Flow and Pressure Scour Analysis of an Open Channel

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Flow and Pressure Scour Analysis of an Open Channel Powered By Docstoc
					   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
     steady operating conditions.
                     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
STEADY-STATE DEVELOPMENT
      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
      3.0                                                                              Quadratic
                                                                                       High-Re
      2.5                                                                              k-ep Suga
                                                                                       Quadratic


                                                                                                                    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
                                                                                                                                                              Quadratic
                                                                                                                                                              High-Re
                                                                            -0.5
                                                                                                                                                              k-ep Suga



      Lift Coefficient
                                                                            -1.0                                                                              Quadratic
                                                                                                                                                              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                                                                     Quadratic High-Re
        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
                                                                              Quadratic High-Re
         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
                                          h*                                  Quadratic High-Re



                                                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
Solution Method              Steady-State
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:

       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 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 ???

More information at:
  www.kostic.niu.edu