Numerical Studies on the Influence of Step-Like Surface Irregularities on the Development of Tollmien-Schlichting Waves

Abstract

The effect of a single step-like surface irregularity on the spatial development of Tollmien-Schlichting (TS) waves is investigated by the recently developed Adaptive Harmonic Linearized Navier-Stokes (AHLNS) methodology. The steps considered in the present work, forward- and backward-facing steps (FFS & BFS), are varied not only in height but also in shape (rectangular and rounded). This work is motivated by the growing interest in the aeronautical industry on the effect of surface irregularities on the location of laminar-turbulent transition. The main contribution of this paper is to present, for fixed flow conditions, the combined influence of the height and shape of step-like irregularities on the expected transition location. A second motivation of this paper is to demonstrate the AHLNS methodology used in the course of this investigation as a perfectly suited stability analysis tool for performing numerical studies on the effect of surface irregularities on the spatial development of traveling instabilities with a relatively moderate computational effort.