Three-dimensional instabilities of compressible flow over open cavities: direct solution of the BiGlobal eigenvalue problem

We report progress in our ongoing effort to compute and understand the instabilities of open cavity flows from incompressible to supersonic speeds. We consider three-dimensional instabilities of nominally two dimensional (spanwise homogeneous) cavity flows (BiGlobal instabilities). Experiments, DNS/LES computations, and preliminary instability computations have shown that the modes of oscillation are influenced by complex interactions between the shear layer and the recirculating flow within the cavity. We present here a framework for computation of the two-dimensional eigenvalue problem for the compressible open cavity. We validate the numerical scheme by computing several canonical flows: square duct flow, boundary layers at speeds from incompressible to supersonic, and two-dimensional parallel shear layers. We present preliminary results for the three-dimensional modes of the compressible open cavity flow with length-to-depth ratio of two at a Mach number of 0.325.