Transition scenario and transition control of the flow over a semi-infinite square leading-edge plate

Abstract

In recent investigations of the flow over a square leading-edge flat plate, elliptic instability and transient growth of perturbations are proposed to explain the turbulent transition mechanism of the separating and reattaching flow reported in early experimental visualizations. An original transition scenario as well as a transition control method is presented by a detailed numerical study in this paper. The transient growth of perturbations in the separation bubble induces the primary instability that causes the 2D unsteady flow consisting of Kelvin-Helmholtz (KH) vortices. The pairing instability of the KH vortices induces the subharmonic secondary instability, and then resonance transition occurs. The streamwise Lorentz force as the control input is applied in the recirculation region where the separation bubble generates. The maximum energy amplification magnitude of perturbations takes a linear attenuation with the interaction number; thus, the primary instability is reduced under control. The interaction number represents the strength of the streamwise Lorentz force relative to the inertial force of the fluid. The reduced primary instability is not strong enough to induce the secondary instability, so the flow is globally stable under control. Three-dimensional direct numerical simulation confirms the results of the linear stability analysis. Although the growth rate of the convectively unstable secondary instability is limited by the flow field scale, the feedback loop of the energy transfer promotes the resonance transition. However, as the separation bubble scale is reduced and the feedback loop is broken by the streamwise Lorentz force, the three-dimensional transition is suppressed and a skin-friction drag reduction is achieved.