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TECHNICAL PAPERS

# RANS-Based Very Large Eddy Simulation of Thermal and Magnetic Convection at Extreme Conditions

[+] Author and Article Information
K. Hanjalić

Department of Multi Scale Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlandshanjalic@ws.tn.tudelft.nl

S. Kenjereš

Department of Multi Scale Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlandskenjeres@ws.tn.tudelft.nl

J. Appl. Mech 73(3), 430-440 (Oct 02, 2005) (11 pages) doi:10.1115/1.2150499 History: Received February 16, 2004; Revised October 02, 2005

## Abstract

For thermal and magnetic convection at very high Rayleigh and Hartman numbers, which are inaccessible to the conventional large eddy simulation, we propose a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach in which the large-scale deterministic motion is fully resolved by time and space solution, whereas the unresolved stochastic motion is modeled by a “subscale” model for which an one-point RANS closure is used. The resolved and modeled contributions to the turbulence moments are of the same order of magnitude and in the near-wall regions the modeled heat transport becomes dominant, emphasizing the role of the subscale model. This T-RANS approach, with an algebraic stress/flux subscale model, verified earlier in comparison with direct numerical simulation and experiments in classic Rayleigh-Bénard convection, is now expanded to simulate Rayleigh-Bénard (RB) convection at very high Ra numbers—at present up to $O(1016)$—and to magnetic convection in strong uniform magnetic fields. The simulations reproduce the convective cell structure and its reorganization caused by an increase in Ra number and effects of the magnetic field. The T-RANS simulations of classic RB indicate expected thinning of both the thermal and hydraulic wall boundary layer with an increase in the Ra number and an increase in the exponent of the $Nu∝Ran$ correlation in accord with recent experimental findings and Kraichnan asymptotic theory.

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## Figures

Figure 2

Instantaneous trajectories in the near-wall region (z∕H=0.925), Ra=6.5×105, Pr=0.71: comparison among DNS, LES, and TRANS

Figure 1

Instantaneous trajectories in the central horizontal plane, Ra=6.5×105, Pr=0.71: comparison among DNS, LES, and TRANS

Figure 12

Temperature distributions in the near-wall region (z∕D=0.075), Ra=107: Ha=0,20,100—from top to bottom

Figure 11

Temperature distributions in the central horizontal plane (z∕D=0.5), Ra=107: Ha=0,20,100—from top to bottom

Figure 10

Diminishing of the Nusselt number with an increase in the Hartmann number in a Rayleigh-Bénard convection subjected to a vertical uniform magnetic field. Open symbols: experiments (Cioni (31)). Closed symbols: T-RANS computations for an 8:8:1 enclosure with open ends.

Figure 9

Effect of a vertical uniform magnetic field on the reorganization of the roll/cell structures in a vertical plane, Ra=107: Ha=0,20,100—from top to bottom.

Figure 8

The thickness of thermal (λθ∕H) and hydrodynamical (λν∕H) boundary layers as functions of Ra, Pr=0.71

Figure 7

Comparison of the computed Nu(Ra) results with several experimental correlations over a range of Ra numbers

Figure 6

The modeled, deterministic, and total contributions of the vertical heat flux in the classical R-B convection: (a) comparison between T-RANS and DNS, Ra=6.5×105; (b) T-RANS computations for ultraturbulent regime Ra=1011–1015; (c) a blowup of the near wall region, 0⩽z∕D⩽5×10−3

Figure 5

Planform structures with fingerlike plumes in between for Ra=6.5×105,109,2×1014, Pr=0.71

Figure 4

The T-RANS instantaneous trajectories close to the top wall (z∕H=0.925) at the high-Ra: (top) Ra=109, (bottom) Ra=2×1014, Pr=0.71

Figure 3

The TRANS instantaneous trajectories at the midplane (z∕H=0.5) for the high-Ra: (top) Ra=109, (bottom) Ra=2×1014, Pr=0.71

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