Modeling plume from pipeline discharge of dredged material
Modeling plume from pipeline discharge of dredged material Sung-Chan Kim1, Paul R. Schroeder2, Terry K. Gerald2, Tahirih C. Lackey1, Joseph Z. Gailani1,Presenter
1Coastal
and Hydraulics Laboratory
2Environmental
Laboratory
October 24, 2012
Outlines •Processes •Existing models •Model improvements •Examples and issues •Concluding remarks BUILDING STRONG®
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Pipeline Discharge Processes
Turbidity Plume Slow Settling Entrainment Hindered Settling Fluid Mud Underflow Accumulated or non-flowing mud
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Pipeline Discharge Processes •Multi-phase plume (open water discharge, overflow, etc) •Both inertial force and buoyancy are important •Koh & Chang (1973) Convective descent Dynamic collapse Passive diffusion ← lacking dense plume dynamics
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Innovative solutions for a safer, better world
Existing Models •Automated Dredging Disposal Alternative Management System (ADDAMS) STFATE– intermittent disposal (Johnson & Fong, 1995) CDFATE – continuous disposal (D-CORMIX: Doneker et al, 2004) •Brandsma & Divoky (1976) – extended Koh & Chang (1973) DIFID – intermittent disposal (became STFATE) DIFCD – continuous disposal •PDFATE (Teeter, 2002) –version 0 Based on turbidity current dynamics over sloped bottom
BUILDING STRONG®
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STFATE
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Schematics of DIFCD
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DIFCD Jet d π r 2 ρ= U ) E ρ a − ∑ Si ρ i ( ds i d π r 2 ρUU = B + E ρ aU a − ∑ Si ρ iU − FD ds i d π r 2 ( ρ a ( 0 ) − ρ )= U E ( ρ a ( 0 ) − ρ a ) − ∑ Si ( ρ a ( 0 ) − ρ i ) ds i = E Emomentum + Ethermal Entrainment
(
)
(
)
Si = 2rw fiCsi
Settling
Dynamic Collapse d = (π abL ) E ρ a − ∑ Si ρ i ds i d M = B + E ρ aU a − ∑ Si ρ iU − D ds i d = ( B ) E ( ρ a ( 0 ) − ρ a ) − ∑ Si ( ρ a ( 0 ) − ρ i ) ds i E = Ecollapse Entrainment
( )
Si = 2bLw fiCsi
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Settling
Innovative solutions for a safer, better world
PDFATE (version 0)
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Innovative solutions for a safer, better world
PDFATE (version 0) Mass conservation
dQ S = B EwU − − PWs dx C Entrainment
Deposition
Water loss
Momentum conservation 1.43C f Ri tan θ Ri ∆ρ dQ Ri ∆ρ dCQ Ri dB h − + − + 2 + − + − 1 ρ ρ 2 2 2 h h Qdx CQdx Bdx dh = 1 − Ri dx Friction
Body force (slope & buoyancy)
Spreading E Ri 1.7 w Cf dB = 1 − dx B 2 − 1 , if Ew ~ 0 1.4 c1hRi
BUILDING STRONG®
Innovative solutions for a safer, better world
Application – Newark Harbor
BUILDING STRONG®
Innovative solutions for a safer, better world
DIFCD
D-CORMIX)
Clouds at t=3600 s
1.6
3
Sand Fines1 Fines2
1.8
C (kg/m )
0.2
2
0.15 0.1 0.05 0 0 10
10
1
10
2
10
3
X (m)
3
Mass Entrained (ft )
1.4
6 BV (m)
1.2 1
4 2
0.8 0 0 10
0.6
10
1
10
2
10
3
X (m) 400 BH (m)
0.4 0.2 0 800
300 200 100
1000
1200
1400 Distance (ft)
1600
1800
2000
0 0 10
10
1
10
2
10
3
X (m)
•Finer – more entrainment •Each time step produces 2 cloudes •Initial entrainment •Entrainment after collapse BUILDING STRONG®
•Discontinuity between jet plume and boundary impingement •Thinning & spreading of plume after impingement Innovative solutions for a safer, better world
Axi-symmetic Flow development
propagation Gravity flow
Distinct ambient and gravity flows BUILDING STRONG®
3D bottom features Innovative solutions for a safer, better world
New PDFATE
Model Schematics
Jet Plume
