Large-Eddy Simulation of Broadband Unsteadiness in a Shock/Boundary-Layer Interaction

The simulation of low-frequency unsteadiness in shock wave/turbulent boundary-layer interactions constitutes a challenging case insofar as very long time integrations are required to describe these broadband motions at frequencies two orders of magnitude lower than those of the turbulent motions. A relatively low-cost numerical strategy is established in the present study. The use of quasi-spectral centered finite differences in conjunction with high-order selective filtering provides an efficient method for compressible large-eddy simulations based on explicit filtering regularization. This strategy is extended to flows containing discontinuities by switching between the high-order filter used in regular zones and a low-order filter acting selectively near the shock locations. The accuracy of the current strategy is assessed for a developing turbulent supersonic boundary layer. The case of an oblique shock wave impinging on a flat plate is then successfully validated against previous experimental and numerical studies. The numerical strategy is finally applied to a configuration involving important low-frequency unsteadiness. A database covering dozens of low-frequency cycles is established to characterize the broadband nature of the low-frequency dynamics, which can be associated with a breathing motion of the decelerated zone. A particular attention is drawn to the important turbulent activity occurring at medium frequencies. It is shown that it corresponds to vortical structures shed in the developing shear layer. Afrequency-wave number analysis of the wall pressure helps to identify their phase speed.