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 $26 \times 10^{6} m^{- 1}$ and $13 \times 10^{6} m^{- 1}$ 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° 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 $S t \sim 0.05$ in the lower-Reynolds-number case and a band of high-energy peaks in the $S t$ range of 0.05–0.2 for the tripped SWBLI case. Through the DMD analysis, an unsteadiness mode was isolated at $S t = 0.057$ 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 $S t = 0.055$ , 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 $S t \sim 0.05 - 0.2$ 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 $S t \sim 0.05$ . 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.

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This material is based upon research supported by the U. S. Office of Naval Research under award number N00014-15-1-2269 and by the Air Force Office of Scientific Research under award number FA9550-20-1-0190. Additional support was also provided by NASA grant 80NSSC19M0194. The authors would like to thank Mark Kulick at NASA Langley Research Center for his assistance with model fabrication and Wayne Page, Kevin Hollingsworth, Sheila Wright, Johnny Ellis, Grace Gleason, Scott Berry, and Matt Rhode at NASA Langley Research Center for their assistance with test setup, execution, and support. Charles Tinney also provided assistance with the development of a preliminary snapshot proper orthogonal decomposition code that was the basis of the proper orthogonal decomposition script written for the current analysis. Support for wind tunnel testing at the NASA Langley Research Center was provided by the Hypersonic Technology Project, Transformational Tools and Technologies project, and the Aeronautics Evaluation and Test Capabilities project.

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Received5 May 2021
Accepted27 November 2021
Published online4 January 2022

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

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