Direct numerical simulation of impinging shock wave and turbulent boundary layer interaction over a wavy-wall

The interaction of an impinging oblique shock wave with an angle of 30° and a supersonic turbulent boundary layer at Ma_∞=2.9 and Re_θ = 2400 over a wavy-wall is investigated through direct numerical simulation and compared with the interaction on a flat-plate under the same flow conditions. A sinusoidal wave with amplitude to wavelength ratio of 0.26 moves in the streamwise direction and is uniformly distributed across the spanwise direction. The influences of the wavy-wall on the interaction, including the characterization of the flow field, the skin-friction, pressure and the budget of turbulence kinetic energy, are systematically studied. The region of separation grows slightly and decomposes into four bubbles. Local peaks of skin-friction are observed at the rear part of the interaction region. The low-frequency shock motion can be seen in the wall pressure spectra. Analyses of the turbulence kinetic energy budget indicate that both diffusion and transport significantly increase near the crests, balanced by an amplified dissipation in the near-wall region. Proper orthogonal decomposition analyses show that the most energetic structures are associated with the separated shock and the shear layer over the bubbles. Only the bubbles in the first two troughs are dominated by a low-frequency enlargement or shrinkage.