2009 January 10-12 www.kostic.niu.edu
1
Computational Fluid Dynamics Computational Fluid Dynamics SimulationSimulation
of Open-Channel Flows Over Bridge-of Open-Channel Flows Over Bridge-DecksDecks
Under Various Flooding ConditionsUnder Various Flooding Conditions
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
S. Patil, M. Kostic and P. Majumdar S. Patil, M. Kostic and P. Majumdar Department of Mechanical EngineeringDepartment of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITYNORTHERN ILLINOIS UNIVERSITY
2009 January 10-12 www.kostic.niu.edu
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Motivation: Bridges are crucial constituents of the nation’s transportation
systems Bridge construction is critical issue as it involves great amount of
money and risk Bridge structures under various flood conditions are studied for
bridge stability analysis Such analyses are carried out by scaled experiments to calculate
drag and lift coefficients on the bridge Scaled experiments are limited to few design variations and flooded
conditions due to high cost and time associated with them Advanced commercial Computational Fluid Dynamics (CFD)
software and parallel computers can be used to overcome such limitations
2009 January 10-12 www.kostic.niu.edu
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CFD is the branch of fluid mechanics which uses numerical methods to solve fluid flow problems
In spite of having simplified equations and high speed computers, CFD can achieve only approximate solutions
CFD is a versatile tool having flexibility is design with an ability to impose and simulate real time phenomena
CFD simulations if properly integrated can complement real time scaled experiments
Available CFD features and powerful parallel computers allow to study wide range of design variations and flooding conditions with different flow characteristics and different flow rates
CFD simulation is a tool for through analysis by providing better insight of what is virtually happening inside the particular design
2009 January 10-12 www.kostic.niu.edu
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Literature Review: Ramamurthy, Qu and Vo, conducted simulation of three
dimensional free surface flows using VOF method and found good agreement between simulation and experimental results
Maronnier, Picasso and Rappaz, conducted simulation of 3D and 2D free surface flows using VOF method and found close agreement between simulation and experimental results.
Harlow, and Welch, wrote Navier stokes equations in finite difference forms with fine step advancement to simulate transient viscous incompressible flow with free surface. This technique is successfully applicable to wide variety of two and three dimensional applications for free surface
Koshizuka, Tamako and Oka, presented particle method for transient incompressible viscous flow with fluid fragmentation of free surfaces. Simulation of fluid fragmentation for collapse of liquid column against an obstacle was carried. A good agreement was found between numerical simulation and experimental data
2009 January 10-12 www.kostic.niu.edu
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Objectives: The objective of the present study is to validate commercial code
STAR-CD for hydraulic research The experimental data conducted by Turner Fairbank Highway
Research Center (TFHRC) at their own laboratories will be simulated using STAR-CD
The base case of Fr = 0.22 and flooding height ratio, h*=1.5 is simulated with appropriate boundary conditions corresponding to experimental testing
The open channel turbulent flow will be simulated using two different methods
First by transient Volume of Fluid (VOF) methodology and other as a steady state closed channel flow with top surface as slip wall
Drag and lift coefficients on the bridge is calculated using six linear eddy viscosity turbulence model and simulation outcome will be compared with experimental results
2009 January 10-12 www.kostic.niu.edu
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The suitable turbulence model will be identified which predicts close to drag and lift coefficients
The parametric study will be performed for time step, mesh density and convergence criteria to identify optimum computational parameters
