1. 2009 January 10-12 www.kostic.niu.edu 1 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

2. 2009 January 10-12 www.kostic.niu.edu 2 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

3. 2009 January 10-12 www.kostic.niu.edu 3  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

4. 2009 January 10-12 www.kostic.niu.edu 4 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

5. 2009 January 10-12 www.kostic.niu.edu 5 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

6. 2009 January 10-12 www.kostic.niu.edu 6  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

7. 2009 January 10-12 www.kostic.niu.edu 7 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) L Bridge =0.34 m S=0.058 m ΔW Simulation =0.00254 L Flow = 0.26 m Flow Direction Schematic of experimental six girder bridge deck model

8. 2009 January 10-12 www.kostic.niu.edu 8 Dimensions of experimental six girder bridge deck model L Flow X Y Nomenclature for bridge dimensions and flooding ratios Theory Flooding Ratio Froude Number

9. 2009 January 10-12 www.kostic.niu.edu 9  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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12. 2009 January 10-12 www.kostic.niu.edu 12 Governing Equations for fluid flow:  Mass conservation equation  Momentum conservation equation  Energy conservation equation

13. 2009 January 10-12 www.kostic.niu.edu 13 Dimensionless parameters for open channel flow:  Reynolds Number y b For 2D open channel flow,

14. 2009 January 10-12 www.kostic.niu.edu 14 Froude Number:  Froude number is dimensionless number which governs character of open channel flow The flow is classified on Froude number Subcritical or tranquil flow Critical Flow Supercritical or rapid flow Open channel flow is dominated by inertial forces for rapid flow and by gravity forces for tranquil flow

15. 2009 January 10-12 www.kostic.niu.edu 15 Froude number is also given by Where Wave speed (m/s) = Flow depth (m)

16. 2009 January 10-12 www.kostic.niu.edu 16 Force Coefficients:  The component of resultant pressure and shear forces in direction of flow is called drag force and component that acts normal to flow direction is called lift force  Drag force coefficient is  Lift force coefficient is  In the experimental testing, the drag reference area is the frontal area normal to the flow direction. The lift reference area is the bridge area perpendicular to Y direction.

17. 2009 January 10-12 www.kostic.niu.edu 17 Drag and lift reference areas for experimental data: For drag, if,then drag area is if,then drag area is For lift, for all,lift area is

18. 2009 January 10-12 www.kostic.niu.edu 18 Turbulent Flow:  Turbulent flow is complex phenomena dominated by rapid and random fluctuations  Turbulent flow is highly unsteady and all the formulae for the turbulent flow are based on experiments or empirical and semi – empirical correlations  Turbulent Intensity  Turbulence mixing length (m)  Turbulent kinetic energy (m 2 /s 2 )

19. 2009 January 10-12 www.kostic.niu.edu 19  Turbulence dissipation rate (m 2 /s 3 )  Specific dissipation rate (1/s)

20. 2009 January 10-12 www.kostic.niu.edu 20 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

21. 2009 January 10-12 www.kostic.niu.edu 21 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

22. 2009 January 10-12 www.kostic.niu.edu 22 k-ω turbulence model:  The k-ω turbulence models are obtained as an alternative to the k-ε model which have some difficulty for near wall treatment  The k-ω turbulence models Standard k-ω model Shear stress transport (SST) model High Reynolds Low Reynolds High ReynoldsLow Reynolds

23. 2009 January 10-12 www.kostic.niu.edu 23 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

24. 2009 January 10-12 www.kostic.niu.edu 24 Computational Model:  STAR-CD (Simulation of Turbulent flow in Arbitrary Regions Computational Dynamics) is CFD analysis software  STAR-CD is finite volume code which solves governing equations for steady state or transient problem  The first method used in STAR-CD to simulate open channel turbulent flow is free surface method which makes use of Volume of Fluid (VOF) methodology  VOF methodology simulates air and water domain  VOF methodology uses volume of fraction variable to capture air- water interface

25. 2009 January 10-12 www.kostic.niu.edu 25 VOF technique:  VOF technique is a transient scheme which captures free surface.  VOF deals with light and heavy fluids  VOF is the ratio of volume of heavy fluid to the total control volume  Volume of fraction is given by  Transport equation for volume of fraction  Volume fraction of the remaining component is given by

26. 2009 January 10-12 www.kostic.niu.edu 26  The properties at the free surface vary according to volume fraction of each component

27. 2009 January 10-12 www.kostic.niu.edu 27 Free Surface method: Dimensions for computational model h*=1.5 generated in STAR-CD (Dimensions not to scale and in SI units) 0 Y X Z 0.08 -1.50 -0.15 0.06 0.30 0303 0.26 1.78

28. 2009 January 10-12 www.kostic.niu.edu 28 Computational Mesh: Full computational domain with non uniform mesh and 2 cells thick in Z direction for =1.5 Y X Y

29. 2009 January 10-12 www.kostic.niu.edu 29 Boundary Conditions: Bottom Wall (No Slip) Top wall (slip) Water Inlet Air Inlet Outlet Symmetry Plane X Y Z Y

