Spectral Proper Orthogonal Decomposition Analysis of Shock-wave/Boundary-layer Interactions

Shock-wave/boundary-layer interactions (SWBLIs) are a major concern in the development of high-speed aircraft. SWBLIs generate low-frequency unsteadiness in many aerodynamic applications which can result in vehicle failure. Building upon previous work, the current research focuses on analyzing high-speed Schlieren images of cylinder-induced SWBLIs in a Mach 5 wind tunnel using spectral proper orthogonal decomposition (SPOD). Using a set of 8,000 Schlieren images an SPOD analysis was conducted. The initial results serve as a proof of concept for the practicality of SPOD analysis of SWBLIs. Lower-order SPOD modes were found to develop coherent physical shock structures, which dissipate as frequency and mode number increase. Plots of modal energy vs. Strouhal number (St) indicate low-frequency shock unsteadiness between St = 0.02 – 0.08. Two-dimensional renderings of Mode 1 at these Strouhal numbers highlight the motion of the primary shock structures while renderings of Mode 2 revealed large-scale turbulence and Mach waves in the separation bubble. This ability to examine unsteady shock motion in conjunction with the physics occurring in the separation bubble may provide vital insights into the underlying driving mechanisms behind SWBLI unsteadiness. An additional study was conducted by adjusting the spectral estimation parameters within the SPOD algorithm. Altering the size of the window the algorithm used to calculate the SPOD modes did not significantly affect the results of the analysis, and again indicated low-frequency shock unsteadiness between St = 0.02 – 0.08. Applying this same parameter study to a supplementary set of Schlieren image data yielded similar results to the previous analyses, indicating shock unsteadiness between St = 0.015 – 0.07 regardless of the parameter change. The consistency of the results seen in the analysis of both the primary and supplementary data sets establish the repeatability of SPOD analysis and confirm it’s suitability for investigating SWBLI unsteadiness mechanisms.