The suitable turbulence model will be used to simulate 13 different flooding height ratio from h*=0.3 to 3 for Fr =0.22
2009 January 10-12 www.kostic.niu.edu
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Experimental Data: Experiments are conducted for open channel turbulent flow
over six girder bridge deck for different flooding height ratios (h*) and with various flow conditions (Fr)
LBridge =0.34 m S=0.058 m
ΔWSimulation=0.00254
LFlow = 0.26 m
Flow Direction
Schematic of experimental six girder bridge deck model
2009 January 10-12 www.kostic.niu.edu
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Dimensions of experimental six girder bridge deck model
W L Flow
X
Y
Nomenclature for bridge dimensions and flooding ratios
gW
VFr avg
u
avg
gh
VFr
Theory
S
hhh bu *Flooding
Ratio
Froude Number
2009 January 10-12 www.kostic.niu.edu
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Experimental data consists of drag and lift coefficients as the function of Froude number, Fr and dimensionless flooding height ratio h*
Experimental data consists of five different sets of experiments for Froude numbers from Fr =0.12 to 0.40 and upstream average velocity 0.20 m/s to 0.65 m/s
The experiments for the Froude number, Fr=0.22 are repeated four times with an average velocity of 0.35 m/s
for h*=0.3 to 3 The lift coefficient is calculated by excluding buoyancy forces
in Y (vertical) direction
2009 January 10-12 www.kostic.niu.edu
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Drag Coefficients vs h* for Fr = 0.22
0.00
0.50
1.00
1.50
2.00
2.50
3.00
-0.10 0.40 0.90 1.40 1.90 2.40 2.90 3.40
h*
Dra
g C
oe
ffic
ien
t -
CD
12-29-06_2 01-03-07_1 01-29-07_1
01-31-07_3 AVG Drag
2009 January 10-12 www.kostic.niu.edu
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Lift Coefficient vs h* for Fr = 0.22
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
-0.10 0.40 0.90 1.40 1.90 2.40 2.90 3.40
h*
Lif
t C
oe
ffic
ien
t -
CL
12-29-06_2 01-03-07_1 01-29-07_1
01-31-07_3 AVG Lift
2009 January 10-12 www.kostic.niu.edu
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Governing Equations for fluid flow:
Mass conservation equation
Momentum conservation equation
Energy conservation equation
0.
Vt
gVPDt
VD .2
dt
dEEE CVoutin
2009 January 10-12 www.kostic.niu.edu
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Dimensionless parameters for open channel flow: Reynolds Number
havgRVRe
y
b
yb
yb
p
AR Ch 2
b yRh For 2D open channel flow
,
2009 January 10-12 www.kostic.niu.edu
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Froude Number: Froude number is dimensionless number which governs
character of open channel flow
The flow is classified on Froude number
Subcritical or tranquil flow
Critical Flow
Supercritical or rapid flow
Open channel flow is dominated by inertial forces for rapid flow
and by gravity forces for tranquil flow
C
avg
gL
VFr
1Fr
1Fr
1Fr
ceGravityFor
ceInertiaForFr 2
2009 January 10-12 www.kostic.niu.edu
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Froude number is also given by
Where
gy
V
C
VFr avgavg
0
0C Wave speed (m/s)
y = Flow depth (m)
2009 January 10-12 www.kostic.niu.edu
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Force Coefficients: The component of resultant pressure and shear forces in direction of flow
is called drag force and component that acts normal to flow direction is called lift force
Drag force coefficient is
Lift force coefficient is
In the experimental testing, the drag reference area is the frontal area normal to the flow direction. The lift reference area is the bridge area
perpendicular to Y direction.
Davg
DD
AV
FC
25.0
Lavg
LL
AV
FC 25.0
2009 January 10-12 www.kostic.niu.edu
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Drag and lift reference areas for experimental data:
For drag, if ,then drag area is
if ,then drag area is
For lift, for all ,lift area is
1* h Bridgebu Lhh *)(
1* h BridgeLS *
*h BridgeFlow LL *
2009 January 10-12 www.kostic.niu.edu
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Turbulent Flow: Turbulent flow is complex phenomena dominated by rapid and
random fluctuations Turbulent flow is highly unsteady and all the formulae for the
turbulent flow are based on experiments or empirical and semi –empirical correlations
