Leading edge instability and generation of Tollmien-Schlichting waves and wave packets

This thesis is concerned with the effect that boundary layer instabilities have on laminar-turbulent transition over an aircraft wing. The receptivity analysis of the two-dimensional marginal separation flow with respect to suction/blowing is considered. The solution of the linearised perturbation equation is sought in the form of perturbations that are periodic in time. Numerical results are obtained and it is observed that for large enough frequencies Tollmien-Schlicting wave packets begin to form downstream of a source of perturbations. A receptivity analysis of an incompressible steady two-dimensional marginally separated laminar boundary layer with respect to three-dimensional unsteady perturbations is then considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier-Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. Two particular cases are considered, one in which we assume that the solution is periodic in both time $T$ and the spanwise coordinate $Z$, and the second where the solution is periodic in time only. As a result an integro-differential equation is derived and studied numerically by means of a spectral method. The next mathematical formulation is the study of marginal separation theory for a swept wing. In this formulation, an additional equation for the spanwise velocity component $w$ is needed. Upon solving the triple-deck equations, an algebraic Fourier transform equation is obtained and solved numerically. Finally, the last chapter concerns itself with a numerical global stability of the two-dimensional unsteady marginal separation equation.Open Acces