Effect of roughness elements on receptivity of hypersonic blunt cone boundary layers

Roughness-element-induced transition influences various aspects including aerodynamic heating, surface frictional drag, intake flow control, engine combustion efficiency, and overall operational performance. Receptivity, as the precursor to natural transition, plays a pivotal role here. This study uses direct numerical simulations (DNS) coupled with linear stability theory (LST) to investigate boundary-layer receptivity to a single-frequency slow acoustic wave in a Mach 6 flow over a blunt cone. The effects of various heights and positions of a roughness element are systematically investigated. It is revealed that receptivity modulation is affected by the existence of reflected waves resulting from the interaction of shock waves with compression and expansion waves downstream of the roughness element. Specifically, receptivity is attenuated by reflected waves from expansion waves and augmented by those from compression waves. The receptivity is slightly strengthened, then weakened, and subsequently strengthened as the roughness element moves away from the nose stagnation point. The receptivity is strengthened as the roughness element increases in height. Finally, a receptivity coefficient is established to enable the effects of receptivity to be considered in transition prediction methods and thereby improve their accuracy.