Computational Investigation of Buoyancy Influenced Flows and Benchmarking exercise

Presenter: Yacine Addad (PDRA) (KNOO Team: D. Laurence, M. Cotton, A. Keshmiri, S. Rolfo) (Collaborators: S. Benhamadouche, R. Howard, F. di Mare)

School of Mechanical, Aerospace & Civil Engineering (MACE)The University of Manchester7th Int. ERCOFTAC Symposium-ETMM7- 4-6 June 2008,Limassol, Cyprus

AGR working schemeThe Heated pipe: Relevance to AGR and VHTR

RANS models predictions buoyancy aiding

Chart6

0.984671910.9882160220.98837907140.91865845590.99711996020.98416261660.98829893280.9624094410.89167000040.7946670.7521970.4920.8611610.3809596837

0.87375853950.91191080110.91172458940.80467848390.98677432860.90500645530.97617980990.92066877690.43245760060.4817780.548330.8480.42179310.4526039974

0.7739824330.86017755230.86131267390.70516616690.97402525710.4941312650.96313594760.38095968370.43522521410.5813330.5799650.9670.572935

0.43127619270.76321073770.74919526430.43244680170.83978439760.51734994530.9361309030.27540150.46257762230.7484440.984

0.43380791090.44743711690.60581592010.44053656320.71838276490.62570738810.87784173640.45260399740.47286766870.93

0.48509673350.46443140980.55202138690.58156513220.79147506590.7248607110.73589111270.54417709620.59650325240.858

0.54889488490.53064891140.67303180750.67856590511.04045989570.95772380.83474576230.64030904380.527

0.57953958320.56277742550.80091658030.90284277711.45778944581.34641217971.10788688320.87168092150.8

0.72179803660.89637497361.06246931091.27884865751.9556861861.54207872041.25298236780.925

0.89408117571.30168040581.87221820991.83825314090.544

1.01544290721.96824138660.453

1.26568689360.871

1.49118778350.474

1.8655491130.538

0.833

0.595

0.551

0.556

0.478

Launder & Sharma Model (CONVERT)

Cotton & Ismael Model (CONVERT)

Suga Non-Linear Eddy Viscosity Model (CONVERT)

Lien-Chen-Leschziner k-eps Model (STAR-CD)

k-omega-SST Model (STAR-CD)

Lien & Durbin v2f Model (STAR-CD)

k-omega-SST Model (Code_Saturne)

Manchester v2f Model (Code_Saturne)

Large Eddy Simulation (STAR-CD)

Data of Steiner (1971)

Data of Carr et al (1973)

Data of Parlatan et al (1996)

DNS - You et al (2003)

Bo

Nu/Nu0

Ascend

Present LS for Ascending FlowCI Model for Ascending FlowSuga-NLEVM for Ascending flowLES - YacineLinear k-e -STAR-cd - LKEv2f- Star-CDk-w-SSt-Star-CDk-w-SST-SATURNEManchester V2f (Saturne)

Gr/Re2NuCfNu/NuoCf/CfoBo*qdTb/Tb(start)

Gr/Re2NuCfNu/NuoCf/CfoBo*qq+dTb/Tb(start)01.892E+019.166E-031.000E+001.000E+000.000E+0010.0000Gr/Re2NuCfNu/NufCf/Cf0Bo*qdTb/Tb(start)BoNuCfNu/Nu0Cf/Cf0BoNuCfNu/Nu0Cf/Cf0BoNuCfNu/Nu0Cf/Cf0BoNuCfNu/Nu0Cf/Cf0BoNuCfNu/Nu0Cf/Cf0BoNuCfNu/Nu0Cf/Cf0

01.742E+018.519E-031.000E+001.000E+000.000E+0010.00007.0456210E-0500.011.870E+019.149E-039.882E-019.981E-010.02071158820.1229680161max z/d=10001.833E+018.930E-031.000E+001.000E+000.000E+000.000E+000.00000E+002.01016E+019.39253E-031.00000E+001.00000E+000.00000E+001.78587E+017.63251E-031.00000E+001.00000E+000.00000E+001.73625E+019.07577E-031.00000E+001.00000E+000.00000E+002.19178E+019.83786E-031.00000E+001.00000E+000.00000E+001.98132E+019.62183E-031.00000E+001.00000E+000.00000E+001.86217E+018.94668E-031.00000E+001.00000E+00