Turbulent Intensity Turbulence mixing length (m)
Turbulent kinetic energy (m2/s2)
avgV
uTI
'
5.175.0 k
Clm
225.1 TIVk avg
2009 January 10-12 www.kostic.niu.edu
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Turbulence dissipation rate (m2/s3)
Specific dissipation rate (1/s)
ml
kC 5.175.0
kC
2009 January 10-12 www.kostic.niu.edu
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Turbulence Models: Six eddy viscosity turbulence models are studied from STAR-CD
turbulence options Two major groups of turbulence models k-ε and k-ω are studied The k- ε turbulence model The k-ω turbulence models
a. Standard High Reynolds a. Standard High Reynolds
b. Renormalization Group b. Standard Low Reynolds
c. SST High Reynolds
d. SST Low Reynolds
2009 January 10-12 www.kostic.niu.edu
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The k-ε High Reynolds turbulence model: Most widely used turbulent transport model First two equation model to be used in CFD This model uses transport equations for k and ε in
conjunction with the law-of-the wall representation of the boundary layer
The k-ε RNG turbulence model: This turbulence model is obtained after modifying k-ε
standard turbulence model using normalization group method to renormalize Navier Stokes equations
This model takes into account effects of different scales of motions on turbulent diffusion
2009 January 10-12 www.kostic.niu.edu
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k-ω turbulence model: The k-ω turbulence models are obtained as an alternative to the k-ε
model which have some difficulty for near wall treatment The k-ω turbulence models
Standard k-ω model Shear stress transport (SST) model
High Reynolds Low Reynolds
High Reynolds Low Reynolds
2009 January 10-12 www.kostic.niu.edu
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SST k-ω turbulence model: SST turbulence model is obtained after combining best features of
k-ε and k-ω turbulence model SST turbulence model is the result of blending of k-ω model near
the wall and k-ε model near the wall
2009 January 10-12 www.kostic.niu.edu
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Computational Model: STAR-CD (Simulation of Turbulent flow in Arbitrary Regions
Computational Dynamics) is CFD analysis software STAR-CD is finite volume code which solves governing equations
for steady state or transient problem The first method used in STAR-CD to simulate open channel
turbulent flow is free surface method which makes use of Volume of Fluid (VOF) methodology
VOF methodology simulates air and water domain VOF methodology uses volume of fraction variable to capture air-
water interface
2009 January 10-12 www.kostic.niu.edu
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VOF technique: VOF technique is a transient scheme which captures free
surface. VOF deals with light and heavy fluids VOF is the ratio of volume of heavy fluid to the total control
volume Volume of fraction is given by
Transport equation for volume of fraction
Volume fraction of the remaining component is given by
V
Vii
0).(
ut ii
12
1
i
i
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The properties at the free surface vary according to volume fraction of each component
2
1
.i
ii
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Free Surface method:
Dimensions for computational model h*=1.5 generated in STAR-CD (Dimensions not to scale and in SI units)
0
Y
XZ
0.08
-1.50
-0.15
0.06
0.30
03
0.26 1.78
2009 January 10-12 www.kostic.niu.edu
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Computational Mesh:
Full computational domain with non uniform mesh and 2 cells thick in Z direction for =1.5
Y
X
Y
2009 January 10-12 www.kostic.niu.edu
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Boundary Conditions:
Bottom Wall(No Slip)
Top wall (slip)
Water Inlet
Air Inlet
Outlet
Symmetry Plane
X
Y
Z
Y
1w
0w
2009 January 10-12 www.kostic.niu.edu
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Computational parameters for VOF methodology:
Inlet velocity, U 0.35 m/s
Turbulent kinetic energy, k 0.00125 m2/s2
Turbulent Dissipation Rate, ε 0.000175 m2/s3
Solution method Transient
Solver method Algebraic Multigrid approach (AMG)
Solution algorithm SIMPLE
