Laminar-Turbulent Transition Over a Flat Plate With Surface Imperfections

Abstract

The present work attempted to explore the fundamental instability mechanisms that govern the laminar-turbulent transition over a flat plate with surface imperfections, to mimick the flow over an engine nacelle-lip, either with uniform freestream velocity or in the presence of pressure gradients. These studies were performed via direct numerical simulations. Geometries considered included backward- and forward-facing steps, and cavities representative of roughness commonly seen in manufacturing; the step-sizes and cavity depth were fairly small compared to the local boundary-layer thickness. The pressure gradients were similar to those encountered on nacelle lips. We considered both two- and three-dimensional configurations; the former highlighted the linear behaviour of Tollmien-Schlichting waves, whereas the latter showed the flow evolution from weak to essential non-linearity. A narrow ribbon, placed upstream of the surface imperfection, generated the perturbations for both configurations; a controlled Klebanoff-type transition was initiated in three-dimensional domain. The perturbations were stabilised and onset of transition was delayed for the a medium-height forward-facing step, whereas in all other cases they were amplified and transition was accelerated. In backward-facing step and cavity cases, the Kelvin–Helmholtz instability was the dominant mechanism that drove the amplification in the separation region. Gortler vortices, typical of centrifugal instability, were not observed within the cavity, although multiple regions were identified where curvature effects could play a role. Although the local instability mechanisms for each surface imperfection differed, the impact was localised; the route to turbulence via the Klebanoff regime remained qualitatively the same independent of stabilising or destabilising effect.