On the Impact of Forward-Facing Steps on Disturbance Amplification in Boundary-Layer Flows

Abstract

Using our DNS code NS3D boundary-layer flows over smooth walls and walls containing a forward-facing step have been simulated using a so-called disturbance formulation, i.e., by first computing a steady two-dimensional base flow and then an unsteady disturbance flow. The influence of step height and free-stream Mach number on streamwise pressure gradient and the occurrence or absence of laminar separation bubbles are shown for some base flows. A fundamental difference between subsonic and a supersonic flow over the same step height is that the flow directly after the step exhibits an adverse pressure gradient with laminar separation in the subsonic case but due to an expansion of the supersonic flow around the corner, a favourable pressure gradient without separation in the supersonic case. The unsteady disturbance flow is initialised by a wave packet in the upstream part of the integration domain that contains all frequencies which become unstable in the considered area. Amplification factors, so called N-factors, are then extracted from the frequency spectra of the disturbance flow for quantification of the impact of step parameters on disturbance amplification. Our results show that the observed differences between different cases are fully due to the local flow properties of the base flow, i.e. streamwise pressure gradient and Mach number. Three-dimensional simulation results for a supersonic case with a large step height where the N-factor approach is no longer applicable are presented towards the end. Self-excited three-dimensional disturbances appear in this case, probably due to a three-dimensional global instability.