Nonlinear Evolution and Breakdown of Azimuthally Compact Crossflow Vortex Pattern over a Yawed Cone

Abstract

Hypersonic boundary-layer flows over a circular cone at moderate angle of incidence can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to the more efficient excitation of stationary crossflow vortices by surface roughness, a possible path to transition in such flows corresponds to rapid amplification of the high-frequency secondary instabilities of finite amplitude stationary crossflow vortices. In the present paper, the previous analyses of crossflow instability over a 7- degree half-angle, yawed circular cone in a Mach 6 free stream have been extended to the nonlinear evolution of azimuthally localized crossflow vortex packets and the amplification characteristics and nonlinear breakdown of high-frequency secondary instabilities associated with those packets. A comparison between plane marching PSE and direct Navier-Stokes simulations (DNS) reveals favorable agreement in regard to mode shapes, most amplified disturbance frequencies, and N-factor evolution. In contrast, the quasi-parallel predictions are found to result in severe underprediction of the N-factors. The direct numerical simulations also indicate that the breakdown of secondary instabilities in a 3D hypersonic boundary layer shares certain common features with the previous computations of crossflow transition over subsonic swept wings.