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A numerical study of shock-interface interaction and prediction of the mixing zone growth in inhomogeneous medium

非均匀介质中激波-界面相互作用的数值研究以及混合区增长预测

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Abstract

The growth of mixing zone on an interface induced by Richtmyer-Meshkov (RM) instability occurs frequently in natural phenomena and in engineering applications. Usually, the medium on which the RM instability happens is inhomogeneous, the effect of medium inhomogeneity on the growth of the mixing zone during the RM instability is still not clear. Therefore, it is necessary to investigate the RM instability in inhomogeneous medium. Based on a high-order computational scheme, the interactions of a density interface with an incident shock wave (ISW) in inhomogeneous medium are numerically simulated by solving the compressible Navier-Stokes equations. The effect of the inhomogeneity on the interface evolution after the passage of ISW through the interface is investigated. The results show that the interface morphology develops in a distinctive “spike-spike” structure in inhomogeneous medium. Particularly, the spike structure on the bottom of the interface is due to the reverse induction of RM instability by curved ISW or reflected shock wave. With the increase of inhomogeneity, the growth rate of the mixing zone width on interface increases, and the wave patterns caused by interaction between the shock wave and interface are more complex. Compared with RM instability in homogeneous medium, the inhomogeneous distribution of the density in medium further enhances the baroclinic effect and induces larger vorticity in flow field. Therefore, the interface is stretched much more significantly under the induction of enhanced vorticity in inhomogeneous medium. Based on above analyses, a model for predicting the growth of mixing zone width on the interface after the passage of ISW is proposed, in order to provide a useful method for evaluations of perturbation growth behavior during the RM instability in inhomogeneous medium.

摘要

Richtmyer-Meshkov (RM) 不稳定所诱导的界面混合区增长的现象在自然现象和工程应用中非常常见. 发生RM不稳定现象 的介质通常是非均匀的, 而在RM不稳定过程中介质非均匀性对混合区的增长的影响尚不清楚, 因此, 研究非均匀介质中的RM不稳 定现象是非常必要的. 本文基于高阶精度计算格式, 通过求解二维可压缩Navier-Stokes (NS) 方程, 数值模拟了非均匀介质中密度界 面与入射激波(ISW)的相互作用, 研究了入射激波通过界面后, 介质非均匀性对界面演化的影响. 研究结果表明: 在非均匀介质中, 界面以独特的“钉-钉”结构发展, 界面底部的“钉”结构是弯曲入射激波(CISW)或反射激波(RSW)与界面相互作用后产生的RM不稳 定反向诱导所导致的. 随着非均匀性的增大, 界面混合区宽度的增长速率逐渐增大, 激波与界面相互作用引起的波系结构更为复 杂. 与均匀介质中的RM不稳定过程相比, 介质密度的非均匀分布进一步增**了斜压效应, 导致流场中沉积更大量级的涡量. 因此, 在非均匀介质中, **化的涡量的诱导作用使得界面更大程度被拉伸. 在上述分析的基础上, 本文提出了一个预测入射激波通过界面 后, 界面混合区宽度增长的模型, 这为评估非均匀介质下RM不稳定过程中的扰动增长行为提供了一种有效的方法.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11872213).

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Authors and Affiliations

  1. Key Laboratory of Transient Physics, Nan**g University of Science and Technology, Nan**g, 210094, China

    Yang Wang  (汪洋) & Gang Dong  (董刚)

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  1. Yang Wang  (汪洋)
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  2. Gang Dong  (董刚)
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Contributions

Yang Wang and Gang Dong designed the research. Yang Wang wrote the first draft of the manuscript. Yang Wang carried out the numerical simulation and processed the data. Gang Dong helped organize the manuscript. Yang Wang and Gang Dong revised and edited the final version.

Corresponding author

Correspondence to Gang Dong  (董刚).

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Wang, Y., Dong, G. A numerical study of shock-interface interaction and prediction of the mixing zone growth in inhomogeneous medium. Acta Mech. Sin. 38, 122163 (2022). https://doi.org/10.1007/s10409-022-22163-x

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