偏心对汇聚激波诱导的RM不稳定性影响的数值研究

Numerical Investigation on Eccentricity Effect in Richtmyer-Meshkov Instability Induced by Converging Shock Wave

数值研究汇聚激波与四种形状(圆形、小振幅单模、大振幅单模和正方形)的二维气柱界面相互作用,激波汇聚中心与界面同心和不同心(即偏心)时Richtmyer-Meshkov(RM)不稳定性的发展规律,重点考察界面中心的压力及混合区面积在两种情况下随时间的变化.数值方法使用VAS2D程序,该方法采用有限体积法结合网格自适应技术,能够达到时间和空间的二阶精度.结果表明,偏心情况下RM不稳定性是其在同心情况下的扰动和偏心小扰动叠加的结果.在本文采用的偏心程度下(20%),偏心对于圆形无扰动界面发展的影响主要表现在后期界面出现微小扰动结构;而对于单模和正方形这种原本有扰动的界面,偏心使扰动结构呈现不对称及扭曲,同时也影响了界面中心压力和混合区面积,因而加剧了不稳定性的发展.

Development of Richtmyer-Meshkov instability induced by a converging shock wave and its reflected shock from converging center is numerically investigated in which emphasis is on eccentricity effect. VAS2D uses finite volume method which has a second- order precision in both temporal and spatial scales. Four types of 2-dimensional SF6 column （circle, small-amplitude single-mode, large-amplitude single mode and square） surrounded by air are adopted. Interface morphologies show that development of RM instability in eccentric case results from perturbation growth in concentric case combined with little perturbation growth caused by eccentricity. For interface without initial perturbation, eccentricity results in appearance of tiny perturbation structures. For interfaces with initial perturbation, eccentricity makes perturbation structures asymmetric and distorted. Meanwhile, eccentricity affects pressure of interface center and area of mixed zone, which are closely related to development of RM instability.