Investigating the Underlying Dynamical Structure of Supersonic Flows Using Effective Model Reduction

The temporal features of a cylinder-generated shock-wave/transitional boundary-layer interaction (XSWBLI) in response to supersonic flow (Mach 2) are investigated using various model reduction techniques. Experimental data are obtained using schlieren imaging at 100 kHz and image analysis is performed using proper orthogonal decomposition (POD). The POD framework is used as a starting point to define a reduced set of data-driven isostable coordinates that characterize the transient behavior of an underlying dynamical system. Observed unsteady behaviors in the shock-wave/boundary-layer interactions are well-represented as an externally forced dynamical system with a pair of complex-conjugate isostable coordinates. Results are validated against well-established reduction methodologies including POD and spectral POD. These results indicate that the isostable reduced coordinate framework can be used to provide an accurate, low-dimensional representation of the dynamical features of supersonic fluid flow, even when the relationships between underlying dynamical model and observed output are not explicitly known.