NUMERICAL STUDY ON THE EVOLUTION OF THREE-DIMENSIONAL CONCAVE CYLINDRICAL INTERFACE ACCELERATED BY REFLECTED SHOCK
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摘要: 激波与气柱相互作用是Richtmyer-Meshkov不稳定性研究的经典案例. 单次激波与二维气柱相互作用已得到广泛关注, 但是反射激波再次冲击气柱 (尤其是三维气柱) 的研究较少, 相关演化规律和机理尚不清楚. 反射激波再次冲击演化中的气柱界面会产生新的斜压涡量, 影响涡量的输运和分布, 从而影响界面的演化. 本文采用自主开发的HOWD (high-order WENO and double-flux methods) 程序, 研究了马赫数为1.29的平面激波冲击N$_{2}$气柱(气柱外为SF$_{6})$的演化过程, 并考察了反射激波对二维和三维凹气柱界面演化的影响规律. 在数值模拟中, 选取了不同的反射距离 (定义为气柱和反射边界的距离), 得到了二维和三维凹气柱在反射激波冲击前后的完整演化图像, 提取了气柱上特征点位置随时间变化的定量数据, 重点分析了不同演化阶段气柱几何特征及斜压涡量分布的变化趋势. 研究表明, 反射距离决定着反射激波作用气柱时的激波形状和气柱形态, 从而影响斜压涡量的生成和分布, 进而改变气柱的不稳定性演化过程. 对于三维气柱, 不同高度截面上的斜压涡量分布不同, 从而诱导出复杂的三维演化结构.
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关键词:
- Richtmyer-Meshkov不稳定性 /
- 反射激波 /
- 气柱 /
- 数值计算
Abstract: The interaction of shock wave with cylindrical interface is fundamental in study of the Richtmyer-Meshkov (RM) instability. Although the RM instability of two-dimensional (2D) cylindrical interfaces under a single shock wave has been extensively studied previously, the interaction of reflected shock (short for reshock) with cylindrical interfaces, especially three-dimensional (3D) cylindrical interfaces has not been investigated thoroughly, with relevant development rules and underlying mechanisms unclear. When the shock wave interacts with the evolving interface after reshock, new baroclinic vorticity appears on the interface and this will have a major influence on the evolution of the interface. In this work, the HOWD (high order WENO and double-flux) solver developed in our group is used to numerically study the reshock effect on the evolution of 2D and 3D concave cylindrical N$_{2}$/SF$_{6}$ (inner/outer phases) interfaces with incident planar shock strength of $Ma=1.29$. This work will focus on the evolution of 2D and 3D concave cylindrical interfaces after the reshock under different reflected distances, which is defined as the distance between the end wall and the center of the gas cylinder. Series of data have been extracted both before and after the reshock, including the schlieren and vorticity images of the evolving gas cylinder and the quantitative data of the geometric position of the feature points on the gas cylinder. The geometrical characteristics of the distorted interface and the generation and distribution of baroclinic vorticity in different stages are analyzed. The results indicate that for different reflected distances, the shapes of the evolving interface and the reshock at the interaction instance affect the generation and distribution of the baroclinic vorticity, resulting in distinct evolution characteristics of the RM instability. For the 3D concave cylindrical interface, the baroclinic vorticity distributed in 3D space at different heights can induce complicated 3D structures of the evolving interface.-
Keywords:
- Richtmyer-Meshkov instability /
- reflected shock /
- gas cylinder /
- numerical simulation
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