Effect of humps and indentations on boundary-layer transition of compressible flows using the AHLNS methodology

Abstract

The presence of surface irregularities like humps or indentations can cause regions of localized strong streamwise gradients in the basic flow quantities. These large gradients can significantly modify the linear mechanisms that lead to laminar-turbulent transition in wall-bounded flows (e.g. Tollmien-Schlichting waves). Standard methodolo- gies like LST (Local Stability Theory) or PSE (Parabolized Stability Equations) can be applied in regions far from the surface irregularities where the streamwise variations are small. However, their formulations are not suited for handling the presence of such large streamwise gradients. The Adaptive Harmonic Linearized Navier-Stokes (AHLNS) equations can handle these large streamwise gradients by using a fully-elliptic system of equations as in DNS (Direct Numerical Simulation). Moreover, as in PSE a wave-like character of the instabilities is assumed, leading to a significant reduction in the number of streamwise grid points required compared with DNS computations. In the present study, smooth humps/indentations with height/depth comparable with the local boundary-layer displacement thickness are investigated. The effect of the hump/indentation on the spatial evolution of convective instabilities, in terms of N-factors, is presented. It is shown that the shape of the surface irregularity plays an important role in the growth of convective instabilities.