Hypersonic Boundary Layer Stability Analysis Using Momentum Potential Theory

Abstract

Linear Stability Theory (LST) and the Parabolized Stability Equations (PSE) have provided valuable tools for analysis and prediction of laminar to turbulent transition for plates, sharp cones, and geometries for which parallel-flow or a slowly-varying boundary layer can be assumed. However, these techniques struggle to capture the complex flow-physics present near the tip of blunt-cones. Input-output analysis has been used in conjunction with direct numerical simulation to capture the effects of nose bluntness on downstream stability. Using the results of the input-output analysis we apply momentum potential theory (MPT) to preform fluid-thermodynamic (FT) decomposition, separating disturbances into their vortical, thermal and acoustic components. A reference case of Mach 6 flow over a flat-plate is computed and output responses are compared to the results for Mach 6 flow over a blunt-cone of $7^{o}$ half angle. Perturbation eigenfunctions and structures are examined in the areas of second-mode amplification. For both the flat-plate and blunt-cone the vortical components are the largest, followed by the thermal then acoustic components. Fluid-thermodynamic structures in the second-mode amplification region of blunt-cone show wall-normal stretching above the critical layer. Fluid-thermodynamic decomposition of full-domain input and output results for the blunt-cone geometry are considered. It is found that input sensitivity is highest at the top of the entropy layer and along the boundary layer edge for the fore-half of the cone. Output response in the streamwise direction is highest in the regions between the generalized inflection point (GIP) and the boundary layer edge and dissipates near the surface, whereas wall-normal response extends to the surface and shows a local minimum between the GIP and boundary layer edge. To compliment existing studies on hypersonic boundary layer response to surface roughness/ vibration we look at input sensitivity and output response at the surface. It is found that there is greater sensitivity to wall-normal forcing than streamwise forcing at the surface and among the three FT components in this direction the vortical had the highest relative output amplitude. Finally, total fluctuating enthalpy (TFE) is considered for both the flat-plate and blunt-cone, in both cases the thermal terms provides the strongest source of TFE.