0.011.715E+018.504E-039.847E-019.982E-012.074E-020.12296801618.6638604E-070.0631.726E+019.021E-039.119E-019.842E-011.299E-010.77469850131.07416E-02max z/d=1000.011.812E+018.926E-039.884E-019.996E-012.074E-021.230E-010.000012.01016E+019.39253E-031.00000E+001.00000E+002.10523E-031.68515E+017.62913E-039.43599E-019.99556E-012.10853E-021.70875E+019.04133E-039.84163E-019.96205E-012.10527E-032.19178E+019.83786E-031.00000E+001.00000E+002.04031E-021.95813E+019.65218E-039.88299E-011.00315E+002.03993E-021.79217E+018.89467E-039.62409E-019.94187E-01

0.0631.522E+018.368E-038.738E-019.822E-011.299E-010.770005.4251282E-060.01074162720.0871.628E+018.915E-038.602E-019.726E-011.805E-011.06982173981.49130E-02max z/d=1000.0631.671E+018.879E-039.117E-019.944E-011.299E-017.700E-011.07419E-031.30712E-011.79240E+019.07743E-038.91670E-019.66452E-012.108495E-021.640608E+017.586490E-039.18658E-019.93970E-011.32815E-011.57131E+018.49640E-039.05006E-019.36163E-012.10859E-022.18546E+019.85162E-039.97120E-011.00140E+001.31626E-011.93412E+019.70291E-039.76180E-011.00843E+001.53021E-011.71444E+018.70580E-039.20669E-019.73077E-01

0.0831.348E+018.197E-037.740E-019.622E-011.719E-011.020637.1910041E-060.1111.444E+018.658E-037.632E-019.446E-010.22989862921.3649449784max z/d=1000.0871.579E+018.827E-038.613E-019.885E-011.805E-011.069E+001.49128E-031.41110E-018.69308E+006.63509E-034.32458E-017.06422E-011.32807E-011.43705E+017.28180E-038.04678E-019.54050E-011.83356E-018.57934E+007.46430E-034.94131E-018.22443E-011.32836E-012.16279E+019.93598E-039.86774E-011.00997E+001.83650E-011.90828E+019.74719E-039.63136E-011.01303E+001.83563E-017.09412E+007.10984E-033.80960E-017.94690E-01

0.0857.512E+008.298E-034.313E-019.740E-011.760E-011.045237.3642813E-060.1158.467E+009.050E-034.474E-019.874E-010.23818326451.4141321849max z/d=1000.1251.373E+018.702E-037.492E-019.745E-012.589E-011.537E+001.55636E-018.74871E+006.83830E-034.35225E-017.28057E-011.58058E-011.25934E+016.97872E-037.05166E-019.14341E-012.10876E-018.98247E+007.45028E-035.17350E-018.20897E-011.83297E-012.13484E+019.97651E-039.74025E-011.01409E+002.75490E-011.85477E+019.83123E-039.36131E-011.02176E+002.75402E-018.14879E-039.10817E-01

0.0877.557E+008.352E-034.338E-019.803E-011.805E-011.070007.5388145E-060.138.789E+009.399E-034.644E-011.025E+002.693E-011.59858max z/d=1000.1651.110E+018.944E-036.058E-011.002E+003.417E-012.029E+001.80500E-019.29854E+007.05769E-034.62578E-017.51415E-011.83099E-017.72295E+007.62409E-034.32447E-019.98896E-015.08239E-011.08638E+011.04422E-026.25707E-011.15056E+005.07654E-011.84062E+011.03945E-028.39784E-011.05659E+004.18327E-011.73928E+019.99403E-038.77842E-011.03868E+002.75402E-018.42825E+008.14879E-034.52604E-019.10817E-01