Relaxation factor Pressure - 0.3Momentum, Turbulence, Viscosity - 0.7
Differencing scheme MARS
Convergence Criteria 10-2
Time Step (Δt) 0.01 s
2009 January 10-12 www.kostic.niu.edu
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Water slip top wall method:
-1.5
0
0.06 Y
XZ
0.08
-0.15
03
0.26 1.78
Dimensions for computational model h*=1.5 for water slip –top-wall method (Dimensions not to scale and in SI units)
2009 January 10-12 www.kostic.niu.edu
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Boundary conditions:
Top wall (slip)
Bottom wall(No slip)
Outlet(Standard)
Symmetry Plane
X
Y
X
Y
Water Inlet
Computational domain with boundary surfaces and boundary conditions for water slip-top-wall method
2009 January 10-12 www.kostic.niu.edu
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Computational parameters for water slip-top-wall method:
U
k
Inlet velocity,
Turbulent kinetic energy,
Turbulent Dissipation Rate,
0.35 m/s
0.00125 m2/s2
0.000175 m2/s3
Solution Method Steady State
Solver Method Algebraic Multigrid approach (AMG)
Solution Algorithm SIMPLE
Relaxation factor Pressure - 0.3Momentum, turbulence, Viscosity - 0.7
Differencing scheme UD
Convergence Criteria 10-6
2009 January 10-12 www.kostic.niu.edu
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STAR-CD simulation Validation with basics of fluid mechanics :
Fully developed velocity profile for laminar pipe flow after STAR-CD simulation
Fully developed velocity profile for laminar pipe flow
-6.00E-02
-4.00E-02
-2.00E-02
0.00E+00
2.00E-02
4.00E-02
6.00E-02
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045
W Velocity (m/s)
Y C
oo
rdin
ate
(m
)
Velocity Profile for Laminar Pipe Flow Average velocity profile
2009 January 10-12 www.kostic.niu.edu
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Fully developed velocity profile for turbulent pipe flow
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 0.05 0.1 0.15 0.2 0.25 0.3
W velocity (m/s)
Y c
oo
rdin
ate
(m
)
Velocity Profile for turbulent pipe flow Average Velocity Profile
Fully developed velocity profile for the turbulent pipe flow after STAR-CD simulation
2009 January 10-12 www.kostic.niu.edu
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Flow type WallRoughness
(m)
Theoreticalfriction factor
(Reference)
Simulation friction factor
AbsoluteDifference
PercentageDifference
Laminar Smooth 0.2844 0.2865 0.0021 0.74
Turbulent Smooth 0.0121 0.0116 0.0005 4.13
Turbulent 0.005 0.053 0.048 0.005 9.43
Turbulent 0.015 0.0872 0.0756 0.0116 13.30
Turbulent 0.075 0.2529 0.2019 0.051 20.17
Comparison between theoretical and simulated friction factor :
2009 January 10-12 www.kostic.niu.edu
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Calculation of entrance length:
DLh Re05.0Shear stress at bottom wall in flow direction
0.00E+00
2.00E-06
4.00E-06
6.00E-06
8.00E-06
1.00E-05
1.20E-05
1.40E-05
1.60E-05
1.80E-05
2.00E-05
0 20 40 60 80 100 120
X distance (m)
Wa
ll s
he
ar
str
es
s (
N/m
2)
Shear stress at bottom wall
Continued on next page
500Re mDh 2
mLh 50
2009 January 10-12 www.kostic.niu.edu
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Developement of velocity profile in laminar duct flow
0.00E+00
1.00E-01
2.00E-01
3.00E-01
4.00E-01
5.00E-01
6.00E-01
7.00E-01
8.00E-01
9.00E-01
1.00E+00
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-03
5.00E-03
6.00E-03
7.00E-03
8.00E-03
9.00E-03
1.00E-02
U velocity (m/s)
Y d
ista
nce
(m
)
At 20 M At 40 M At 50 M At 60 M At 75 M At 90 M
2009 January 10-12 www.kostic.niu.edu
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Verification of power law velocity profile:Comparision for power law velocity profile from
theory and after simulation
-1.00E+00
-8.00E-01
-6.00E-01
-4.00E-01
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
1.00E+00
0 0.2 0.4 0.6 0.8 1 1.2
U/Umax
r/R
h
Theoretical velocity profile Velocity profile from simulation
2009 January 10-12 www.kostic.niu.edu
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Comparison between Fluent and STAR-CD for same geometry:
0 0.254 0.504
0.097
1.016
0.127
0X
Y
Operating Condition Variables
Inlet Velocity U = 2 m/s
Inlet turbulence intensity 10 %
Inlet turbulence mixing length 0.1 m
Outlet gauge pressure 0 Pa
Walls No Slip
Convergence 0.001
2009 January 10-12 www.kostic.niu.edu
