Magnetic field suppression characteristics in interaction process between shock wave and light gas cylinder

Zhang Sheng-Bo; Zhang Huan-Hao; Zhang Jun; Mao Yong-Jian; Chen Zhi-Hua; Shi Qi-Chen; Zheng Chun

doi:10.7498/aps.73.20231916

Abstract

Based on ideal compressible magnetohydrodynamics (MHD) equations, the interface instabilities induced by the interaction between planar shock wave and the light gas (Helium) cylinder under the influence of the magnetic fields with different directions are investigated numerically by using the CTU(corner transport upwind)+CT (constrained transport) algorithm. The numerical results elucidate the evolution of flow field characteristics and wave structures with and without magnetic field. Moreover, we examine the influence of the magnetic field direction on a characteristic scales (including the length, height and width of the central axis of gas cylinder), as well as the volume compressibility. Then, the mechanism of the magnetic field direction affecting the interface instability is studied in depth by integrating the analyses of the circulation, energy, velocity and magnetic force distribution within the flow field. The core of this study, is to explore the suppression mechanism of interface instability by magnetic field force. The results show that the magnetic pressure plays a crucial role in driving vorticity away from the interface, thereby reducing its deposition on the density interface. Simultaneously, it adheres to the divided vortex layer, thereby effectively isolating the influence of Richtmyer-Meshkov instability on the interface. On the other hand, the magnetic tension adheres to the separated vortex layer, and its direction is opposite to that of the vorticity generated by the shear of interface velocity. This action effectively suppresses the Kelvin-Helmholtz instability and the rolling-up of vortices on the density interface. Additionally, under the control of a longitudinal magnetic field, the direction of magnetic tension is opposite to the direction of the central jet, effectively suppressing the development of Rayleigh-Taylor instability.

Keywords:

Authors and contacts

1.
National Key Laboratory of Transient Physics, Nanjing University of Science & Technology, Nanjing 210094, China
2.
Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, China
3.
School of Energy and Power Engineering, Nanjing University of Science & Technology, Nanjing 210094, China

Corresponding author: Zhang Huan-Hao, zhanghuanhao@njsut.edu.cn ; Chen Zhi-Hua, chenzh@njust.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12072162, 12102196, 12072334), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20210322), and the China Postdoctoral Science Foundation (Grant No. 2022M711642).

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References

[1]	Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297 Google Scholar
[2]	Meshkov E E 1969 Fluid Dyn. 4 101
[3]	Kelvin L 1871 Philos. Mag. 42 362 Google Scholar
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Cited By

图 1 (a) 仿真模型; (b) 氦气组分沿y = 0的分布

Figure 1. (a) Simulation model; (b) distribution of helium components along y = 0.

DownLoad: Full-Size Img PowerPoint

图 2 平面激波与He气柱作用过程的计算结果(下)与相关实验结果^[9](上)的对比

Figure 2. Comparison between simulation results of this study (down) and experimental results ^[9] (up) for the interaction between a shock wave and a helium gas cylinder.

DownLoad: Full-Size Img PowerPoint

图 3 无磁场控制下, 激波冲击He气柱过程的阴影图

Figure 3. Shadowgraph images for the interaction of a shock wave with a helium cylinder in HD condition.

DownLoad: Full-Size Img PowerPoint

图 4 流向磁场作用下, 激波冲击He气柱过程的阴影图

Figure 4. Shadowgraph images for interaction of a shock wave with a helium cylinder in the presence of a transverse magnetic field.

DownLoad: Full-Size Img PowerPoint

图 5 纵向磁场作用下, 激波冲击He气柱过程的阴影图

Figure 5. Shadowgraph images for the interaction of a shock wave with a helium cylinder in the presence of a longitudinal magnetic field.

DownLoad: Full-Size Img PowerPoint

图 6 不同磁场方向下的流场涡量分布

Figure 6. Vorticity contour in RMI under various magnetic-field directions.

DownLoad: Full-Size Img PowerPoint

图 7 环量随时间的变化曲线　(a) 正环量Γ₊; (b) 负环量Γ_–; (c) 总环量Γ

Figure 7. History of the circulation: (a) Positive circulation Γ₊; (b) negative circulation Γ_–; (c) total circulation Γ.

DownLoad: Full-Size Img PowerPoint

图 8 激波冲击氦气柱过程中气柱特征尺寸的变化曲线　(a)气柱长度L; (b)气柱高度H; (c)中轴宽度W

Figure 8. The variation curves of characteristic dimensions of helium cylinder during the interaction process with the shock wave: (a) Length of helium cylinder, L; (b) height of helium cylinder, H; (c) axis width of helium cylinder, W.

DownLoad: Full-Size Img PowerPoint

图 9 不同磁场方向下, He气柱体积压缩率V(t)/V(0)变化

Figure 9. Volume compressibility of He cylinder for various magnetic-field directions.

DownLoad: Full-Size Img PowerPoint

图 10 流场能量随时间的变化曲线　(a) 总能E、内能E_p ; (b) 磁能E_b; (c) 横向总动能E_kx; (d) 纵向总动能E_ky

Figure 10. Time history of the flow energy: (a) Total energy E, internal energy E_p; (b) magnetic energy E_b; (c) lateral total kinetic energy E_kx; (d) vertical total kinetic energy E_ky.

DownLoad: Full-Size Img PowerPoint

图 11 内能分布随时间的变化

Figure 11. Distribution of internal energy over time.

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图 12 t = 0.15 ms时, 流场磁场强度与磁能量的分布云图

Figure 12. The distribution of magnetic field strength and magnetic energy in the flow field at t = 0.15 ms.