0.138.450E+009.517E-034.851E-011.117E+002.693E-011.598581.1263019E-050.21.004E+011.076E-025.306E-011.174E+004.142E-012.45936max z/d=1000.2411.012E+011.154E-025.520E-011.292E+004.992E-012.960E+004.12927E-032.07511E-019.50538E+007.44101E-034.72868E-017.92226E-011.95842E-017.86743E+007.77805E-034.40537E-011.01907E+008.43566E-011.25854E+011.22630E-027.24861E-011.35118E+008.42077E-011.57453E+011.22942E-027.18383E-011.24969E+008.46945E-011.45803E+011.23827E-027.35891E-011.28693E+004.99845E-011.01335E+019.82916E-035.44177E-011.09864E+00

0.29.561E+001.096E-025.489E-011.287E+004.142E-012.459361.7327721E-050.0149129540.2411.065E+011.142E-025.628E-011.246E+004.992E-012.963533.752555782E-02max z/d=1000.51.234E+011.640E-026.730E-011.836E+001.036E+006.14840080375.00064E-011.19907E+019.55530E-035.96503E-011.01733E+005.07233E-011.03860E+011.03369E-025.81565E-011.35432E+002.10908E+001.66284E+011.64651E-029.57724E-011.81418E+002.10423E+001.73474E+011.64842E-027.91475E-011.67559E+002.11618E+001.65389E+011.70777E-028.34746E-011.77489E+008.46900E-011.19236E+011.17751E-026.40309E-011.31615E+00

0.2411.010E+011.165E-025.795E-011.368E+004.992E-012.960002.0855038E-0511.696E+011.826E-028.964E-011.992E+002.074E+0012.29700max z/d=6511.468E+012.354E-028.009E-012.636E+002.074E+0012.297008.41606E-011.21183E+011.20275E-026.78566E-011.57583E+006.32868E+002.33770E+012.35928E-021.34641E+002.59954E+006.31724E+002.28045E+012.39219E-021.04046E+002.43162E+006.32369E+002.19507E+012.49756E-021.10789E+002.59572E+002.11708E+001.62322E+011.58540E-028.71681E-011.77205E+00

0.51.257E+011.488E-027.218E-011.746E+001.036E+006.14840080374.3319302E-0532.463E+012.670E-021.302E+002.913E+006.213E+0036.8904048223max z/d=3531.947E+013.897E-021.062E+004.364E+006.213E+0036.89040482232.10274E+001.61236E+011.58082E-029.02843E-012.07117E+002.11027E+013.39555E+013.58156E-021.95569E+003.94629E+002.11564E+013.19515E+013.64238E-021.45779E+003.70242E+002.07423E+013.05534E+013.80553E-021.54208E+003.95509E+006.33250E+002.33327E+012.27067E-021.25298E+002.53800E+00

11.557E+011.882E-028.941E-012.209E+002.074E+0012.297008.6640002E-050.0412934718103.725E+014.140E-021.968E+004.517E+002.071E+01122.968016074250.000E+000.000E+001.037E+0161.48400803716.30495E+002.28386E+012.19182E-021.27885E+002.87169E+002.07894E+013.42314E+013.36634E-021.83825E+003.76267E+00

1.51.769E+012.163E-021.015E+002.539E+003.107E+0018.44520241111.2995791E-04100.000E+000.000E+002.071E+01122.96801607422.10272E+013.34354E+013.15060E-021.87222E+004.12787E+00

32.205E+012.751E-021.266E+003.229E+006.213E+0036.89040482232.5991581E-04

52.598E+013.293E-021.491E+003.866E+001.037E+0161.48400803714.3319302E-04

103.250E+014.221E-021.866E+004.955E+002.071E+01122.96801607428.6638604E-041.58064E-011.30603E+018.12772E-037.52215E-018.95540E-01

