Instabilities of compressible fluid flow over a membrane

Abstract

This paper considers the linearized dynamics of flow of a compressible fluid over a stretched membrane. In particular, the stability of the flow has been studied, and identify the types of instability that occur has been identified. The zones of stability/instability in the Mach number-velocity ratio plane have been obtained. Three regions, namely neutrally stable, convectively unstable, and absolutely unstable, are observed to exist. It is found that low values of Mach number and velocity ratio yield a neutrally stable flow. At high Mach number and/or velocity ratio, the system becomes absolutely unstable. A zone of convective instability is also observed for a range of Mach number and velocity ratio.

Keywords

compressible flow flexible structure fluid-structure interaction instability

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