Spectral Proper Orthogonal Decomposition Analysis of Shock-Wave/Boundary-Layer Interactions

Abstract

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 and often lead to flow separation and an increased likelihood of scramjet engine unstart. Existing research on SWBLIs has focused primarily on either fully laminar or fully turbulent interaction boundary layers and utilizes frequently employed visualization methods such as planar laser scattering (PLS), particle image velocimetry (PIV), and Schlieren imaging. Despite the breadth of research conducted, a definitive driving mechanism of this unsteadiness is still yet to be determined. Building upon previous work, the current research focuses on analyzing high-speed Schlieren images of cylinder-induced transitional SWBLIs (XSWBLIs) in a Mach 5 wind tunnel using spectral proper orthogonal decomposition (SPOD).The appeal of using SPOD analysis over similar methods is that SPOD produces modes that are coherent in both space and time. Using a set of 5,000 Schlieren images previously collected at the Center for Aeromechanics Research Wind Tunnel Laboratory at The University of Texas at Austin, an SPOD analysis of the interaction structure was conducted for the representative XSWBLI test case. These results serve mainly as a proof of concept for the practicality of SPOD analysis of XSWBLIs but also shed light on the underlying physics of the interaction. Upon studying the resulting SPOD modes it was observed that lower order modes develop coherent physical structures in the form of a leading edge shock, Upstream Influence (UI), inviscid shock, forward lambdashock (λ 1),downstream closure shock (λ 2), and the flow separation beneath the lambda-shock structure. These features become less prominentas frequency and mode number increase. Plots of the modal energies of selected modes as a function of Strouhal number show fluctuations in the modal energies for Mode 1. These fluctuations indicate unsteadiness generated by the XSWBLI. The largest of these fluctuations occurs between St = 0.01-0.03 and further analysis produced promising SPOD results. Optimizing certain parameters within the SPOD algorithm should yield more germane modal structures in future analysis.