Effects of surface imperfections on the transitional boundary layer

Abstract

The present work explores the effects of surface imperfections on the transition to turbulence of an incompressible boundary layer over a flat-plate. The analysis focuses on flow mean-dynamics. Visualization of instantaneous coherent structures provides insight into the flow evolution. Geometries considered include forward-facing steps and a step-cavity, representative of roughness commonly seen in manufacturing; the step-sizes and cavity depth are a small fraction of the local boundary layer thickness. A series of well-resolved direct numerical simulations are performed. A controlled Klebanoff-type transition is initiated via a narrow vibrating ribbon placed upstream of the surface imperfection. To distinguish the impact of the forward-facing step and the effect of the cavity, data from a flat-plate and medium-height backward-facing step cases from a previous study [M. Teng and U. Piomelli, “Instability and transition of a boundary layer over a backward-facing step,” Fluids 7, 35 (2022).] is employed as a reference for comparison. The perturbations are found to be locally stabilized, and transition inception is delayed for the medium-height forward-facing step, whereas in all other cases, increased growth-rates promote the onset of transition. The evolution of flow structures in the step-cavity case resembles that of the medium-height backward-facing step: the Kelvin–Helmholtz instability is a predominant mechanism that drives the amplification in the separation region. The phenomenon of stabilization and destabilization is explained from the perspective of energy budget analysis. Although the active instability mechanisms for each surface imperfection are locally influential, the route to turbulence via the Klebanoff regime remains qualitatively the same, independent of stabilizing or destabilizing effect.