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St.-Petersburg State Polytechnic University Department of Aerodynamics, St.-Petersburg, Russia

“FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg. Numerical analysis of turbulent Rayleigh-Bénard convection in confined enclosures using a hybrid RANS/LES approach. A. ABRAMOV, N. IVANOV & E. SMIRNOV. St.-Petersburg State Polytechnic University

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St.-Petersburg State Polytechnic University Department of Aerodynamics, St.-Petersburg, Russia

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  1. “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg Numerical analysis of turbulent Rayleigh-Bénard convection in confined enclosures using a hybrid RANS/LES approach A. ABRAMOV, N. IVANOV & E. SMIRNOV St.-Petersburg State Polytechnic University Department of Aerodynamics, St.-Petersburg, Russia E-mail: aerofmf@citadel.stu.neva.ru

  2. OUTLINE Introduction  Problem description  Mathematical model  Computational aspects  Structure of turbulent convection  Heat transfer predictions  Conclusions Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  3. 3D Unsteady formulations: modeling levels 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 Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  4. Problem description High-Ra Rayleigh-Bénard mercury and water convection in confined enclosures g z Cold walls, Tc z Scales: H r H Adiabaticwalls H - buoyancy velocity Hot walls, Th D = H Water, Pr = 7 Mercury, Pr = 0.025 Ra > 108 Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  5. Mathematical model  Navier-Stokes equations averaged/filtered for a RANS/LES model;  Boussinesq’s approximation for gravity buoyancy where Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  6. Turbulence Modelling: RANS / LES one-equation turbulence model (Abramov & Smirnov, 2002) Modified Wolfshtein model for a RANS zone: Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  7. Computational aspects Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  8. Computational program Mercury convection: 108 < Ra < 5109 Pr= 0.025 Water convection: Ra = 5108;5109 Pr= 7 Grids of about 160000 cells Conditions of experiments: Takeshita et al.(Phys. Rev. Lett.,1996) Cioni et al.(J. Fluid Mech.,1997) Glazier et al.(Nature, 1999) Conditions of experiments: Zocchi et al. (Physica A.,1990) Cioni et al.(J. Fluid Mech.,1997) Qiu et al.(Phys. Rev. E., 1998) etc. Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  9. Vb Vb Structure of turbulent convection Mercury convection: Ra = 108, Pr= 0.025 Temperature isolines Vertical velocity at middle horizontal plane w Velocity vector patterns Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  10. Structure of turbulent convection Mercury convection: Ra = 108, 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

  11. Structure of turbulent convection Water convection: Ra = 5109, Pr= 7 A A Equiscalar surfaces of vertical velocity w = 0.05 (black) and w = -0.05 (gray) B Velocity vector and temperature fields B A A B B Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  12. z 5108 5109 z 5108 5109 z  Th  wm 108 5108 8.7108  Th z wmc=2Vg 108 5108 8.7108  wm Characteristics of the global circulation Profiles of maximum horizontal temperature difference and vertical velocity difference Reynolds number Reg= VgH /, versus Rayleigh number. Mercury Water Mercury Abramov et al. SPTU, Russia

  13. Thermal plumes in high-Ra convection Temperature isosurfaces T= 0.45 and T = 0.55 Temperature isosurface T= 0.9 colored by vertical velocity w Ra = 5108 Ra = 5109 Temperature fluctuations near the top wall (z = 0.96) Temperature fluctuations near the bottom wall (z = 0.03, r = 0) plumes T T plumes   Abramov et al. SPTU, Russia

  14. -5/3 -4 Turbulent vertical velocity and temperature fluctuations Water, Ra = 5109 T  W -5/3 -4  z = 0.5 z z = 0.75 Mercury, Ra = 5108 Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  15. z 5108 5109 z 108 uh 5108 8.7108 T Boundary layers near the isothermal walls Temperature profile near the top wall (mercury) Thermal and viscous boundary layer thicknesses as functions of Ra T T Ra - RANS/LES in water Mercury: V < T Water: V > T - RANS/LES in mercury - DNS Verzicco et al., 99 - Experiment Takeshita et al., 96 Ra Mean horizontal velocity profile (water) V - DNS Verzicco et al., 99 - Experiment Takeshita et al., 96 Ra - RANS/LES in mercury - RANS/LES in water Ra Abramov et al. SPTU, Russia

  16. Eq -5/3 -4 fq f Heat transfer predictions Nusselt number fluctuations in mercury and water convection Ra = 5108 Nu t - RANS/LES in water Nu - RANS/LES in mercury Ra = 5109 - Exp. Cioni et al., 96 Nu - Exp. Goldstein, 80 - Exp. Glazier, 99 t Ra Abramov et al. SPTU, Russia “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg

  17. “FLOMANIA”, DES WORKSHOP, 2/3 July 2003, St.-Petersburg CONCLUSIONS  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

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