Computational simulation of unsteady boundary layer over compliant surfaces

Abstract

This work is concerned with the development and application of spatial direct numerical simulation to an investigation of the interaction between an unstable boundary layer and compliant surfaces. The study covers the propagation of two-dimensional (2D) and three-dimensional (3D) waves over compliant membranes, viscoelastic layers and their comparison with similar waves over rigid surfaces. For 2D simulations, we demonstrate that Tollmien-Schlichting (TS) waves and compliance-induced flow instability (CIFI) waves predicted by linear stability theory frequently coexist on membrane surfaces and viscoelastic layers of finite streamwise length. The results show that well-designed compliant panel surfaces are able bring the CIFI under control and reduce the overall amplification of the TS waves in accordance with the prediction of linear stability theory. Results for 3D oblique linear TS waves propagation over finite compliant membranes generally show the presence and/or modulating influence of coexisting a longer wavelength CIFI, which propagates at a larger oblique wave angle than the TS wave. Simulation reveals that compliant wall response could lessen the secondary instabilities during the early stages of subharmonic and fundamental breakdown. However, during the late stage of fundamental breakdown, the modulating effects of CIFI and other wave modes may increase the amplitudes of original 2D and 3D TS modes and trigger an earlier breakdown on a compliant surface.