2009 january 10-12 cfd simulation of open channel flooding flows and scouring around bridge...
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2009 January 10-12 www.kostic.niu.edu
CFD Simulation of Open Channel CFD Simulation of Open Channel Flooding FlowsFlooding Flows
and Scouring Around Bridge Structuresand Scouring Around Bridge Structures
The 6th WSEAS International Conference on FLUID MECHANICS The 6th WSEAS International Conference on FLUID MECHANICS ((WSEAS - FLUIDS'09WSEAS - FLUIDS'09))
Ningbo, China, January 10-12, 2009Ningbo, China, January 10-12, 2009
B. D. ADHIKARY , P. MajumdarB. D. ADHIKARY , P. Majumdar and M. Kosticand M. Kostic Department of Mechanical EngineeringDepartment of Mechanical EngineeringNORTHERN ILLINOIS UNIVERSITYNORTHERN ILLINOIS UNIVERSITY
Overview INTRODUCTION LITERATURE REVIEW OBJECTIVE PROBLEM DEFINITION COMPUTATIONAL MODEL VALIDATION OF FORCE COEFFICIENTS SCOUR PHENOMENON DESCRIPTION OF SCOUR METHODOLOGY DETERMINATION OF EQUILIBRIUM SCOUR EFFECT OF SCOURING ON FORCE COEFFICIENTS CONCLUSIONS & RECOMMENDATIONS
INTRODUCTIONBridge failure analysis is important from CFD perspectiveMost of the bridge fails due to flood in an open channelUnder flooding conditions, force around the bridge becomes very highHigh stresses caused at the channel bed results in scourDesign and analysis software shows a way to design a cost-effective and quality bridge structureExperimental results throw the challenge to have solution for the real-life problem
Scour hole
Failed bridge Piers
Fig 1: Bridge failure
OBJECTIVE Calculation of force coefficients around the bridge under various flooding conditions Identification of proper turbulence model and modeling option Analysis of turbulence effects on the bridge Comparison of force coefficients with experimental results Study of pressure scour development Development of a methodology to analyze pressure scour Comparison of computational scour depth with experiment Effect of scouring on force coefficients
LITERATURE REVIEWLiteratures related to numerical methods and modeling techniques of open channel flow:
Ramamurthy et al. analyzed the pressure and velocity distributions for an open channel flow using 2-D, Standard k- Turbulence Model.
Koshizuka et al. simulated the free surface of a collapsing liquid column for an incompressible viscous flow using VOF technique and found good agreement between simulation and experimental results.
LITERATURE REVIEWLiteratures related to pressure scour analysis:
Guo et al. projected an analytical model for partially and fully submerged flows around the bridge based on a critical shear stress correlation which showed good agreement with the experimental results.
Benoit et al. proposed a new relationship between the roughness height and the main hydrodynamic and sediment parameters for plane beds, under steady operating conditions.
PROBLEM DEFINITION
x
Y
Z
hu
hb
s
W
Vu
Need to find out a computational model and modeling technique for turbulence and force analysis around the bridge using STAR-CD CFD software.
Fig 2: Characteristic dimensions for the channel and the bridge
Fig 3: Detail bridge dimension
0.029m (1.14")
0.029m (1.15")
0.027m (1.05")
0.25m (9.861")
0.005m (0.188")
0.01m (0.4")
0.034m (1.35") 0.01m
(0.54")
0.00254m (0.159")
0.0045m(0.259")
X
Y
Z
0.004m (0.126")
DIMENSIONLESS PARAMETERS
huDVRe
c
u
gL
VFr
s
hhh bu
*
Du
DD
AV
FC
25.0
Lu
LL
AV
FC
25.0
Reynolds Number: Froude Number:
Inundation Ratio:
Drag Force Coefficient:
Lift Force Coefficient:
COMPUTATIONAL MODELTwo computational model are used.
