On the governing mechanism of unsteadiness in bow shock-induced three-dimensional separation

Abstract

We investigate the driving mechanism of low-frequency unsteadiness in bow shock-turbulent boundary layer interactions due to protuberances. Wind tunnel experiments are conducted at a freestream Mach number of 2.87 with protuberances of different shapes and sizes. From time-resolved surface pressure measurements and schlieren imaging, the unsteadiness is characterized by low-frequency shock oscillations, with a Strouhal number of $St_{\delta}\sim 0.01$ based on the boundary layer thickness ($\delta$), while the separated region exhibits predominantly mid-frequency pressure oscillations, with $St_{\delta} \sim 0.1$. Mid-span separation length, $L_{sep}$, is identified as a key parameter in determining time and length scales of shock oscillations. Further details of the interaction are examined through compressible adaptive detached eddy simulations for one particular case, viz.,the cubical protuberance of side 15 mm. A detailed modal analysis using proper orthogonal decomposition (POD) is performed with the 3-D data from computations. Flapping of shock-foot about mid-span was apparent, over and above the coherent to-and-fro oscillations, with the dominance of anti-symmetric mode in the POD of wall pressure fluctuations. The motion of the shock foot is initiated near mid-span, while the shock foot at other spanwise locations lags behind. The flap and asymmetries are related to the spanwise extent of reverse flow. From the reconstructed 3-D flow field using low-frequency modes, along with corroborating observations from the two-point correlations, it is inferred that the imbalance and time lag between the mass injected into the separated region at reattachment and the mass leaving spanwise at the horseshoe vortex core govern the observed shock motion.