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2009 January 10-12 www.kostic.niu.edu 1 Computational Fluid Dynamics Computational Fluid Dynamics Simulation Simulation of Open-Channel Flows Over Bridge- of Open-Channel Flows Over Bridge- Decks Decks Under Various Flooding Conditions Under Various Flooding Conditions The 6th WSEAS International Conference on FLUID MECHANICS The 6th WSEAS International Conference on FLUID MECHANICS ( WSEAS - FLUIDS'09 WSEAS - FLUIDS'09) Ningbo, China, January 10-12, 2009 Ningbo, China, January 10-12, 2009 S. Patil, M. Kostic and P. S. Patil, M. Kostic and P. Majumdar Majumdar Department of Mechanical Engineering Department of Mechanical Engineering NORTHERN ILLINOIS NORTHERN ILLINOIS UNIVERSITY UNIVERSITY

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  • Computational Fluid Dynamics Simulationof Open-Channel Flows Over Bridge-DecksUnder Various Flooding Conditions The 6th WSEAS International Conference on FLUID MECHANICS (WSEAS - FLUIDS'09)Ningbo, China, January 10-12, 2009

  • Motivation:Bridges are crucial constituents of the nations transportation systemsBridge construction is critical issue as it involves great amount of money and riskBridge structures under various flood conditions are studied for bridge stability analysisSuch analyses are carried out by scaled experiments to calculate drag and lift coefficients on the bridgeScaled experiments are limited to few design variations and flooded conditions due to high cost and time associated with themAdvanced commercial Computational Fluid Dynamics (CFD) software and parallel computers can be used to overcome such limitations

  • CFD is the branch of fluid mechanics which uses numerical methods to solve fluid flow problemsIn spite of having simplified equations and high speed computers, CFD can achieve only approximate solutionsCFD is a versatile tool having flexibility is design with an ability to impose and simulate real time phenomenaCFD 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 ratesCFD simulation is a tool for through analysis by providing better insight of what is virtually happening inside the particular design

  • 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 surfaceKoshizuka, 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

  • Objectives:The objective of the present study is to validate commercial code STAR-CD for hydraulic researchThe experimental data conducted by Turner Fairbank Highway Research Center (TFHRC) at their own laboratories will be simulated using STAR-CDThe base case of Fr = 0.22 and flooding height ratio, h*=1.5 is simulated with appropriate boundary conditions corresponding to experimental testingThe open channel turbulent flow will be simulated using two different methodsFirst by transient Volume of Fluid (VOF) methodology and other as a steady state closed channel flow with top surface as slip wallDrag and lift coefficients on the bridge is calculated using six linear eddy viscosity turbulence model and simulation outcome will be compared with experimental results

  • 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 parametersThe suitable turbulence model will be used to simulate 13 different flooding height ratio from h*=0.3 to 3 for Fr =0.22

  • 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)

    Schematic of experimental six girder bridge deck model

  • Dimensions of experimental six girder bridge deck model Nomenclature for bridge dimensions and flooding ratiosTheoryFlooding RatioFroude Number

  • 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/sThe 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 3The lift coefficient is calculated by excluding buoyancy forces in Y (vertical) direction

  • Governing Equations for fluid flow:

    Mass conservation equation

    Momentum conservation equation

    Energy conservation equation

  • Dimensionless parameters for open channel flow:Reynolds Number For 2D open channel flow,

  • 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 flowand by gravity forces for tranquil flow

  • Froude number is also given by

    Where

    Wave speed (m/s) = Flow depth (m)

  • 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 forceDrag 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.

  • 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

  • Turbulent Flow:Turbulent flow is complex phenomena dominated by rapid and random fluctuationsTurbulent flow is highly unsteady and all the formulae for the turbulent flow are based on experiments or empirical and semi empirical correlationsTurbulent Intensity Turbulence mixing length (m)

    Turbulent kinetic energy (m2/s2)

  • Turbulence dissipation rate (m2/s3)

    Specific dissipation rate (1/s)

  • Turbulence Models:Six eddy viscosity turbulence models are studied from STAR-CD turbulence optionsTwo major groups of turbulence models k- and k- are studied The k- turbulence model The k- 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

  • The k- High Reynolds turbulence model:Most widely used turbulent transport modelFirst two equation model to be used in CFDThis model uses transport equations for k and in conjunction with the law-of-the wall representation of the boundary layer

    The k- RNG turbulence model:This turbulence model is obtained after modifying k- standard turbulence model using normalization group method to renormalize Navier Stokes equationsThis model takes into account effects of different scales of motions on turbulent diffusion

  • k- turbulence model:The k- turbulence models are obtained as an alternative to the k- model which have some difficulty for near wall treatment The k- turbulence models

    Standard k- model Shear stress transport (SST) model

    High ReynoldsLow ReynoldsHigh ReynoldsLow Reynolds

  • SST k- turbulence model:SST turbulence model is obtained after combining best features of k- and k- turbulence modelSST turbulence model is the result of blending of k- model near the wall and k- model near the wall

  • Computational Model:STAR-CD (Simulation of Turbulent flow in Arbitrary Regions Computational Dynamics) is CFD analysis softwareSTAR-CD is finite volume code which solves governing equations for steady state or transient problemThe first method used in STAR-CD to simulate open channel turbulent flow is free surface method which makes use of Volume of Fluid (VOF) methodologyVOF methodology simulates air and water domainVOF methodology uses volume of fraction variable to capture air-water interface

  • VOF technique:VOF technique is a transient scheme which captures free surface.VOF deals with light and heavy fluidsVOF is the ratio of volume of heavy fluid to the total control volumeVolume of fraction is given by

    Transport equation for volume of fraction Volume fraction of the remaining component is given by

  • The properties at the free surface vary according to volume fraction of each component

  • Free Surface method:

    Dimensions for computational model h*=1.5 generated in STAR-CD (Dimensions not to scale and in SI units)

  • Computational Mesh:

    Full computational domain with non uniform mesh and 2 cells thick in Z direction for =1.5Y

  • Boundary Conditions:

  • Computational parameters for VOF methodology:

  • Water slip top wall method:

    Dimensions for computational model h*=1.5 for water slip top-wall method (Dimensions not to scale and in SI units)

  • Boundary conditions:Computational domain with boundary surfaces and boundary conditions for water slip-top-wall method

  • Computational parameters for water slip-top-wall method:

    Inlet velocity, Turbulent kinetic energy, Turbulent Dissipation Rate,

    0.35 m/s0.00125 m2/s20.000175 m2/s3Solution MethodSteady StateSolver MethodAlgebraic Multigrid approach (AMG)Solution AlgorithmSIMPLERelaxation factorPressure - 0.3Momentum, turbulence, Viscosity - 0.7Differencing schemeUDConvergence Criteria10-6

  • STAR-CD simulation Validation with basics of fluid mechanics :

    Fully developed velocity profile for laminar pipe flow after STAR-CD simulation

  • Fully developed velocity profile for the turbulent pipe flow after STAR-CD simulation

  • Comparison between theoretical and simulated friction factor :

  • Calculation of entrance length:

    Continued on next page

  • Verification of power law velocity profile:

  • Comparison between Fluent and STAR-CD for same geometry:

  • Comparison for velocity contours between STAR-CD and Fluent

  • Comparison for velocity vectors between STAR-CD and Fluent

  • Comparison for X velocities between Fluent and STAR-CD

  • Pressure difference (Pa)3.97 %0.28-7.05-6.77CL5.5 %0.112.001.89CDPercentageDifferenceAbsolute Difference STAR-CD(Reference Data)FluentForceCoefficientsForce Coefficients

  • VOF simulation of experimental data:Effect of time steps on drag coefficients

  • Effect of time steps on lift coefficients:

  • Effect of decreased downstream length on force coefficients

  • Effect of decrease in under bridge water depth

  • Effect of top boundary condition at top as slip wall and symmetry

  • Free Surface Development:

    Nomenclature for VOF contour plot

    Volume fraction for water

  • Effect of k- standard turbulence model on free surface development:

  • Effect of different turbulence models on drag coefficients:

    Chart1

    2.78714201092.68097466153.72858845448.51995746582.65573362333.32871726982.022

    3.00324072422.51070835984.342012107210.61330304442.78337799643.68917700872.022

    3.00235507372.62495726974.534419670511.01992731372.78935613713.73445588872.022

    3.05759752142.65827986844.604164644611.06730961362.86186876883.72869916072.022

    3.1034299332.74407725714.633169697311.06254924232.88345649893.80619357632.022

    3.14738033722.71783986214.647118692111.01937378222.95519418653.84671208512.022

    3.18834167122.80673702744.654093189511.00464984322.94766615763.83829840562.022

    3.1922163922.79345227054.650772000310.99645757643.05139796823.94723341272.022

    3.20472620482.89917679464.667710065410.98538694563.05150867453.99882255232.022

    3.18889520282.92253582564.673023968210.96700969853.04220934464.01321437232.022

    3.24203423062.76278662324.674352443910.96601334173.08184220293.93505571892.022

    3.2605221843.05128726194.680994822410.95151081543.078631723.9911838172.022

    3.23505973322.89563419284.68841214510.93778323323.05029090514.03148091322.022

    3.16121862572.80053747424.696493705510.92582695193.02615692994.22078869992.022

    3.16952159882.70676923134.691954746810.93944382783.0082225084.1982046132.022

    3.16254710142.93194586184.686751550410.92471988883.03357425264.18060231012.022

    3.17472479532.82710698814.683319654810.92593765823.08372421014.2158069162.022

    3.17804598462.75415153114.689519208110.92372353213.02261432814.19200505982.022

    3.18922732172.96283292184.686751550410.9254948333.08272785344.01432143542.022

    3.15036940762.8511302574.695054523510.91840962933.00014094764.02240299592.022

    3.1936555742.89939820734.693061809910.9194059863.01552912443.94136597842.022

    3.19110932893.01353641084.689408501810.91110301293.04796607263.94679058752.022

    3.23860233512.75736201414.685644487310.90125015152.99261291863.99860113972.022

    3.25387980563.16575758444.679334227710.90446063453.03733826714.12580268762.022

    3.25133356052.92530348334.678891402510.9197381053.0171897194.17074944872.022

    3.19199497942.61300098844.69129050910.91110301293.04763395374.06137161632.022

    3.12878167752.60491942794.696161586610.9122100763.04984807993.9911838172.022

    3.0739820552.53993482514.696493705510.91674903473.0200680833.99483712522.022

    3.10996160512.48524590894.696604411810.92272717533.06302213053.96882114282.022

    3.13719535692.62672857064.688854970210.92062375543.03213507064.19233717872.022

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimenal Results

    time (sec)

