Assessment of Linear Methods for Analysis of Boundary Layer Instabilities on a Finned Cone at Mach 6

Abstract

Boundary-layer instabilities of a finned cone at Mach = 6, Re = 8.4 x 10⁶ /m, 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 (BAM6QT) at Purdue University. Where possible, a common mean flow 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 (LST), planar Parabolized Stability Equations (planar-PSE), One-Way Navier Stokes (OWNS), forced direct numerical simulation (DNS), and Adaptive Mesh Refinement Wavepacket Tracking (AMR-WPT) are presented. One of the major findings of the work includes identification of a dominant three-dimensional vortex instability occurring at approximately 250 kHz that correlates well with experimental measurements of transition onset. With the exception of LST, 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. OWNS analysis utilizing randomized wavenumber forcing identified possible nonmodal interactions contributing to the development of this vortex instability. Both forced DNS and AMR-WPT analysis demonstrated the utility of these methods in tracking either linear or nonlinear growth of disturbances. Finally, a new implementation of Input/Output (I/O) analysis is discussed and some of the challenges, opportunities, and development needs for all of the stability methods are presented.