30. 2009 January 10-12 www.kostic.niu.edu 30 Computational parameters for VOF methodology: Inlet velocity, U0.35 m/s Turbulent kinetic energy, k 0.00125 m 2 /s 2 Turbulent Dissipation Rate, ε 0.000175 m 2 /s 3 Solution methodTransient Solver methodAlgebraic Multigrid approach (AMG) Solution algorithmSIMPLE Relaxation factorPressure - 0.3 Momentum, Turbulence, Viscosity - 0.7 Differencing schemeMARS Convergence Criteria10 -2 Time Step (Δt)0.01 s

31. 2009 January 10-12 www.kostic.niu.edu 31 Water slip top wall method: -1.5 0 0.06 Y X Z 0.08 -0.15 0303 0.26 1.78 Dimensions for computational model h*=1.5 for water slip –top-wall method (Dimensions not to scale and in SI units)

32. 2009 January 10-12 www.kostic.niu.edu 32 Boundary conditions: Top wall (slip) Bottom wall (No slip) Outlet (Standard) Symmetry Plane X Y X Y Water Inlet Computational domain with boundary surfaces and boundary conditions for water slip-top-wall method

33. 2009 January 10-12 www.kostic.niu.edu 33 Computational parameters for water slip-top-wall method: Inlet velocity, Turbulent kinetic energy, Turbulent Dissipation Rate, 0.35 m/s 0.00125 m 2 /s 2 0.000175 m 2 /s 3 Solution MethodSteady State Solver MethodAlgebraic Multigrid approach (AMG) Solution AlgorithmSIMPLE Relaxation factorPressure - 0.3 Momentum, turbulence, Viscosity - 0.7 Differencing schemeUD Convergence Criteria10 -6

34. 2009 January 10-12 www.kostic.niu.edu 34 STAR-CD simulation Validation with basics of fluid mechanics : Fully developed velocity profile for laminar pipe flow after STAR-CD simulation

35. 2009 January 10-12 www.kostic.niu.edu 35 Fully developed velocity profile for the turbulent pipe flow after STAR-CD simulation

36. 2009 January 10-12 www.kostic.niu.edu 36 Flow typeWall Roughness (m) Theoretical friction factor (Reference) Simulation friction factor Absolute Difference Percentage Difference LaminarSmooth0.28440.2865 0.00210.74 TurbulentSmooth0.01210.0116 0.00054.13 Turbulent0.0050.0530.048 0.0059.43 Turbulent0.0150.08720.0756 0.011613.30 Turbulent0.0750.25290.2019 0.05120.17 Comparison between theoretical and simulated friction factor :

37. 2009 January 10-12 www.kostic.niu.edu 37 Calculation of entrance length: Continued on next page

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39. 2009 January 10-12 www.kostic.niu.edu 39 Verification of power law velocity profile:

40. 2009 January 10-12 www.kostic.niu.edu 40 Comparison between Fluent and STAR-CD for same geometry: 0 0.254 0.504 0.097 1.016 0.127 0 X Y Operating ConditionVariables Inlet VelocityU = 2 m/s Inlet turbulence intensity10 % Inlet turbulence mixing length0.1 m Outlet gauge pressure0 Pa WallsNo Slip Convergence0.001

41. 2009 January 10-12 www.kostic.niu.edu 41 Comparison for velocity contours between STAR-CD and Fluent

42. 2009 January 10-12 www.kostic.niu.edu 42 Comparison for velocity vectors between STAR-CD and Fluent

43. 2009 January 10-12 www.kostic.niu.edu 43 Comparison for X velocities between Fluent and STAR-CD

44. 2009 January 10-12 www.kostic.niu.edu 44 ParameterFluentSTAR-CD (Reference Data) Absolute Difference Percentage Difference ΔP STAT 11201161413.53 % ΔP TOT 10831120373.30 % Pressure difference ( Pa ) 3.97 %0.28-7.05-6.77CLCL 5.5 %0.112.001.89CDCD Percentage Difference Absolute Difference STAR-CD (Reference Data) FluentForce Coefficients Force Coefficients

45. 2009 January 10-12 www.kostic.niu.edu 45 VOF simulation of experimental data: Effect of time steps on drag coefficients

46. 2009 January 10-12 www.kostic.niu.edu 46 Effect of time steps on lift coefficients:

47. 2009 January 10-12 www.kostic.niu.edu 47 Effect of decreased downstream length on force coefficients

48. 2009 January 10-12 www.kostic.niu.edu 48 Effect of decrease in under bridge water depth

49. 2009 January 10-12 www.kostic.niu.edu 49 Effect of top boundary condition at top as slip wall and symmetry

50. 2009 January 10-12 www.kostic.niu.edu 50 Free Surface Development: Nomenclature for VOF contour plot Free surface, Volume fraction for water

51. 2009 January 10-12 www.kostic.niu.edu 51 t=10sec t=30sec t=50 sec t=150 sec t=200 sec sec t=300 sec t =250 sec t=100se c Effect of k-ε standard turbulence model on free surface development:

52. 2009 January 10-12 www.kostic.niu.edu 52 Effect of different turbulence models on drag coefficients:

53. 2009 January 10-12 www.kostic.niu.edu 53 Effect of different turbulence models on lift coefficients:

54. 2009 January 10-12 www.kostic.niu.edu 54 Turbulence Models h* up h* dw h* avg C D avg C D exp C L avg C L exp k-ε High Re1.401.301.353.171.98-0.83-1.04 k-ε RNG1.45 2.772.02-1.39-0.73 k-ω STD High Re1.151.301.384.691.99-0.55 k-ω STD Low Re1.841.501.6710.911.97-0.29-0.60 k-ω SST High Re1.301.201.253.031.98-1.15-1.10 k-ω SST Low Re1.351.201.284.031.96-0.91-1.07 h* up h* dw h* avg C D avg C D exp C L avg C L exp Count6.00 Maximum1.841.501.6710.912.02-0.29-0.60 Average1.411.331.404.771.98-0.85-0.92 Std. Dev.0.230.130.153.090.020.400.21 Minimum1.151.201.252.771.96-1.39-1.10 Comparison between simulation results for different turbulence model and experimental results:

55. 2009 January 10-12 www.kostic.niu.edu 55 Water slip-top-wall method: (a) Basic Coarse mesh (b) Refined near bridge (c) Fully refined model 0 % (Ref)-1.384390 % (Ref)2.93109 Fully refined model 0.08 %-1.383280.08 %2.93367 Refined near bridge 0.54%-1.391881 %2.96061 Basic coarse grid % DifferenceCLCL CDCD Mesh Density

56. 2009 January 10-12 www.kostic.niu.edu 56 0.94 %-1.378770.2 %2.9544510 -4 0.0022 %-1.391850.00033 %2.9606210 -5 0 % (ref)-1.391880 % (ref)2.9606110 -6 % differenceCLCL CDCD Convergence criteria Effect of convergence criteria on final solution:

57. 2009 January 10-12 www.kostic.niu.edu 57 Comparison between VOF and Water slip-top-wall method with experimental results:

58. 2009 January 10-12 www.kostic.niu.edu 58 Drag coefficient, C D Lift Coefficient, C L Turbulence modelVOFExp.Water slip-top- wall VOFExp. Water slip- top-wall k-ε High Re 3.172.022.96-0.83-0.70-1.39 k-ε RNG 2.772.022.57-1.39-0.70-1.08 k-ω STD High Re 4.692.023.19-0.55-0.70-1.43 k-ω STD Low Re 10.912.0210.59-0.29-0.70-1.35 k-ω SST High Re 3.032.022.78-1.15-0.70-1.26 k-ω SST Low Re 4.032.024.03-0.91-0.70-1.63 The k-ε RNG predicts closet drag and lift coefficients

59. 2009 January 10-12 www.kostic.niu.edu 59 Effect of inlet turbulence on drag and lift coefficients:

60. 2009 January 10-12 www.kostic.niu.edu 60 Fully developed velocity profile after selected runs:

61. 2009 January 10-12 www.kostic.niu.edu 61 Fully developed turbulence kinetic energy after selected runs:

62. 2009 January 10-12 www.kostic.niu.edu 62 Fully developed turbulence dissipation rate after selected runs:

63. 2009 January 10-12 www.kostic.niu.edu 63 h *CFD Simulation Experimental (Reference) Absolute Difference Percentage Difference 0.2891.631.92 0.2915.10 0.4931.781.21 0.5747.10 0.681.921.57 0.3522.29 0.9722.291.37 0.9267.15 1.2812.681.98 0.735.35 1.5002.662.02 0.6431.68 1.7092.621.95 0.6734.35 2.0152.511.89 0.6232.80 2.3092.391.82 0.5731.31 2.5172.331.79 0.5430.16 2.7062.281.73 0.5531.79 3.0082.191.71 0.4828.07 3.0972.171.69 0.4828.40 Comparison between CFD simulations and experimental data for Fr=0.22 for drag coefficients:

64. 2009 January 10-12 www.kostic.niu.edu 64 h *CFD Simulation Experimental (Reference) Absolute Difference Percentage Difference 0.289 -0.42-1.701.2875.29 0.493 -0.77-1.280.5139.84 0.68 -1.760.7643.18 0.972 -1.44-1.750.3117.71 1.281 -1.53-1.130.4035.40 1.500 -1.01-0.700.3144.29 1.709 -0.81-0.530.2852.83 2.015 -0.46-0.290.1758.62 2.309 -0.10-0.140.0428.57 2.517 -0.12-0.040.08233.33 2.706 -0.050.030.08275.00 3.008 -0.060.060.13201.59 3.097 -0.100.100.19198.97 Comparison between CFD simulation and experimental data for Fr=0.22 for lift coefficients:

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67. 2009 January 10-12 www.kostic.niu.edu 67 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 lower lift than experimental

68. 2009 January 10-12 www.kostic.niu.edu 68 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

69. 2009 January 10-12 www.kostic.niu.edu 69 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).

70. 2009 January 10-12 www.kostic.niu.edu 70 QUESTIONS ??? More information at: www.kostic.niu.edu