    CD

    Effect of different turbulence models on drag coefficient

    Sheet1

    Force calculations for Jazz runs for water level of 3.4350 inches

    same as of geometry sent to us by Dr. Tanju

    for kepsilon high Re TM

    top wall as slip

    TimeFTXCD%differenceFTYCL

    Sec

    100.025182.78714-0.00282-0.06972

    200.027133.00324-0.01398-0.34614

    300.027123.00236-0.01838-0.45525

    400.027623.05760-0.02324-0.57541

    500.028033.10343-0.02755-0.68230

    600.028433.14738-0.03089-0.76496

    700.028803.18834-0.03320-0.82227

    800.028843.19222-0.03369-0.83428

    900.028953.20473-0.03466-0.85843

    1000.028813.18890-0.03383-0.83785

    1100.029293.24203-0.03649-0.90362

    1200.029453.26052-0.04131-1.02304

    1300.029223.23506-0.03787-0.93787

    1400.028563.16122-0.03132-0.77551

    1500.028633.16952-0.03167-0.78418

    1600.028573.16255-0.03155-0.78136

    1700.028683.17472-0.03277-0.81164

    1800.028713.17805-0.03376-0.83614

    1900.028813.18923-0.03447-0.85374

    2000.028463.15037-0.03418-0.84651

    2100.028853.19366-0.03528-0.87368

    2200.028833.19111-0.03525-0.87284

    2300.029253.23860-0.03969-0.98284

    2400.029393.25388-0.03990-0.98800

    2500.029373.25133-0.03968-0.98277

    2600.028833.19199-0.03701-0.91645

    2700.028263.12878-0.02609-0.64599

    2800.027773.07398-0.02470-0.61179

    2900.028093.10996-0.02729-0.67593

    3000.028343.13720-0.03006-0.74448

    AVG3.17-0.83

    STD DEV.0.060.14

    K-epsilon High Re with top wall symmetry

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.025282.79821-0.00314-0.07772

    200.027012.98985-0.01334-0.33039

    300.027062.99604-0.01781-0.44099

    400.027523.04608-0.02262-0.56028

    500.028003.10000-0.02691-0.66647

    600.028373.14074-0.03029-0.75008

    700.028723.17960-0.03326-0.82361

    800.028903.19941-0.03421-0.84713

    900.028883.19709-0.03422-0.84743

    1000.028673.17340-0.03240-0.80246

    1100.028883.19698-0.03270-0.80991

    1200.028563.16133-0.03202-0.79305

    1300.028703.17716-0.03255-0.80597

    1400.028963.20617-0.03417-0.84624

    1500.028883.19742-0.03421-0.84721

    1600.029513.26650-0.03871-0.95875

    1700.029233.23617-0.04023-0.99637

    1800.029503.26561-0.03924-0.97177

    1900.028633.16952-0.03547-0.87834

    2000.028393.14284-0.02849-0.70545

    2100.028273.12945-0.02875-0.71206

    2200.028503.15513-0.03058-0.75719

    2300.028453.15004-0.03231-0.80003

    2400.028803.18845-0.03367-0.83381

    2500.028983.20827-0.03474-0.86028

    2600.029343.24834-0.03792-0.93896

    2700.029193.23141-0.03968-0.98277

    2800.029533.26960-0.03942-0.97623

    2900.029003.21026-0.03292-0.81533

    3000.028463.15092-0.03027-0.74973

    AVG3.19-0.83

    STD DEV.0.050.10

    kepsilon RNG with top wall as slip

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.024222.68097-0.00979-0.24246

    200.022682.51071-0.02010-0.49777

    300.023712.62496-0.02840-0.70320

    400.024012.65828-0.03578-0.88599

    500.024792.74408-0.04555-1.12802

    600.024552.71784-0.05245-1.29882

    700.025352.80674-0.05794-1.43495

    800.025232.79345-0.06342-1.57047

    900.026192.89918-0.06668-1.65137

    1000.026402.92254-0.06911-1.71158

    1100.024962.76279-0.06879-1.70363

    1200.027563.05129-0.07058-1.74791

    1300.026162.89563-0.07713-1.91017

    1400.025302.80054-0.06088-1.50776

    1500.024452.70677-0.05515-1.36571

    1600.026482.93195-0.05439-1.34686

    1700.025542.82711-0.05381-1.33260

    1800.024882.75415-0.06007-1.48763

    1900.026762.96283-0.06524-1.61574

    2000.025752.85113-0.06737-1.66836

    2100.026192.89940-0.07008-1.73555

    2200.027223.01354-0.07327-1.81460

    2300.024912.75736-0.07854-1.94496

    2400.028603.16576-0.07505-1.85863

    2500.026422.92530-0.07501-1.85754

    2600.023602.61300-0.05785-1.43257

    2700.023532.60492-0.04241-1.05030

    2800.022942.53993-0.03391-0.83980

    2900.022452.48525-0.02249-0.55694

    3000.023732.62673-0.02252-0.55763

    AVG2.77-1.39

    STD DEV.0.220.54

    K omega STD High Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.033683.72859-0.00833-0.20621

    200.039224.34201-0.01213-0.30037

    300.040964.53442-0.01453-0.35971

    400.041594.60416-0.01660-0.41117

    500.041854.63317-0.01788-0.44290

    600.041984.64712-0.01881-0.46575

    700.042044.65409-0.01907-0.47224

    800.042014.65077-0.01913-0.47370

    900.042164.66771-0.01997-0.49455

    1000.042214.67302-0.02045-0.50644

    1100.042224.67435-0.02078-0.51456

    1200.042284.68099-0.02140-0.52989

    1300.042354.68841-0.02196-0.54379

    1400.042424.69649-0.02248-0.55659

    1500.042384.69195-0.02247-0.55654

    1600.042344.68675-0.02232-0.55280

    1700.042304.68332-0.02203-0.54550

    1800.042364.68952-0.02221-0.55010

    1900.042344.68675-0.02224-0.55082

    2000.042414.69505-0.02250-0.55711

    2100.042394.69306-0.02261-0.55981

    2200.042364.68941-0.02241-0.55503

    2300.042334.68564-0.02211-0.54763

    2400.042274.67933-0.02174-0.53831

    2500.042264.67889-0.02159-0.53477

    2600.042384.69129-0.02207-0.54656

    2700.042424.69616-0.02241-0.55496

    2800.042424.69649-0.02276-0.56372

    2900.042424.69660-0.02292-0.56756

    3000.042354.68885-0.02236-0.55377

    AVG4.69-0.55

    STD DEV.0.010.01

    K omega STD Low RE TM

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.076968.51996-0.01272-0.31489

    200.0958710.61330-0.01322-0.32749

    300.0995411.01993-0.01352-0.33487

    400.0999711.06731-0.01333-0.33019

    500.0999311.06255-0.01316-0.32581

    600.0995411.01937-0.01274-0.31543

    700.0994011.00465-0.01268-0.31407

    800.0993310.99646-0.01255-0.31073

    900.0992310.98539-0.01253-0.31021

    1000.0990610.96701-0.01228-0.30406

    1100.0990610.96601-0.01221-0.30238

    1200.0989210.95151-0.01215-0.30097

    1300.0988010.93778-0.01187-0.29406

    1400.0986910.92583-0.01183-0.29292

    1500.0988210.93944-0.01196-0.29614

    1600.0986810.92472-0.01184-0.29327

    1700.0986910.92594-0.01184-0.29317

    1800.0986710.92372-0.01183-0.29294

    1900.0986910.92549-0.01177-0.29136

    2000.0986310.91841-0.01177-0.29143

    2100.0986310.91941-0.01178-0.29163

    2200.0985610.91110-0.01167-0.28906

    2300.0984710.90125-0.01157-0.28655

    2400.0985010.90446-0.01165-0.28849

    2500.0986410.91974-0.01184-0.29332

    2600.0985610.91110-0.01173-0.29059

    2700.0985710.91221-0.01170-0.28970

    2800.0986110.91675-0.01176-0.29131

    2900.0986610.92273-0.01177-0.29146

    3000.0986510.92062-0.01177-0.29158

    AVG10.91-0.29

    STD DEV.0.010.00

    K omega SST High Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.023992.65573-0.00868-0.21496

    200.025142.78338-0.01517-0.37576

    300.025202.78936-0.02376-0.58841

    400.025852.86187-0.02982-0.73841

    500.026052.88346-0.03507-0.86841

    600.026692.95519-0.04273-1.05830

    700.026632.94767-0.04629-1.14644

    800.027563.05140-0.04592-1.13725

    900.027563.05151-0.04793-1.18708

    1000.027483.04221-0.04613-1.14235

    1100.027843.08184-0.04597-1.13832

    1200.027813.07863-0.04749-1.17608

    1300.027553.05029-0.04531-1.12215

    1400.027343.02616-0.04611-1.14198

    1500.027173.00822-0.04517-1.11861

    1600.027403.03357-0.04553-1.12757

    1700.027863.08372-0.04629-1.14642

    1800.027303.02261-0.04731-1.17173

    1900.027853.08273-0.04527-1.12101

    2000.027103.00014-0.04613-1.14235

    2100.027243.01553-0.04823-1.19446

    2200.027533.04797-0.04695-1.16264

    2300.027032.99261-0.04644-1.14998

    2400.027443.03734-0.04532-1.12239

    2500.027253.01719-0.04697-1.16328

    2600.027533.04763-0.04672-1.15707

    2700.027553.04985-0.04706-1.16551

    2800.027283.02007-0.04614-1.14263

    2900.027673.06302-0.04470-1.10697

    3000.027393.03214-0.04517-1.11870

    AVG3.03-1.15

    STD DEV.0.020.03

    K omega SST Low Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.030073.32872-0.01026-0.25406

