Computational Fluid Dynamics Simulation
of Open-Channel Flows Over Bridge-Decks
Under Various Flooding Conditions
The 6th WSEAS International Conference on FLUID MECHANICS
(WSEAS - FLUIDS'09)
Ningbo, China, January 10-12, 2009
S. Patil, M. Kostic and P. Majumdar
Department of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
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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
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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
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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
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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
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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
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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)
ΔWSimulation=0.00254
S=0.058 m
LBridge =0.34 m
LFlow = 0.26 m
Flow Direction
Schematic of experimental six girder bridge deck model
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Theory
Dimensions of experimental six girder bridge deck model
W
Fr 
Vavg
Fr 
Vavg
L Flow
Froude
Number
Y
Flooding
Ratio
h* 
ghu
gW
hu  hb
S
X
Nomenclature for bridge dimensions and flooding ratios
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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
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Drag Coefficients vs h* for Fr = 0.22
3.00
Drag Coefficient - C D
2.50
2.00
1.50
1.00
0.50
0.00
-0.10
0.40
0.90
12-29-06_2
01-03-07_1
01-31-07_3
AVG Drag
1.40
1.90
2.40
01-29-07_1
2.90
3.40
h*
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Lift Coefficient vs h* for Fr = 0.22
0.50
Lift Coefficient - C L
0.00
-0.10
0.40
0.90
1.40
1.90
2.40
2.90
3.40
-0.50
-1.00
-1.50
-2.00
12-29-06_2
01-03-07_1
01-31-07_3
AVG Lift
01-29-07_1
-2.50
h*
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Governing Equations for fluid flow:
 Mass conservation equation

 . V  0
t
 
 Momentum conservation equation

DV
 P   2 .V   g
Dt
 Energy conservation equation
Ein  Eout
dECV

dt
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Dimensionless parameters for open channel flow:
 Reynolds Number
Vavg Rh
Re 

Rh 
AC
yb

p b  2y
For 2D open channel flow
b 
,
Rh  y
y
b
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Froude Number:
 Froude number is dimensionless number which governs
character of open channel flow
Vavg
Fr 
gLC
The flow is classified on Froude number
Fr  1
Fr  1
Subcritical or tranquil flow
Critical Flow
Fr  1
Supercritical or rapid flow
InertiaForce
Fr 
GravityForce
2
Open channel flow is dominated by inertial forces for rapid flow
and by gravity forces for tranquil flow
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Froude number is also given by
Fr 
Vavg
C0

Vavg
gy
Where
C 0  Wave speed (m/s)
y = Flow depth (m)
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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
CD 
FD
0.5 Vavg AD
2
 Lift force coefficient is
FL
CL 
2
0.5Vavg AL
 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.
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Drag and lift reference areas for experimental data:
For drag, if h*  1 ,then drag area is (hu  hb ) * LBridge
if h*  1 ,then drag area is S * LBridge
For lift, for all h * ,lift area is LFlow * LBridge
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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
u'
TI 
Vavg
 Turbulence mixing length (m)
lm  C
0.75
k 1.5

 Turbulent kinetic energy (m2/s2)
k  1.5Vavg TI 2
2
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 Turbulence dissipation rate (m2/s3)

C
0.75 1.5
k
lm
 Specific dissipation rate (1/s)


C k
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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
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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
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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
High Reynolds
Shear stress transport (SST) model
Low Reynolds
High Reynolds Low Reynolds
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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
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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 airwater interface
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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
i 
Vi
V
 Transport equation for volume of fraction
 i
 .( i u)  0
t
2
 Volume
fraction of the remaining component is given by

