Abstract: To reveal the expansion effects on the complicated flow phenomena, direct numerical simulations of impinging shock wave and turbulent boundary layer interaction for the incident shock of 30° at Mach number 2.9 in an expansion corner of 10° are performed. Three cases, corresponding to the impingement point upstream, in the vicinity and downstream of the expansion corner, are systematically studied to investigate the intricate flow mechanisms, including separation bubble, fluctuating wall pressure and unsteady motion of shock wave, statistical characteristics of turbulent boundary layer, and dynamical processes of coherent structure. The results indicate that the variations of impingement point have significant influence on the streamwise and wall-normal scales of separation bubble, especially when the shock wave is located at the corner or in its downstream region. It is found that the intensities of fluctuating wall pressure are dramatically reduced in the expansion region, and the downstream-propagating speed of wall pressure waves is significantly reduced in the separation region and relatively accelerated in the expansion region. The low-frequency unsteady oscillations of separated shock waves are dramatically suppressed by the expansion effects. Compared with the inter-actions between oblique shock-wave and turbulent boundary layer of flat-plate, the logarithmic and wake regions of the mean velocity profile in the reattachment boundary layer are evidently changed by the variations of impingement point. The structure parameter for the Reynolds stress is increased in the inner region and decreased in the outer layer. The anisotropy invariant maps suggest that the turbulence in the near wall region gradually deviates from the one-component state. Furthermore, the proper orthogonal decomposition analysis of the fluctuating streamwise velocity indicates that the dominant mode is associated with the separated shock and the foot of separated shear layer, whereas the high-order mode is characterized by the small-scale sign-alternating fluctuation structures. The obtained low-order reconstruction illustrates that the dominant mode is corresponding to the dilation and contraction of separation bubble, but the high-order mode is associated with the high frequency ossification of separation bubble.

Key words: shock wave/turbulent boundary layer interaction, expansion corner, proper orthogonal decomposition, direct numerical simulation, supersonic