Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach

Abstract

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer. Various direct numerical simulations were carried out of a shock-wave/laminar-boundary-layer interaction (SWBLI). Three-dimensional unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.