Direct numerical simulation of laminar and turbulent Bénard convection

Abstract

The TURBIT-3 computer code has been used for the direct numerical simulation of Bénard convection in an infinite plane channel filled with air. The method is based on the three-dimensional non-steady-state equations for the conservation of mass, momentum and enthalpy. Subgrid-scale models of turbulence are not required, as calculations with different grids show that the spatial resolution of grids with about 322 × 16 nodes provides sufficient accuracy for Rayleigh numbers up to Ra = 3·8 × 105. Hence this simulation model contains no tuning parameters.The simulations start from nearly random initial conditions. This has been found to be essential for calculating flow patterns and statistical data insensitive to grid parameters and agreeing with experimental experience. The numerical results show the theoretically predicted ‘skewed varicose’ instability at Ra = 4000. Warm and cold ‘blobs’ are identified as causing temperature-gradient reversals for all the high Rayleigh numbers under consideration. The calculated wavelengths and the corresponding flow regimes observed in the transition range confirm the stability maps determined theoretically. In the turbulent range the wavelengths agree qualitatively with low-aspect-ratio experiments. Accordingly, the Nusselt numbers lie at the upper end of the scatter band of experimental data, as these also depend on the aspect ratio. Appropriately normalized, the velocity and temperature fluctuation peaks are independent of the Rayleigh number. The vertical profiles agree largely with experimental data and, especially in case of temperature statistics, exhibit comparable or less scatter.