Flow Stability around Forward Facing Steps in Unswept Incompressible Boundary Layers

Abstract

The location of laminar to turbulent transition is an important consideration as turbulent flow is associated with higher skin friction drag and, by extension, lower fuel economy. In unswept boundary layers, natural transition proceeds by the amplification of Tollmien–Schlichting waves. Tollmien–Schlichting waves are convective instabilities with spanwise oriented vorticity. The amplification of these instabilities/perturbations is sensitive to roughness elements, such as forward-facing steps. These surface imperfections are inevitable as steps, gaps, and humps are a byproduct of mismatch between panels of a wing. However, their interaction with Tollmien–Schlichting waves is not very well understood. Direct numerical simulation of the flow field around forward facing steps has been performed in this thesis to gain an in-depth understanding of the particular flow features that stabilise or destabilise the incoming Tollmien–Schlichting wave, with respect to a flat plate zero pressure gradient flow. The forward facing step is found to significantly distort the base flow, its effect scaling with the roughness Reynolds number in the upstream regime. This distortion of the base flow is observed to amplify the incoming instability, both upstream and far downstream. At the step location, however, stabilisation or destabilisation can be observed, depending upon the height of the step. The step causes the incoming Tollmien–Schlichting wave to split into two, just upstream of the step, and leads to two counter-rotating structures at the step location. The interaction of these structures influences downstream growth. Localised stabilisation is observed, at the step location, for step heights that are smaller than the boundary layer displacement thickness. Destabilisation is observed for larger step heights. The upstream base flow distortion is due to an adverse pressure gradient imposed by the forward facing step. The magnitude of the pressure gradient is found to scale with the roughness Reynolds number. The upstream amplification is due to the Tollmien–Schlichting wave encountering the distorted base flow. The response of the Tollmien–Schlichting wave to the distorted base flow is observed to scale with its wavelength. The ratio of the roughness Reynolds number to the wavelength ($\gls{Rehh}/\lambda$) is found to be the governing parameter for the upstream interaction of the step with the instability.