An adaptation of the low Mach number approximation for supercritical fluid buoyant flows

Gilbert Accary (1) , Isabelle Raspo (1) , Patrick Bontoux (1) , Bernard Zappoli (2)

1 M2P2 - Modélisation et Simulation Numérique (en mécanique des fluides)
2 CNES - Centre National d'Études Spatiales [Toulouse]

This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh-Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating.

Mots clés: Fluid mechanics; Supercritical fluid; Low Mach number; Rayleigh-Bénard instability; Piston effect

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Gilbert Accary, Isabelle Raspo, Patrick Bontoux, Bernard Zappoli. An adaptation of the low Mach number approximation for supercritical fluid buoyant flows. Comptes Rendus Mécanique, 2005, 333 (5), pp.397-404. ⟨10.1016/j.crme.2005.03.004⟩. ⟨hal-00836294⟩