高马赫数激波作用下单模界面的Richtmyer-Meshkov不稳定性数值模拟  

Numerical simulation of single-mode Richtmyer-Meshkov instability caused by high-Mach number shock wave

作　　者：高士清 邹立勇[1,2] 唐久棚 李季 林健宇 GAO Shiqing;ZOU Liyong;TANG Jiupeng;LI Ji;LIN Jianyu(Institute of Fluid Physics,China Academy of Engineering Physics,Mianyang 621999,Sichuan,China;National Key Laboratory of Shock Wave and Detonation Physics,Institute of Fluid Physics,China Academy of Engineering Physics,Mianyang 621999,Sichuan,China;Aerospace Technology Institute,China Aerodynamics Research and Development Center,Mianyang 621000,Sichuan,China)

机构地区：[1]中国工程物理研究院流体物理研究所,四川绵阳621999 [2]中国工程物理研究院流体物理研究所冲击波物理与爆轰物理全国重点实验室,四川绵阳621999 [3]中国空气动力研究与发展中心空天技术研究所,四川绵阳621000

出　　处：《爆炸与冲击》2024年第7期36-56,共21页Explosion and Shock Waves

基　　金：国家自然科学基金重大研究计划培育项目(92052108,12202419);冲击波物理与爆轰物理全国重点实验室稳定支持项目(JCKYS2022212006,JCKYS2023212003)。

摘　　要：为了研究高马赫数激波冲击下的单模界面Richtmyer-Meshkov(RM)不稳定性,特别是高马赫数激波带来的热化学非平衡效应的影响,采用基于有限体积方法的二维高温非平衡流动程序,利用自适应非结构网格模拟了空气中高马赫数激波冲击两侧温度不同的单模界面导致的RM不稳定现象。研究中涵盖了轻/重界面和重/轻界面2种情况,涉及的激波马赫数范围分别为6~9和8~11。对比了冻结流、热非平衡流和热化学非平衡流3种气体模式下的流场演化过程,揭示了扰动增长和增长率的变化规律。通过对比扰动增长的线性理论和非线性理论,分析了初始激波马赫数和初始扰动尺度的变化对RM不稳定性的影响,同时讨论了涡量场分布和环量的演化规律。结果表明,与冻结流相比,热化学非平衡流中透射激波、反射波及界面速度明显不同,扰动振幅增长率峰值降低,界面增长率脉动减弱,界面不稳定性增长速度变慢。通过对比多种理论模型和本文的数值模拟结果,发现Zhang-Sohn模型相对于其他模型更适用于高马赫数激波作用下的单模界面RM不稳定性问题。对涡量场的研究发现,有2个较强的涡量生成区域,一个位于界面上,另一个位于透射激波波后,这同低马赫数下涡量主要在界面上生成的结论显著不同。此外,热化学非平衡流中环量的幅值大小低于冻结流中的结果,这与热化学非平衡流中扰动的增长低于冻结流的结论对应。Richtmyer-Meshkov(RM)instabilities are observed in various fields,including inertial confinement fusion,supernova explosions,and supersonic combustion engines.While considerable research has been conducted on the singlemode RM instability induced by low-Mach number shock waves,there is a notable gap in studies on the RM instability of a single-mode interface under high-Mach number shock waves.Additionally,the influence of thermo-chemical non-equilibrium effects resulting from high-Mach number shock waves remains unknown.In this study,a two-dimensional code for high-temperature non-equilibrium gas based on the finite volume method with unstructured adaptive grids was employed to simulate the single-mode RM instability caused by high-Mach number shock waves in air.In the numerical solution process,a splitting method was employed to separately solve the convective and source terms.The convective term was solved using the MUSCL-HANCOCK method for second-order space-time reconstruction and the HLL(Harten-Lax-van Leer)scheme for calculating numerical fluxes.The source term was solved using a single-step implicit time format with A-stability.Two scenarios were considered:light/heavy interface and heavy/light interface,with shock Mach numbers ranging from 6 to 9 and 8 to 11,respectively.The research compared the evolution of flow fields under three gas models:frozen gas,thermal non-equilibrium gas,and thermo-chemical non-equilibrium gas.The disturbance growth and growth rate of each gas model were presented,and the numerical results were compared with linear and nonlinear theories.The influence of the initial shock Mach number and the initial disturbance scale on RM instability was analyzed.Furthermore,the distribution of vorticity fields and the evolution of circulation were discussed.The findings reveal significant differences in thermo-chemical non-equilibrium flow compared to frozen flow,particularly in the transmission and reflection waves,as well as the interface velocity.Thermo-chemical non-equilibrium flow exhibi

关 键 词：RICHTMYER-MESHKOV不稳定性 高马赫数激波 高温非平衡效应 Zhang-Sohn模型 

分 类 号：O354.5[理学—流体力学]