i 1
i
1
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 The properties at the free surface vary according to volume fraction
of each component
2
    i . i
i 1
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Free Surface
method:
0.30
0.08
0.06
Y
0
X
Z
-0.15
-1.50
0
0.26
1.78
3
Dimensions for computational model h*=1.5 generated
in STAR-CD (Dimensions not to scale and in SI units)
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Computational Mesh:
Y
Y
X
Full computational domain with non uniform mesh
and 2 cells thick in Z direction for =1.5
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Boundary Conditions:
Top wall (slip)
Symmetry
Plane
w  0
Air Inlet
w  1
Water Inlet
Y
Y
X
Z
Bottom Wall
(No Slip)
Outlet
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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 - 0.3
Momentum, Turbulence, Viscosity - 0.7
Differencing scheme
MARS
Convergence Criteria
10-2
Time Step (Δt)
0.01 s
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Water slip top wall method:
0.08
Y
0.06
0
X
Z
-0.15
-1.5
0
0.26
1.78
3
Dimensions for computational model h*=1.5 for water
slip –top-wall method (Dimensions not to scale and in
SI units)
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Boundary conditions:
Top wall (slip)
Symmetry
Plane
Water Inlet
Y
Y
X
X
Bottom wall
(No slip)
Outlet
(Standard)
Computational domain with boundary surfaces and
boundary conditions for water slip-top-wall method
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Computational parameters for water slip-top-wall
method:
0.35 m/s
Inlet velocity, U
0.00125 m2/s2
Turbulent kinetic energy, k
0.000175 m2/s3
Turbulent Dissipation Rate, 
Solution Method
Steady State
Solver Method
Algebraic Multigrid approach (AMG)
Solution Algorithm
SIMPLE
Relaxation factor
Pressure - 0.3
Momentum, turbulence, Viscosity - 0.7
Differencing scheme
UD
Convergence Criteria
10-6
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STAR-CD simulation Validation with basics of fluid
mechanics :
Fully developed velocity profile for laminar pipe flow
6.00E-02
Y Coordinate (m)
4.00E-02
2.00E-02
0.00E+00
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
-2.00E-02
-4.00E-02
-6.00E-02
W Velocity (m/s)
Velocity Profile for Laminar Pipe Flow
Average velocity profile
Fully developed velocity profile for laminar pipe flow after
STAR-CD simulation
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Fully developed velocity profile for turbulent pipe flow
0.06
Y coordinate (m)
0.04
0.02
0
0
0.05
0.1
0.15
0.2
0.25
0.3
-0.02
-0.04
-0.06
W velocity (m/s)
Velocity Profile for turbulent pipe flow
Average Velocity Profile
Fully developed velocity profile for the turbulent pipe flow
after STAR-CD simulation
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Comparison between theoretical and simulated friction factor :
Flow type
Wall
Roughness
(m)
Theoretical
friction factor
(Reference)
Simulation
friction
factor
Absolute
Difference
Percentage
Difference
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
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Calculation of entrance length:
Lh  0.05 Re D
Re  500
Shear stress at bottom wall in flow direction
Wall shear stress (N/m2)
2.00E-05
Dh  2m
1.80E-05
1.60E-05
1.40E-05
Lh  50m
1.20E-05
1.00E-05
8.00E-06
6.00E-06
4.00E-06
2.00E-06
0.00E+00
0
20
40
60
80
100
120
X distance (m)
Shear stress at bottom wall
Continued on next page
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Developement of velocity profile in laminar duct flow
1.00E+00
9.00E-01
Y distance (m)
8.00E-01
7.00E-01
6.00E-01
5.00E-01
4.00E-01
3.00E-01
2.00E-01
1.00E-01
0.00E+00
0.00E+ 1.00E- 2.00E- 3.00E- 4.00E- 5.00E- 6.00E- 7.00E- 8.00E- 9.00E- 1.00E00
03
03
03
03
03
03
03
03
03
02
U velocity (m/s)
At 20 M
At 40 M
At 50 M
At 60 M
At 75 M
At 90 M
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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
r/Rh
4.00E-01
2.00E-01
0.00E+00
-2.00E-01 0
0.2
0.4
0.6
0.8
1
1.2
-4.00E-01
-6.00E-01
-8.00E-01
-1.00E+00
U/Umax
Theoretical velocity profile
Velocity profile from simulation
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Comparison between Fluent and STAR-CD for same geometry:
0
0.254
1.016
0.504
0.127
0.097
Y
0
X
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
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Comparison for velocity contours between
STAR-CD and
Fluent