    200.033323.68918-0.01510-0.37405

    300.033733.73446-0.02034-0.50382

    400.033683.72870-0.02464-0.61028

    500.034383.80619-0.02942-0.72846

    600.034753.84671-0.03446-0.85332

    700.034673.83830-0.03664-0.90748

    800.035663.94723-0.03871-0.95875

    900.036123.99882-0.03341-0.82739

    1000.036254.01321-0.03448-0.85389

    1100.035553.93506-0.03539-0.87633

    1200.036053.99118-0.04128-1.02220

    1300.036424.03148-0.03920-0.97071

    1400.038134.22079-0.03883-0.96169

    1500.037924.19820-0.03886-0.96239

    1600.037764.18060-0.03962-0.98106

    1700.038084.21581-0.03937-0.97492

    1800.037874.19201-0.03851-0.95377

    1900.036264.01432-0.03028-0.74993

    2000.036334.02240-0.03287-0.81407

    2100.035603.94137-0.03457-0.85610

    2200.035653.94679-0.03651-0.90417

    2300.036123.99860-0.04170-1.03257

    2400.037274.12580-0.03916-0.96977

    2500.037674.17075-0.03568-0.88359

    2600.036694.06137-0.03285-0.81355

    2700.036053.99118-0.03498-0.86637

    2800.036093.99484-0.03888-0.96274

    2900.035853.96882-0.03969-0.98284

    3000.037874.19234-0.03860-0.95583

    AVG4.04-0.91

    STD DEV.0.090.07

    kepsilon High Re without Buoyancy, no Buoyancy

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.010641.177920.014230.35243

    200.011241.244560.011320.28026

    300.011491.271680.010910.27028

    400.011361.257620.011960.29616

    500.011341.254970.012010.29748

    600.011051.223420.011760.29116

    700.011051.223530.011660.28876

    800.011051.223080.011660.28876

    900.011051.223530.011660.28883

    1000.011051.223300.011660.28863

    1100.011041.222530.011660.28878

    1200.011051.222970.011670.28888

    1300.011051.223080.011660.28876

    1400.011041.222420.011660.28863

    1500.011041.222310.011670.28888

    1600.011041.222640.011660.28886

    1700.011041.222200.011660.28871

    1800.011041.221870.011670.28888

    1900.011041.222200.011670.28898

    2000.011041.221870.011660.28878

    2100.011031.221310.011660.28883

    2200.011041.221640.011670.28903

    2300.011041.221750.011670.28893

    2400.011031.220980.011670.28896

    2500.011031.221090.011670.28911

    2600.011031.221420.011670.28906

    2700.011031.220870.011670.28893

    2800.011021.220430.011670.28911

    2900.011031.220870.011680.28920

    3000.011031.220540.011670.28903

    AVG1.221200.28891

    STD DEV.

    kepsilon High Re TM with Non equil wall function

    TimeFTXCDDifferenceFTY

    Sec

    100.031703.50961-0.05666-1.40305

    200.027623.05760-0.00106-0.02621

    300.010821.197290.042751.05880

    400.023662.61920-0.01372-0.33985

    500.024872.753490.010970.27172

    600.019902.203060.034700.85922

    700.018612.060360.032660.80872

    800.018182.012860.038330.94931

    900.009931.099780.053621.32797

    1000.015431.708090.033310.82497

    1100.018142.008540.045911.13698

    1200.017071.889420.050171.24243

    1300.016671.844920.043551.07861

    1400.020972.321730.036490.90372

    1500.006970.771200.049681.23022

    1600.016631.841490.048641.20461

    1700.008810.975510.054041.33820

    1800.011551.278100.048671.20523

    1900.005820.644680.058121.43921

    2000.008300.918640.044761.10855

    2100.002720.300820.046931.16224

    220-0.00254-0.280920.076301.88954

    2300.003870.428870.075111.86004

    2400.004240.469870.032370.80164

    2500.010491.161420.071101.76086

    2600.011821.308880.053941.33572

    2700.016101.782590.045081.11633

    2800.010901.206260.067181.66358

    2900.021382.367120.021900.54243

    3000.015681.735650.074971.85660

    AVG1.327151.48257

    Experimental Average values

    timeCDCL

    sec

    102.022-0.707

    202.022-0.707

    302.022-0.707

    402.022-0.707

    502.022-0.707

    602.022-0.707

    702.022-0.707

    802.022-0.707

    902.022-0.707

    1002.022-0.707

    1102.022-0.707

    1202.022-0.707

    1302.022-0.707

    1402.022-0.707

    1502.022-0.707

    1602.022-0.707

    1702.022-0.707

    1802.022-0.707

    1902.022-0.707

    2002.022-0.707

    2102.022-0.707

    2202.022-0.707

    2302.022-0.707

    2402.022-0.707

    2502.022-0.707

    2602.022-0.707

    2702.022-0.707

    2802.022-0.707

    2902.022-0.707

    3002.022-0.707

    Sheet1

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimenal Results

    time (sec)

    Drag Coefficient

    Effect of Different Turbulence Models on Drag Coefficient

    Sheet2

    Sheet2

    2.78714201092.7982126417

    3.00324072422.9898452609

    3.00235507372.9960448142

    3.05759752143.0460840654

    3.1034299333.0999980374

    3.14738033723.1407379588

    3.18834167123.1795958729

    3.1922163923.199412302

    3.20472620483.1970874695

    3.18889520283.1733963196

    3.24203423063.1969767632

    3.2605221843.1613293321

    3.23505973323.1771603341

    3.16121862573.2061653868

    3.16952159883.1974195885

    3.16254710143.2665003247

    3.17472479533.2361667963

    3.17804598463.2656146742

    3.18922732173.1695215988

    3.15036940763.1428413786

    3.1936555743.1294459153

    3.19110932893.1551297788

    3.23860233513.1500372886

    3.25387980563.1884523775

    3.25133356053.2082688067

    3.19199497943.2483444902

    3.12878167753.231406425

    3.0739820553.2696001013

    3.10996160513.2102615202

    3.13719535693.1509229391

    Slip wall

    symmetry wall

    time (sec)

    CD

    Comparision between top wall as a slip and symmetry for k-e High Reynolds turbulence model

    Sheet3

    -0.0697156408-0.0777246061

    -0.3461388625-0.3303883926

    -0.4552529662-0.4409883898

    -0.5754122107-0.5602808631

    -0.6822974744-0.6664727099

    -0.764962676-0.7500789773

    -0.8222686306-0.8236059347

    -0.8342796021-0.8471325798

    -0.8584253695-0.8474297585

    -0.8378457462-0.8024567189

    -0.9036212931-0.8099109507

    -1.0230375909-0.7930460608

    -0.9378711354-0.8059733332

    -0.775512519-0.8462410438

    -0.7841802304-0.8472068745

    -0.7813570329-0.9587479374

    -0.811644493-0.9963658048

    -0.8361369688-0.9717742694

    -0.8537448053-0.8783363408

    -0.8465134576-0.7054526462

    -0.8736805415-0.7120648717

    -0.8728385353-0.7571865006

    -0.982844175-0.8000297597

    -0.9879952721-0.8338090692

    -0.9827698804-0.8602827362

    -0.9164495059-0.9389607906

    -0.6459921462-0.9827698804

    -0.6117918336-0.9762319495

    -0.6759328977-0.8153344615

    -0.7444821123-0.7497322689

    Slip wall

    Symmetry wall

    time (sec)

    CL

    Comparision between top wall as a slip and symmetry for k-e High Reynolds turbulence model

    2.78714201092.68097466152.022

    3.00324072422.51070835982.022

    3.00235507372.62495726972.022

    3.05759752142.65827986842.022

    3.1034299332.74407725712.022

    3.14738033722.71783986212.022

    3.18834167122.80673702742.022

    3.1922163922.79345227052.022

    3.20472620482.89917679462.022

    3.18889520282.92253582562.022

    3.24203423062.76278662322.022

    3.2605221843.05128726192.022

    3.23505973322.89563419282.022

    3.16121862572.80053747422.022

    3.16952159882.70676923132.022

    3.16254710142.93194586182.022

    3.17472479532.82710698812.022

    3.17804598462.75415153112.022

    3.18922732172.96283292182.022

    3.15036940762.8511302572.022

    3.1936555742.89939820732.022

    3.19110932893.01353641082.022

    3.23860233512.75736201412.022

    3.25387980563.16575758442.022

    3.25133356052.92530348332.022

    3.19199497942.61300098842.022

    3.12878167752.60491942792.022

    3.0739820552.53993482512.022

    3.10996160512.48524590892.022

    3.13719535692.62672857062.022

    High Re

    RNG

    Experimental

    time (sec)

    CD

    Comparision between K epsilon models

    -0.0697156408-0.2424631285-0.707

    -0.3461388625-0.4977742817-0.707

    -0.4552529662-0.7031990412-0.707

    -0.5754122107-0.8859886916-0.707

    -0.6822974744-1.1280159581-0.707

    -0.764962676-1.2988194019-0.707

    -0.8222686306-1.4349520002-0.707

    -0.8342796021-1.5704654763-0.707

    -0.8584253695-1.6513723708-0.707

    -0.8378457462-1.7115758175-0.707

    -0.9036212931-1.7036262879-0.707

    -1.0230375909-1.7479059106-0.707

    -0.9378711354-1.9101654675-0.707

    -0.775512519-1.5077607758-0.707

    -0.7841802304-1.3657093688-0.707

    -0.7813570329-1.3468632878-0.707

    -0.811644493-1.3325987114-0.707

    -0.8361369688-1.4876269205-0.707

    -0.8537448053-1.6157356946-0.707

    -0.8465134576-1.6683610851-0.707

    -0.8736805415-1.7355482306-0.707

    -0.8728385353-1.8145977584-0.707

    -0.982844175-1.9449601374-0.707

    -0.9879952721-1.8586297321-0.707

    -0.9827698804-1.857540077-0.707

    -0.9164495059-1.4325745708-0.707

    -0.6459921462-1.0503037344-0.707

    -0.6117918336-0.8398021725-0.707

    -0.6759328977-0.556937603-0.707

    -0.7444821123-0.55763102-0.707

    High Re TM

    RNG TM

    Experimental

    time (sec)

    CL

    Comparision between k epsilon models

    3.72858845448.51995746582.65573362333.32871726982.022

    4.342012107210.61330304442.78337799643.68917700872.022

    4.534419670511.01992731372.78935613713.73445588872.022

    4.604164644611.06730961362.86186876883.72869916072.022

    4.633169697311.06254924232.88345649893.80619357632.022

    4.647118692111.01937378222.95519418653.84671208512.022

    4.654093189511.00464984322.94766615763.83829840562.022

    4.650772000310.99645757643.05139796823.94723341272.022

    4.667710065410.98538694563.05150867453.99882255232.022

    4.673023968210.96700969853.04220934464.01321437232.022

    4.674352443910.96601334173.08184220293.93505571892.022

    4.680994822410.95151081543.078631723.9911838172.022

    4.68841214510.93778323323.05029090514.03148091322.022

    4.696493705510.92582695193.02615692994.22078869992.022

    4.691954746810.93944382783.0082225084.1982046132.022

    4.686751550410.92471988883.03357425264.18060231012.022

    4.683319654810.92593765823.08372421014.2158069162.022

    4.689519208110.92372353213.02261432814.19200505982.022

    4.686751550410.9254948333.08272785344.01432143542.022

    4.695054523510.91840962933.00014094764.02240299592.022

    4.693061809910.9194059863.01552912443.94136597842.022

    4.689408501810.91110301293.04796607263.94679058752.022

    4.685644487310.90125015152.99261291863.99860113972.022

    4.679334227710.90446063453.03733826714.12580268762.022

    4.678891402510.9197381053.0171897194.17074944872.022

    4.69129050910.91110301293.04763395374.06137161632.022

    4.696161586610.9122100763.04984807993.9911838172.022

    4.696493705510.91674903473.0200680833.99483712522.022

    4.696604411810.92272717533.06302213053.96882114282.022

    4.688854970210.92062375543.03213507064.19233717872.022

    STD High Re TM

    STD Low Re TM

    SST High Re TM

    SST Low Re TM

    Experimental

    time (sec)

