Unsteady Dynamics of Shock-Wave Boundary-Layer Interactions

Abstract

Shock-wave/turbulent boundary-layer interactions (SWTBLIs) are characterized by low-frequency unsteadiness, amplified aerothermal loads, and a complex three-dimensional flowfield. Presence of a broad range of length and time-scales associated with compressible turbulence generates additional gasdynamic features that interact with different parts of the flowfield via feedback mechanisms. Determining the physics of such flows is of practical importance as they occur frequently in different components of a supersonic/hypersonic aircraft such as inlets operating in both on- and off-design conditions, exhaust nozzles, and control surfaces. SWTBLIs can cause massive flow separation which may trigger unstart by choking the flow in an inlet. On control surfaces, fatigue loading caused by low-frequency shock unsteadiness, coupled with high skin-friction and heat transfer at the surface, can result in failure of the structure.The objective of this study is twofold. The first aspect involves examining the causes of unsteadiness in SWTBLIs associated with two geometries – a backward facing step flow reattaching on to a ramp, and a highly confined duct flow. Signal processing and statistical techniques are performed on the results obtained from Delayed Detached-Eddy Simulations (DDES) and Implicit Large-Eddy Simulations (ILES). Dynamic Mode Decomposition (DMD) is used as a complement to this analysis, by obtaining a low-dimensional approximation of the flowfield and associating a discrete frequency value to individual modes. In case of the backward facing step, Fourier analysis of wall-pressure data brought out several energy dominant frequency bands such as separation bubble breathing, oscillations of the reattachment shock, shear-layer flapping, and shedding of vortices from the recirculation zone. The spectra of reattachment shock motion suggested a broadband nature of the oscillations, wherein separation bubble breathing affected the low-frequency motion and shear-layer flapping, and vortex shedding correlated well at higher frequencies. A similar exercise was carried out on the highly confined duct flow which featured separation on the floor and sidewalls. In addition to the low-frequency shock motions, the entire interaction exhibited a cohesive back-and-forth in the streamwise direction as well as a left-right motion along the span. Mode reconstruction using DMD was used in this case to recover complex secondary flows induced by the presence of sidewalls.For the final aspect of this study, a flow-control actuator was computationally modeled as a sinusoidally varying body-force function. Effects of high-frequency forcing at F+ =1.6 on the flowfield corresponding to a backward facing step flow reattaching on to a ramp were examined. Conditionally averaged profile of streamwise velocity fluctuations, based on reattachment shock position, was used for the formulation of spatial distribution of the actuator. The forcing did not change the mean and RMS profiles significantly, but affected the unsteadiness of the interaction significantly. The effects of forcing were localized to the recirculation zone and did not affect the evolution of the shear-layer. The acoustic disturbances propagating through the freestream and recirculation zone drove the motion of the reattachment shock, and did not alter the low-frequency dynamics of the interaction.