41Comparison for velocity contours between STAR-CD and Fluent
2009 January 10-12 www.kostic.niu.edu
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Comparison for velocity vectors between STAR-CD and Fluent
2009 January 10-12 www.kostic.niu.edu
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Comparison for X velocities between Fluent and STAR-CD
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Parameter Fluent STAR-CD(Reference Data)
Absolute Difference
Percentage Difference
ΔP STAT 1120 1161 41 3.53 %
ΔP TOT 1083 1120 37 3.30 %
Pressure difference (Pa)
3.97 %0.28-7.05-6.77CL
5.5 %0.112.001.89CD
PercentageDifference
Absolute Difference
STAR-CD(Reference
Data)
FluentForceCoefficients
Force Coefficients
2009 January 10-12 www.kostic.niu.edu
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VOF simulation of experimental data:Effect of time steps on drag coefficients
Effect of time steps for k- High Re TM on drag coefficients
2.20000
2.40000
2.60000
2.80000
3.00000
3.20000
3.40000
3.60000
-40 10 60 110 160 210 260 310
time (sec)
CD
time step 0.01 sec time step 0.05 sec time step 0.1 sec
2009 January 10-12 www.kostic.niu.edu
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Effect of time steps on lift coefficients:
Effect of time steps for k- High Re TM on lift coefficients
-1.40000
-1.20000
-1.00000
-0.80000
-0.60000
-0.40000
-0.20000
0.00000
-40 10 60 110 160 210 260 310
time (sec)
CL
time step 0.01 sec time step 0.05 sec time step 0.1 sec
2009 January 10-12 www.kostic.niu.edu
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Comparision for CD between full computational model and
computational model with decreased downstream length for k-
High Re TM for 0.05 s time step
1.00000
1.50000
2.00000
2.50000
3.00000
3.50000
4.00000
0 50 100 150 200 250
time (sec)
CD
Full Computational model Computational model with decreased downstream length
Comparision for CL between full computational domain and
computational model with decreased downstream length for k-
High Re TM for 0.05 s time step
-3.00000
-2.50000
-2.00000
-1.50000
-1.00000
-0.50000
0.00000
0.50000
1.00000
1.50000
2.00000
2.50000
0 50 100 150 200 250
time (sec)
CL
Full computational domain Computatioanl domain with decreased downstream length
Effect of decreased downstream length on force coefficients
2009 January 10-12 www.kostic.niu.edu
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Comparision for CD between full computational model and
computational model with decrease in under bridge water depth for k- High Re TM for time step 0.05 s
0.00000
2.00000
4.00000
6.00000
8.00000
10.00000
12.00000
0 50 100 150 200 250
time (step)
CD
Full Cvomputational model Compuatational model with decrease in under bridge water depth
Effect of decrease in under bridge water depth
Comparision for CL between full computational model and
computational model with decrease in under bridge water depth for k- High Re TM for time step of 0.05 s
-6.00000
-5.00000
-4.00000
-3.00000
-2.00000
-1.00000
0.00000
0 50 100 150 200 250
time (sec)
CL
Full computational model Computational model with decrease in under bridge water depth
2009 January 10-12 www.kostic.niu.edu
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Comparision between top wall as a slip and symmetry for k-
High Reynolds turbulence model
2.70000
2.95000
3.20000
3.45000
0 50 100 150 200 250 300 350
time (sec)
CD
Slip wall symmetry wall
Comparision between top wall as a slip and symmetry for k-
High Reynolds turbulence model
-1.20000
-1.00000
-0.80000
-0.60000
-0.40000
-0.20000
0.00000
0 50 100 150 200 250 300 350
time (sec)
CL
Slip wall Symmetry wall
Effect of top boundary condition at top as slip wall and symmetry
2009 January 10-12 www.kostic.niu.edu
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Free Surface Development:
Nomenclature for VOF contour plot
Free surface,
1w
0w
w Volume fraction for water
99.001.0 w
2009 January 10-12 www.kostic.niu.edu
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t=10sec t=30sec
t=50 sec
t=150 sec t=200 sec sec
t=300 sect =250 sec
t=100sec
Effect of k-ε standard turbulence model on free surface development:
2009 January 10-12 www.kostic.niu.edu
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Effect of different turbulence models on drag coefficient
