A finite Reynolds-number approach for the prediction of boundary-layer receptivity in localized regions

Abstract

Earlier theoretical work on the boundary-layer receptivity problem utilized the triple-deck framework, and typically produced only the leading-order asymptotic result. The applicability of these predictions was limited to the generation of Tollmien–Schlichting-type (viscosity-conditioned) instabilities and rather high values of an appropriate Reynolds number. Generalizing the concepts behind the asymptotic theory of Goldstein and Ruban, the classical Orr–Sommerfeld theory is utilized to predict the receptivity due to small-amplitude surface nonuniformities. This approach accounts for the finite Reynolds-number effects, and can also be extended easily to problems involving other types of instabilities. It is illustrated here for the case of the Tollmien–Schlichting wave generation in a Blasius boundary layer, due to the interaction of a free-stream acoustic wave with a region of short-scale variation in one of the surface boundary conditions. The type of surface disturbances examined include regions of short-scale variations in wall suction, wall admittance, and wall geometry (roughness). Results from the finite Reynolds-number approach are compared in detail with previous asymptotic predictions, as well as the available experimental data.