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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 0.5Vu AD 0.5Vu 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 0.0541 exp 23 s gd 50 d * Where s 1g 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: 100S 1d 6 5 2M 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

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bridge scour, the bridge, open channels, cross section, shear stress, water surface, critical velocity, uniform flow, bridge deck, bed material, bridge abutment, water surface profiles, the flume, open channel flow, tidal scour

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posted: | 1/13/2010 |

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