-1.00000
1.00000
3.00000
5.00000
7.00000
9.00000
11.00000
13.00000
0 50 100 150 200 250 300 350
time (sec)
CD
k-epsilon High Re k-epsilon RNG k-omega STD High Re
k-omega STD Low Re k-omega SST High Re k-omega SST Low Re
Experimenal Results
Effect of different turbulence models on drag coefficients:
2009 January 10-12 www.kostic.niu.edu
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Effect of different turbulence models on lift coefficient
-2.00000
-1.80000
-1.60000
-1.40000
-1.20000
-1.00000
-0.80000
-0.60000
-0.40000
-0.20000
0.00000
0 50 100 150 200 250 300 350
Time (sec)
CL
k-epsilon High Re k-epsilon RNG k-omega STD High Re
k-omega STD Low Re k-omega SST High Re k-omega SST Low Re
Experimental Results
Effect of different turbulence models on lift coefficients:
2009 January 10-12 www.kostic.niu.edu
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TurbulenceModels
h*up h*dw h*avg CD avg CD exp CL avg CL exp
k-ε High Re 1.40 1.30 1.35 3.17 1.98 -0.83 -1.04
k-ε RNG 1.45 1.45 1.45 2.77 2.02 -1.39 -0.73
k-ω STD High Re 1.15 1.30 1.38 4.69 1.99 -0.55 -1.00
k-ω STD Low Re 1.84 1.50 1.67 10.91 1.97 -0.29 -0.60
k-ω SST High Re 1.30 1.20 1.25 3.03 1.98 -1.15 -1.10
k-ω SST Low Re 1.35 1.20 1.28 4.03 1.96 -0.91 -1.07
h*up h*dw h*avg CD avg CD exp CL avg CL exp
Count 6.00 6.00 6.00 6.00 6.00 6.00 6.00
Maximum 1.84 1.50 1.67 10.91 2.02 -0.29 -0.60
Average 1.41 1.33 1.40 4.77 1.98 -0.85 -0.92
Std. Dev. 0.23 0.13 0.15 3.09 0.02 0.40 0.21
Minimum 1.15 1.20 1.25 2.77 1.96 -1.39 -1.10
Comparison between simulation results for different turbulence model and experimental results:
2009 January 10-12 www.kostic.niu.edu
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Water slip-top-wall method:
(a) Basic Coarse mesh (b) Refined near bridge (c) Fully refined model
0 % (Ref)-1.384390 % (Ref)2.93109Fully refined
model
0.08 %-1.383280.08 %2.93367Refined near
bridge
0.54%-1.391881 % 2.96061Basic coarse
grid
% DifferenceCL% DifferenceCDMesh Density
2009 January 10-12 www.kostic.niu.edu
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0.94 %-1.378770.2 %2.9544510-4
0.0022 %-1.391850.00033 %2.9606210-5
0 % (ref)-1.391880 % (ref)2.9606110-6
% differenceCL% differenceCDConvergence
criteria
Effect of convergence criteria on final solution:
2009 January 10-12 www.kostic.niu.edu
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Comparison between VOF and Water slip-top-wall method with experimental results:
Comparision between VOF and steady state simulation for different turbulence models for base case of Fr= 0.22 and h*=1.5
0.00
2.00
4.00
6.00
8.00
10.00
12.00
k-epsilonHigh Re
k-epsilonRNG
k-omegaSTD High Re
k-omegaSTD Low Re
k-omega SSTHigh Re
k-omega SSTLow Re
Turbulence models
CD
VOF simulation Steady state simulation Experimental data
Comparision between VOF and steady state simulation for different turbulence models for base case of Fr=0.22 and h*=1.5
-1.80
-1.60
-1.40
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.00k-epsilonHigh Re
k-epsilonRNG
k-omegaSTD High Re
k-omegaSTD Low Re
k-omega SSTHigh Re
k-omega SSTLow Re
Turbulence models
CL
VOF Simulation Steady State Simulation Experimental data
`
2009 January 10-12 www.kostic.niu.edu
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Drag coefficient, CD Lift Coefficient, CL
Turbulence model VOF Exp. Water slip-top-wall
VOF Exp. Water slip-top-wall
k-ε High Re 3.17 2.02 2.96 -0.83 -0.70 -1.39
k-ε RNG 2.77 2.02 2.57 -1.39 -0.70 -1.08
k-ω STD High Re4.69 2.02 3.19 -0.55 -0.70 -1.43
k-ω STD Low Re10.91 2.02 10.59 -0.29 -0.70 -1.35
k-ω SST High Re 3.03 2.02 2.78 -1.15 -0.70 -1.26
k-ω SST Low Re 4.03 2.02 4.03 -0.91 -0.70 -1.63
The k-ε RNG predicts closet drag and lift coefficients
2009 January 10-12 www.kostic.niu.edu
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Effect of inlet turbulence on drag and lift coefficients:
Effect of inlet turbulence intensity on force coefficients when mixing length is 1 mm
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0% 5% 10% 15% 20% 25% 30%
Inlet turbulence intensity
Effect of inlet turbulence intensity on drag coefficient
Effect of inlet turbulence intensity on lift coefficient
CL
CD
Effect of inlet turbulence intensity on force coefficients when mixing length is 41.5 mm
