High-frequency instabilities along the windward face of a hypersonic yawed circular cone
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abstract
Instability analysis of the three-dimensional boundary layer over a 7 half-angle circular cone at 6 angle of attack, ying at Mach 6, is considered. The yawed straight cone has to-date been analyzed using modal local and non-local theories, respectively based on the solution of the one-dimensional eigenvalue problem and the Parabolized Stability Equations (PSE). Both approaches assume the flow to be homogeneous either in one or two spatial directions. The aim of the present work is to analyze this flow using multidimensional stability analysis techniques, namely the spatial BiGlobal analysis, relaxing the azimuthal homogeneity assumption. Multiple instabilities are known to be simultaneously present in a three-dimensional hypersonic boundary layer from earlier stability predictions, as for example the low-frequency disturbances related to traveling crossow modes or the high- frequency second modes. The multidimensional instability analysis is used to unraveled the high-frequency instability modes occurring on the windward face of the cone, where the main heating happens and therefore it is the most critical for the performance of the modeled high-speed vehicle. Different instability modes are found in the present analysis, namely a two-dimensional second mode peaking on the windward plane and oblique second modes peaking at a certain distance from the windward plane. The instability properties of these instabilities are studied at different axial positions and in a wide range of frequencies. The results are in line with previous numerical and experimental predictions.
