Direct numerical simulation of separation bubble in shock wave turbulent boundary layer interaction

Characteristics of separation bubbles in the interaction of a supersonic turbulent boundary layer at Mach number 2.25 with an impinging shock wave of 33.2° are investigated by means of Direct Numerical Simulation (DNS). After verifying the reliability of the numerical results, fundamental mechanisms associated with separation bubbles, including unsteadiness, separation micro-clusters geometries features and coherent structures, at three different spanwise locations are quantitatively compared to analyze the influence of the three-dimensionality in the spanwise direction. It is found that the separation bubble is highly three-dimensional, with the streamwise extent significantly larger than the wall-normal height and spanwise width. In the spanwise direction, the bubble height is generally large in the middle and small on both sides, exhibiting a single flat peak behavior. The pre-multiplied power spectrum density of the fluctuating separation bubble area suggests that the separation bubble unsteadiness is characterized by large-scale low-frequency contraction and dilation, which is less affected by the spanwise three-dimensionality. The bubbles on both sides lag slightly behind that in the middle. Conditional analysis based on Empirical Mode Decomposition (EMD) is performed to analyze the influence of the bubble dilation and contraction on geometries features of the separation micro-clusters. The statistical results indicate no essential changes in both motions, where the probability peak of the aspect ratio appears around 0.1, and the area and the normal height of the micro-clusters approximately satisfy the quadratic distribution. In addition, the Proper Orthogonal Decomposition (POD) analysis of the fluctuating streamwise velocity indicates that the unsteady motion of the separation bubble is strongly related to the low-order modes, whereas the contribution from the high-order modes is rather small. With the first ten low-order modes, the low-frequency dilation and contraction process of separation bubbles is accurately reconstructed. © 2022 AAAS Press of Chinese Society of Aeronautics and Astronautics. All rights reserved.