    CD

    Comparision between k omega models

    -0.206212283-0.3148855717-0.2149617185-0.2540630028-0.707

    -0.3003733464-0.3274909006-0.3757576705-0.3740488931-0.707

    -0.359710022-0.3348708377-0.5884137778-0.5038169148-0.707

    -0.4111714626-0.3301902735-0.7384147143-0.6102811753-0.707

    -0.4428952863-0.3258068881-0.86840562-0.7284592287-0.707

    -0.4657532794-0.3154303993-1.0583027937-0.8533238022-0.707

    -0.4722416805-0.3140683304-1.146441036-0.9074846159-0.707

    -0.473702809-0.3107250703-1.1372532619-0.9587479374-0.707

    -0.494554846-0.3102050076-1.1870802199-0.8273949628-0.707

    -0.5064419931-0.304063315-1.1423548292-0.8538933947-0.707

    -0.5145648769-0.3023793025-1.1383181522-0.8763303847-0.707

    -0.5298943436-0.3009677038-1.1760846089-1.0221955847-0.707

    -0.5437874466-0.2940582995-1.1221466792-0.9707093791-0.707

    -0.5565908946-0.2929191146-1.1419833558-0.9616949593-0.707

    -0.5565413648-0.2961385503-1.1186053-0.9623883762-0.707

    -0.5528018665-0.2932658231-1.1275701901-0.981061103-0.707

    -0.545496224-0.2931667635-1.1464162711-0.9749194103-0.707

    -0.5501024935-0.2929438795-1.1717259883-0.9537701946-0.707

    -0.5508206753-0.2913589266-1.1210074943-0.749930388-0.707

    -0.5571109573-0.2914332212-1.1423548292-0.8140714521-0.707

    -0.5598103302-0.2916313404-1.194460157-0.8560974699-0.707

    -0.5550307065-0.2890557918-1.1626372738-0.9041661206-0.707

    -0.5476260045-0.286554538-1.1499824152-1.0325720734-0.707

    -0.538314406-0.2884861994-1.1223943281-0.9697683133-0.707

    -0.5347730268-0.2933153529-1.1632811609-0.8835864974-0.707

    -0.5465611143-0.290591215-1.1570651736-0.8135513895-0.707

    -0.5549564119-0.289699679-1.165510001-0.8663748991-0.707

    -0.5637231828-0.2913093968-1.142627243-0.9627350846-0.707

    -0.5675617407-0.2914579861-1.1069658019-0.982844175-0.707

    -0.5537676972-0.2915818106-1.1187043596-0.9558256804-0.707

    STD High Re TM

    STD Low Re TM

    SST High Re TM

    SST Low Re TM

    Experimental

    time (sec)

    CL

    Comparision between K omega models

    2.78714201091.1779151174

    3.00324072421.2445603149

    3.00235507371.2716833603

    3.05759752141.2576236592

    3.1034299331.2549667078

    3.14738033721.22341541

    3.18834167121.2235261163

    3.1922163921.2230832911

    3.20472620481.2235261163

    3.18889520281.2233047037

    3.24203423061.2225297596

    3.2605221841.2229725848

    3.23505973321.2230832911

    3.16121862571.2224190532

    3.16952159881.2223083469

    3.16254710141.2226404659

    3.17472479531.2221976406

    3.17804598461.2218655217

    3.18922732171.2221976406

    3.15036940761.2218655217

    3.1936555741.2213119902

    3.19110932891.2216441091

    3.23860233511.2217548154

    3.25387980561.2209798712

    3.25133356051.2210905776

    3.19199497941.2214226965

    3.12878167751.2208691649

    3.0739820551.2204263397

    3.10996160511.2208691649

    3.13719535691.220537046

    Buoyancy

    No Buoyancy

    time (sec)

    CD

    Effect of buoyancy on CD

    -0.06971564080.3524291444

    -0.34613886250.280264256

    -0.45525296620.2702840055

    -0.57541221070.2961633152

    -0.68229747440.2974758543

    -0.7649626760.2911608075

    -0.82226863060.2887586132

    -0.83427960210.2887586132

    -0.85842536950.2888329078

    -0.83784574620.2886347887

    -0.90362129310.2887833781

    -1.02303759090.2888824376

    -0.93787113540.2887586132

    -0.7755125190.2886347887

    -0.78418023040.2888824376

    -0.78135703290.2888576727

    -0.8116444930.2887090834

    -0.83613696880.2888824376

    -0.85374480530.2889814972

    -0.84651345760.2887833781

    -0.87368054150.2888329078

    -0.87283853530.289031027

    -0.9828441750.2889319674

    -0.98799527210.2889567323

    -0.98276988040.2891053216

    -0.91644950590.2890557918

    -0.64599214620.2889319674

    -0.61179183360.2891053216

    -0.67593289770.2892043812

    -0.74448211230.289031027

    Buoyancy

    No Buoyancy

    time (sec)

    CL

    Effect of Buoyancy

    FTYFTY

    BOUYANCYNo Buoyancy

    -0.002820.01423-0.01705

    -0.013980.01132-0.02529

    -0.018380.01091-0.02930

    -0.023240.01196-0.03519

    -0.027550.01201-0.03956

    -0.030890.01176-0.04265

    -0.033200.01166-0.04486

    -0.033690.01166-0.04535

    -0.034660.01166-0.04633

    -0.033830.01166-0.04549

    -0.036490.01166-0.04815

    -0.041310.01167-0.05298

    -0.037870.01166-0.04953

    -0.031320.01166-0.04297

    -0.031670.01167-0.04333

    -0.031550.01166-0.04322

    -0.032770.01166-0.04443

    -0.033760.01167-0.04543

    -0.034470.01167-0.04614

    -0.034180.01166-0.04584

    -0.035280.01166-0.04694

    -0.035250.01167-0.04692

    -0.039690.01167-0.05135

    -0.039900.01167-0.05156

    -0.039680.01167-0.05136

    -0.037010.01167-0.04868

    -0.026090.01167-0.03775

    -0.024700.01167-0.03638

    -0.027290.01168-0.03897

    -0.030060.01167

    2.78714201092.68097466153.72858845448.51995746582.65573362333.32871726982.022

    3.00324072422.51070835984.342012107210.61330304442.78337799643.68917700872.022

    3.00235507372.62495726974.534419670511.01992731372.78935613713.73445588872.022

    3.05759752142.65827986844.604164644611.06730961362.86186876883.72869916072.022

    3.1034299332.74407725714.633169697311.06254924232.88345649893.80619357632.022

    3.14738033722.71783986214.647118692111.01937378222.95519418653.84671208512.022

    3.18834167122.80673702744.654093189511.00464984322.94766615763.83829840562.022

    3.1922163922.79345227054.650772000310.99645757643.05139796823.94723341272.022

    3.20472620482.89917679464.667710065410.98538694563.05150867453.99882255232.022

    3.18889520282.92253582564.673023968210.96700969853.04220934464.01321437232.022

    3.24203423062.76278662324.674352443910.96601334173.08184220293.93505571892.022

    3.2605221843.05128726194.680994822410.95151081543.078631723.9911838172.022

    3.23505973322.89563419284.68841214510.93778323323.05029090514.03148091322.022

    3.16121862572.80053747424.696493705510.92582695193.02615692994.22078869992.022

    3.16952159882.70676923134.691954746810.93944382783.0082225084.1982046132.022

    3.16254710142.93194586184.686751550410.92471988883.03357425264.18060231012.022

    3.17472479532.82710698814.683319654810.92593765823.08372421014.2158069162.022

    3.17804598462.75415153114.689519208110.92372353213.02261432814.19200505982.022

    3.18922732172.96283292184.686751550410.9254948333.08272785344.01432143542.022

    3.15036940762.8511302574.695054523510.91840962933.00014094764.02240299592.022

    3.1936555742.89939820734.693061809910.9194059863.01552912443.94136597842.022

    3.19110932893.01353641084.689408501810.91110301293.04796607263.94679058752.022

    3.23860233512.75736201414.685644487310.90125015152.99261291863.99860113972.022

    3.25387980563.16575758444.679334227710.90446063453.03733826714.12580268762.022

    3.25133356052.92530348334.678891402510.9197381053.0171897194.17074944872.022

    3.19199497942.61300098844.69129050910.91110301293.04763395374.06137161632.022

    3.12878167752.60491942794.696161586610.9122100763.04984807993.9911838172.022

    3.0739820552.53993482514.696493705510.91674903473.0200680833.99483712522.022

    3.10996160512.48524590894.696604411810.92272717533.06302213053.96882114282.022

    3.13719535692.62672857064.688854970210.92062375543.03213507064.19233717872.022

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimenal Results

    time (sec)

    CD

    Effect of different turbulence models on drag coefficient

    -0.0697156408-0.2424631285-0.206212283-0.3148855717-0.2149617185-0.2540630028-0.707

    -0.3461388625-0.4977742817-0.3003733464-0.3274909006-0.3757576705-0.3740488931-0.707

    -0.4552529662-0.7031990412-0.359710022-0.3348708377-0.5884137778-0.5038169148-0.707

    -0.5754122107-0.8859886916-0.4111714626-0.3301902735-0.7384147143-0.6102811753-0.707

    -0.6822974744-1.1280159581-0.4428952863-0.3258068881-0.86840562-0.7284592287-0.707

    -0.764962676-1.2988194019-0.4657532794-0.3154303993-1.0583027937-0.8533238022-0.707

    -0.8222686306-1.4349520002-0.4722416805-0.3140683304-1.146441036-0.9074846159-0.707

    -0.8342796021-1.5704654763-0.473702809-0.3107250703-1.1372532619-0.9587479374-0.707

