Hypersonic Boundary-Layer Receptivity over Circular Cones with Ellipsoidal/Spherical Noses

Abstract

The hypersonic boundary-layer receptivity to planar and axisymmetric freestream slow acoustic waves is investigated for a Mach 6 flow over a 5 deg half-angle circular cone with three different ellipsoidal/spherical noses. To fully characterize the boundary-layer response, a wide frequency range of the first and second instability modes is considered. The results show that the receptivity mechanisms for both instability modes are similar to those for a previously investigated sphere-nosed cone. Furthermore, the variation of the receptivity coefficient with the frequency is obtained. For the second mode, the nose effect on the receptivity coefficient is dependent on the forcing frequency; whereas for the first mode, the receptivity coefficient monotonously decreases with increasing bluntness. An empirical similarity parameter is identified to collapse the receptivity coefficient of the first mode for the cones investigated. Considering that the receptivity coefficient of the first mode is nearly two orders of magnitude higher than that of the second mode, the traditional method, which ignores receptivity, may underestimate the role of the first mode in causing transition.