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St.-Petersburg State Polytechnic University Department of Aerodynamics, St.-Petersburg, Russia A. ABRAMOV, N. IVANOV & E. SMIRNOV Numerical analysis of turbulent Rayleigh-Bénard convection in confined enclosures using a hybrid RANS/LES approach E-mail: aerofmf@citadel.stu.neva.ru “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg
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Introduction Problem description Mathematical model Computational aspects Structure of turbulent convection Heat transfer predictions Conclusions OUTLINE Abramov et al. SPTU, Russia
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1. Full Direct Numerical Simulation (DNS): no turbulence model 2. Under-resolved (coarse-grid) DNS: no turbulence model 3. Unsteady Reynolds-Averaged Navier-Stokes (RANS): modeling of all-scales background turbulence 4. Large Eddy Simulation (LES): modeling of subgrid-scale turbulence 5. RANS/LES hybridization, in particular, non-standard DES 3D Unsteady formulations: modeling levels “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Problem description High-Ra Rayleigh-Bénard mercury and water convection in confined enclosures H z H D = H z r g Cold walls, T c Hot walls, T h Adiabatic walls Mercury, Pr = 0.025 Water, Pr = 7 Ra > 10 8 - buoyancy velocity Scales: H “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Mathematical model Navier-Stokes equations averaged/filtered for a RANS/LES model; Boussinesq’s approximation for gravity buoyancy where “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Turbulence Modelling: RANS / LES one-equation turbulence model (Abramov & Smirnov, 2002) Modified Wolfshtein model for a RANS zone: “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Computational aspects “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Computational program Grids of about 160000 cells Water convection: Ra = 5 10 8 ; 5 10 9 Pr = 7 Conditions of experiments: Zocchi et al. (Physica A.,1990) Cioni et al. (J. Fluid Mech.,1997) Qiu et al. (Phys. Rev. E., 1998) etc. Mercury convection: 10 8 < Ra < 5 10 9 Pr = 0.025 Conditions of experiments: Takeshita et al. (Phys. Rev. Lett.,1996) Cioni et al. (J. Fluid Mech.,1997) Glazier et al. (Nature, 1999) “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Structure of turbulent convection VbVb Mercury convection: Ra = 10 8, Pr = 0.025 VbVb Velocity vector patterns Temperature isolines Vertical velocity at middle horizontal plane w “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Structure of turbulent convection Mercury convection: Ra = 10 8, Pr = 0.025 Equiscalar surfaces of vertical velocity w = 0.25 (gray) and w = -0.25 (black) Temperature and velocity vector fields Vertical velocity distributions (time-averaging over the interval of 10 time units) w Abramov et al. SPTU, Russia
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Structure of turbulent convection B A A B A B Velocity vector and temperature fields Water convection: Ra = 5 10 9, Pr = 7 Equiscalar surfaces of vertical velocity w = 0.05 (black) and w = -0.05 (gray) A B “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Characteristics of the global circulation 10 8 5 10 8 8.7 10 8 z Th Th 10 8 5 10 8 8.7 10 8 w m z w mc =2V g 5 10 8 5 10 9 z Th Th w m z 5 10 8 5 10 9 Profiles of maximum horizontal temperature difference and vertical velocity difference Water Mercury Reynolds number Re g = V g H /, versus Rayleigh number. Mercury Abramov et al. SPTU, Russia
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Temperature isosurface T = 0.9 colored by vertical velocity Temperature fluctuations near the bottom wall (z = 0.03, r = 0) Thermal plumes in high-Ra convection Temperature isosurfaces T = 0.45 and T = 0.55 Temperature fluctuations near the top wall (z = 0.96) T T Ra = 5 10 9 Ra = 5 10 8 w plumes Abramov et al. SPTU, Russia
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-5/3 -4 Mercury, Ra = 5 10 8 z = 0.5 -5/3 -4 Turbulent vertical velocity and temperature fluctuations z = 0.75 T W Water, Ra = 5 10 9 z “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Boundary layers near the isothermal walls 5 10 8 5 10 9 z uhuh Thermal and viscous boundary layer thicknesses as functions of Ra Temperature profile near the top wall (mercury) Mean horizontal velocity profile (water) Mercury: V < T Water: V > T TT z T 10 8 5 10 8 8.7 10 8 - RANS/LES in water - RANS/LES in mercury - DNS Verzicco et al., 99 - Experiment Takeshita et al., 96 Ra TT - DNS Verzicco et al., 99 - Experiment Takeshita et al., 96 - RANS/LES in water - RANS/LES in mercury Ra VV Abramov et al. SPTU, Russia
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Heat transfer predictions Ra = 5 10 8 t Nu -5/3 -4 fqfq f EqEq Nu Nusselt number fluctuations in mercury and water convection Ra = 5 10 9 - RANS/LES in water - RANS/LES in mercury - Exp. Cioni et al., 96 - Exp. Goldstein, 80 - Exp. Glazier, 99 Nu Ra t “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Abramov et al. SPTU, Russia
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Numerical simulations of high-Ra R-B convection was performed with a non-standard DES approach based on the one-equation k-model of unresolved turbulence The specific patterns of fully developed turbulent convection were analyzed, especially the formation of a large-scale circulation cell and thermal plumes for both the configurations In mercury the global circulation, velocity and temperature fluctuations are considerably more intensive than in water Relation between the thicknesses of the viscous layer and the thermal boundary layer was established Numerically predicted Nusselt numbers were in quantitative agreement with registered experimental laws CONCLUSIONS “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg
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