Abstract Direct numerical simulations of incident shock wave and supersonic turbulent boundary layer interactions near an expansion corner are performed at Mach number M∞ = 2.9 and Reynolds number Re∞ = 5581 to investigate the expansion effect on the characteristic features of this phenomenon. Four expansion angles, i.e. α = 00 (flat-plate), 20, 50 and 100 are considered. The nominal impingement point of the oblique shock wave with a flow deflection angle of 120 is fixed at the onset of the expansion corner, and flow conditions are kept the same for all cases. The numerical results are in good agreement with previous experimental and numerical data. Various flow phenomena, including the flow separation, the post-shock turbulent boundary layer and the flow unsteadiness in the interaction region, have been systematically studied. Analysis of the instantaneous and mean flow fields indicates that the main effect of the expansion corner is to significantly decrease the size and three-dimensionality of the separation bubble. A modified scaling analysis is proposed for the expansion effect on the interaction length scale, and a satisfactory result is obtained. Distributions of the mean velocity, the Reynolds shear stress and the turbulent kinetic energy show that the post-shock turbulent boundary layer in the downstream region experiences a faster recovery to the equilibrium state as the expansion angle is increased. The flow unsteadiness is studied using spectral analysis and dynamic mode decomposition, and dynamically relevant modes associated with flow structures originated from the incoming turbulent boundary layer are clearly identified. At large expansion angle (α=100), the unsteadiness of the separated shock is dominated by medium frequencies motions, and no low frequency unsteadiness is observed. The present study confirms that the driving mechanism of the low frequency unsteadiness is strongly related to the separated shock and the detached shear layer.

中文翻译：

---

膨胀角附近的入射激波和超音速湍流边界层相互作用

摘要 在马赫数M∞ = 2.9 和雷诺数Re∞ = 5581 下对膨胀角附近的入射激波和超音速湍流边界层相互作用进行了直接数值模拟，以研究膨胀对这种现象特征的影响。考虑了四个膨胀角，即α=00（平板）、20、50和100。流动偏转角为120°的斜激波的标称冲击点固定在膨胀角的开始处，并且所有情况下的流动条件保持相同。数值结果与先前的实验和数值数据非常吻合。系统研究了各种流动现象，包括流动分离、冲击后湍流边界层和相互作用区域的流动不稳定。对瞬时和平均流场的分析表明，膨胀角的主要作用是显着减小分离气泡的尺寸和三维度。针对相互作用长度尺度上的扩展效应提出了修正尺度分析，取得了满意的结果。平均速度、雷诺剪应力和湍流动能的分布表明，随着膨胀角的增加，下游区域的震后湍流边界层恢复到平衡状态的速度更快。使用谱分析和动态模式分解来研究流动的不稳定，并清楚地识别出与源自传入湍流边界层的流动结构相关的动态相关模式。在大膨胀角（α=100）时，分离激波的不稳定性以中频运动为主，未观察到低频不稳定性。目前的研究证实，低频不稳定的驱动机制与分离的冲击和分离的剪切层密切相关。