshaft Angle [°]
80
100
120
14
Knock model The CHRNET, however, depends on other factors (e.g., combustion phasing, synthesized by MFB50): only cycles with a given value of MFB50 must be taken into account. MAPO values are randomly distributed in non-knocking conditions; as knock happens the correlation between MAPO MAPO-CHR CHRNET becomes high high. For a given SA only the cycles with average MFB50 are considered (cycles filt i ) filtering)
The correlation between MAPO and CHRNET is then introduced:
KNOCK SEVERITY INDEX
Knock model KNOCK SEVERITY INDEX The Cumulative Heat Release based index is sensitive to knock severity (increases with SA, after knock takes place) and is almost linearly related to the simulated heat losses
Conclusion - knock model A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: •Spark main electrical characteristics (Lump model) •Mixture Mi t thermophysical th h i l properties ti (thermodynamic (th d i lagrangian l i model) d l) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against g experimental p data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA
Conclusion - knock model The choice of knock model has been driven by the needs of the research: a deeper insight in knocking combustion for better understanding experimental pressure signal The AnB empirical model has been developed and tuned against experimental data. The reconstruction of pressure evolution at spark location is good good. The analysis of results has allowed to create a knock severity index based on the Cumulative Net Heat Release in the chamber chamber. The index is based on both on the high and low frequency content of pressure signals and proved to be position in-sensitive.
OUTLINE SPARK IGNITION MODEL
COMBUSTION MODEL
KNOCK MODEL
ANALYSIS OF CYCLE BY CYCLE VARIABILITY
Cycle by Cycle Variation Reduction of consumption Î Leaner CombustionÎ Cyclic Variability Cycle by Cycle Variation defined as the non-repeatability of the combustion process on a cycle p y resolved basis CAUSES AND INFLUENCING FACTORS MIXTURE COMPOSITION CYLINDER CHARGING IGNITION FACTORS IN CYLINDER FLOW FACTORS
MIXTURE COMPOSITION
•Air to fuel ratio •Mixture non-homogeneity •Fuel type •Residual gas fraction
Evaluation Of Cyclic Variation Configurations Examined Regime
FIXED > 15000rpm
Spark Advance
Fixed
Load
WOT
Mean Lambda
> Lambda of Maximum Laminar Flame Speed
Chain Measurement Encoder Indicating System
AVL 365, 360 pulses per revolution AVL Indimodul 621 (14 bit max 800kHz) bit,
Pressure Sensor
Kistler
Charge g amplifier p
Kistler
Analog Filter
Bessel, 6 poles
The pressure traces of 200 consecutive cycles have been recorded end filtered with a lowpass analog filter The methodology for the measurement of cyclic variability of an internal combustion engine g strongly influences its evaluation
Pressure Related Parameters
Pmax and ϑPmax ⎛ ∂P ⎞ and ϑ⎛ ∂P ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ∂ϑ ⎠max ⎝ ∂ϑ ⎠max IMEP
Coefficient Of Variation of IMEP COVIMEP
Std ( IMEP) = ×100 × 100 mean( IMEP)
IMEP ↓ ⇔ COV(IMEP) ↑ λREF
+0.04
+0.08 +0.10
Work output variations strongly influence engine driveability and performance and it has been demonstrated that they are well related to combustion instability
Frequency distribution of IMEP
IMEP
IMEP
pd df
pd df
Asymmetric
IMEP
IMEP
Care must be taken when using the COV of IMEP for the identification of the variability y of an engine, g because samples for leaner combustions are not compatible with a gaussian distribution
Analysis of exp. pressure traces The higher differences in pressure variability occur during the expansion phase where the positive phase, work output is generated. This well correlates with the differences in the variability of IMEP
Inlet Valve Closing Noise
Combustion Start
Analysis y of heat release Minimum in COV(P) on a crank angle b i can b basis be used d as th the ““starting t ti point of combustion”
Heat Release extracted from pressure by using the First Law of Thermodynamics HYPOTHESES: •No heat transfer to wall (adiabatic chamber) •Fixed Fixed Specific Heat Capacity Ratio k=1 k=1.3 3 •Theoretical (Rigid) Piston Displacement
Combustion angles g of MFB •Moving towards leaner mixture, the combustion durations increase affecting g all the combustion angles •Differences are mainly formed in the early stages of combustion (0-5%) and are not sensitively incremented for later angles •The laminar flame speed’s dependence on air to fuel ratio cannot justify this tendency because it should have been amplified p the different trends •Increase in the variability of combustion duration as the mixture air index is increased •This variability maintains nearly constant during the evolution of the first half of combustion
The A/F ratio influences the combustion duration and cyclic variability of the early stages of combustion b ti
Experimental analysis: conclusion The statistical investigation of the experimental in-cylinder pressure d t recorded data d d for f the th different diff t mean lambda l bd shows h that: th t •The cycle-by-cycle variation increases when leaner mixture are considered with respect to the optimum value for the highest flame speed •The reduction of IMEP well correlates with the increase of COV of IMEP •The The variability of work output is closely related to the instability of the early stages of combustion •The The IMEP distribution can not be described in terms of a gaussian function when the COV increases with leaner conbustion •The statistical analysis of combustion angles shows that the cyclic variation affects mainly the initial flame development i.e, 0-5% MFB duration thus suggesting that the cyclic variation is closely related to mixture tu e qua quality ty a around ou d spark spa