Free-Surface or VOF Model Single-Phase Flat-Top Model
Governing Equations:
0)(
ii
uxt
iii
ijjij
i Fgx
Puu
xu
t
)()(
Where
ijk
k
i
j
j
iij x
u
x
u
x
u
3
2For Laminar Flow
''3
2jiij
k
ktot
i
j
j
itotij uu
x
u
x
u
x
u
For Turbulent Flow
0)(
ut ii
Additional Transport Equation for VOF:
Where V
Vii
‘VOF’ MODELAIR (VOF=0)
WATER (VOF = 1)
x
Y
Z
1.524m (60") 0.26m (10.237") 1.518m (59.763")
3.302m (130")
0.15m(5.9055")
0.058m(2.29")
0.029m(1.145")
0.2178m(8.565")
0.3048m(12")
Fig 4: Computational Domain for VOF Model
Fig 5: Mesh Structure for VOF Model
BOUNDARY CONDITIONS SLIP WALL
OUTLET
NO SLIP WALL
WATER INLET
AIR INLET
SYMPLANE
Air & Water Inlet:Velocity inlet having 0.35 m/s free-stream
velocityOutlet:
Constant pressure gradient at boundary surface
Bottom Wall: Hydro-dynamically smooth no-slip wall
Fig 6: Boundary conditions for VOF Model
‘VOF’ SIMULATION PARAMETERSAir & Water Inlet Velocity 0.35 m/s
Turbulent Kinetic Energy 0.00125 m2/s2
Turbulent Dissipation Rate 0.000175m2/s3
Solution Method Transient
Solver Algebric Multigrid (AMG)
Solution Algorithm SIMPLE
Relaxation FactorPressure - 0.3Momentum, Turbulence,Viscosity - 0.7
Differencing Scheme MARS
Convergence Criteria 10-2Computation time 200 sec
TURBULENCE MODELS USED
Two-Equation Models• k- High Reynolds• k- Low Reynolds• k- Chen• k- Standard Quadratic High Reynolds• k- Suga Quadratic High Reynolds
Reynolds Stress Models• RSM/Gibson-Launder (Standard) • RSM/Gibson-Launder (Craft)• RSM/Speziale, Sarkar and Gatski
STEADY-STATE DEVELOPMENTt = 10 sec t = 50 sec
t = 90 sec t = 100 sec
t = 120 sec t = 150 sec
t = 190 sec t = 200 sec
Fig 7: Steady-state development of k-Low-Re VOF Model
PARAMETRIC EFFECT ON FORCE COEFFICIENTS
-2.0
-1.6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CL
0.1
0.05
0.02
0.01
Effect of Time Steps on Lift Coefficient for k-e Low-Re TM
Temporal Effect:
Drag Coefficient
Lift Coefficient
Fig 8
Effect of Time Steps on Drag Coefficient for k- Low-Re TM
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CD
0.1
0.05
0.02
0.01
Effect of Slip & Symmetry BC at the Flat-Top:
Drag Coefficient
Lift Coefficient
Fig 9
Comparison Between Symmetry and Slip top-wall for Low-Re TM for CL Calculation
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CL Symmetry
Slip
Comparison Between Symmetry and Slip top-wall for Low-Re TM for CD Calculation
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CD Symmetry
Slip
Effect of Bridge Opening:
Drag Coefficient
Fig 10
Effect of bridge openings (hb) on CD
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CD
hb=15cm
hb=12cm
hb=10.125cm
FORCE COEFFICIENT COMPARISON OF FORCE COEFFICIENT COMPARISON OF k-k- MODELS MODELS
Comparison of CD among k- Models
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CD
k-ep High-Re
k-ep StandardQuadraticHigh-Re
k-ep SugaQuadraticHigh-Re
k-ep Low-Re
k-ep Chen
ExperimentalData
Comparison of CL among k- Models
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CL
k-ep High-Re
k-ep StandardQuadraticHigh-Re
k-ep SugaQuadraticHigh-Re
k-ep Low-Re
k-ep Chen
ExperimentalData
Drag Coefficient
Lift Coefficient
Fig 11
FORCE COEFFICIENT COMPARISON OF RSM MODELS FORCE COEFFICIENT COMPARISON OF RSM MODELS
Drag Coefficient
Lift Coefficient
Fig 12
Comparison of CL among RSM Models
-3.2
-2.8
-2.4
-2.0
-1.6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CL
RSM-GL-Craft
RSM-GL-Standard
RSM-SSG
ExperimentalData
