Mechanisms and control of sharp-edged roughness-induced transition in a supersonic boundary layer

Abstract

Abstract

Active control of transition induced by an isolated sharp-edged roughness element in a supersonic boundary layer is investigated via direct numerical simulation and biglobal stability analysis. The blowing/suction strips and distributed blowing/suction configurations are employed for transition control, respectively. A parametric study of control amplitudes for the blowing/suction strip reveals that multiple distinct mechanisms govern the control efficacy. Specifically, small-amplitude blowing suppresses sharp-edged roughness-induced transition, while large-amplitude blowing promotes it. Analysis via the flow-freezing technique discloses an intrinsic competition mechanism: the blowing strip suppresses the wake mode while simultaneously inducing very-low-frequency unsteadiness related to the horseshoe vortices on both sides of the roughness. Conversely, suction strip control exhibits the opposite behaviour: low amplitudes sharply promote transition, while high amplitudes effectively delay it. Dynamic mode decomposition indicates that the small-amplitude suction strip will excite an ultra-low-frequency unstable mode, and the transition is driven by non-modal growth rather than the wake mode. To mitigate the limitations of strip-based control, we propose three distributed blowing/suction configurations that can significantly reduce the growth rates of both sinuous and varicose modes, thereby delaying the transition more effectively. To investigate the underlying control mechanisms, the linearised vorticity transport equation is derived. This framework enables quantitative analysis of sinuous and varicose mode growth mechanisms from a vortex dynamics perspective, elucidating the growth-promoting interactions among different vorticity components within wake modes and accounting for their enhanced growth rates relative to the Tollmien–Schlichting waves. Based on perturbed vorticity transport equations, it is revealed that the key mode stabilisation mechanism is mainly associated with marked suppression of the tilting terms for wall-normal perturbation vorticity and the production term for the spanwise perturbation vorticity for strip control. However, the proposed distributed blowing/suction configurations not only suppress the spanwise perturbation vorticity generation but also totally inhibit the wall-normal perturbation vorticity production term, leading to effective transition delay.