Simulation of combustion: λ uniform Initial Flow condition mapped from results of the simulation of intake process (AVL (AVLFIRE v8.4)
KIVA
Good reconstruction of the mean pressure curve tendencies t d i No information on Cyclic Variation
Slam = f ( λ , P, T ) Laminar Flame Speed Velocità Laminare 0.6
EXP
0.55 0.5 04 0.45 0.4 0.35 0.7 0.75 0.8 0.85 0.9 0.95 0.7
1
1.05 1.1 1.15 1.2
LambdaX
1.2
Mixture quality at ignition The analysis of the experimental pressure traces clearly indicated the early l stages t off combustion b ti as th the kkey processes iin th the onsett off cycle l by cycle variation. It is necessary to characterize the local mixture quality at the ignition with respect to: 1. The local cycle by cycle variability of the mixture composition 2 The fuel distribution at the spark plug location and its 2. homogeneity in the combustion chamber Any attempt A tt t to t reconstruct t t the th combustion b ti iinstability t bilit trends t d with ith leaner l mixture composition must concern with the imposition of these two information: a RANS methodology is presented for a preliminary parametric assessment of cycle by cycle variation in SI engine
Local A/F variability and mixture homogeneity
Local Lambda variability, (Baritaud et Al., Combustion And Diagnostics 2006)
Mixture homogeneity Length Scale
∫
λ ( s )ds
Sphere ( Lu )
4π L
2 u
= λmean
Lu
Description of RANS methodlogy λmean = REF Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
The variability of the local value of lambda at ignition is forced in the simulations of combustion The combustion process is initialized by forcing a local lambda different from the mean one one. As the flame kernel grows up, the chemical and physical proprieties tend to those of the mean mixture with a linear interpolation based on the ratio between the flame radius and Lu.
Description of RANS methodlogy λmean = REF Laminar Velocità Flame LaminareSpeed
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.04 Laminar Velocità Flame LaminareSpeed
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.08 Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Description of RANS methodlogy λmean = REF + 0.10 Laminar Flame Speed Velocità Laminare
0.7 0.7
Lu
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
Statistical analysis y of results Velocità Laminare
The stochastic variability of the local lambda at the ignition is represented by four different perturbations from the mean value 0.7 0.7
0.75
0.8
0.85
0.9
0.95 LambdaX
1
1.05
1.1
1.15
1.2 1.2
A statistical analysis of the results of the RANS simulations is possible by imposing the cumulative probability of each sample as a weighting factor
Pressure variation analysis y EXP
The numerical methodology gy p performance in predicting the influence of the AFR on cyclic variability are aligned to experimental evidence The mixture non homogeneity together with the variation on the local value of lambda cause higher variation of pressure traces with leaner combustion
KIVA
This variation is located in the expansion phase, where the IMEP is mainly created
Variation of MFB angles g EXP
KIVA
Variation of IMEP
IM MEP
IMEP
STD L Locall L Lambda bd 0 0.02 02 STD Local Lambda 0.08 STD Local Lambda 0.12
Mean Lambda
COV of IMEP STD Local Lambda 0.02
COV V of IMEP
The combustion simulations clearly reveal a decrease in IMEP when increasing Air to Fuel ratio
STD Local Lambda 0.08 STD Local Lambda 0.12
Mean Lambda
The imposition of the variability of local lambda at the ignition has resulted in the identification of an increase in the variation of IMEP for leaner mixture An increase A i i the in th variability i bilit off the th initial local lambda causes not only an increase of COV of IMEP, but also a decrease of IMEP, IMEP because of the non-symmetrically distribution of IMEP over the mean value
STD ⇒ PMI
Variation of IMEP – lambda REF+0.1
The numerical methodology has well reconstructed the predominant non-symmetric behaviour of the system, though excite with a symmetric one
CCV - Conclusion A combined experimental and numerical methodology for the evaluation of the dependence of Cycle by Cycle Variation on mixture composition has been presented The estimation of the cyclic variation was based on the evaluation of the COV of IMEP, but for leanest combustion it has been demonstrated that the distribution of the IMEP is far from being well represented by a gauss-distribution The analysis of pressure data for different air to fuel ratios has revealed the close relation between the early stages of combustion and the cyclic variability A numerical methodology has been developed to analyze the influence of the air to fuel composition on the combustion process. The non-homogeneity of the mixture proved to influence much more the leaner combustions. The cyclic variability has been described by means of RANS simulation, by imposing a given local lambda variability on the combustion models. The results well reconstruct the increase in the cyclic variability of the leaner combustion in terms of IMEP statistic distributions and allow a better understanding of the root causes of cyclic variability of internal combustion engines
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