Gravity Plume UN xN
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Gravity plume 2πrhu = Q
Mass conservation reach
thickness
Flux (from jet plume)
speed Froude Number
Momentum conservation
dr u= = Fr g 0' φh dt Reduced gravity Sediment fraction
Settling velocity
φ dφ = wsf dt h
Particle conservation
r u BUILDING STRONG®
h Innovative solutions for a safer, better world
Gravity plume Length scale
r 2 η ≈ η 0 exp − r*
Plume thickness
Deposit
r* = Q πw fs
Radial distance BUILDING STRONG®
Innovative solutions for a safer, better world
Shallow Water Equation Mass conservation
∂h ∂ + ( uh ) ∂t ∂x
Momentum conservation
∂ ∂ 2 1 2 0 ( uh ) + u h + g ′h = 2 ∂t ∂x
Particle conservation
∂ ∂ − w fsφ (φ h ) + ( uφ h ) = ∂t ∂x
BC
u ( 0, t ) = 0 u ( xN , t ) = Fr ( g ′hN )
1 2
h X=0
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u
hN X=xN
Innovative solutions for a safer, better world
Tribell Shoal, James River
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Innovative solutions for a safer, better world
TSA018r
TSA017r 200
1
200
2 180 2
4
160
6
140
160
140 3
10
120
Bin
120
Secondary plume
8
Bin
Hourly snapshot of ADCP backscatter
180
100
4
100
80
80 5
12
60
14
40
60
40 6
20 16 TSA019r 400
350
200 300
2
250
200 Progress
100
150
7
0
50
Stripping (very small) 50
100
150 Progress
200
20
0
250
180 4
160
6
140
120
Bin
8 100 10 80 12
60
14
40
20
TSA021r
TSA020r 200
200
16 2 50
100
150
200
250
300 350 Progress
400
450
500
2
0
550
180
180
160
4
160
4
140
140
6
6
100
120
Bin
Bin
120 8
8
100
80
10
80 10
60
60
12 40
12
40
14 20
BUILDING STRONG®
20 14
16
50
100
150
200 250 Progress
300
350
400
450
0
Innovative solutions for a safer, better world 0 500
450
400
350
300
250 Progress
200
150
100
50
Concluding Remarks •New PDFATE Jet plume from DIFCD Axi-symmetric Gravity plume (box model)
•Ongoing effort 2-D shallow water equation Implement stripping function
•Future plan 3 dimensional bedforms Multiphase flows BUILDING STRONG®
Innovative solutions for a safer, better world
1Coastal
and Hydraulics Laboratory
2Environmental
Laboratory
October 24, 2012
Outlines •Processes •Existing models •Model improvements •Examples and issues •Concluding remarks BUILDING STRONG®
Innovative solutions for a safer, better world
Pipeline Discharge Processes
Turbidity Plume Slow Settling Entrainment Hindered Settling Fluid Mud Underflow Accumulated or non-flowing mud
BUILDING STRONG®
Innovative solutions for a safer, better world
Pipeline Discharge Processes •Multi-phase plume (open water discharge, overflow, etc) •Both inertial force and buoyancy are important •Koh & Chang (1973) Convective descent Dynamic collapse Passive diffusion ← lacking dense plume dynamics
BUILDING STRONG®
Innovative solutions for a safer, better world
Existing Models •Automated Dredging Disposal Alternative Management System (ADDAMS) STFATE– intermittent disposal (Johnson & Fong, 1995) CDFATE – continuous disposal (D-CORMIX: Doneker et al, 2004) •Brandsma & Divoky (1976) – extended Koh & Chang (1973) DIFID – intermittent disposal (became STFATE) DIFCD – continuous disposal •PDFATE (Teeter, 2002) –version 0 Based on turbidity current dynamics over sloped bottom
BUILDING STRONG®
Innovative solutions for a safer, better world
STFATE
BUILDING STRONG®
Innovative solutions for a safer, better world
Schematics of DIFCD
BUILDING STRONG®
Innovative solutions for a safer, better world
DIFCD Jet d π r 2 ρ= U ) E ρ a − ∑ Si ρ i ( ds i d π r 2 ρUU = B + E ρ aU a − ∑ Si ρ iU − FD ds i d π r 2 ( ρ a ( 0 ) − ρ )= U E ( ρ a ( 0 ) − ρ a ) − ∑ Si ( ρ a ( 0 ) − ρ i ) ds i = E Emomentum + Ethermal Entrainment
(
)
(
)
