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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).
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