1. 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

2.  Introduction  Problem description  Mathematical model  Computational aspects  Structure of turbulent convection  Heat transfer predictions  Conclusions OUTLINE Abramov et al. SPTU, Russia

3. 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

4. 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

5. 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

6. 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

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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. -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

15. 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 TT 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 TT - DNS Verzicco et al., 99 - Experiment Takeshita et al., 96 - RANS/LES in water - RANS/LES in mercury Ra VV Abramov et al. SPTU, Russia

16. 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

17.  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