-2
-1
0
1
2
3
4
0% 5% 10% 15% 20% 25% 30%
Inlet turbulence intensity
Effect of inlet turbulence intensity on drag coefficients
Effect of inlet turbulence intensity on lift coeffcients
CD
CL
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Fully developed velocity profile after selected runs:
Development of velocity profile for open channel flow for selected runs
-8
-6
-4
-2
0
2
4
0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4
U velocity (m/s)
Y c
oo
rdin
ate
s (
m)
1st Run 3rd Run 5th Run 9th Run 13th Run 15th Run
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Development of turbulence kinetic energy for open channel flow for selected runs
-8
-6
-4
-2
0
2
4
0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04 7.00E-04
Kinetic energy per unit mass (m2/s2)
Y c
oo
rdin
ate
(m
)
1st Run 3rd Run 5th Run 9th Run 13th Run 15th Run
Fully developed turbulence kinetic energy after selected runs:
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Fully developed turbulence dissipation rate after selected runs:
Development of turbulence dissipation rate for open channel flow for selected runs
-8
-6
-4
-2
0
2
4
0.00E+00
4.10E-04
8.20E-04
1.23E-03
1.64E-03
2.05E-03
2.46E-03
2.87E-03
3.28E-03
3.69E-03
4.10E-03
Turbulence dissipation rate (m2/s3)
Y c
oo
rdin
ate
(m)
1st Run 3rd Run 5th Run 9th Run 13th Run 15th Run
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h * CFDSimulation
Experimental(Reference)
Absolute Difference
Percentage Difference
0.289 1.63 1.92 0.29 15.10
0.493 1.78 1.21 0.57 47.10
0.68 1.92 1.57 0.35 22.29
0.972 2.29 1.37 0.92 67.15
1.281 2.68 1.98 0.7 35.35
1.500 2.66 2.02 0.64 31.68
1.709 2.62 1.95 0.67 34.35
2.015 2.51 1.89 0.62 32.80
2.309 2.39 1.82 0.57 31.31
2.517 2.33 1.79 0.54 30.16
2.706 2.28 1.73 0.55 31.79
3.008 2.19 1.71 0.48 28.07
3.097 2.17 1.69 0.48 28.40
Comparison between CFD simulations and experimental data for Fr=0.22 for drag coefficients:
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h * CFD Simulation
Experimental(Reference)
Absolute Difference
Percentage Difference
0.289 -0.42 -1.70 1.28 75.29
0.493 -0.77 -1.28 0.51 39.84
0.68 -1.00 -1.76 0.76 43.18
0.972 -1.44 -1.75 0.31 17.71
1.281 -1.53 -1.13 0.40 35.40
1.500 -1.01 -0.70 0.31 44.29
1.709 -0.81 -0.53 0.28 52.83
2.015 -0.46 -0.29 0.17 58.62
2.309 -0.10 -0.14 0.04 28.57
2.517 -0.12 -0.04 0.08 233.33
2.706 -0.05 0.03 0.08 275.00
3.008 -0.06 0.06 0.13 201.59
3.097 -0.10 0.10 0.19 198.97
Comparison between CFD simulation and experimental data for Fr=0.22 for lift coefficients:
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Comparision between CFD simulations and experimental results for drag coefficients for case of Fr=0.22
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0 0.5 1 1.5 2 2.5 3 3.5
h*
CD
CFD simulation Experimental results
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Comparision between CFD simulation and experimental results for lift coefficients for case of Fr=0.22
-2.00
-1.50
-1.00
-0.50
0.00
0.50
0 0.5 1 1.5 2 2.5 3 3.5
h*
CL
CFD Simulation Experimental results
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Conclusion: CFD simulations by STAR-CD for Fr=0.22 case , predicts more drag than
experimental drag except for h*=0.289 The percentage difference if the experimental data is taken as reference, is
maximum of 67% for h*=0.972 and minimum of 15% for h* =0.289 For lift predictions, for cases of h*<1, CFD simulations predict more lift
than experimental . For h*>1, CFD simulations predict lower lift than experimental
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Recommendations for future work: VOF simulations are run for convergence criterion of 0.01.
VOF should be run for more convergence criterion and that is only available with large computing power.
VOF simulations should be run for lower time step than 0.01 sec and for longer simulation time up to 500 sec.
In this study only linear eddy viscosity turbulence models are used. The effect of Large Eddy Simulation, Reynolds stress models and non linear eddy viscosity turbulence models should be tested on force coefficients
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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).
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