Numerical solutions of thermoacoustic and buoyancy-driven transport in a near critical fluid

Abstract

This paper presents the mechanisms of heat and mass transport of 1D and 2D low Mach number, unsteady, viscous, low heat diffusing, hypercompressible Navier-Stokes equations of a van der Waals gas (CO₂). The results have been focused on some striking behaviours compared to those obtained for normally compressible gases: i) heat equilibration is still achieved very fast under normal gravity conditions, as under zero-g conditions, by the Piston Effect before buoyancy convection has time to enhance heat transport; ii) mass equilibration is achieved on a much longer time scale by a quasi isothermal buoyant convection; iii) due to the very high compressibility, a stagnation point effect as that encountered in high speed flows provokes an overheating of the upper wall of a heated square cavity; iv) a significant difference with the convective single roll pattern generated under the same condition in normal CO₂ is also found: on the Piston Effect time scale, under the form of a Marangoni-like pattern due to the very thin boundary layer-localised density gradients; on the heat diffusion time scale under the form of a double roll convective structure.