姬隽泽, 李祝飞, 司东现, 等. 轴对称内锥流动中马赫盘的形成与演化[J]. 空气动力学学报, 2022, 40(1): 129−140. doi: 10.7638/kqdlxxb-2021.0360
引用本文: 姬隽泽, 李祝飞, 司东现, 等. 轴对称内锥流动中马赫盘的形成与演化[J]. 空气动力学学报, 2022, 40(1): 129−140. doi: 10.7638/kqdlxxb-2021.0360
JI J Z, LI Z F, SI D X, et al. Formation and evolution of Mach disk in axisymmetric internal conical flow[J]. Acta Aerodynamica Sinica, 2022, 40(1): 129−140. doi: 10.7638/kqdlxxb-2021.0360
Citation: JI J Z, LI Z F, SI D X, et al. Formation and evolution of Mach disk in axisymmetric internal conical flow[J]. Acta Aerodynamica Sinica, 2022, 40(1): 129−140. doi: 10.7638/kqdlxxb-2021.0360

轴对称内锥流动中马赫盘的形成与演化

Formation and evolution of Mach disk in axisymmetric internal conical flow

  • 摘要: 针对轴对称内收缩直锥流场中的马赫反射问题,采用无黏数值模拟结合理论分析,在来流马赫数6及直锥入口半径R恒定的条件下,以模型壁面前缘角度θw和壁面长度w/R为几何参数,研究了内锥形激波汇聚增强过程以及马赫盘下游流动对马赫盘位置的影响。结果表明,壁面前缘角度θw通过改变轴对称内锥形入射激波汇聚增强过程中达到von Neumann强度的位置,限定了马赫盘可能存在的位置范围;马赫盘位置还受其下游流动的影响,在不同的θww/R条件下,马赫盘下游流管内声速喉道的形成机制可以划分为依赖或不依赖壁面尾缘膨胀波两种类型;对于不依赖于壁面尾缘膨胀波的情况,声速喉道形成之前流管内的压力仅与反射激波的波后非均匀压力相匹配,马赫盘的位置不随w/R而变化;对于依赖于壁面尾缘膨胀波的情况,声速喉道形成之前流管还需要匹配壁面尾缘膨胀波引起的压力变化;根据反射激波下游与马赫盘下游流管的压力匹配关系,可以求解马赫盘位置。

     

    Abstract: The Mach reflection in axisymmetric flows, which is compressed by an internal cone, is investigated by using a combination of numerical simulations and theoretical analyses at a free-stream Mach number of 6. The effects of the leading-edge angle and cone length on the convergence behaviour of incident shocks and the flow downstream of Mach disk are examined. The results show that the leading-edge angle determines the point of von Neumann strength of the convergent incident shock, and also the location of the Mach disk. In addition to the shock convergence, the position of Mach disk is influenced by the downstream flow as well. According to whether the sonic throat of the stream tube downstream of the Mach disk is affected by the expansion waves generated from the trailing edge of the wall or not, two types of flow patterns downstream of the Mach disk can be classified depending on the leading-edge angle and the cone length. When the sonic throat is independent of the expansion waves, the pressure upstream of the sonic throat is balanced by the post-shock pressure of the reflected shock, and the position of Mach disk will not shift even if the cone length changes. On the other hand, when the sonic throat depends on the expansion waves, the stream tube upstream of the sonic throat needs to match the change of the pressure resulting from expansion waves. The position of Mach disk can be theoretically predicted based on the matching relations between the flow downstream of reflected shocks and the flow downstream of Mach disk.

     

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