Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers

Abstract

We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh-Bénard convection (RBC) for Rayleigh numbers ranging from $10^6$ to $10^{1}5$ and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. (Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598), albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at $Ra=10^{1}3$, we use grids that are 1/120 times the grid-resolution as that of the DNS (Iyer et al., Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598). The Reynolds numbers in our simulations span 3 orders of magnitude from 1,000 to 1,700,000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as $Nu\sim R{a}^{0.317}$ and $Re\sim R{a}^{0.497}$. We also perform LES of RBC with periodic side-walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477 respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers, and hence enable us to test the transition to ultimate convection regime.

37 pages, 15 figures

References in corpus (7)

• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Energy Spectrum of Buoyancy-Driven Turbulence
• Scaling of large-scale quantities in Rayleigh-Bénard convection
• Dynamics of reorientations and reversals of large scale flow in Rayleigh-Benard convection
• Dynamics of large-scale quantities in Rayleigh-Bénard convection
• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection

Cited by in corpus (2)

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