Rayleigh-Bénard Convection in a Near-Critical Fluid Using 3D Direct Numerical Simulation

Abstract

Convection in a fluid close to its gas-liquid critical point (CP) has been a subject of growing interest since the exhibition of the piston-effect (PE), this thermo-acoustic effect responsible for the fast thermal equilibrium observed in such a fluid in the absence of convection. In 1987, under microgravity conditions, Nitsche and Straub observed a fast and homogeneous increase of the temperature inside a spherical cell containing SF6 slightly above the CP when it was subjected to a heating impulse. This phenomenon was then explained theoretically (Zappoli et al., 1990; Onuki et al., 1990; Boukari et al., 1990) by the well-known critical anomalies, more precisely by the divergence of the thermal expansion coefficient and the vanishing of its thermal diffusivity when approaching the CP. Indeed, the heating of a cell containing a supercritical fluid (SCF) induces along the heated wall a thin thermal boundary layer in which density shows large variations because of the divergence of the thermal expansion coefficient; this thermal layer expands compressing adiabatically the rest of the fluid leading by thermo-acoustic effects (the socalled PE) to a fast and homogeneous heating of the bulk of the cell. Several experiments were carried out subsequently, mainly in microgravity (Guenoun et al., 1993; Straub et al., 1995; Garrabos et al., 1998) but also on Earth (Kogan & Meyer, 1998), and confirmed the existence of the PE.