    -0.8584253695-1.6513723708-0.494554846-0.3102050076-1.1870802199-0.8273949628-0.707

    -0.8378457462-1.7115758175-0.5064419931-0.304063315-1.1423548292-0.8538933947-0.707

    -0.9036212931-1.7036262879-0.5145648769-0.3023793025-1.1383181522-0.8763303847-0.707

    -1.0230375909-1.7479059106-0.5298943436-0.3009677038-1.1760846089-1.0221955847-0.707

    -0.9378711354-1.9101654675-0.5437874466-0.2940582995-1.1221466792-0.9707093791-0.707

    -0.775512519-1.5077607758-0.5565908946-0.2929191146-1.1419833558-0.9616949593-0.707

    -0.7841802304-1.3657093688-0.5565413648-0.2961385503-1.1186053-0.9623883762-0.707

    -0.7813570329-1.3468632878-0.5528018665-0.2932658231-1.1275701901-0.981061103-0.707

    -0.811644493-1.3325987114-0.545496224-0.2931667635-1.1464162711-0.9749194103-0.707

    -0.8361369688-1.4876269205-0.5501024935-0.2929438795-1.1717259883-0.9537701946-0.707

    -0.8537448053-1.6157356946-0.5508206753-0.2913589266-1.1210074943-0.749930388-0.707

    -0.8465134576-1.6683610851-0.5571109573-0.2914332212-1.1423548292-0.8140714521-0.707

    -0.8736805415-1.7355482306-0.5598103302-0.2916313404-1.194460157-0.8560974699-0.707

    -0.8728385353-1.8145977584-0.5550307065-0.2890557918-1.1626372738-0.9041661206-0.707

    -0.982844175-1.9449601374-0.5476260045-0.286554538-1.1499824152-1.0325720734-0.707

    -0.9879952721-1.8586297321-0.538314406-0.2884861994-1.1223943281-0.9697683133-0.707

    -0.9827698804-1.857540077-0.5347730268-0.2933153529-1.1632811609-0.8835864974-0.707

    -0.9164495059-1.4325745708-0.5465611143-0.290591215-1.1570651736-0.8135513895-0.707

    -0.6459921462-1.0503037344-0.5549564119-0.289699679-1.165510001-0.8663748991-0.707

    -0.6117918336-0.8398021725-0.5637231828-0.2913093968-1.142627243-0.9627350846-0.707

    -0.6759328977-0.556937603-0.5675617407-0.2914579861-1.1069658019-0.982844175-0.707

    -0.7444821123-0.55763102-0.5537676972-0.2915818106-1.1187043596-0.9558256804-0.707

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimental Results

    Time (sec)

    CL

    Effect of different turbulence models on lift coefficient

  • Effect of different turbulence models on lift coefficients:

    Chart2

    -0.0697156408-0.2424631285-0.206212283-0.3148855717-0.2149617185-0.2540630028-0.707

    -0.3461388625-0.4977742817-0.3003733464-0.3274909006-0.3757576705-0.3740488931-0.707

    -0.4552529662-0.7031990412-0.359710022-0.3348708377-0.5884137778-0.5038169148-0.707

    -0.5754122107-0.8859886916-0.4111714626-0.3301902735-0.7384147143-0.6102811753-0.707

    -0.6822974744-1.1280159581-0.4428952863-0.3258068881-0.86840562-0.7284592287-0.707

    -0.764962676-1.2988194019-0.4657532794-0.3154303993-1.0583027937-0.8533238022-0.707

    -0.8222686306-1.4349520002-0.4722416805-0.3140683304-1.146441036-0.9074846159-0.707

    -0.8342796021-1.5704654763-0.473702809-0.3107250703-1.1372532619-0.9587479374-0.707

    -0.8584253695-1.6513723708-0.494554846-0.3102050076-1.1870802199-0.8273949628-0.707

    -0.8378457462-1.7115758175-0.5064419931-0.304063315-1.1423548292-0.8538933947-0.707

    -0.9036212931-1.7036262879-0.5145648769-0.3023793025-1.1383181522-0.8763303847-0.707

    -1.0230375909-1.7479059106-0.5298943436-0.3009677038-1.1760846089-1.0221955847-0.707

    -0.9378711354-1.9101654675-0.5437874466-0.2940582995-1.1221466792-0.9707093791-0.707

    -0.775512519-1.5077607758-0.5565908946-0.2929191146-1.1419833558-0.9616949593-0.707

    -0.7841802304-1.3657093688-0.5565413648-0.2961385503-1.1186053-0.9623883762-0.707

    -0.7813570329-1.3468632878-0.5528018665-0.2932658231-1.1275701901-0.981061103-0.707

    -0.811644493-1.3325987114-0.545496224-0.2931667635-1.1464162711-0.9749194103-0.707

    -0.8361369688-1.4876269205-0.5501024935-0.2929438795-1.1717259883-0.9537701946-0.707

    -0.8537448053-1.6157356946-0.5508206753-0.2913589266-1.1210074943-0.749930388-0.707

    -0.8465134576-1.6683610851-0.5571109573-0.2914332212-1.1423548292-0.8140714521-0.707

    -0.8736805415-1.7355482306-0.5598103302-0.2916313404-1.194460157-0.8560974699-0.707

    -0.8728385353-1.8145977584-0.5550307065-0.2890557918-1.1626372738-0.9041661206-0.707

    -0.982844175-1.9449601374-0.5476260045-0.286554538-1.1499824152-1.0325720734-0.707

    -0.9879952721-1.8586297321-0.538314406-0.2884861994-1.1223943281-0.9697683133-0.707

    -0.9827698804-1.857540077-0.5347730268-0.2933153529-1.1632811609-0.8835864974-0.707

    -0.9164495059-1.4325745708-0.5465611143-0.290591215-1.1570651736-0.8135513895-0.707

    -0.6459921462-1.0503037344-0.5549564119-0.289699679-1.165510001-0.8663748991-0.707

    -0.6117918336-0.8398021725-0.5637231828-0.2913093968-1.142627243-0.9627350846-0.707

    -0.6759328977-0.556937603-0.5675617407-0.2914579861-1.1069658019-0.982844175-0.707

    -0.7444821123-0.55763102-0.5537676972-0.2915818106-1.1187043596-0.9558256804-0.707

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimental Results

    Time (sec)

    CL

    Effect of different turbulence models on lift coefficient

    Sheet1

    Force calculations for Jazz runs for water level of 3.4350 inches

    same as of geometry sent to us by Dr. Tanju

    for kepsilon high Re TM

    top wall as slip

    TimeFTXCD%differenceFTYCL

    Sec

    100.025182.78714-0.00282-0.06972

    200.027133.00324-0.01398-0.34614

    300.027123.00236-0.01838-0.45525

    400.027623.05760-0.02324-0.57541

    500.028033.10343-0.02755-0.68230

    600.028433.14738-0.03089-0.76496

    700.028803.18834-0.03320-0.82227

    800.028843.19222-0.03369-0.83428

    900.028953.20473-0.03466-0.85843

    1000.028813.18890-0.03383-0.83785

    1100.029293.24203-0.03649-0.90362

    1200.029453.26052-0.04131-1.02304

    1300.029223.23506-0.03787-0.93787

    1400.028563.16122-0.03132-0.77551

    1500.028633.16952-0.03167-0.78418

    1600.028573.16255-0.03155-0.78136

    1700.028683.17472-0.03277-0.81164

    1800.028713.17805-0.03376-0.83614

    1900.028813.18923-0.03447-0.85374

    2000.028463.15037-0.03418-0.84651

    2100.028853.19366-0.03528-0.87368

    2200.028833.19111-0.03525-0.87284

    2300.029253.23860-0.03969-0.98284

    2400.029393.25388-0.03990-0.98800

    2500.029373.25133-0.03968-0.98277

    2600.028833.19199-0.03701-0.91645

    2700.028263.12878-0.02609-0.64599

    2800.027773.07398-0.02470-0.61179

    2900.028093.10996-0.02729-0.67593

    3000.028343.13720-0.03006-0.74448

    AVG3.17-0.83

    STD DEV.0.060.14

    K-epsilon High Re with top wall symmetry

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.025282.79821-0.00314-0.07772

    200.027012.98985-0.01334-0.33039

    300.027062.99604-0.01781-0.44099

    400.027523.04608-0.02262-0.56028

    500.028003.10000-0.02691-0.66647

    600.028373.14074-0.03029-0.75008

    700.028723.17960-0.03326-0.82361

    800.028903.19941-0.03421-0.84713

    900.028883.19709-0.03422-0.84743

    1000.028673.17340-0.03240-0.80246

    1100.028883.19698-0.03270-0.80991

    1200.028563.16133-0.03202-0.79305

    1300.028703.17716-0.03255-0.80597

    1400.028963.20617-0.03417-0.84624

    1500.028883.19742-0.03421-0.84721

    1600.029513.26650-0.03871-0.95875

    1700.029233.23617-0.04023-0.99637

    1800.029503.26561-0.03924-0.97177

    1900.028633.16952-0.03547-0.87834

    2000.028393.14284-0.02849-0.70545

    2100.028273.12945-0.02875-0.71206

    2200.028503.15513-0.03058-0.75719

    2300.028453.15004-0.03231-0.80003

    2400.028803.18845-0.03367-0.83381

    2500.028983.20827-0.03474-0.86028

    2600.029343.24834-0.03792-0.93896

    2700.029193.23141-0.03968-0.98277

    2800.029533.26960-0.03942-0.97623

    2900.029003.21026-0.03292-0.81533

    3000.028463.15092-0.03027-0.74973

    AVG3.19-0.83

    STD DEV.0.050.10

    kepsilon RNG with top wall as slip

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.024222.68097-0.00979-0.24246

    200.022682.51071-0.02010-0.49777

    300.023712.62496-0.02840-0.70320

    400.024012.65828-0.03578-0.88599

    500.024792.74408-0.04555-1.12802

    600.024552.71784-0.05245-1.29882

    700.025352.80674-0.05794-1.43495

    800.025232.79345-0.06342-1.57047

    900.026192.89918-0.06668-1.65137

    1000.026402.92254-0.06911-1.71158

    1100.024962.76279-0.06879-1.70363

    1200.027563.05129-0.07058-1.74791

    1300.026162.89563-0.07713-1.91017

    1400.025302.80054-0.06088-1.50776

    1500.024452.70677-0.05515-1.36571

    1600.026482.93195-0.05439-1.34686

    1700.025542.82711-0.05381-1.33260

    1800.024882.75415-0.06007-1.48763

    1900.026762.96283-0.06524-1.61574

    2000.025752.85113-0.06737-1.66836

    2100.026192.89940-0.07008-1.73555

    2200.027223.01354-0.07327-1.81460

    2300.024912.75736-0.07854-1.94496

    2400.028603.16576-0.07505-1.85863

    2500.026422.92530-0.07501-1.85754

    2600.023602.61300-0.05785-1.43257

    2700.023532.60492-0.04241-1.05030

    2800.022942.53993-0.03391-0.83980

    2900.022452.48525-0.02249-0.55694

    3000.023732.62673-0.02252-0.55763

    AVG2.77-1.39

    STD DEV.0.220.54

    K omega STD High Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.033683.72859-0.00833-0.20621

