Forced response of a laminar shock-induced separation bubble

Abstract

The source of unsteadiness in shock-wave/boundary-layer interactions is currently disputed. This paper considers a two-dimensional separation bubble induced by an oblique shock wave interacting with a laminar boundary layer at a free-stream Mach number of 1.5. The global response of the separated region to white noise forcing is analyzed for different interaction strengths, which generate small and large separation bubbles. Forcing location and amplitude effects have been examined. For both interaction strengths and for forcing both upstream and inside the bubble, the wall-pressure spectra downstream of the separation show a high-frequency peak that is demonstrated to be a Kelvin-Helmholtz instability. A low-frequency response at the separation point is also found when the separation bubble is only forced internally, therefore with a disturbance-free upstream boundary layer. For low-amplitude internal forcing, the low-frequency response at the separation point and downstream of the bubble is linear. However, when forced upstream the low-frequency unsteadiness of the large separation bubble is found to be driven by nonlinearities coming from the downstream shedding. The same nonlinear behavior is found when the separation bubble is internally forced over a narrowband around the shedding frequency, without low-frequency disturbances. This analysis for a laminar interaction is used to interpret the low-frequency unsteadiness found at the foot of the shock of turbulent interactions. Here, the low-frequency unsteadiness occurs in the absence of upstream disturbances and a linear relationship is found between the internal forcing and the response near the separation point. When low-frequencies are not present in the forcing they are generated from weak nonlinearities of the shear-layer instability modes.

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ORCID for N.D. Sandham: orcid.org/0000-0002-5107-0944

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