Boundary layer receptivity to free‐stream vorticity
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The receptivity to free-stream vorticity of the boundary layer over a flat plate with an elliptic leading edge is investigated numerically by solving the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and streamfunction as dependent variables. A small-amplitude vortical disturbance is introduced at the upstream boundary and the governing equations solved time accurately to evaluate the spatial and temporal growth of the perturbations leading to instability waves [Tollmien-Schlichting (TS) waves] in the boundary layer. The effect of disturbance amplitude, orientation, and the effect of the leading edge and of surface curvature are investigated for the case of spanwise vorticity. Simulations reveal, for the conditions considered, a linear variation in the TS response with forcing amplitude for perturbations of free-stream velocity that are either symmetrical or asymmetrical with respect to the basic-state stagnation streamline. The presence near the leading edge of a large, oscillating component of velocity normal to the airfoil axis for the case of asymmetrical forcing results, for the same strength of input disturbance, in an increase in the TS response aft of the juncture and in the appearance of a superharmonic component of the disturbance motion near the tip of the nose. This superharmonic decays rapidly in the streamwise direction. In all cases considered, the first clear appearance of the TS mode occurs aft of the surface pressure-gradient maximum. Changes to the geometry that increase the maximum in steady surface pressure gradient are found to increase receptivity. © 1994 American Institute of Physics.
author list (cited authors)
Buter, T. A., & Reed, H. L.