# Flow and Pressure Scour Analysis of an Open Channel

Document Sample

```					   CFD Simulation of Open Channel Flooding Flows
and Scouring Around Bridge Structures

The 6th WSEAS International Conference on FLUID MECHANICS
(WSEAS - FLUIDS'09)
Ningbo, China, January 10-12, 2009

B. D. ADHIKARY , P. Majumdar and M. Kostic
Department of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY

2009 January 10-12                    www.kostic.niu.edu
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
INTRODUCTION
Bridge failure analysis is important from CFD
perspective
Most of the bridge fails due to flood in an open
channel
Under flooding conditions, force around the bridge
becomes very high
High stresses caused at the channel bed results in
scour
Design and analysis software shows a way to
design a cost-effective and quality bridge structure
Experimental 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 REVIEW
Literatures 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-e 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 REVIEW
Literatures 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
PROBLEM DEFINITION
Need to find out a computational model and modeling
technique for turbulence and force analysis around
the bridge using STAR-CD CFD software.
W
Vu              Y                             s           hu
x                   hb
Z

Fig 2: Characteristic dimensions for the channel and the bridge

0.005m (0.188")
0.25m (9.861")

0.00254m
0.0045m
0.029m                            0.004m (0.126")                                 (0.159")
(0.259")
(1.14")

Y
0.029m     0.027m
(1.15")     (1.05")

X

Z                     0.034m
0.01m          (1.35")
(0.4")                                              0.01m
(0.54")

Fig 3: Detail bridge dimension
DIMENSIONLESS PARAMETERS
Reynolds Number:                 Froude Number:
Vu Dh                                Vu
Re                                 Fr 
                                    gLc
Inundation Ratio:
hu  hb
h* 
s
Drag Force Coefficient:              Lift Force Coefficient:
FD                                FL
CD                                 CL 
0.5Vu AD                           0.5Vu AL
2                                 2
COMPUTATIONAL MODEL
Two computational model are used.
 Free-Surface or VOF Model
 Single-Phase Flat-Top Model

Governing Equations:
   
   ( u i )  0
t xi

                                         P
( u i )       ( u i u j   ij )        g i  Fi
t            x j                         xi
Where
  u i u j     2 u k
 ij    
 x
         
 3 x
 ij For Laminar Flow
  j xi
                      k

  u i u j     2
 ij    tot           tot u k  ij   u i ' u j '
 x
  j xi         3       x k
                
For Turbulent Flow

Additional Transport Equation for VOF:
 i                                                  Vi
   ( i u )  0           Where            i 
t                                                    V
‘VOF’ MODEL
0.2178m                                 AIR (VOF=0)
(8.565")
0.029m                                                                       0.3048m
(1.145")                                                                       (12")

0.058m                     Y
(2.29")                                                  WATER (VOF = 1)
0.15m                             x
(5.9055")                       Z
1.524m (60")               0.26m (10.237")    1.518m (59.763")

3.302m (130")

Fig 4: Computational Domain for VOF Model

Fig 5: Mesh Structure for VOF Model
BOUNDARY CONDITIONS
SLIP WALL

AIR
INLET

OUTLET

WATER
INLET

NO SLIP WALL                     SYMPLANE

Fig 6: Boundary conditions for VOF Model

Air & Water Inlet:
Velocity inlet having 0.35 m/s free-stream velocity
Outlet:
Constant pressure gradient at boundary surface
Bottom Wall:
Hydro-dynamically smooth no-slip wall
‘VOF’ SIMULATION PARAMETERS
Air & 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
Pressure - 0.3