Removed points

0.0711.472E+018.324E-038.448E-019.770E-011.471E-010.873076.1513409E-06

0.0791.404E+018.258E-038.062E-019.693E-011.636E-010.971456.8444497E-06

Removed points

Removed pointsRemoved points

Gr/Re2Boq+dTb/Tb(start) (LS)dTb/Tb(start) (CI)dTb/Tb(start) (Suga)1.96055E-012.12730E+019.98729E-039.70582E-011.01519E+001.53052E-011.92421E+019.72187E-039.71177E-011.01040E+004.18234E-019.49749E+009.31002E-035.10023E-011.04061E+00

FCModelCfNu00.00E+000.00E+000002.34669E-011.87975E+019.79187E-039.48739E-011.01767E+001.31591E-011.71822E+018.65807E-039.22700E-019.67741E-01

DNS9.20E+0018.20.0630.1305.43E-061.074E-021.074E-021.074E-03Fine Grid2.44880E-011.87367E+019.80094E-039.45669E-011.01861E+002.34571E-018.21536E+007.62499E-034.41171E-018.52270E-01

Present8.55E+001.75E+010.0870.1807.54E-061.491E-021.491E-021.491E-0301.91857E+018.99321E-031.00000E+001.00000E+004.99923E-011.55331E+011.02520E-027.83978E-011.06549E+00

LS-Kim et al8.50E+0017.30.2410.4992.09E-054.129E-023.753E-024.129E-03

Correlation-19

dTBdTBdTB

000

3.14729677813.14729677660.3147382039

DNSLSConstant line4.36949550854.36949550650.4369458392

12.0989872410.99498844091.2098773958

Gr/Re2Bo*Nu/NufNuBo*Nu/Nu0BoNu/Nu01.83563E-017.09412E+007.10984E-033.80960E-017.94690E-01

0118.3010.0112.75402E-018.42825E+008.14879E-034.52604E-019.10817E-01

0.0630.1307010.8611615.7592288.043E-029.243E-011001

0.0870.1817550.4217937.71881191.318E-018.586E-01

0.2410.5013290.57293510.48471051.819E-014.371E-01

2.417E-014.674E-01

3.212E-015.116E-01

4.025E-015.418E-01

LS Kim et al.5.042E-015.810E-01

6.385E-016.226E-01

nu/nufBo*8.086E-016.756E-01

01.269E+007.880E-01

0.12952081211.752E+008.700E-01

0.17886211752.391E+009.495E-01

0.4954688737

DNSLS

Bo*Cf/Cf0Bo*Cf/Cf0

0.1302040.9581757.958E-029.812E-01

0.1790460.866921.315E-019.680E-01

0.4961951.186311.835E-019.614E-01

2.403E-011.057E+00

3.197E-011.156E+00

3.992E-011.245E+00

5.037E-011.337E+00

6.424E-011.449E+00

8.021E-011.571E+00

1.174E+001.805E+00

1.545E+001.989E+00

2.002E+002.151E+00

2.409E+002.266E+00

Descend

LS Results for Descending FlowCI Model for Descending FlowSuga Results for Descending Flow

Gr/Re2NuCfNu/NuoCf/CfoBo*qGr/Re2NuCfNu/NuoCf/CfoBo*qGr/Re2NuCfNu/NuoCf/CfoBo*q

01.747E+018.547E-031.000E+001.000E+000.000E+0010.000001.892E+019.166E-031.000E+001.000E+000.000E+0010.000001.823E+018.878E-031.000E+001.000E+000.000E+000.0000

0.011.772E+018.560E-031.014E+001.001E+002.071E-020.12300.011.914E+019.181E-031.011E+001.002E+002.074E-020.12296801610.011.844E+018.882E-031.011E+001.000E+002.071E-020.1230

0.0631.883E+018.610E-031.078E+001.007E+001.299E-010.770000.0632.012E+019.246E-031.063E+001.009E+001.299E-010.77469850130.0631.939E+018.890E-031.063E+001.001E+001.299E-010.77000

0.0871.926E+018.627E-031.103E+001.009E+001.805E-011.070000.0872.051E+019.270E-031.084E+001.011E+001.805E-011.06982173980.0871.977E+018.889E-031.084E+001.001E+001.805E-011.07000

