Parallel direct numerical simulation and analysis of turbulent Rayleigh–Bénard convection at moderate Rayleigh numbers using an efficient algorithm

Abstract

Direct numerical simulation of turbulent Rayleigh-Bénard convection up to Rayleigh number 108 is performed using a fully-implicit, non-dissipative, discrete kinetic energy-conserving algorithm and a parallel flow solver based on it. The algorithm is especially suitable for simulating low-Mach number, variable density/viscosity, transitional and turbulent flows with or without heat transfer. Furthermore, since it does not rely on the Boussinesq assumption, large temperature differences and high Rayleigh numbers can be handled without loss of accuracy, unlike the pure incompressible ones. It is first shown that the algorithm is able to predict the evolution of thermally-driven instability to turbulent regime and all the characteristics of turbulent convection accurately, using low- and high-order turbulent statistics and various secondary diagnostics derived. Then, effects of increasing Rayleigh numbers on the development of the instability are analyzed in detail. Additionally, Nusselt-Rayleigh scaling properties are studied and a scaling relation is provided. Results show that Rayleigh-Bénard convection at relatively high Rayleigh numbers, corresponding to a boundary layer-dominated regime and little beyond it to a bulk-dominated regime, is characterized by weakening thermal fluctuations, thinning thermal boundary layers, increasing vertical velocity fluctuations and decreasing skewness. It is also observed that the turbulent heat flux dominates the heat transfer. Finally, the corresponding Nusselt-Rayleigh scaling relation is predicted as Nu=0.132Ra0.297.