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Comparison for velocity vectors between STAR-CD and Fluent
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Comparison for X velocities between Fluent and STAR-CD
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Pressure difference (Pa)
Parameter
Fluent
STAR-CD
(Reference Data)
Absolute
Difference
Percentage
Difference
ΔP STAT
1120
1161
41
3.53 %
ΔP TOT
1083
1120
37
3.30 %
Force Coefficients
Force
Coefficients
Fluent
STAR-CD
(Reference
Data)
Absolute
Difference
Percentage
Difference
CD
1.89
2.00
0.11
5.5 %
CL
-6.77
-7.05
0.28
3.97 %
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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
3.60000
3.40000
3.20000
3.00000
CD
2.80000
2.60000
2.40000
2.20000
-40
10
60
110
160
210
260
310
time (sec)
time step 0.01 sec
time step 0.05 sec
time step 0.1 sec
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Effect of time steps on lift coefficients:
Effect of time steps for k- High Re TM on lift coefficients
0.00000
-40
-0.20000
10
60
110
160
210
260
310
-0.40000
-0.60000
CL
-0.80000
-1.00000
-1.20000
-1.40000
time (sec)
time step 0.01 sec
time step 0.05 sec
time step 0.1 sec
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Effect of decreased downstream length on force
coefficients
Comparision for C L between full computational domain and
computational model with decreased downstream length for k-
High Re TM for 0.05 s time step
Comparision for C D between full computational model and
computational model with decreased downstream length for k-
High Re TM for 0.05 s time step
4.00000
2.50000
2.00000
3.50000
1.50000
1.00000
3.00000
0.50000
CD 2.50000
CL
2.00000
0.00000
-0.50000 0
50
100
150
200
250
-1.00000
-1.50000
1.50000
-2.00000
-2.50000
1.00000
0
50
100
150
200
250
-3.00000
time (sec)
time (sec)
Full Computational model
Computational model with decreased downstream length
Full computational domain
Computatioanl domain with decreased downstream length
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Effect of decrease in under bridge water depth
Comparision for C D 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
Comparision for C L 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
12.00000
0.00000
10.00000
-1.00000
8.00000
-2.00000
0
CD 6.00000
50
100
150
200
250
CL -3.00000
4.00000
-4.00000
2.00000
-5.00000
0.00000
0
50
100
150
200
250
-6.00000
time (sec)
time (step)
Full Cvomputational model
Compuatational model with decrease in under bridge water depth
Full computational model
Computational model with decrease in under bridge water depth
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Effect of top boundary condition at top as slip wall and
symmetry
Comparision between top wall as a slip and symmetry for k-
High Reynolds turbulence model
Comparision between top wall as a slip and symmetry for k-
High Reynolds turbulence model
3.45000
0.00000
0
50
100
150
200
250
300
350
-0.20000
3.20000
-0.40000
CD
CL -0.60000
2.95000
-0.80000
-1.00000
2.70000
0
50
100
150
200
250
300
350
-1.20000
time (sec)
time (sec)
Slip wall
Slip wall
symmetry wall
Symmetry wall
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Free Surface Development:
Nomenclature for VOF contour plot
Free surface,
w  0
0.01   w  0.99
w  1
 w Volume fraction for water
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Effect of k-ε standard turbulence model on free surface
development:
t=10sec
t=50 sec
t=30sec
t=100se
c
t=150 sec
t=200 sec
sec
t =250 sec
t=300 sec
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Effect of different turbulence models on drag coefficients:
Effect of different turbulence models on drag coefficient
13.00000
11.00000
9.00000
CD
7.00000
5.00000
3.00000
1.00000
-1.00000 0
50
100
150
200
250
300
350
time (sec)
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
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Effect of different turbulence models on lift coefficients:
Effect of different turbulence models on lift coefficient
0.00000
-0.20000 0
50
100
150
200
250
300
350
-0.40000
-0.60000
-0.80000
CL -1.00000
-1.20000
-1.40000
-1.60000
-1.80000
-2.00000
Time (sec)
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
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Comparison between simulation results for different
turbulence model and experimental results:
Turbulence
Models
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
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Water slip-top-wall method:
