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

高士清; 邹立勇; 唐久棚; 李季; 林健宇

doi:10.11883/bzycj-2023-0458

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

doi: 10.11883/bzycj-2023-0458

高士清^{1, 2,},
邹立勇^{1, 2},
唐久棚¹,
李季³,
林健宇^{1, 2, ,}

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

基金项目: 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）

详细信息

作者简介:
高士清（1998－　），男，硕士，gaoshiqing21@gscaep.ac.cn

通讯作者:
林健宇（1988－　），男，博士，副研究员，linjiany@mail.ustc.edu.cn

中图分类号: O354.5
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-21
- 修回日期: 2024-04-08
- 网络出版日期: 2024-04-09
- 刊出日期: 2024-07-15

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

GAO Shiqing^{1, 2
,},
ZOU Liyong^{1, 2},
TANG Jiupeng¹,
LI Ji³,
LIN Jianyu^{1, 2
, ,}

1.
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China
2.
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China
3.
Aerospace Technology Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China

摘要

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不稳定性 /
- 高马赫数激波 /
- 高温非平衡效应 /
- Zhang-Sohn模型
Abstract: 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 single-mode 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 exhibits a decreased peak amplitude growth rate, weakened fluctuations in the interface growth rate, and a slowed-down growth of interface instability compared to frozen flow. Comparative analysis with multiple theoretical models indicates that the Zhang-Sohn model is more suitable than other models for describing single-mode interface RM instability under high-Mach number shock waves. The study of vorticity reveals two main regions with strong vorticity generation: one near the interface and the other behind the transmitted shock wave, which is notably different from RM instability induced by low-Mach number shock, where vorticity is primarily generated at the interface. Additionally, the investigation into circulation demonstrates that the amplitude of vortices in thermo-chemical non-equilibrium flow is smaller than in frozen flow, aligning with the conclusion that disturbances grow more slowly in thermo-chemical non-equilibrium flow compared to frozen flow. This study contributes valuable insights into the RM instability under high-Mach number shock waves, expanding the understanding within the RM instability research community.
- Richtmyer-Meshkov instability /
- high-Mach number shock wave /
- high-temperature nonequilibrium effect /
- Zhang-Sohn model

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图 1 激波冲击轻/重单模界面初始示意图

Figure 1. Schematic of shock wave impact on a light/heavy single-mode interface

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图 2 正激波后的压力和密度分布

Figure 2. Pressure and density distributions after the normal shock wave

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图 3 不同网格尺度下重/轻界面的振幅增长率

Figure 3. Amplitude growth rates at different grid resolutions for the heavy/light interface

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图 4 轻/重界面时的界面和压力场演化

Figure 4. Evolution of interface and pressure field for the light/heavy interface

Top: FG; middle: TNG; bottom: TCNG.

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图 5 重/轻界面时的界面和压力场演化

Figure 5. Evolution of interface and pressure field for the heavy/light interface

Top: FG; middle: TNG; bottom: TCNG.

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图 6 激波与轻/重和重/轻界面作用界面及波系随时间的变化

Figure 6. Positions of the interfaces and wave systems of the shock wave-light/heavy and -heavy/light interface interaction at different times

The positions of the interface, transmitted and reflected shock waves are indicated in red, black and blue, respectively.

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图 7 轻/重界面振幅的数值模拟结果与理论解的对比

Figure 7. Comparison of the amplitudes of the light/heavy interface between numerical simulation results and theoretical solutions

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图 8 重/轻界面振幅的数值模拟结果与理论解的对比

Figure 8. Comparison of the amplitudes of the heavy/light interface between numerical simulation results and theoretical solutions

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图 9 不同气体模式中轻/重界面振幅及其振幅增长率对比

Figure 9. Comparison of amplitudes and amplitude growth rates of the light/heavy interface among different gas models

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图 10 不同气体模式中重/轻界面振幅及其振幅增长率对比

Figure 10. Comparison of amplitudes and amplitude growth rates of the heavy/light interface among different gas models

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图 11 不同初始扰动尺度下轻/重界面振幅增长对比

Figure 11. Comparison of amplitude growths of the light/heavy interface among different initial disturbance scales

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图 12 不同初始扰动尺度下重/轻界面振幅增长对比

Figure 12. Comparison of amplitude growths of the heavy/light interface among different initial disturbance scales

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图 13 不同激波马赫数时轻/重界面振幅增长对比

Figure 13. Comparison of amplitude growths of the light/heavy interfaces at different Mach numbers of shock waves

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图 14 不同激波马赫数时重/轻界面振幅增长对比

Figure 14. Comparison of amplitude growths of the heavy/light interface at different Mach numbers of shock waves

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图 15 不同时刻冻结流中轻/重界面涡量场和涡量生成项

Figure 15. Vorticity field and generation terms of the light/heavy interface in frozen gas at different times

Top: vorticity field; bottom: vorticity generation term.

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图 16 不同时刻冻结流中重/轻界面涡量场与涡量生成项

Figure 16. Vorticity field and generation terms of the heavy/light interface in frozen gas at different times

Top: vorticity field; bottom: vorticity generation term.

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图 17 冻结流中轻/重和重/轻界面环量的演化

Figure 17. Evolution of circulations of the light/heavy and heavy/light interfaces in frozen gas

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图 18 不同气体模式轻/重和重/轻界面环量演化

Figure 18. Evolution of circulations of the light/heavy and heavy/light interfaces in different gases

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表 1 初始条件

Table 1. Initial conditions

界面类型	气体模式	M_s	a₀/mm	界面类型	气体模式	M_s	a₀/mm
轻/重界面	冻结流	6, 7, 8, 9	0.75, 7.5, 75	重/轻界面	冻结流	8, 9, 10, 11	0.75, 7.5, 75
	热非平衡流				热非平衡流
	热化学非平衡流				热化学非平衡流

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表 2 不同马赫数非平衡距离

Table 2. Non-equilibrium distances at different Mach numbers

界面类型	M_s	L_eq/mm	界面类型	M_s	L_eq/mm
轻/重界面	6	582.5	重/轻界面	8	569.4
	7	129.6		9	133.0
	8	41.4		10	47.5
	9	20.0		11	20.6

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