The sensitivity of flow and surface instabilities to changes in compliant wall properties

Abstract

A spatial stability analysis is performed for a transitional boundary layer over a non-isotropic compliant wall. A simple mechanical model is used for the wall. A spectral approximation is used to obtain the solution of the Orr-Sommerfeld problem. From the spectrum of eigenvalues a measure of the growth rate of instabilities in the boundary layer is obtained. These instabilities are the Tollmien-Schlichting (TSI) and Travelling-Wave Flutter (TWF) instabilities. A measure of the critical velocity at which the surface instability-static divergence-occurs is made for given compliant walls. The sensitivity of the instabilities to changes in the wall properties is evaluated. The TSI is found to be more sensitive to changes in the surface properties than the TWF. It is found that by decreasing the plate thickness or the modulus of elasticity the TSI growth rate is reduced. The variation of the instability growth rates with the degree of non-isotropy of the surface is also examined. The sensitivity calculations show the effect of compliant wall properties on the flow and surface instabilities. From the results of the sensitivity analysis, the most effective wall properties are varied leading to reduced growth rates of instabilities without static divergence occurring.