Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M=2.25

Abstract

The interaction of a spatially developing adiabatic boundary layer flow at M∞=2.25 and Reθ=3725 with an impinging oblique shock wave (β=33.2°) is analyzed by means of direct numerical simulation of the compressible Navier-Stokes equations. Under the selected flow conditions the incoming boundary layer undergoes mild separation due to the adverse pressure gradient. Coherent structures are shed near the average separation point and the flow field exhibits large-scale low-frequency unsteadiness. The formation of the mixing layer is primarily responsible for the amplification of turbulence, which relaxes to an equilibrium state past the interaction. Complete equilibrium is attained in the inner part of the boundary layer, while in the outer region the relaxation process is incomplete. Far from the interaction zone, turbulence exhibits a universal behavior and it shows similarities with the incompressible case. The interaction of the coherent structures with the incident shock produces acoustic waves that propagate upstream, thus inducing an oscillatory motion of the separation bubble and a subsequent flapping motion of the reflected shock. The simulation indicates the occurrence of low-frequency tones in the interaction zone associated with peaks in the pressure spectra at discrete frequencies. We propose that such large-scale low-frequency unsteadiness is due to a resonance mechanism that establishes in the interaction region, and which has close similarities with those responsible for the generation of tones in cavity flows and screeching jets. In order to support our claim, we develop a simplified model for the acoustic resonance that is capable to predict the characteristic frequencies of the tones.