Comparison of CD among RSM Models
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
0 20 40 60 80 100 120 140 160 180 200 220
Time (sec)
CD
RSM-GL-Craft
RSM-GL-Standard
RSM-SSG
ExperimentalData
DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models
Fig 13
Comparison of CD for different TM wrt h*
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
h*
CD
Experimental
k-ep High-Re
k-ep low-Re
RNG
Chen
RSM_GL_Craft
RSM_GL_Standard
RSM_SSG
k-omega StandardHigh-Re
k-omega SST High-Re
k-omega SST Low-Re
k-ep StandardQuadratic High-Re
k-ep Suga QuadraticHigh-Re
LIFT COEFFICIENT COMPARISON FOR ALL Turb. ModelsLIFT COEFFICIENT COMPARISON FOR ALL Turb. Models
Fig 14
Comparison of CL for different TM wrt h*
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
h*
CL
Experimental
k-epsilon High-Re
k-epsilon Low-Re
k-epsilon RNG
k-epsilon Chen
RSM_GL_Craft
RSM_GL_Standard
RSM_SSG
k-omega Standard High-Re
k-omega SST High-Re
k-omega SST Low-Re
k-epsilon StandardQuadratic High-Re
k-epsilon SugaQuadratic High-Re
Turbulence Models CD avg CD exp
(Ref.)%Differen
ceCL avg CL exp
(Ref.)%
Difference
k-ε High Re (top wall slip) 3.17 1.98 60.10 -0.83 -1.04 20.19
k-ε High Re (top wall symmetry)
3.19 1.97 61.92 -0.83 -1.05 20.95
k-ε Low Re (top wall slip) 3.07 1.87 63.73 -1.01 -1.25 18.19
k-ε Low Re (top wall symmetry)
3.09 1.82 69.45 -1.11 -1.3 14.46
k-ε RNG 2.77 2.2 25.90 -1.39 -0.73 90.41
k-ε Chen 3.6 1.67 115.56 -0.97 -1.4 30.28
k-ε Standard Quadratic High Re
2.38 2 19.3 -0.067 -0.7 90.45
k-ε Suga Quadratic High Re 3.27 1.4 133.88 -2.67 -1.85 44.21
k-ω STD High Re 4.66 1.99 135.67 -0.55 -1 45
k-ω STD Low Re10.9
11.965 455.21 -0.29 -0.6 51.66
k-ω SST High Re 3.03 1.98 53.03 -1.15 -1.1 4.55
k-ω SST Low Re 4.03 1.96 105.61 -0.91 -1.07 14.95
RSM_GL_craft
2.21
1.95 13.33 -0.015 -0.5 97
RSM_SSG0.36
7N/A N/A 1.341 N/A N/A
RSM_GL_Standard0.53
5 N/A N/A 1.628 N/A N/A
Comparison of force coefficients for different turbulence models:Comparison of force coefficients for different turbulence models:
SINGLE-PHASE MODEL
NO SLIP WALL
WATER INLET OUTLET
SLIP WALL
SYMPLANE
Fig 15: Mesh structure of Single-phase Model
Fig 16: Boundary conditions of Single-Phase Model
SIMULATION PARAMETERSWater Inlet Velocity 0.35 m/s
Turbulent Kinetic Energy 0.00125 m2/s2
Turbulent Dissipation Rate 0.000175m2/s3
Solution Method Steady-State
Solver Algebric Multigrid (AMG)
Solution Algorithm SIMPLE
Relaxation FactorPressure - 0.3Momentum, Turbulence,Viscosity - 0.7
Differencing Scheme MARS
Convergence Criteria 10-6
TURBULENCE MODELS USED
Two-Equation Models
• k- High Reynolds
• k- Low Reynolds
•k- Standard High Reynolds
• k- SST High Reynolds
DRAG COEFFICIENT COMPARISON FOR THE TM
Fig 17
Variation of CD wrt h*
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
h*
CD
Experimental k-epsilon_High-Re
k-epsilon_Low-Re k-omega_Standard_High-Re
k-omega_SST_High-Re
LIFT COEFFICIENT COMPARISON FOR THE TM
Fig 18
Variation of CL wrt h*
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
h*
CL
Experimental k-epsilon_High-Re
k-epsilon_Low-Re k-omega_Standard_High-Re
k-omega_SST_High-Re
SCOUR PHENOMENONCaused by high stress at the river bed
Types of Scour:
Aggradation or Degradation Scour
Contraction Scour• Lateral Contraction• Longitudinal Contraction causes pressure scour
Local Scour
SCOUR MODELING OPTIONS
A theoretical model proposed by Guo employing semi-analytical solution for flow-hydrodynamics.
