Nonlocal and Local Instability Analysis of Hypersonic Flows

Summary

A nonlocal, linear instability theory is used to model convective amplification of waves with weakly divergent or curved wave-rays and wave-fronts, propagating in a weakly nonuniform flow. The compressible, nonlocal stability equations, which represent an eighth order system of parabolic differential equations in generalized coordinates, are derived from a consistent scaling method. Amplification rates from spatial DNS and nonlocal instability analysis of unstable first mode disturbances in hypersonic flow past a flat plate are shown to be in excellent agreement. Conical Divergence is shown to be stabilizing on first mode disturbances in nonuniform, nonparallel hypersonic flow past a pointed cone. Convex wall camber is found to have a strongly stabilizing effect, concave wall camber a strongly destabilizing effect on first and second mode disturbances. Due to concave curvature a third mode unstable region develops merged with the second mode.