Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

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英文篇名：Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability 作者：ZhiGang ; Zhai ; Fu ; Zhang ; ZhangBo ; Zhou ; JuChun ; Ding ; Chih-Yung ; Wen 英文作者：ZhiGang Zhai;Fu Zhang;ZhangBo Zhou;JuChun Ding;Chih-Yung Wen;Department of Modern Mechanics, University of Science and Technology of China;Beijing Institute of Space Long March Vehicle;Department of Mechanical Engineering, The Hong Kong Polytechnic University; 英文关键词：converging shock wave;;Rayleigh-Taylor effect;;Richtmyer-Meshkov instability 中文刊名：Science China(Physics,Mechanics & Astronomy) 英文刊名：中国科学:物理学 力学 天文学(英文版) 机构：Department of Modern Mechanics, University of Science and Technology of China;Beijing Institute of Space Long March Vehicle;Department of Mechanical Engineering, The Hong Kong Polytechnic University; 出版日期：2019-12-01 出版单位：Science China(Physics,Mechanics & Astronomy) 年：2019 期：12 基金：supported by the National Natural Science Foundation of China(Grant Nos.11772329,11802304,and U1530103);; the Science Challenge Project(Grant No.TZ2016001);; the Research Grants Council,Hong Kong(Grant No.152151/16E) 语种：英文; 页：72-81 页数：10 CN：11-5849/N ISSN：1674-7348 分类号：TL334

摘要

Evolution of a two-dimensional air/SF_6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a_0), the azimuthal mode number(k_0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k_0, a_0), a critical a_0 for the RTPI occurrence is solved for each k_0, and there exists a threshold value of k_0 below which the RTPI will not occur no matter what a_0 is. There exists a special k_0 corresponding to the largest critical a_0, and the reduction rule of critical a_0 with k_0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a_0 which should be less than a critical value, a large k_0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k_0 and on the maximum critical a_0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.
        Evolution of a two-dimensional air/SF_6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a_0), the azimuthal mode number(k_0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k_0, a_0), a critical a_0 for the RTPI occurrence is solved for each k_0, and there exists a threshold value of k_0 below which the RTPI will not occur no matter what a_0 is. There exists a special k_0 corresponding to the largest critical a_0, and the reduction rule of critical a_0 with k_0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a_0 which should be less than a critical value, a large k_0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k_0 and on the maximum critical a_0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.

引文

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