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

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-  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. Fig 2: Characteristic dimensions for the channel and the bridge Fig 3: Detail bridge dimension

DIMENSIONLESS PARAMETERS Reynolds Number:Froude Number: Inundation Ratio: Drag Force Coefficient:Lift Force Coefficient:

COMPUTATIONAL MODEL Two computational model are used.   Free-Surface or VOF Model   Single-Phase Flat-Top Model Governing Equations:

Where For Laminar Flow For Turbulent Flow Additional Transport Equation for VOF: Where

‘VOF’ MODEL Fig 4: Computational Domain for VOF Model Fig 5: Mesh Structure for VOF Model

BOUNDARY CONDITIONS SLIP WALL OUTLET NO SLIP WALL WATER INLET AIR INLET SYMPLANE   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 Fig 6: Boundary conditions for VOF Model

‘VOF’ SIMULATION PARAMETERS Air & Water Inlet Velocity0.35 m/s Turbulent Kinetic Energy m 2 /s 2 Turbulent Dissipation Rate m 2 /s 3 Solution MethodTransient SolverAlgebric Multigrid (AMG) Solution AlgorithmSIMPLE Relaxation Factor Pressure Momentum, Turbulence, Viscosity Differencing SchemeMARS Convergence Criteria10 -2 Computation time 200 sec

TURBULENCE MODELS USED   Two-Equation Models k-  High Reynolds k-  Low Reynolds k-  Chen k-  Standard Quadratic High Reynolds k-  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 sect = 50 sec t = 90 sect = 100 sec t = 120 sect = 150 sec t = 190 sect = 200 sec Fig 7: Steady-state development of k-  Low-Re VOF Model

PARAMETRIC EFFECT ON FORCE COEFFICIENTS Temporal Effect: Drag Coefficient Lift Coefficient Fig 8

Effect of Slip & Symmetry BC at the Flat-Top: Drag Coefficient Lift Coefficient Fig 9

Effect of Bridge Opening: Drag Coefficient Fig 10

FORCE COEFFICIENT COMPARISON OF k-  MODELS Drag Coefficient Lift Coefficient Fig 11

FORCE COEFFICIENT COMPARISON OF RSM MODELS Drag Coefficient Lift Coefficient Fig 12

DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models Fig 13

LIFT COEFFICIENT COMPARISON FOR ALL Turb. Models Fig 14

Turbulence ModelsC D avg C D exp (Ref.) %Differenc e C L avg C L exp (Ref.) % Difference k-ε High Re (top wall slip) k-ε High Re (top wall symmetry) k-ε Low Re (top wall slip) k-ε Low Re (top wall symmetry) k-ε RNG k-ε Chen k-ε Standard Quadratic High Re k-ε Suga Quadratic High Re k-ω STD High Re k-ω STD Low Re k-ω SST High Re k-ω SST Low Re RSM_GL_craft RSM_SSG0.367N/A N/A RSM_GL_Standard0.535 N/A N/A Comparison of force coefficients for different turbulence models:

SINGLE-PHASE MODEL NO SLIP WALL WATER INLET OUTLET SLIP WALL SYMPLANE Fig 15: Mesh structure of Single-phase Model Fig 16: Boundary conditions of Single-Phase Model

SIMULATION PARAMETERS Water Inlet Velocity0.35 m/s Turbulent Kinetic Energy m 2 /s 2 Turbulent Dissipation Rate m 2 /s 3 Solution MethodSteady-State SolverAlgebric Multigrid (AMG) Solution AlgorithmSIMPLE Relaxation Factor Pressure Momentum, Turbulence, Viscosity Differencing SchemeMARS Convergence Criteria10 -6

TURBULENCE MODELS USED   Two-Equation Models k-  High Reynolds k-  Low Reynolds k-  Standard High Reynolds k-  SST High Reynolds

DRAG COEFFICIENT COMPARISON FOR THE TM Fig 17

LIFT COEFFICIENT COMPARISON FOR THE TM 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 (y s ) 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. Where

OTHER CRITICAL SHEAR STRESS FORMULAE Based on Shields Coefficient: USWES Formula: Sakai Formula: Etc…..

CRITICAL SHEAR STRESS CURVE 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 Where, = Bed load transport rate = Bed Shear Stress = Critical Shear Stress

FLOW CHART

Geometrical and Operating Variables and Parameters Values 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 m 3 /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/m 2 Computational parameters: Fig 20: Model geometry

After 19 th iteration, final y s of 2.4 cm is obtained. Fig 21: Final scoured model Fig 22: Shear stress distribution

Fig 23 SCOUR AUTOMATION PROCESS

Automation has been implemented for same geometry Mentioned in Fig. 19. After 24 th iteration, final y s of 1.2 cm is obtained. Fig 24 Fig 25

VALIDATION OF EXPERIMENT Geometrical and Operating Variables and Parameters Values Channel water depth 0.25 m Bridge opening m Type of bridge deck Girder Rectangular obstacle instead of bridge Height of bridge deck, s 0.04 m Inundation ratio, h* Water discharge rate 5.125E-4 m 3 /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/m 2

Fig 26: Final scour shape After 20 th iteration, final y s 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: Formula by Wilson: Formula by Yalin: Formula by Bayram et al. Based on these different formulae roughness (k s ) varies from mm to 2.5 mm for d 50 = 1 mm.

VERIFICATION OF GUO’S PROFILE Guo proposed, For

Fig 29: Without using factor Fig 30: Using 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.

INITIAL BED PROFILE Fig 31: Model geometry Fig 32

ITERATION # 02 Fig 34 Fig 33

ITERATION # 03 Fig 36 Fig 35

ITERATION # 04 Fig 38 Fig 37

ITERATION # 05 Fig 40 Fig 39

ITERATION # 06 Fig 42 Fig 41

ITERATION # 07 Fig 44 Fig 43

ITERATION # 08 Fig 46 Fig 45

  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 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.

  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 CONCLUSIONS & RECOMMENDATIONS

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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