Relaxation Factor            Momentum, Turbulence,
Viscosity - 0.7
Differencing Scheme          MARS
Convergence Criteria         10-2
Computation time             200 sec
TURBULENCE MODELS USED
 Two-Equation Models
• k-e High Reynolds
• k-e Low Reynolds
• k-e Chen
• k-e Standard Quadratic High Reynolds
• k-e Suga Quadratic High Reynolds

 Reynolds Stress Models
• RSM/Gibson-Launder (Standard)
• RSM/Gibson-Launder (Craft)
• RSM/Speziale, Sarkar and Gatski
t = 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-e Low-Re VOF Model
PARAMETRIC EFFECT ON FORCE COEFFICIENTS
Temporal Effect:
Effect of Time Steps on Drag Coefficient for k-e Low-Re TM

4.0

3.6

3.2

2.8

Drag Coefficient
0.1
2.4
0.05
CD

2.0
0.02
1.6
0.01
1.2

0.8

0.4

0.0
0      20    40   60    80   100    120   140   160   180   200     220

Time (sec)

Effect of Time Steps on Lift Coefficient for k-e Low-Re TM
2.0

1.6

1.2

0.8
0.1
0.4

Lift Coefficient
0.05
CL

0.0
0.02
-0.4
0.01
-0.8

-1.2

-1.6

-2.0
0   20     40   60   80   100   120    140   160   180   200   220
Time (sec)

Fig 8
Effect of Slip & Symmetry BC at the Flat-Top:
Comparison Between Symmetry and Slip top-wall for
Low-Re TM for CD Calculation

3.5

3.0

2.5

2.0
Symmetry                   Drag Coefficient
CD

1.5
Slip

1.0

0.5

0.0
0     20   40   60   80    100   120   140   160   180   200   220
Time (sec)

Comparison Between Symmetry and Slip top-wall for
Low-Re TM for CL Calculation

0.0

-0.2

-0.4

Lift Coefficient                                                      -0.6
Symmetry
CL

-0.8
Slip

-1.0

-1.2

-1.4
0   20   40   60   80   100   120    140   160   180   200   220

Fig 9
Time (sec)
Effect of Bridge Opening:

Effect of bridge openings (h b) on CD

4.4
4.0
3.6
3.2
2.8                                                                       hb=15cm
2.4
CD

hb=12cm
2.0
1.6                                                                       hb=10.125cm
1.2
0.8
0.4
0.0
0   20    40   60   80   100    120   140   160   180   200   220
Time (sec)

Drag Coefficient
Fig 10
FORCE COEFFICIENT COMPARISON OF k-e MODELS
Comparison of CD among k-e Models
4.0                                                                              k-ep High-Re

3.5
k-ep Standard
High-Re
2.5                                                                              k-ep Suga

Drag Coefficient
High-Re
CD

2.0
k-ep Low-Re
1.5

1.0                                                                              k-ep Chen

0.5
Experimental
Data
0.0
0   20   40   60    80    100   120    140   160   180   200     220
Time (sec)

Comparison of CL among k-e Models

1.0
k-ep High-Re
0.5

0.0                                                                              k-ep Standard
High-Re
-0.5
k-ep Suga

Lift Coefficient
High-Re
CL

-1.5                                                                              k-ep Low-Re

-2.0
k-ep Chen
-2.5

-3.0
Experimental
Data
-3.5
0     20    40      60     80   100   120    140   160   180   200   220

Time (sec)

Fig 11
FORCE COEFFICIENT COMPARISON OF RSM MODELS
Comparison of CD among RSM Models

4.0

3.6

3.2

2.8                                                                                  RSM-GL-Craft
2.4

2.0                                                                                  RSM-GL-
Standard
Drag Coefficient
CD

1.6
RSM-SSG
1.2

0.8
Experimental
0.4                                                                                  Data
0.0

-0.4

-0.8
0   20   40    60   80     100   120   140   160   180   200    220

Time (sec)

Comparison of CL among RSM Models

2.8
2.4
2.0
1.6
1.2                                                                             RSM-GL-Craft
0.8
0.4
RSM-GL-

Lift Coefficient
0.0                                                                             Standard
CL

-0.4
RSM-SSG
-0.8
-1.2
-1.6                                                                            Experimental