    200.039224.34201-0.01213-0.30037

    300.040964.53442-0.01453-0.35971

    400.041594.60416-0.01660-0.41117

    500.041854.63317-0.01788-0.44290

    600.041984.64712-0.01881-0.46575

    700.042044.65409-0.01907-0.47224

    800.042014.65077-0.01913-0.47370

    900.042164.66771-0.01997-0.49455

    1000.042214.67302-0.02045-0.50644

    1100.042224.67435-0.02078-0.51456

    1200.042284.68099-0.02140-0.52989

    1300.042354.68841-0.02196-0.54379

    1400.042424.69649-0.02248-0.55659

    1500.042384.69195-0.02247-0.55654

    1600.042344.68675-0.02232-0.55280

    1700.042304.68332-0.02203-0.54550

    1800.042364.68952-0.02221-0.55010

    1900.042344.68675-0.02224-0.55082

    2000.042414.69505-0.02250-0.55711

    2100.042394.69306-0.02261-0.55981

    2200.042364.68941-0.02241-0.55503

    2300.042334.68564-0.02211-0.54763

    2400.042274.67933-0.02174-0.53831

    2500.042264.67889-0.02159-0.53477

    2600.042384.69129-0.02207-0.54656

    2700.042424.69616-0.02241-0.55496

    2800.042424.69649-0.02276-0.56372

    2900.042424.69660-0.02292-0.56756

    3000.042354.68885-0.02236-0.55377

    AVG4.69-0.55

    STD DEV.0.010.01

    K omega STD Low RE TM

    TimeFTXCD% DifferenceFTYCL

    Sec

    100.076968.51996-0.01272-0.31489

    200.0958710.61330-0.01322-0.32749

    300.0995411.01993-0.01352-0.33487

    400.0999711.06731-0.01333-0.33019

    500.0999311.06255-0.01316-0.32581

    600.0995411.01937-0.01274-0.31543

    700.0994011.00465-0.01268-0.31407

    800.0993310.99646-0.01255-0.31073

    900.0992310.98539-0.01253-0.31021

    1000.0990610.96701-0.01228-0.30406

    1100.0990610.96601-0.01221-0.30238

    1200.0989210.95151-0.01215-0.30097

    1300.0988010.93778-0.01187-0.29406

    1400.0986910.92583-0.01183-0.29292

    1500.0988210.93944-0.01196-0.29614

    1600.0986810.92472-0.01184-0.29327

    1700.0986910.92594-0.01184-0.29317

    1800.0986710.92372-0.01183-0.29294

    1900.0986910.92549-0.01177-0.29136

    2000.0986310.91841-0.01177-0.29143

    2100.0986310.91941-0.01178-0.29163

    2200.0985610.91110-0.01167-0.28906

    2300.0984710.90125-0.01157-0.28655

    2400.0985010.90446-0.01165-0.28849

    2500.0986410.91974-0.01184-0.29332

    2600.0985610.91110-0.01173-0.29059

    2700.0985710.91221-0.01170-0.28970

    2800.0986110.91675-0.01176-0.29131

    2900.0986610.92273-0.01177-0.29146

    3000.0986510.92062-0.01177-0.29158

    AVG10.91-0.29

    STD DEV.0.010.00

    K omega SST High Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.023992.65573-0.00868-0.21496

    200.025142.78338-0.01517-0.37576

    300.025202.78936-0.02376-0.58841

    400.025852.86187-0.02982-0.73841

    500.026052.88346-0.03507-0.86841

    600.026692.95519-0.04273-1.05830

    700.026632.94767-0.04629-1.14644

    800.027563.05140-0.04592-1.13725

    900.027563.05151-0.04793-1.18708

    1000.027483.04221-0.04613-1.14235

    1100.027843.08184-0.04597-1.13832

    1200.027813.07863-0.04749-1.17608

    1300.027553.05029-0.04531-1.12215

    1400.027343.02616-0.04611-1.14198

    1500.027173.00822-0.04517-1.11861

    1600.027403.03357-0.04553-1.12757

    1700.027863.08372-0.04629-1.14642

    1800.027303.02261-0.04731-1.17173

    1900.027853.08273-0.04527-1.12101

    2000.027103.00014-0.04613-1.14235

    2100.027243.01553-0.04823-1.19446

    2200.027533.04797-0.04695-1.16264

    2300.027032.99261-0.04644-1.14998

    2400.027443.03734-0.04532-1.12239

    2500.027253.01719-0.04697-1.16328

    2600.027533.04763-0.04672-1.15707

    2700.027553.04985-0.04706-1.16551

    2800.027283.02007-0.04614-1.14263

    2900.027673.06302-0.04470-1.10697

    3000.027393.03214-0.04517-1.11870

    AVG3.03-1.15

    STD DEV.0.020.03

    K omega SST Low Re TM

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.030073.32872-0.01026-0.25406

    200.033323.68918-0.01510-0.37405

    300.033733.73446-0.02034-0.50382

    400.033683.72870-0.02464-0.61028

    500.034383.80619-0.02942-0.72846

    600.034753.84671-0.03446-0.85332

    700.034673.83830-0.03664-0.90748

    800.035663.94723-0.03871-0.95875

    900.036123.99882-0.03341-0.82739

    1000.036254.01321-0.03448-0.85389

    1100.035553.93506-0.03539-0.87633

    1200.036053.99118-0.04128-1.02220

    1300.036424.03148-0.03920-0.97071

    1400.038134.22079-0.03883-0.96169

    1500.037924.19820-0.03886-0.96239

    1600.037764.18060-0.03962-0.98106

    1700.038084.21581-0.03937-0.97492

    1800.037874.19201-0.03851-0.95377

    1900.036264.01432-0.03028-0.74993

    2000.036334.02240-0.03287-0.81407

    2100.035603.94137-0.03457-0.85610

    2200.035653.94679-0.03651-0.90417

    2300.036123.99860-0.04170-1.03257

    2400.037274.12580-0.03916-0.96977

    2500.037674.17075-0.03568-0.88359

    2600.036694.06137-0.03285-0.81355

    2700.036053.99118-0.03498-0.86637

    2800.036093.99484-0.03888-0.96274

    2900.035853.96882-0.03969-0.98284

    3000.037874.19234-0.03860-0.95583

    AVG4.04-0.91

    STD DEV.0.090.07

    kepsilon High Re without Buoyancy, no Buoyancy

    TimeFTXCD%DifferenceFTYCL

    Sec

    100.010641.177920.014230.35243

    200.011241.244560.011320.28026

    300.011491.271680.010910.27028

    400.011361.257620.011960.29616

    500.011341.254970.012010.29748

    600.011051.223420.011760.29116

    700.011051.223530.011660.28876

    800.011051.223080.011660.28876

    900.011051.223530.011660.28883

    1000.011051.223300.011660.28863

    1100.011041.222530.011660.28878

    1200.011051.222970.011670.28888

    1300.011051.223080.011660.28876

    1400.011041.222420.011660.28863

    1500.011041.222310.011670.28888

    1600.011041.222640.011660.28886

    1700.011041.222200.011660.28871

    1800.011041.221870.011670.28888

    1900.011041.222200.011670.28898

    2000.011041.221870.011660.28878

    2100.011031.221310.011660.28883

    2200.011041.221640.011670.28903

    2300.011041.221750.011670.28893

    2400.011031.220980.011670.28896

    2500.011031.221090.011670.28911

    2600.011031.221420.011670.28906

    2700.011031.220870.011670.28893

    2800.011021.220430.011670.28911

    2900.011031.220870.011680.28920

    3000.011031.220540.011670.28903

    AVG1.221200.28891

    STD DEV.

    kepsilon High Re TM with Non equil wall function

    TimeFTXCDDifferenceFTY

    Sec

    100.031703.50961-0.05666-1.40305

    200.027623.05760-0.00106-0.02621

    300.010821.197290.042751.05880

    400.023662.61920-0.01372-0.33985

    500.024872.753490.010970.27172

    600.019902.203060.034700.85922

    700.018612.060360.032660.80872

    800.018182.012860.038330.94931

    900.009931.099780.053621.32797

    1000.015431.708090.033310.82497

    1100.018142.008540.045911.13698

    1200.017071.889420.050171.24243

    1300.016671.844920.043551.07861

    1400.020972.321730.036490.90372

    1500.006970.771200.049681.23022

    1600.016631.841490.048641.20461

    1700.008810.975510.054041.33820

    1800.011551.278100.048671.20523

    1900.005820.644680.058121.43921

    2000.008300.918640.044761.10855

    2100.002720.300820.046931.16224

    220-0.00254-0.280920.076301.88954

    2300.003870.428870.075111.86004

    2400.004240.469870.032370.80164

    2500.010491.161420.071101.76086

    2600.011821.308880.053941.33572

    2700.016101.782590.045081.11633

    2800.010901.206260.067181.66358

    2900.021382.367120.021900.54243

    3000.015681.735650.074971.85660

    AVG1.327151.48257

    Experimental Average values

    timeCDCL

    sec

    102.022-0.707

    202.022-0.707

    302.022-0.707

    402.022-0.707

    502.022-0.707

    602.022-0.707

    702.022-0.707

    802.022-0.707

    902.022-0.707

    1002.022-0.707

    1102.022-0.707

    1202.022-0.707

    1302.022-0.707

    1402.022-0.707

    1502.022-0.707

    1602.022-0.707

    1702.022-0.707

    1802.022-0.707

    1902.022-0.707

    2002.022-0.707

    2102.022-0.707

    2202.022-0.707

    2302.022-0.707

    2402.022-0.707

    2502.022-0.707

    2602.022-0.707

    2702.022-0.707

    2802.022-0.707

    2902.022-0.707

    3002.022-0.707

    Sheet1

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    0000000

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimenal Results

    time (sec)