Considering a two-phase flow and using VOF methodology, scour modeling has been done by Heather D. Smith in Flow-3D.
Eulerian two-phase model with coupled governing equations for fluid and solid sediment transport
In STAR-CD, VOF methodology found to be slow,numerically unstable and very sensitive towardsComputational parameters.
Eulerian two-phase model is also very complex in Terms of considering sediment transportation, Suspension and settlement.
Single-phase model has been chosen for initial scour depth (ys) analysis.
SCOUR METHODOLOGY
Scour methodology using a single-phase model hasbeen developed based on the critical shear stressFormula proposed by Guo, known as Rouse-Shieldsequation.
23exp1054.0
23.0 85.0*
*50
d
dgds
c
Where 50
31
2*
1d
gd s
OTHER CRITICAL SHEAR STRESS FORMULAE
Based on Shields Coefficient:
ds
c
USWES Formula:
2
1
100595.0
M
dSc
Sakai Formula:
M
MdSc 21
2
3
1100 56
Etc…..
CRITICAL SHEAR STRESS CURVE
Fig 19: Variation of c with diameter based on different formulae
Variation of Critical Shear Stress with Bed Size
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
0 1 2 3 4 5 6 7Median Bed Diameter d50 (mm)
c (Pa)
Rouse-Shields Equation Based Shields Coefficient Based
USWES Formula Based Chang's Formula Based
Sakai Formula Based Chien & Wan Approach Based
For mean diameter of 1 mm, c varies from 0.43 Pato 0.72 Pa, based on different formula.
VAN RIJN FORMULA
1.0
23.0
1.2
5.1
053.0
w
ws
c
c
w
ws
b
gd
gd
q
Where,
bq= Bed load transport rate
= Bed Shear Stress
c = Critical Shear Stress
IS τX AND τC ?
SCRIPT FILE
IMPLY ALL THE FLOW CONDITIONS AND
RELEVANT PRE-PROCESSING DATA
RUN THE GEOMETRY
GET THE SHEAR FORCE
STORE SHEAR STRESS IN STRESS.OUT FILE
MAKE CELL BY CELL COMPARISON OF τX AND τC
WRITE THE CELL NUMBER IN THE FORTRAN OUTPUT FILE,
OUTPUT.TXT
END OF FILE?
CHANGE OF SCRIPT FILE BY BRINGING THE BOTTOM BOUNDARY OF THE CELLS, WHERE τX > τC,
ONE CELL DOWN
YES
YES
END OF FILE?NO
YES
NO
NO
FIND OUT τC USING DIFFERENT CORRELATIONS
FLOW CHART
Geometrical and Operating Variables and Parameters
Values
Channel water depth 0.06 m
Bridge opening 0.03 m
Type of bridge deck Girder Rectangular obstacle instead of bridge
Height of bridge deck, s 0.02 m
Inundation ratio, h* 1.5
Water discharge rate 1.05E-4 m3/s
Average upstream velocity 0.35 m/s
Bed sediment diameter 1 mm
Sediment bed roughness Hydro-dynamically smooth
Critical bed shear stress 0.58 N/m2
Computational parameters:
Fig 20: Model geometry
After 19th iteration, final ys of 2.4 cm is obtained.
Fig 21: Final scoured model
Fig 22: Shear stressdistribution
Fig 23
SCOUR AUTOMATION PROCESS
Automation has been implemented for same geometryMentioned in Fig. 19.
