Abstract: Direct numerical simulations of impinging shock waves and turbulent boundary layer interactions in an expansion corner for the incident shock of 30° at Mach number 2.9 are performed. The nominal impingement point of incident shock waves at the wall is fixed at the apex of the expansion corner. Four cases for expansion angles of 0°, 2°, 5° and 10° are considered. By changing the expansion angle, this research studies the impact of the expansion effect on the complicated flow phenomena in the interaction region, including the separation bubble, wall pressure fluctuations, the turbulent boundary layer in the expansion region and the fluctuating wall shear stress. Results indicate that the streamwise length and height of the separation region are dramatically decreased when the expansion angle is increased, particularly in the condition of strong expansion effect where the shape of the separation bubble is characterized by double peaks with downstream migration. The power spectrum density of wall pressure fluctuations suggests that the unsteady motion of the separation shock is still dominated by the large-scale low frequency oscillation for the expansion angles of 2° and 5°. When the angle is increased to be 10°, the low-frequency unsteady motion of the separated shock is strongly suppressed and the recovery process of fluctuating wall pressure in the expansion region is obviously accelerated. The quadrant analysis of Reynolds shear stress shows that the contribution and occurrence probability of each quadrant experience a faster recovery as the expansion angle is increased. The Görtler-like vortex structures are dramatically destroyed and more small-scale streamwise vortices are generated in the near-wall region. In addition, the proper orthogonal decomposition analysis of the fluctuating wall shear stress indicates that the influence of the expansion effect is mainly reflected in the sharp decrease of the low-order modes energy and the relative increase of overall contribution of high-order modes.

Key words: shock wave/turbulent boundary layer interaction, expansion corner, proper orthogonal decomposition, wall shear stress fluctuation, separation bubble, direct numerical simulation