Distributed two-dimensional boundary-layer receptivity to non-stationary vortical disturbances in the presence of surface roughness

Abstract

The distributed (over the longitudinal coordinate) excitation of two-dimensional (2D) Tollmien — Schlichting (TS) waves by weak non-stationary free-stream vortices propagating along the edge of the laminar boundary layer developing over a surface with small-amplitude 2D roughness is examined. The vorticity vector of the free-stream vortices was oriented over the span of the model, i. e., did not depend on the transverse coordinate. The theoretical analysis of the excitation mechanism reported in [1] was refined to develop, around it, a procedure making it possible to experimentally determine the coefficients of distributed vortical receptivity of the flow and the coefficients of “vortex-roughness” receptivity by fitting the experimental distributions with analytical solutions. Under conditions with controllable excitation of disturbances, a detailed hot-wire study of free-stream disturbances and boundary-layer disturbances at several vortex frequencies and at several surface-roughness periods was performed, and the shape of the controllable surface roughness was measured. The point-source method was employed to experimentally examine the characteristics of linear three-dimensional (3D) stability of the flow to TS waves, necessary for determination of the coefficients of distributed receptivity. It was found that the free-stream vortices with transverse orientation of the vorticity vector excited boundary-layer TS waves via two receptivity mechanisms: (a) on the smooth surface (due to natural non-uniformity of the flow) and (b) during interaction of the vortices with the surface roughness. The developed approach was used to experimentally estimate the amplitudes and phases of the coefficients of both types of distributed vortical receptivity as dependent on problem parameters. The absolute values of both types of receptivity coefficients were found to rapidly grow in value with increasing vortex frequency. It is shown that the most efficient excitation of TS waves is observed in the situation with satisfied resonance conditions for streamwise vortex, surface-roughness, and TS-wave streamwise wavenumbers, resulting in strong deviation of the increments of the TS waves from the linear-stability increments. Under no-resonance conditions, only amplitude beats of boundary-layer disturbances were observed.