(b) Refined near bridge
(a) Basic Coarse mesh
Mesh Density
(c) Fully refined model
CD
% Difference
CL
% Difference
Basic coarse
grid
2.96061
1%
-1.39188
0.54%
Refined near
bridge
2.93367
0.08 %
-1.38328
0.08 %
Fully refined
model
2.93109
0 % (Ref)
-1.38439
0 % (Ref)
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Effect of convergence criteria on final solution:
Convergence
criteria
CD
% difference
CL
% difference
10-6
2.96061
0 % (ref)
-1.39188
0 % (ref)
10-5
2.96062
0.00033 %
-1.39185
0.0022 %
10-4
2.95445
0.2 %
-1.37877
0.94 %
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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
Comparision between VOF and steady state simulation for
different turbulence models for base case of Fr= 0.22 and h*=1.5
-1.80
12.00
-1.60
10.00
-1.40
-1.20
8.00
-1.00
CL
CD 6.00
-0.80
`
-0.60
4.00
-0.40
2.00
-0.20
0.00
0.00
k-epsilon
High Re
k-epsilon
RNG
k-omega
k-omega k-omega SST k-omega SST
STD High Re STD Low Re High Re
Low Re
k-epsilon
High Re
k-epsilon
RNG
Turbulence models
Turbulence models
VOF simulation
Steady state simulation
k-omega
k-omega k-omega SST k-omega SST
STD High Re STD Low Re High Re
Low Re
Experimental data
VOF Simulation
Steady State Simulation
Experimental data
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Drag coefficient, CD
Lift Coefficient, CL
VOF
Exp.
Water slip-topwall
VOF
Exp.
Water sliptop-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
4.69
2.02
3.19
-0.55
-0.70
-1.43
k-ω STD Low Re
10.91
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
Turbulence model
k-ω STD High Re
The k-ε RNG predicts closet drag and lift coefficients
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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
3
2.5
CD
2
1.5
1
0.5
0
-0.5 0%
CL -1
-1.5
-2
Effect of inlet turbulence intensity on force coefficients when
mixing length is 41.5 mm
4
CD 3
2
1
5%
10%
15%
20%
25%
30%
0
0%
CL
5%
10%
15%
20%
25%
30%
-1
-2
Inlet turbulence intensity
Inlet turbulence intensity
Effect of inlet turbulence intensity on drag coefficient
Effect of inlet turbulence intensity on drag coefficients
Effect of inlet turbulence intensity on lift coefficient
Effect of inlet turbulence intensity on lift coeffcients
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Fully developed velocity profile after selected runs:
Development of velocity profile for open channel flow for selected runs
4
Y coordinates (m)
2
0
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
-2
-4
-6
-8
U velocity (m/s)
1st Run
3rd Run
5th Run
9th Run
13th Run
15th Run
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Fully developed turbulence kinetic energy after selected
runs:
Development of turbulence kinetic energy for open channel flow for
selected runs
4
Y coordinate (m)
2
0
0.00E+00
1.00E-04
2.00E-04
3.00E-04
4.00E-04
5.00E-04
6.00E-04
7.00E-04
-2
-4
-6
-8
Kinetic energy per unit mass (m2/s2)
1st Run
3rd Run
5th Run
9th Run
13th Run
15th Run
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Fully developed turbulence dissipation rate after selected
runs:
Development of turbulence dissipation rate for open channel flow
for selected runs
4
Y coordinate (m)
2
0
0.00E+0 4.10E04
-2 0
8.20E04
1.23E03
1.64E03
2.05E03
2.46E03
2.87E03
3.28E03
3.69E03
4.10E03
-4
-6
-8
Turbulence dissipation rate (m2/s3)
1st Run
3rd Run
5th Run
9th Run
13th Run
15th Run
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Comparison between CFD simulations and experimental data
for Fr=0.22 for drag coefficients:
h*
CFD
Simulation
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
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Comparison between CFD simulation and experimental data for
Fr=0.22 for lift coefficients:
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
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Comparision between CFD simulations and experimental
results for drag coefficients for case of Fr=0.22
3.00
2.50
CD
2.00
1.50
1.00
0.50
0.00
0
0.5
1
1.5
2
2.5
3
3.5
h*
CFD simulation
Experimental results
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Comparision between CFD simulation and experimental
results for lift coefficients for case of Fr=0.22
0.50
0.00
0
0.5
1
1.5
2
2.5
3
3.5
CL
-0.50
-1.00
-1.50
-2.00
h*
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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QUESTIONS ???
More information at:
www.kostic.niu.edu
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