| In this study, the effect of the incidence angle of free strewn acoustic waves on the leading edge boundary layer receptivity of a two dimensional laminar incompressible flow over parabolic bodies is investigated. For this, the full Navier-Stokes equations in parabolic coordinates in streamfunction and vorticity variables were solved numerically. For the receptivity problem a spatial approach is used. With this approach, the free stream flow variables are composed of a uniform flow with a superimposed perturbation fluctuations of small amplitude. Using Normal Mode form and linearization assuming that the perturbations are small, the unsteady governing equations are converted into two systems of equations; the steady nonlinear basic flow equations and the steady linear complex perturbation flow equations.; For the solution of nonlinear basic flow equations, a new numerical technique is developed which provides very accurate solutions. The perturbation equations are solved using a direct linear solver (LINPACK subroutines). In the numerical calculations, the numerical domain extends downstream of Branch II predicted by the linear theory for Blasius flow, for the frequency of the free stream oscillations used in the problem. The numerical codes for the solution of both the basic flow and the perturbation flow equations are first tested extensively to validate the solutions.; In order to determine the receptivity coefficient, KLE, three steps are followed. First the basic flow equations are solved. Second, using the basic flow solution, the perturbation equations are solved. Third, the Stokes wave solution is obtained and subtracted from the perturbation solution. Using this final solution, the receptivity coefficient is extrapolated to the leading edge. The results obtained are compared with the past numerical results of Haddad [17], where they were found to be in excellent quantitative agreement. Quantitative comparisons with the analytical results of Hammerton and Kerschen [20] could not be made because of differences between the semi-infinite geometry used here and the finite geometry used by them. However, we observed excellent qualitative comparisons which indicate that the essential physics were represented by our numerical approach. |