    Drag Coefficient

    Effect of Different Turbulence Models on Drag Coefficient

    Sheet2

    Sheet2

    2.78714201092.7982126417

    3.00324072422.9898452609

    3.00235507372.9960448142

    3.05759752143.0460840654

    3.1034299333.0999980374

    3.14738033723.1407379588

    3.18834167123.1795958729

    3.1922163923.199412302

    3.20472620483.1970874695

    3.18889520283.1733963196

    3.24203423063.1969767632

    3.2605221843.1613293321

    3.23505973323.1771603341

    3.16121862573.2061653868

    3.16952159883.1974195885

    3.16254710143.2665003247

    3.17472479533.2361667963

    3.17804598463.2656146742

    3.18922732173.1695215988

    3.15036940763.1428413786

    3.1936555743.1294459153

    3.19110932893.1551297788

    3.23860233513.1500372886

    3.25387980563.1884523775

    3.25133356053.2082688067

    3.19199497943.2483444902

    3.12878167753.231406425

    3.0739820553.2696001013

    3.10996160513.2102615202

    3.13719535693.1509229391

    Slip wall

    symmetry wall

    time (sec)

    CD

    Comparision between top wall as a slip and symmetry for k-e High Reynolds turbulence model

    Sheet3

    -0.0697156408-0.0777246061

    -0.3461388625-0.3303883926

    -0.4552529662-0.4409883898

    -0.5754122107-0.5602808631

    -0.6822974744-0.6664727099

    -0.764962676-0.7500789773

    -0.8222686306-0.8236059347

    -0.8342796021-0.8471325798

    -0.8584253695-0.8474297585

    -0.8378457462-0.8024567189

    -0.9036212931-0.8099109507

    -1.0230375909-0.7930460608

    -0.9378711354-0.8059733332

    -0.775512519-0.8462410438

    -0.7841802304-0.8472068745

    -0.7813570329-0.9587479374

    -0.811644493-0.9963658048

    -0.8361369688-0.9717742694

    -0.8537448053-0.8783363408

    -0.8465134576-0.7054526462

    -0.8736805415-0.7120648717

    -0.8728385353-0.7571865006

    -0.982844175-0.8000297597

    -0.9879952721-0.8338090692

    -0.9827698804-0.8602827362

    -0.9164495059-0.9389607906

    -0.6459921462-0.9827698804

    -0.6117918336-0.9762319495

    -0.6759328977-0.8153344615

    -0.7444821123-0.7497322689

    Slip wall

    Symmetry wall

    time (sec)

    CL

    Comparision between top wall as a slip and symmetry for k-e High Reynolds turbulence model

    2.78714201092.68097466152.022

    3.00324072422.51070835982.022

    3.00235507372.62495726972.022

    3.05759752142.65827986842.022

    3.1034299332.74407725712.022

    3.14738033722.71783986212.022

    3.18834167122.80673702742.022

    3.1922163922.79345227052.022

    3.20472620482.89917679462.022

    3.18889520282.92253582562.022

    3.24203423062.76278662322.022

    3.2605221843.05128726192.022

    3.23505973322.89563419282.022

    3.16121862572.80053747422.022

    3.16952159882.70676923132.022

    3.16254710142.93194586182.022

    3.17472479532.82710698812.022

    3.17804598462.75415153112.022

    3.18922732172.96283292182.022

    3.15036940762.8511302572.022

    3.1936555742.89939820732.022

    3.19110932893.01353641082.022

    3.23860233512.75736201412.022

    3.25387980563.16575758442.022

    3.25133356052.92530348332.022

    3.19199497942.61300098842.022

    3.12878167752.60491942792.022

    3.0739820552.53993482512.022

    3.10996160512.48524590892.022

    3.13719535692.62672857062.022

    High Re

    RNG

    Experimental

    time (sec)

    CD

    Comparision between K epsilon models

    -0.0697156408-0.2424631285-0.707

    -0.3461388625-0.4977742817-0.707

    -0.4552529662-0.7031990412-0.707

    -0.5754122107-0.8859886916-0.707

    -0.6822974744-1.1280159581-0.707

    -0.764962676-1.2988194019-0.707

    -0.8222686306-1.4349520002-0.707

    -0.8342796021-1.5704654763-0.707

    -0.8584253695-1.6513723708-0.707

    -0.8378457462-1.7115758175-0.707

    -0.9036212931-1.7036262879-0.707

    -1.0230375909-1.7479059106-0.707

    -0.9378711354-1.9101654675-0.707

    -0.775512519-1.5077607758-0.707

    -0.7841802304-1.3657093688-0.707

    -0.7813570329-1.3468632878-0.707

    -0.811644493-1.3325987114-0.707

    -0.8361369688-1.4876269205-0.707

    -0.8537448053-1.6157356946-0.707

    -0.8465134576-1.6683610851-0.707

    -0.8736805415-1.7355482306-0.707

    -0.8728385353-1.8145977584-0.707

    -0.982844175-1.9449601374-0.707

    -0.9879952721-1.8586297321-0.707

    -0.9827698804-1.857540077-0.707

    -0.9164495059-1.4325745708-0.707

    -0.6459921462-1.0503037344-0.707

    -0.6117918336-0.8398021725-0.707

    -0.6759328977-0.556937603-0.707

    -0.7444821123-0.55763102-0.707

    High Re TM

    RNG TM

    Experimental

    time (sec)

    CL

    Comparision between k epsilon models

    3.72858845448.51995746582.65573362333.32871726982.022

    4.342012107210.61330304442.78337799643.68917700872.022

    4.534419670511.01992731372.78935613713.73445588872.022

    4.604164644611.06730961362.86186876883.72869916072.022

    4.633169697311.06254924232.88345649893.80619357632.022

    4.647118692111.01937378222.95519418653.84671208512.022

    4.654093189511.00464984322.94766615763.83829840562.022

    4.650772000310.99645757643.05139796823.94723341272.022

    4.667710065410.98538694563.05150867453.99882255232.022

    4.673023968210.96700969853.04220934464.01321437232.022

    4.674352443910.96601334173.08184220293.93505571892.022

    4.680994822410.95151081543.078631723.9911838172.022

    4.68841214510.93778323323.05029090514.03148091322.022

    4.696493705510.92582695193.02615692994.22078869992.022

    4.691954746810.93944382783.0082225084.1982046132.022

    4.686751550410.92471988883.03357425264.18060231012.022

    4.683319654810.92593765823.08372421014.2158069162.022

    4.689519208110.92372353213.02261432814.19200505982.022

    4.686751550410.9254948333.08272785344.01432143542.022

    4.695054523510.91840962933.00014094764.02240299592.022

    4.693061809910.9194059863.01552912443.94136597842.022

    4.689408501810.91110301293.04796607263.94679058752.022

    4.685644487310.90125015152.99261291863.99860113972.022

    4.679334227710.90446063453.03733826714.12580268762.022

    4.678891402510.9197381053.0171897194.17074944872.022

    4.69129050910.91110301293.04763395374.06137161632.022

    4.696161586610.9122100763.04984807993.9911838172.022

    4.696493705510.91674903473.0200680833.99483712522.022

    4.696604411810.92272717533.06302213053.96882114282.022

    4.688854970210.92062375543.03213507064.19233717872.022

    STD High Re TM

    STD Low Re TM

    SST High Re TM

    SST Low Re TM

    Experimental

    time (sec)

    CD

    Comparision between k omega models

    -0.206212283-0.3148855717-0.2149617185-0.2540630028-0.707

    -0.3003733464-0.3274909006-0.3757576705-0.3740488931-0.707

    -0.359710022-0.3348708377-0.5884137778-0.5038169148-0.707

    -0.4111714626-0.3301902735-0.7384147143-0.6102811753-0.707

    -0.4428952863-0.3258068881-0.86840562-0.7284592287-0.707

    -0.4657532794-0.3154303993-1.0583027937-0.8533238022-0.707

    -0.4722416805-0.3140683304-1.146441036-0.9074846159-0.707

    -0.473702809-0.3107250703-1.1372532619-0.9587479374-0.707

    -0.494554846-0.3102050076-1.1870802199-0.8273949628-0.707

    -0.5064419931-0.304063315-1.1423548292-0.8538933947-0.707

    -0.5145648769-0.3023793025-1.1383181522-0.8763303847-0.707

    -0.5298943436-0.3009677038-1.1760846089-1.0221955847-0.707

    -0.5437874466-0.2940582995-1.1221466792-0.9707093791-0.707

    -0.5565908946-0.2929191146-1.1419833558-0.9616949593-0.707

    -0.5565413648-0.2961385503-1.1186053-0.9623883762-0.707

    -0.5528018665-0.2932658231-1.1275701901-0.981061103-0.707

    -0.545496224-0.2931667635-1.1464162711-0.9749194103-0.707

    -0.5501024935-0.2929438795-1.1717259883-0.9537701946-0.707

    -0.5508206753-0.2913589266-1.1210074943-0.749930388-0.707

    -0.5571109573-0.2914332212-1.1423548292-0.8140714521-0.707

    -0.5598103302-0.2916313404-1.194460157-0.8560974699-0.707

    -0.5550307065-0.2890557918-1.1626372738-0.9041661206-0.707

    -0.5476260045-0.286554538-1.1499824152-1.0325720734-0.707

    -0.538314406-0.2884861994-1.1223943281-0.9697683133-0.707

    -0.5347730268-0.2933153529-1.1632811609-0.8835864974-0.707

    -0.5465611143-0.290591215-1.1570651736-0.8135513895-0.707

    -0.5549564119-0.289699679-1.165510001-0.8663748991-0.707

    -0.5637231828-0.2913093968-1.142627243-0.9627350846-0.707

    -0.5675617407-0.2914579861-1.1069658019-0.982844175-0.707

    -0.5537676972-0.2915818106-1.1187043596-0.9558256804-0.707

    STD High Re TM

    STD Low Re TM

    SST High Re TM

    SST Low Re TM

    Experimental

    time (sec)

    CL

    Comparision between K omega models

    2.78714201091.1779151174

    3.00324072421.2445603149

    3.00235507371.2716833603

    3.05759752141.2576236592

    3.1034299331.2549667078

    3.14738033721.22341541

    3.18834167121.2235261163

    3.1922163921.2230832911

    3.20472620481.2235261163

    3.18889520281.2233047037

    3.24203423061.2225297596

    3.2605221841.2229725848

    3.23505973321.2230832911

    3.16121862571.2224190532

    3.16952159881.2223083469

    3.16254710141.2226404659

    3.17472479531.2221976406

    3.17804598461.2218655217

    3.18922732171.2221976406

    3.15036940761.2218655217

    3.1936555741.2213119902

    3.19110932891.2216441091

    3.23860233511.2217548154

    3.25387980561.2209798712

    3.25133356051.2210905776

    3.19199497941.2214226965

    3.12878167751.2208691649

    3.0739820551.2204263397

    3.10996160511.2208691649

    3.13719535691.220537046

    Buoyancy

    No Buoyancy

    time (sec)

