Numerical Study of Boundary Layer Receptivity to Free-stream Disturbances and Surface Excrescences

Abstract

Numerous studies conducted over the years have shown that the transition onset in boundary layer flows is strongly dependent on the receptivity to various environmental disturbances. The objective of this paper is to study the mechanism by which free-stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat-plate featuring a small excrescence located at a certain distance from a blunt leading edge. The numerical tool is a high-fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier-Stokes equations in a body-fitted curvilinear coordinates, and employing high accurate compact differencing schemes with Pade type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free-stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien-Schlichting waves than the vorticity disturbance. The latter generates TS waves that are grouped in wave packets with the length consistent with the wavelength of the free-stream disturbance.