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

TL;DR

This study investigates the linear and nonlinear disturbance evolution on a hypersonic ogive-cylinder, revealing dominant Mack mode instabilities and secondary resonance mechanisms through spectral analysis and wave packet modeling.

Contribution

It provides new insights into the disturbance evolution mechanisms, including the effects of amplitude and location on instability development in hypersonic flow.

Findings

Mack modes are the primary instabilities in the flow.

Nonlinear wave packets exhibit a three-legged pressure signature due to spanwise curvature.

Secondary instabilities involve fundamental resonance, with sub-harmonic and oblique resonances at higher amplitudes.

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.