    CD

    Effect of buoyancy on CD

    -0.06971564080.3524291444

    -0.34613886250.280264256

    -0.45525296620.2702840055

    -0.57541221070.2961633152

    -0.68229747440.2974758543

    -0.7649626760.2911608075

    -0.82226863060.2887586132

    -0.83427960210.2887586132

    -0.85842536950.2888329078

    -0.83784574620.2886347887

    -0.90362129310.2887833781

    -1.02303759090.2888824376

    -0.93787113540.2887586132

    -0.7755125190.2886347887

    -0.78418023040.2888824376

    -0.78135703290.2888576727

    -0.8116444930.2887090834

    -0.83613696880.2888824376

    -0.85374480530.2889814972

    -0.84651345760.2887833781

    -0.87368054150.2888329078

    -0.87283853530.289031027

    -0.9828441750.2889319674

    -0.98799527210.2889567323

    -0.98276988040.2891053216

    -0.91644950590.2890557918

    -0.64599214620.2889319674

    -0.61179183360.2891053216

    -0.67593289770.2892043812

    -0.74448211230.289031027

    Buoyancy

    No Buoyancy

    time (sec)

    CL

    Effect of Buoyancy

    FTYFTY

    BOUYANCYNo Buoyancy

    -0.002820.01423-0.01705

    -0.013980.01132-0.02529

    -0.018380.01091-0.02930

    -0.023240.01196-0.03519

    -0.027550.01201-0.03956

    -0.030890.01176-0.04265

    -0.033200.01166-0.04486

    -0.033690.01166-0.04535

    -0.034660.01166-0.04633

    -0.033830.01166-0.04549

    -0.036490.01166-0.04815

    -0.041310.01167-0.05298

    -0.037870.01166-0.04953

    -0.031320.01166-0.04297

    -0.031670.01167-0.04333

    -0.031550.01166-0.04322

    -0.032770.01166-0.04443

    -0.033760.01167-0.04543

    -0.034470.01167-0.04614

    -0.034180.01166-0.04584

    -0.035280.01166-0.04694

    -0.035250.01167-0.04692

    -0.039690.01167-0.05135

    -0.039900.01167-0.05156

    -0.039680.01167-0.05136

    -0.037010.01167-0.04868

    -0.026090.01167-0.03775

    -0.024700.01167-0.03638

    -0.027290.01168-0.03897

    -0.030060.01167

    2.78714201092.68097466153.72858845448.51995746582.65573362333.32871726982.022

    3.00324072422.51070835984.342012107210.61330304442.78337799643.68917700872.022

    3.00235507372.62495726974.534419670511.01992731372.78935613713.73445588872.022

    3.05759752142.65827986844.604164644611.06730961362.86186876883.72869916072.022

    3.1034299332.74407725714.633169697311.06254924232.88345649893.80619357632.022

    3.14738033722.71783986214.647118692111.01937378222.95519418653.84671208512.022

    3.18834167122.80673702744.654093189511.00464984322.94766615763.83829840562.022

    3.1922163922.79345227054.650772000310.99645757643.05139796823.94723341272.022

    3.20472620482.89917679464.667710065410.98538694563.05150867453.99882255232.022

    3.18889520282.92253582564.673023968210.96700969853.04220934464.01321437232.022

    3.24203423062.76278662324.674352443910.96601334173.08184220293.93505571892.022

    3.2605221843.05128726194.680994822410.95151081543.078631723.9911838172.022

    3.23505973322.89563419284.68841214510.93778323323.05029090514.03148091322.022

    3.16121862572.80053747424.696493705510.92582695193.02615692994.22078869992.022

    3.16952159882.70676923134.691954746810.93944382783.0082225084.1982046132.022

    3.16254710142.93194586184.686751550410.92471988883.03357425264.18060231012.022

    3.17472479532.82710698814.683319654810.92593765823.08372421014.2158069162.022

    3.17804598462.75415153114.689519208110.92372353213.02261432814.19200505982.022

    3.18922732172.96283292184.686751550410.9254948333.08272785344.01432143542.022

    3.15036940762.8511302574.695054523510.91840962933.00014094764.02240299592.022

    3.1936555742.89939820734.693061809910.9194059863.01552912443.94136597842.022

    3.19110932893.01353641084.689408501810.91110301293.04796607263.94679058752.022

    3.23860233512.75736201414.685644487310.90125015152.99261291863.99860113972.022

    3.25387980563.16575758444.679334227710.90446063453.03733826714.12580268762.022

    3.25133356052.92530348334.678891402510.9197381053.0171897194.17074944872.022

    3.19199497942.61300098844.69129050910.91110301293.04763395374.06137161632.022

    3.12878167752.60491942794.696161586610.9122100763.04984807993.9911838172.022

    3.0739820552.53993482514.696493705510.91674903473.0200680833.99483712522.022

    3.10996160512.48524590894.696604411810.92272717533.06302213053.96882114282.022

    3.13719535692.62672857064.688854970210.92062375543.03213507064.19233717872.022

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimenal Results

    time (sec)

    CD

    Effect of different turbulence models on drag coefficient

    -0.0697156408-0.2424631285-0.206212283-0.3148855717-0.2149617185-0.2540630028-0.707

    -0.3461388625-0.4977742817-0.3003733464-0.3274909006-0.3757576705-0.3740488931-0.707

    -0.4552529662-0.7031990412-0.359710022-0.3348708377-0.5884137778-0.5038169148-0.707

    -0.5754122107-0.8859886916-0.4111714626-0.3301902735-0.7384147143-0.6102811753-0.707

    -0.6822974744-1.1280159581-0.4428952863-0.3258068881-0.86840562-0.7284592287-0.707

    -0.764962676-1.2988194019-0.4657532794-0.3154303993-1.0583027937-0.8533238022-0.707

    -0.8222686306-1.4349520002-0.4722416805-0.3140683304-1.146441036-0.9074846159-0.707

    -0.8342796021-1.5704654763-0.473702809-0.3107250703-1.1372532619-0.9587479374-0.707

    -0.8584253695-1.6513723708-0.494554846-0.3102050076-1.1870802199-0.8273949628-0.707

    -0.8378457462-1.7115758175-0.5064419931-0.304063315-1.1423548292-0.8538933947-0.707

    -0.9036212931-1.7036262879-0.5145648769-0.3023793025-1.1383181522-0.8763303847-0.707

    -1.0230375909-1.7479059106-0.5298943436-0.3009677038-1.1760846089-1.0221955847-0.707

    -0.9378711354-1.9101654675-0.5437874466-0.2940582995-1.1221466792-0.9707093791-0.707

    -0.775512519-1.5077607758-0.5565908946-0.2929191146-1.1419833558-0.9616949593-0.707

    -0.7841802304-1.3657093688-0.5565413648-0.2961385503-1.1186053-0.9623883762-0.707

    -0.7813570329-1.3468632878-0.5528018665-0.2932658231-1.1275701901-0.981061103-0.707

    -0.811644493-1.3325987114-0.545496224-0.2931667635-1.1464162711-0.9749194103-0.707

    -0.8361369688-1.4876269205-0.5501024935-0.2929438795-1.1717259883-0.9537701946-0.707

    -0.8537448053-1.6157356946-0.5508206753-0.2913589266-1.1210074943-0.749930388-0.707

    -0.8465134576-1.6683610851-0.5571109573-0.2914332212-1.1423548292-0.8140714521-0.707

    -0.8736805415-1.7355482306-0.5598103302-0.2916313404-1.194460157-0.8560974699-0.707

    -0.8728385353-1.8145977584-0.5550307065-0.2890557918-1.1626372738-0.9041661206-0.707

    -0.982844175-1.9449601374-0.5476260045-0.286554538-1.1499824152-1.0325720734-0.707

    -0.9879952721-1.8586297321-0.538314406-0.2884861994-1.1223943281-0.9697683133-0.707

    -0.9827698804-1.857540077-0.5347730268-0.2933153529-1.1632811609-0.8835864974-0.707

    -0.9164495059-1.4325745708-0.5465611143-0.290591215-1.1570651736-0.8135513895-0.707

    -0.6459921462-1.0503037344-0.5549564119-0.289699679-1.165510001-0.8663748991-0.707

    -0.6117918336-0.8398021725-0.5637231828-0.2913093968-1.142627243-0.9627350846-0.707

    -0.6759328977-0.556937603-0.5675617407-0.2914579861-1.1069658019-0.982844175-0.707

    -0.7444821123-0.55763102-0.5537676972-0.2915818106-1.1187043596-0.9558256804-0.707

    k-epsilon High Re

    k-epsilon RNG

    k-omega STD High Re

    k-omega STD Low Re

    k-omega SST High Re

    k-omega SST Low Re

    Experimental Results

    Time (sec)

    CL

    Effect of different turbulence models on lift coefficient

  • Comparison between simulation results for different turbulence model and experimental results:

  • Water slip-top-wall method:

    0 % (Ref)-1.384390 % (Ref)2.93109Fully refined model0.08 %-1.383280.08 %2.93367Refined near bridge0.54%-1.391881 % 2.96061Basic coarse grid% DifferenceCL% DifferenceCDMesh Density

  • 0.94 %-1.378770.2 %2.9544510-40.0022 %-1.391850.00033 %2.9606210-50 % (ref)-1.391880 % (ref)2.9606110-6% differenceCL% differenceCDConvergence criteria

    Effect of convergence criteria on final solution:

  • Comparison between VOF and Water slip-top-wall method with experimental results:

  • The k- RNG predicts closet drag and lift coefficients

  • Effect of inlet turbulence on drag and lift coefficients:

  • Fully developed velocity profile after selected runs:

  • Fully developed turbulence kinetic energy after selected runs:

  • Fully developed turbulence dissipation rate after selected runs:

  • Comparison between CFD simulations and experimental data for Fr=0.22 for drag coefficients:

  • Comparison between CFD simulation and experimental data for Fr=0.22 for lift coefficients:

  • Conclusion:CFD simulations by STAR-CD for Fr=0.22 case , predicts more drag than experimental drag except for h*=0.289The 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

  • 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

  • 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 ANLs Transportation Research and Analysis Computing Center (TRACC).

  • QUESTIONS ???More information at:www.kostic.niu.edu


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