Artikel

Receptivity of Three-Dimensional Boundary Layers to Surface Roughness

Abstract

Aircrafts have usually swept wings for the benefit of a reduced static pressure along the leading edge of the wing. The sweep leads to a three-dimensional boundary layer along the wing surface, characterized by a misalignment between the incoming flow and the pressure gradient along the profile, and hence by curved external streamlines. The streamline curvature in conjunction with the no-slip condition on the wing surface causes a force imbalance and thus a cross-chordwise flow within the boundary layer. The resulting cross-flow profile tends to zero towards the wing surface and the boundary-layer edge and gives therefore rise to inflectional instability, the cross-flow (CF) instability. Although many different types of instabilities can occur in a 3D boundary layer, e.g. Tollmien-Schlichting (TS) waves or Görtler vortices, we focus on CF instability waves in this paper, since they dominate the boundary-layer instability scenario for sufficiently large sweep angles.

Here, we deal with two model flow configurations for 3D boundary layers rather than a realistic flow past an aircraft wing: First, the flow over a swept cylinder is studied to model the flow around the leading edge of the wing. Secondly, we investigate a swept flat-plate boundary layer subject to a chordwise pressure gradient - the Falkner-Skan-Cooke boundary layer. This configuration models the flow over the aircraft wing slightly downstream of the leading edge. Both flow configurations are studied by means of Direct Numerical Simulation (DNS). The aim of this work is to investigate the receptivity phase of the boundary-layer instability, taking place upstream of the regions of linear and nonlinear growth of the CF instability wave. Receptivity denotes the process by which disturbances enter the boundary layer and establish the initial conditions for the boundary-layer instability. One can think of many different external disturbances - either in the free stream or on the body surface - e.g. acoustic or vortical free-stream disturbances or surface irregularities as suction holes or bumps. We want to focus on the latter and study the receptivity of three-dimensional boundary layers to surface roughness. Already in the eighties, Goldstein (1985) pointed out that a boundary-layer flow becomes receptive to external disturbances in particular in regions of substantial streamwise mean-flow variations, e.g. around a roughness bump. Roughness receptivity in three-dimensional boundary layers was studied by Ng & Crouch (1999), among others.