Instabilités bi-et tridimensionnelles dans une couche limite décollée compressible subsonique

Abstract

Flow separation is a common feature in wall-bounded flow, where it is generally induced by an adverse pressure gradient. Here we reconsider a bump-type geometry which has been used in previous numerical investigations of the stability of the laminar recirculation bubble for incompressible flow. It has been shown for low Reynolds number that the first bifurcation of the 2D stationnary flow is characterized by a zero-frequency 3D instability mode. For larger Reynolds number a second bifurcation appears (Hopfbifurcation) and separated boundary-layer is then subject to a low frequency phenomenon known as’flapping’. The influence of compressibility for this type of flow is assessed.We first solve the compressible Navier-Stokes equations in order to obtain an equilibrium solution for increasing compressibility effects. Two-dimensional global stability of this solution is then investigatesand we assess the influence of Mach number on the critical Reynolds number for which the separated flow becomes unstable with respect to oscillatory perturbations.Three-dimensional transverse instabilities are addressed as well and in particular the evolution of growth rate and transverse wave length of the most unstable mode for several Mach numbers.