After 24th iteration, final ys of 1.2 cm is obtained.
Fig 24
Fig 25
VALIDATION OF EXPERIMENTGeometrical and
Operating Variables and Parameters
Values
Channel water depth 0.25 m
Bridge opening 0.115 m
Type of bridge deck Girder Rectangular obstacle instead of bridge
Height of bridge deck, s 0.04 m
Inundation ratio, h* 3.375
Water discharge rate 5.125E-4 m3/s
Average upstream velocity 0.41 m/s
Bed sediment diameter 1 mm
Sediment bed roughness Hydro-dynamically smooth
Critical bed shear stress 0.58 N/m2
Fig 26: Final scour shape
After 20th iteration, final ys of 0.95 cm is obtained.
Fig 27
Fig 28: Effect of roughness on bed shear stress
EFFECT OF ROUGHNESSBed shear stress depends on roughness.
Roughness Formulae:
Formula by Wilson: 550
d
k s
Formula by Yalin:
125.0203.0289.0043.045 232
50
d
k s
Formula by Bayram et al. )5.2,5.2max( 5.1
50
d
k s
Based on these different formulae roughness (ks)varies from 0.195 mm to 2.5 mm for d50 = 1 mm.
VERIFICATION OF GUO’S PROFILEGuo proposed,
,0x
5.2
expW
x
y
y
s
For
For ,0x
055.02
1exp055.1
8.1
W
x
y
y
s
Fig 29: Without using 0.055 factor
Fig 30: Using 0.055 factor
NEW SCOUR SCHEMEIn order to improve this scheme, the cell removal scheme is modified based on the magnitude of the deviation of computed shear stress from the critical shear stress.
Below is the empirical formula for this.
c
csyy
max
INITIAL BED PROFILE
Fig 31: Model geometry
Fig 32
ITERATION # 02
Fig 34
Fig 33
ITERATION # 03
Fig 36
Fig 35
ITERATION # 04
Fig 38
Fig 37
ITERATION # 05
Fig 40
Fig 39
ITERATION # 06
Fig 42
Fig 41
ITERATION # 07
Fig 44
Fig 43
ITERATION # 08
Fig 46
Fig 45
Maximum scour depth obtained from simulation = 6.1cm
Maximum scour depth obtained from experiment = 6.4 cm
Relative error = 5% (Experimental value is the reference)
EFFECT OF FORCE COEFFICIENTS
Effect of Scour Depth on Force Coefficients
-0.5
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6 7
Scour depth (cm)
Force Coefficients
Drag Coefficient Lift Coefficient
Fig 47
CONCLUSIONS & RECOMMENDATIONS For CFD analysis in STAR-CD, VOF methodology showed lot of noise, unsteadiness and divergence to calculate force coefficients. Total computational time of 300 sec needs to be used in VOF A time-step of 0.01 sec is fine for the VOF method For drag coefficient calculation, RSM_GL_Craft TM showed 13.33% of relative error compared to the experiment For lift coefficient calculation, k-w SST High Re TM showed 4.555% of relative error Single-phase model showed a right trend of drag and lift coefficient variation.
Consideration of roughness is a very important factor for scour analysis Critical shear stress formulation for the scour bed depends on bed load, slope of the scoured bottom and sediment properties Sediment transportation, suspension and bed settlement phenomenon needs to be considered for scour analysis A transient methodology needs to be formulated to capture the time-varying effect of sediment transportation
CONCLUSIONS & RECOMMENDATIONS
Acknowledgments:
The authors like to acknowledge support by Dean Promod Vohra, College of Engineering and Engineering Technology of Northern Illinois University (NIU), and Dr. David P. Weber of Argonne National Laboratory (ANL); and especially the contributions by Dr. Tanju Sofu, and Dr. Steven A. Lottes of ANL, as well as financial support by U.S. Department of Transportation (USDOT) and computational support by ANL’s Transportation Research and Analysis Computing Center (TRACC).
QUESTIONS ???
More information at:More information at:www.kostic.niu.edu