-2.0                                                                            Data
-2.4
-2.8
-3.2
0     20       40   60   80   100   120    140   160   180   200   220

Fig 12
Time (sec)
DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models

Comparison of CD for different TM wrt h*
Experimental
5.0
k-ep High-Re
4.5
k-ep low-Re

4.0
RNG

3.5                                                                     Chen

3.0                                                                     RSM_GL_Craft

RSM_GL_Standard
CD

2.5

2.0                                                                     RSM_SSG

k-omega Standard
1.5
High-Re
k-omega SST High-Re
1.0

k-omega SST Low-Re
0.5

k-ep Standard
0.0   0.5   1.0   1.5   2.0   2.5    3.0     3.5   4.0   4.5   5.0   k-ep Suga Quadratic
h*                                     High-Re

Fig 13
LIFT COEFFICIENT COMPARISON FOR ALL Turb. Models

Comparison of CL for different TM wrt h*
Experimental
2.0
k-epsilon High-Re
1.5
k-epsilon Low-Re
1.0
k-epsilon RNG

0.5
k-epsilon Chen

0.0                                                                     RSM_GL_Craft
CL

-0.5                                                                     RSM_GL_Standard

-1.0                                                                     RSM_SSG

-1.5                                                                     k-omega Standard High-
Re
-2.0                                                                     k-omega SST High-Re

k-omega SST Low-Re
-2.5

k-epsilon Standard
-3.0
0.0   0.5      1.0   1.5   2.0   2.5   3.0   3.5   4.0   4.5   5.0
k-epsilon Suga

Fig 14
Comparison of force coefficients for different turbulence models:
Turbulence Models          CD avg   CD exp   %Differenc   CL avg   CL exp   % Difference
(Ref.)         e               (Ref.)
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            3.19     1.97       61.92       -0.83   -1.05       20.95
symmetry)
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 Re                   10.91    1.965      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_SSG                          0.367    N/A        N/A        1.341    N/A         N/A
RSM_GL_Standard                  0.535    N/A        N/A         1.628   N/A         N/A
SINGLE-PHASE MODEL

Fig 15: Mesh structure of Single-phase Model

SLIP WALL

WATER
OUTLET
INLET

SYMPLANE
NO SLIP WALL

Fig 16: Boundary conditions of Single-Phase Model
SIMULATION PARAMETERS
Water Inlet Velocity         0.35 m/s
Turbulent Kinetic Energy     0.00125 m2/s2
Turbulent Dissipation Rate   0.000175m2/s3
Solver                       Algebric Multigrid (AMG)
Solution Algorithm           SIMPLE
Pressure - 0.3
Relaxation Factor            Momentum, Turbulence,
Viscosity - 0.7
Differencing Scheme          MARS
Convergence Criteria         10-6
TURBULENCE MODELS USED
 Two-Equation Models

• k-e High Reynolds

• k-e Low Reynolds

•k-w Standard High Reynolds

• k-w SST High Reynolds
DRAG COEFFICIENT COMPARISON FOR THE TM
Variation of CD wrt h*

3.5

3.0

2.5

2.0
CD

1.5

1.0

0.5

0.0
0.0      0.5         1.0    1.5        2.0      2.5          3.0    3.5

h*

Experimental                       k-epsilon_High-Re
k-epsilon_Low-Re                   k-omega_Standard_High-Re
k-omega_SST_High-Re

Fig 17
LIFT COEFFICIENT COMPARISON FOR THE TM
Variation of CL wrt h*

0.5

0.0

-0.5

-1.0
CL

-1.5

-2.0

-2.5
0.0       0.5        1.0    1.5        2.0     2.5      3.0        3.5
h*

Experimental                      k-epsilon_High-Re
k-epsilon_Low-Re                  k-omega_Standard_High-Re
k-omega_SST_High-Re

Fig 18
SCOUR PHENOMENON
Caused by high stress at the river bed

Types of 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 towards
Computational 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 has
been developed based on the critical shear stress
Formula proposed by Guo, known as Rouse-Shields
equation.

