Energy-Budget Analysis of the Crossflow Instability on a Hypersonic Yawed Cone

The Amplification Factor Transport (AFT) model is run in parallel to computational fluid dynamics codes to judiciously activate turbulence models. The model does this by monitoring single-point surrogates for integral parameters indicative of the growth of the Tollmien-Schlichting instability; it is presently leveraged toward the low-speed regime. The overarching goal of the present work is to extend the applicability of this model by capturing the instability mechanisms pertinent to hypersonic boundary layers. The present study focuses on the Mach 6 yawed-cone geometry for which the stationary crossflow instability mechanism drives the process of transition. The instability mechanism that dominates the transition process in this case is the stationary crossflow instability. To identify which mechanisms play a dominant role in amplifying perturbation energy, a energy-budget analysis is performed based on a parabolized stability equation analysis with EPIC, as applied to a laminar basic state computed with OVERFLOW. By studying the most dominant terms in the budget equations, the surprising discovery is made that the total perturbation energy budget is dictated by terms from the conservation of energy equation instead of those from the crossflow perturbation velocity equation. In tracking the two most dominant contributions: the Reynolds wall-normal heat-flux term and the dissipation related to perturbation-temperature gradients in the wall-normal direction, it is found that their sum yields a reasonable estimate for the location of the neutral point in the streamwise direction across all considered wavenumbers and all considered paths along the azimuth of the cone. Furthermore, they yield very high correlation coefficients when evaluating their streamwise variation with respect to the computed spatial growth rate. It is concluded that an understanding of the behavior of these terms, especially as expressed with respect to integral parameters of the boundary layer, is essential to improve the AFT model.