Numerical studies on the influence of step-like surface irregularities on the development of Tollmien-Schlichting waves

Abstract

The recently developed adaptive harmonic linearized Navier-Stokes (AHLNS) equations offer an efficient approach for the study of the spatial evolution of Tollmien-Schlichting (TS) waves in flows where a surface irregularity is present. This new methodology combines some of the concepts involved in the parabolized stability equations (PSE) and direct numerical simulation (DNS) methods. On the one hand, the “wave-like” character of the TS wave is kept (like in PSE), leading to a significant reduction in the number of streamwise grid points required compared with DNS computations. On the other hand, the fully elliptic nature of the AHLNS equations (like DNS) allows to study the possible upstream influence of the large streamwise flow gradients introduced by the presence of the steps on the TS waves. Moreover, the use of an arbitrarily fine grid in these regions of strong streamwise flow gradients is also possible. In addition, a coordinate transformation has been implemented which facilitates the application of AHLNS to curved surfaces.