Spectral Proper Orthogonal Decomposition of Unsteady High Speed Flows over Compression Expansion Corners

High speed flows over several compression-expansion ramp configurations with high angles that create large separation regions have been studied with direct simulation Monte Carlo (DSMC). These large separation regions enable the detailed investigation of mean flow parameters such as scaled angle of the triple deck theory or recirculation strength when the flow reached the maximum separation size, i.e. when the whole flow region is separated up until the expansion corner. It is shown that the stability of the single recirculation in the separation region, that is characterized by the appearance of the secondary recirculation and unsteadiness in two dimensional simulations, is more sensitive to the wall temperature and the free stream velocity than the physical ramp angle. In addition, the flows are observed to be unsteady for the configurations when the secondary recirculation regions are present in the flow. Spectral proper orthogonal decomposition analysis reveals that low frequency unsteadiness is present in these configurations and confirms the power spectral density analysis from the DSMC probe data. Mode shapes of the discrete frequencies with highest mode energies shows that unsteadiness originates mainly from the reattachment shock and reattachment location, with some contribution from secondary separation for configurations with low wall temperature. Travelling waves resembling Kelvin-Helmholtz instabilities are also observed in the mode shapes within the shear layer.