Interaction of panel flutter with inviscid boundary layer instability in supersonic flow

Abstract

AbstractWe investigate the stability of an elastic plate in supersonic gas flow. This problem has been studied in many papers regarding panel flutter, where uniform flow is usually considered. In this paper, we take the boundary layer on the plate into account and investigate its influence on plate stability. Three problem formulations are studied. First, we investigate the stability of travelling waves in an infinite-length plate. Second, the nature of the instability (absolute or convective instability) is examined. Finally, by using solutions of the first two problems, instability of a long finite-length plate is studied by using Kulikovskii’s global instability criterion. The following results are obtained. All the eigenmodes of a finite-length plate are split into two types, which we call subsonic and supersonic. The influence of the boundary layer on these eigenmodes can be of two kinds. First, for a generalized convex boundary layer profile (typical for accelerating flow), supersonic eigenmodes are stabilized by the boundary layer, whereas subsonic disturbances are destabilized. Second, for a profile with a generalized inflection point (typical for constant and decelerating flows), supersonic eigenmodes are destabilized in a thin boundary layer and stabilized in a thick layer; subsonic eigenmodes are damped. The correspondence between the influence of the boundary layer on panel flutter and the stability of the boundary layer over a rigid wall is established. Examples of stable boundary layer profiles of both types are given.