NUMERICAL-SIMULATION OF THE EVOLUTION OF TOLLMIEN-SCHLICHTING WAVES OVER FINITE COMPLIANT PANELS

The evolution of two-dimensional Tollmien-Schlichting waves propagatin g along a wall shear layer as it passes over a compliant panel of fini te length is investigated by means of numerical simulation. It is show n that the interaction of such waves with the edges of the panel can l ead to complex patterns of behaviour. The behaviour of the Tollmien-Sc hlichting waves in this situation, particularly the effect on their gr owth rate, is pertinent to the practical application of compliant wall s for the delay of laminar-turbulent transition. If compliant panels c ould be made sufficiently short whilst retaining the capability to sta bilize Tollmien-Schlichting waves, there is a good prospect that multi ple-panel compliant walls could be used to maintain laminar flow at in definitely high Reynolds numbers. We consider a model problem whereby a section of a plane channel is replaced with a compliant panel. A gro wing Tollmien-Schlichting wave is then introduced into the plane, rigi d-walled, channel flow upstream of the compliant panel. The results ob tained are very encouraging from the viewpoint of laminar-flow control . They indicate that compliant panels as short as a single Tollmien-Sc hlichting wavelength can have a strong stabilizing effect. In some cas es the passage of the Tollmien-Schlichting wave over the panel edges l eads to the excitation of stable flow-induced surface waves. The prese nce of these additional waves does not appear to be associated with an y adverse effect on the stability of the Tollmien-Schlichting waves. E xcept very near the panel edges the panel response and flow perturbati on can be represented by a superposition of the Tollmien-Schlichting w ave and two other eigenmodes of the coupled Orr-Sommerfeld/compliant-w all eigensystem. The numerical scheme employed for the simulations is derived from a novel vorticity-velocity formulation of the linearized Navier-Stokes equations and uses a mixed finite-difference/spectral sp atial discretization. This approach facilitated the development of a h ighly efficient solution procedure. Problems with numerical stability were overcome by combining the inertias of the compliant wall and flui d when imposing the boundary conditions. This allowed the interactivel y coupled fluid and wall motions to be computed without any prior rest riction on the form taken by the disturbances.