On flow unsteadiness in strongly separated high-speed ramp flows using kinetic and data-driven methods

The gas dynamics of high-speed flows over several compression–expansion ramp geometries with large separation regions were investigated using a particle-kinetic approach and data-driven methods. These large separation regions allow study of the role of scaled angle predicted by triple deck theory on recirculation strength, separation size, and appearance of secondary recirculation regions, all of which lead to flow unsteadiness. Examining four different free-stream conditions for the same geometry using the direct simulation Monte Carlo (DSMC) approach, we show that the stability of single recirculation in the separation region is more sensitive to wall temperature and free-stream velocity than physical ramp angle. Stability in this context refers to appearance of secondary separation regions. In addition, configurations with similar types of recirculation regions from literature considered, we find that general trends regarding unsteadiness, such as appearance of secondary recirculation regions, mostly hold; however, the flows are too complex to be characterized by only scaled angle. Thus, stochastic flowfields generated by DSMC were investigated using data-driven methods, namely, spectral proper orthogonal decomposition (SPOD) and dynamic mode decomposition (DMD). We found that both methods yield similar frequency components and mode shapes for spatiotemporal coherent structures of unsteady DSMC flows. With the help of these structures, the main mechanisms of unsteadiness were identified as oscillations of the reattachment shock, Kelvin–Helmholtz-like instability of the shear layer, and c-shaped mode of the separation bubble. This is the first time SPOD has been applied to a DSMC generated flowfield and compared with DMD.