0.2412.144E+018.694E-031.227E+001.017E+004.992E-012.963530.2412.254E+019.366E-031.191E+001.022E+004.992E-012.963530.2412.171E+018.868E-031.191E+009.989E-014.992E-012.96353

12.756E+018.820E-031.577E+001.032E+002.074E+0012.2970012.827E+019.357E-031.494E+001.021E+002.074E+0012.297000.8542.645E+018.704E-031.451E+009.804E-011.771E+0010.5

1.53.024E+018.884E-031.731E+001.039E+003.107E+0018.44520241111.53.024E+018.884E-031.607E+001.032E+003.107E+0018.4452024111

Results for Fully-Developed Forced Convection. (no buoyancy)

Test Case Description Re=180 based on R and u. Boussinesq Approximation. Periodic Flow. Lz=30R Grid1: 1.61 million Grid2: 4.83 million

Grid1 Resolution: r+min=1.0, +=6.28, z+=18.

Grid2 Resolution: r+min=1.0, +=6.28, z+=7.03.

Buoyancy effects on turbulence in VHTR channels: WR-LES

Nusselt number as a function of the buoyancy parameterfrom You et al. For RANS models predictions, see the paper by Amir Keshmiri et al.Ratio of SGS to molecular viscosity

Case1: Forced convection Gr/Re2=0.0Buoyancy effects on turbulence in VHTR channels: WR-LESData normalized by the bulk velocity

Cases from Gr/Re2=0.063 to Gr/Re2=0.241Buoyancy effects on turbulence in VHTR channels: WR-LESData normalized by the bulk velocity

NEARLY-HORIZONTAL SHALLOW CAVITY TEST CASE Ra= 4.16108 NCELL= 3 million Boussinesq approximation Pr=0.71 (Air) =5 LES Grid (Case1)

NEARLY-HORIZONTAL SHALLOW CAVITY TEST CASELES RESULTS Q=0.05

NEARLY-HORIZONTAL SHALLOW CAVITY TEST CASELES RESULTS

NEARLY-HORIZONTAL SHALLOW CAVITY TEST CASERANS RESULTS

Low-Re. models tested:

k- Lien et al. (1996)

k- Wilcox (1998)

k- SST Menter (1993)

v2-f Lien & Durbin (1996) Buoyancy term included in k-equation

thermal fluxes

Energy conservation: Taylor-Green vortices test case.

Taylor-Green vortices test case: mesh generation.Resolution: 60 x 60Time step: 0.01 => CFLmax < 0.2

Effects of the velocity/pressure coupling

Comparison between the codes for RR=0.75 (6/8)RR=0.75 6/8

Re=395 Domain 2 2 LES Ncells= 443,272 DNS Ncells = 9,486,336 (Ref: Moser et al. 1999)Channel flow test case

N xNyNzLES68 to 2004642 to 100DNS256193192

Channel flow test case: Mean Velocity predictions

Channel flow test case: Reynolds Stresses

Budgets of the Reynolds stress components Ref: T. Omori et al. Int. J. Heat and fluid flow 2008

Viscus diffusion termDissipation termChannel flow test case: Budget for k

Budget for kSTAR: Grid (141x184x177) = 4.59 millionDNS : Grid (256x193x192)= 9.48 million

STAR: Grid (141x184x177) = 4.59 millionDNS : Grid (256x193x192)= 9.48 millionBudget for uu

STAR: Grid (141x184x177) = 4.59 millionDNS : Grid (256x193x192)= 9.48 millionBudget for vv

STAR: Grid (141x184x177) = 4.59 millionDNS : Grid (256x193x192)= 9.48 millionBudget for ww

STAR: Grid (141x184x177) = 4.59 millionDNS : Grid (256x193x192)= 9.48 millionBudget for uv

ConclusionsAcknowledgements: TSEC programme 'KNOO' EPSRC funding under grant EP/C549465/1 for PDRA and Computer resources

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