Receptivity to Freestream Periodic Vorticity Disturbance on a Flat Plate with an Elliptic Leading Edge

Abstract

The receptivity of the Blasius boundary layer over a semi-infinite flat plate with an elliptic leading edge and of aspect ratio five was investigated using a direct numerical solution of two-dimensional Navier-Stokes equations. The result of the computation where the slip condition is applied to the fluctuating component of velocity at the wall surface is compared with that of an ordinary computation using a nonslip condition. Another numerical experiment is performed where no vorticity fluctuation is supplied from a freestream while prerecorded values of vorticities at the wall in response to the passage of convecting fluctuations are used as the wall vorticity boundary condition. It is shown that vorticity fluctuations in the boundary layer can be classified according to their wavelengths. Waves with longer wavelengths originate from the freestream, whereas waves with shorter wavelengths close to T-S waves originate from the surface of the plate. In another numerical experiment, the slip boundary condition against the fluctuation component of vorticity is applied to the limited area of the wall surface. The aim of the study is to determine the part of the elliptic leading edge or flat plate that induces vorticity fluctuations, thereby resulting in the creation of T-S waves. The numerical results show that the contribution of vorticity fluctuations originating from the juncture is the most crucial, whereas the vorticities supplied in the elliptic leading-edge surface negatively affect the amplitude of vorticity fluctuations inside the boundary layer. And, the stagnation section did not show positive contribution.