School of Engineering, The University of Queensland
Abstract
A method and preliminary results are presented for the determination of eigenvalues and eigenmodes from fully viscous boundary layer flow interacting with a finite length one-sided compliant wall. This is an extension to the analysis of inviscid flow-structure systems which has been established in previous work. A combination of spectral and finite-difference methods are applied to a linear perturbation form of the full Navier-Stokes equations and one-dimensional beam equation. This yields a system of coupled linear equations that accurately define the spatio-temporal development of linear perturbations to a boundary layer flow over a finite-length compliant surface. Standard Krylov subspace projection methods are used to extract the eigenvalues from this complex system of equations. To date, the analysis of the development of Tollmien-Schlichting (TS) instabilities over a finite compliant surface have relied upon DNS-type results across a narrow (or even singular) spectrum of TS waves. The results from this method have the potential to describe conclusively the role that a finite length compliant surface has in the development of two-dimensional TS instabilities and other FSI instabilities across a broad spectrum
