Modal Analysis of Cylinder-Induced Transitional Shock-Wave/Boundary-Layer Interaction Unsteadiness

Shock-wave/boundary-layer interactions (SWBLIs) are critical phenomena in the design of high-speed vehicles as they exhibit inherent unsteadiness that can damage airframes and lead to engine unstart. This paper presents a novel characterization of the unsteady dynamics of cylinder-induced SWBLIs at Reynolds numbers of 26x106 m-1 and 13x106 m-1 using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). Data sets analyzed in this paper were obtained from experiments conducted in the NASA Langley Research Center's 20-Inch Mach 6 blowdown wind tunnel. The experiments used a cylinder protuberance model mounted on a 10 & DEG; half-angle wedge to create the interaction. The lower-Reynolds-number case was observed to have a transitional incoming boundary layer, whereas a swept ramp array trip was used in the higher-Reynolds-number case to generate a turbulent incoming boundary layer. The POD analysis from both cases helped isolate spatial regions in the separation bubble that contained the highest percentage of energy for each case, which correlate to the dominant structures in the flow. A power spectral density analysis on the POD temporal components of the highest-energy POD mode (mode 1) revealed a frequency spectrum with a distinct peak at St & SIM;0.05 in the lower-Reynolds-number case and a band of high-energy peaks in the St range of 0.05-0.2 for the tripped SWBLI case. Through the DMD analysis, an unsteadiness mode was isolated at St=0.057 and an asymmetric motion of the forward lambda shock was identified in the lower-Reynolds-number case. This dynamic asymmetry was not detected in the higher-Reynolds-number case, suggesting that the asymmetric effect may be unique to interactions in transitional incoming boundary layers. Additional spectral-kernel-based POD analysis identified primary unsteadiness frequencies that were in agreement with the DMD findings. A low-frequency mode at St=0.055, exhibiting relatively high energy, was obtained for the lower-Reynolds-number (transitional) case, whereas a broadband "bump " with increased energy over a frequency range of St & SIM;0.05-0.2 was observed for the higher-Reynolds-number (tripped) case. Through these analysis techniques, a mode, likely connected to a shock-breathing mechanism, was identified at St & SIM;0.05. In the assessment of the structural motion occurring in the shock-breathing mode, the phenomenon in the lower-Reynolds-number case was found to traverse a longer upstream distance and compress to a larger degree when compared with the breathing behavior in the higher-Reynolds-number case.