Linear and Nonlinear Disturbance Evolution on the Frustum of Hypersonic Ogive-Cylinders

Abstract

Aspects of transition mechanisms on a $14^{\circ}$ sharp-nosed ogive-cylinder at Mach~$6$ are elucidated by considering linear and nonlinear disturbance evolution of freestream stochastic and wave packet forcing at different locations downstream of the ogive-cylinder junction. The spectral response of the stochastic forcing displays favorable agreement with experimental observations from AFRL on which the configuration is based. Intermittent wave packets are generated from small-amplitude continuous freestream pressure forcing. Linear wave packet evolution reveals that Mack modes are the dominant primary instabilities, followed by relatively weaker first-mode waves. The non-linear wavepacket displays a three-legged wall pressure perturbation signature, which is traced to spanwise curvature effects, and fundamental resonance is the dominant secondary instability mechanism. At higher amplitudes of excitation, weak signatures of sub-harmonic and oblique resonance phenomena are identified. Downstream placement of the small-amplitude disturbance diminishes receptivity of first-mode waves; however, with high-amplitude forcing, the location of actuation does not significantly vary the disturbance evolution signature or the secondary instability mechanisms.