Linear Analysis of Boundary-Layer Instabilities on a Finned Cone at Mach 6

Boundary-layer instabilities for a finned cone at Mach = 6, Re = 8.4 × 10⁶ [m⁻¹ [, and zero incidence angle are examined using linear stability methods of varying fidelity and maturity. The geometry and laminar flow conditions correspond to experiments conducted at the Boeing Air Force Mach 6 Quiet Tunnel at Purdue University. Where possible, a common baseflow is utilized among the stability computations, and comparisons are made along the acreage of the cone where transition is first observed in the experiment. Stability results utilizing linear stability theory, planar parabolized stability equations, one-way Navier–Stokes, forced direct numerical simulation, and adaptive mesh refinement wavepacket tracking are presented. A dominant three-dimensional vortex instability occurring at ≈250 kHz is identified and correlates well with experimental measurements of transition onset. With the exception of linear stability theory, all of the higher-fidelity linear methods considered in this work were consistent in predicting the initial growth and general structure of the vortex instability as it evolved downstream. Some of the challenges, opportunities, and development needs of the stability methods considered are discussed.