Si = 2rw fiCsi
Settling
Dynamic Collapse d = (π abL ) E ρ a − ∑ Si ρ i ds i d M = B + E ρ aU a − ∑ Si ρ iU − D ds i d = ( B ) E ( ρ a ( 0 ) − ρ a ) − ∑ Si ( ρ a ( 0 ) − ρ i ) ds i E = Ecollapse Entrainment
( )
Si = 2bLw fiCsi
BUILDING STRONG®
Settling
Innovative solutions for a safer, better world
PDFATE (version 0)
BUILDING STRONG®
Innovative solutions for a safer, better world
PDFATE (version 0) Mass conservation
dQ S = B EwU − − PWs dx C Entrainment
Deposition
Water loss
Momentum conservation 1.43C f Ri tan θ Ri ∆ρ dQ Ri ∆ρ dCQ Ri dB h − + − + 2 + − + − 1 ρ ρ 2 2 2 h h Qdx CQdx Bdx dh = 1 − Ri dx Friction
Body force (slope & buoyancy)
Spreading E Ri 1.7 w Cf dB = 1 − dx B 2 − 1 , if Ew ~ 0 1.4 c1hRi
BUILDING STRONG®
Innovative solutions for a safer, better world
Application – Newark Harbor
BUILDING STRONG®
Innovative solutions for a safer, better world
DIFCD
D-CORMIX)
Clouds at t=3600 s
1.6
3
Sand Fines1 Fines2
1.8
C (kg/m )
0.2
2
0.15 0.1 0.05 0 0 10
10
1
10
2
10
3
X (m)
3
Mass Entrained (ft )
1.4
6 BV (m)
1.2 1
4 2
0.8 0 0 10
0.6
10
1
10
2
10
3
X (m) 400 BH (m)
0.4 0.2 0 800
300 200 100
1000
1200
1400 Distance (ft)
1600
1800
2000
0 0 10
10
1
10
2
10
3
X (m)
•Finer – more entrainment •Each time step produces 2 cloudes •Initial entrainment •Entrainment after collapse BUILDING STRONG®
•Discontinuity between jet plume and boundary impingement •Thinning & spreading of plume after impingement Innovative solutions for a safer, better world
Axi-symmetic Flow development
propagation Gravity flow
Distinct ambient and gravity flows BUILDING STRONG®
3D bottom features Innovative solutions for a safer, better world
New PDFATE
Model Schematics
Jet Plume
Gravity Plume UN xN
BUILDING STRONG®
Innovative solutions for a safer, better world
Gravity plume 2πrhu = Q
Mass conservation reach
thickness
Flux (from jet plume)
speed Froude Number
Momentum conservation
dr u= = Fr g 0' φh dt Reduced gravity Sediment fraction
Settling velocity
φ dφ = wsf dt h
Particle conservation
r u BUILDING STRONG®
h Innovative solutions for a safer, better world
Gravity plume Length scale
r 2 η ≈ η 0 exp − r*
Plume thickness
Deposit
r* = Q πw fs
Radial distance BUILDING STRONG®
Innovative solutions for a safer, better world
Shallow Water Equation Mass conservation
∂h ∂ + ( uh ) ∂t ∂x
Momentum conservation
∂ ∂ 2 1 2 0 ( uh ) + u h + g ′h = 2 ∂t ∂x
Particle conservation
∂ ∂ − w fsφ (φ h ) + ( uφ h ) = ∂t ∂x
BC
u ( 0, t ) = 0 u ( xN , t ) = Fr ( g ′hN )
1 2
h X=0
BUILDING STRONG®
u
hN X=xN
Innovative solutions for a safer, better world
Tribell Shoal, James River
BUILDING STRONG®
Innovative solutions for a safer, better world
TSA018r
TSA017r 200
1
200
2 180 2
4
160
6
140
160
140 3
10
120
Bin
120
Secondary plume
8
Bin
Hourly snapshot of ADCP backscatter
180
100
4
100
80
80 5
12
60
14
40
60
40 6
20 16 TSA019r 400
350
200 300
2
250
200 Progress
100
150
7
0
50
Stripping (very small) 50
100
150 Progress
200
20
0
250
180 4
160
6
140
120
Bin
8 100 10 80 12
60
14
40
20
TSA021r
TSA020r 200
200
16 2 50
100
150
200
250
300 350 Progress
400
450
500
2
0
550
180
180
160
4
160
4
140
140
6
6
100
120
Bin
Bin
120 8
8
100
80
10
80 10
60
60
12 40
12
40
14 20
BUILDING STRONG®
20 14
16
50
100
150
200 250 Progress
300
350
400
450
0
Innovative solutions for a safer, better world 0 500
450
400
350
300
250 Progress
200
150
100
50
Concluding Remarks •New PDFATE Jet plume from DIFCD Axi-symmetric Gravity plume (box model)
•Ongoing effort 2-D shallow water equation Implement stripping function
•Future plan 3 dimensional bedforms Multiphase flows BUILDING STRONG®
Innovative solutions for a safer, better world
