Hypersonic boundary layer transition on a concave wall induced by low-frequency blowing and suction

Abstract

Hypersonic boundary layer transitions caused by unsteady blowing and suction are investigated with linear stability analyses and direct numerical simulations (DNS). Three blowing–suction frequencies, i.e., 15, 30, and 45 kHz, are separately utilized to excite a pair of unsteady Görtler instability waves (the first two cases) or first-mode instability waves (the last case). These two primary instabilities, respectively, induce diamond-shaped and Λ-shaped structures through self-interactions. These structures are highly susceptible to high-frequency secondary instabilities, as is demonstrated by global Floquet analyses that take into account both temporal unsteadiness and spanwise spatial variations of the base flow. The secondary instability manifests as hairpin packets riding on the downstream end of the diamond-shaped structures or reside in the outward sides of the two legs of the Λ-shaped structures. The theoretical results quantitatively agree with the DNS results. Energy analyses further reveal that the wall-normal productions dominate the energy transfer for the secondary instability of the unsteady Görtler vortices, while the spanwise productions are crucial to the secondary instabilities in the first-mode oblique breakdown. Quasi-steady analyses based on the “frozen” base flow are also performed, whose results compare favorably with those from Floquet analyses in the lowest-frequency case.