c         0.23                d *0.85 
       0.0541  exp 
 23 

 s   gd 50 d *          
                

Where
  s   1g 
13

d*                 d 50
       2

OTHER CRITICAL SHEAR STRESS FORMULAE
Based on Shields Coefficient:
c

 s   d
USWES Formula:
1
        d             2
 c  0.00595 S  1 
        M
Sakai Formula:

100S  1d
6
5
 2M        Etc…..
c                                
3                1  2M 
CRITICAL SHEAR STRESS CURVE
Variation of Critical Shear Stress with Bed Size

6.5

6.0

5.5

5.0

4.5

4.0
c (Pa)

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0
0     1          2          3             4          5        6      7
Median Bed Diameter d50 (mm)

Rouse-Shields Equation Based        Shields Coefficient Based
USWES Formula Based                 Chang's Formula Based
Sakai Formula Based                 Chien & Wan Approach Based

Fig 19: Variation of c with diameter based on different formulae

For mean diameter of 1 mm, c varies from 0.43 Pa
to 0.72 Pa, based on different formula.
VAN RIJN FORMULA
2.1
   c 
        
qb
 0.053               c 
1.5    s   w g                          s   w g 
0. 1

d                                   d   0. 3
               
w                              w
2

Where,
q b = Bed load transport rate
     = Bed Shear Stress

c    = Critical Shear Stress
FLOW CHART                      SCRIPT FILE                  FIND OUT τC
USING DIFFERENT
CORRELATIONS
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

NO

NO
END OF FILE?            IS τX AND τC ?

YES

WRITE THE CELL NUMBER IN THE
FORTRAN OUTPUT FILE,
YES                  OUTPUT.TXT

END OF FILE?           NO

YES

CHANGE OF SCRIPT FILE BY
BRINGING THE BOTTOM BOUNDARY
OF THE CELLS, WHERE τX > τC,
ONE CELL DOWN
Fig 20: Model geometry

Computational parameters:
Geometrical and Operating Variables                   Values
and Parameters
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
After 19th iteration, final ys of 2.4 cm is obtained.

Fig 21: Final
scoured model

Fig 22: Shear stress
distribution
SCOUR AUTOMATION PROCESS

Fig 23
Automation has been implemented for same geometry
Mentioned in Fig. 19.
Fig 24

After 24th iteration, final ys of 1.2 cm is obtained.

Fig 25
VALIDATION OF EXPERIMENT
Geometrical and Operating              Values
Variables and Parameters
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 ROUGHNESS
Bed shear stress depends on roughness.
Roughness Formulae:
ks
Formula by Wilson:                      5
d 50
Formula by Yalin:
ks
d 50

 5    4  0.043 3  0.289  2  0.203  0.125
2

ks
Formula by Bayram et al.                max( 2.5,2.5 1.5 )
d 50
Based on these different formulae roughness (ks)
varies from 0.195 mm to 2.5 mm for d50 = 1 mm.
VERIFICATION OF GUO’S PROFILE
Guo proposed,
For x  0,
y           x   2.5

  exp           
ys          W         
           

For x  0,

y                1  x  1. 8 
 1.055 exp      0.055
ys               2 W  
              
Fig 29: Without using 0.055 factor

Fig 30: Using 0.055 factor
NEW SCOUR SCHEME
In 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 
y  ys 
   
 max c 
INITIAL BED PROFILE

Fig 31: Model geometry

Fig 32
ITERATION # 02

Fig 33

Fig 34
ITERATION # 03

Fig 35

Fig 36
ITERATION # 04

Fig 37

Fig 38
ITERATION # 05

Fig 39

Fig 40
ITERATION # 06

Fig 41

Fig 42
ITERATION # 07

Fig 43

Fig 44
ITERATION # 08

Fig 45

Fig 46
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

2.0

1.5
Force Coefficients

1.0

0.5

0.0

-0.5
0        1         2       3         4         5        6   7
Scour depth (cm)

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.
CONCLUSIONS & RECOMMENDATIONS
 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
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 ???