DownLoad: Full-Size Img PowerPoint

图 13 氦气柱附近速度矢量分布图

Figure 13. Velocity vector distribution near the He cylinder.

DownLoad: Full-Size Img PowerPoint

图 14 涡量层上的磁张力和磁压力分布

Figure 14. Magnetic tension and magnetic pressure distributions on the vorticity layers.

DownLoad: Full-Size Img PowerPoint

图 15 纵向动能分布(upper)和涡量(lower)对照图

Figure 15. Comparison of longitudinal kinetic energy distribution (upper) with vorticity (lower).

DownLoad: Full-Size Img PowerPoint

表 1 气体参数

Table 1. Gas parameters.

Gas Density
ρ/(kg·m^–3) Specific-heat ratio γ Molar mass
M/(g·mol^–1) Speed of sound
c_A/(m·s^–1)

Air 1.176 1.40 28.96 347

He 0.162 1.67 4.00 1021

DownLoad: CSV

表 2 不同工况下的初始条件

Table 2. The initial conditions of different cases.

Case a $\beta^{-1}$ Magnetic field direction

1 0.8 0 —

2 0.8 0.0005 Transverse

3 0.8 0.0005 Longitudinal

DownLoad: CSV

[1]	Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297 Google Scholar
[2]	Meshkov E E 1969 Fluid Dyn. 4 101
[3]	Kelvin L 1871 Philos. Mag. 42 362 Google Scholar
[4]	Helmholtz H V 1868 Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin 23 215
[5]	Rayleigh L 1882 Proc. R. Math. Soc. s1-14 170 Google Scholar
[6]	Taylor S G 1950 Proc. R Soc. London Ser. A 201 192 Google Scholar
[7]	Zheng C, Zhang H H, Chen Z H, Wu W T, Sha S 2019 Phys. Fluids 31 086104 Google Scholar
[8]	林震亚, 张焕好, 陈志华, 刘迎 2017 爆炸与冲击 37 748 Google Scholar Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explo. Shock Waves 37 748 Google Scholar
[9]	Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41 Google Scholar
[10]	Jacobs J 1993 Phys. Fluids 5 2239 Google Scholar
[11]	Layes G, Metayer O L 2007 Phys. Fluids 19 042105 Google Scholar
[12]	Jacobs J and Krivets V 2005 Phys. Fluids 17 034105 Google Scholar
[13]	Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800 Google Scholar
[14]	Wang X S, Yang D G, Wu J Q, Luo X S 2015 Phys. Fluids 27 064104 Google Scholar
[15]	Bai J S, Zou L Y, Wang T, Liu K, Huang W B, Liu J G, Li P, Tan D W, Liu C L 2010 Phys. Rev. E 82 056318 Google Scholar
[16]	Si T, Long T, Zhai Z G, Luo X S 2015 J. Fluid Mech. 784 225 Google Scholar
[17]	Luo X S, Ding J C, Wang M H, Zhai Z G, Si T 2015 Phys. Fluids 27 091702 Google Scholar
[18]	Lei F, Ding J C, Si T, Zhai Z G, Luo X S 2017 J. Fluid Mech. 826 819 Google Scholar
[19]	Ding J C, Si T, Yang J M, Lu X Y, Zhai Z G, Luo X S 2017 Phys. Rev. Lett. 119 014501 Google Scholar
[20]	Liang Y, Ding J C, Zhai Z G, Si T, Luo X S 2017 Phys. Fluids 29 086101 Google Scholar
[21]	李冬冬, 王革, 张斌 2018 物理学报 67 184702 Google Scholar Li D D, Wang G, Zhang B 2018 Acta Phys. Sin. 67 184702 Google Scholar
[22]	Guo X, Zhai Z G, Si T, Luo X S 2019 Phys. Rev. Fluids 4 092001(R
[23]	王显圣, 司廷, 罗喜盛, 杨基明 2012 力学学报 44 664 Google Scholar Wang X S, Si T, Luo X S, Yang J M 2012 Acta Mech. Sin. 44 664 Google Scholar
[24]	张升博, 张焕好, 陈志华, 郑纯 2023 物理学报 72 105202 Google Scholar Zhang S B, Zhang H H, Chen Z H, Zheng C 2023 Acta Phys. Sin. 72 105202 Google Scholar
[25]	Zhang S B, Zhang H H, Chen Z H, Zheng C 2023 Phys. Plasmas 30 022107 Google Scholar
[26]	Samtaney R 2003 Phys. Fluids 15 53 Google Scholar
[27]	Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 016102 Google Scholar
[28]	Sano T 2021 Astrophys. J. 920 29 Google Scholar
[29]	李源, 罗喜胜 2014 计算物理 31 659 Google Scholar Li Y, Luo X S 2014 Chin. J. Comput. Phys. 31 659 Google Scholar
[30]	Qiu Z Y, Wu Z W, Cao J T, Li D 2008 Phys. Plasmas 15 042305 Google Scholar
[31]	Tapinou K C, Wheatley V, Bond D, Jahn I 2023 Phys. Plasmas 30 022707 Google Scholar
[32]	Tapinou K C, Wheatley V, Bond D 2023 J. Fluid Mech. 977 A19 Google Scholar
[33]	Rinderknecht H G, Amendt P, Wilks S, Collins G 2018 Plasma Phys. Controlled Fusion 60 064001 Google Scholar
[34]	Xu A G, Zhang G C, Gan Y B, Chen F, Yu X J 2012 Front. Phys. 7 582 Google Scholar
[35]	Gan Y B, Xu A G, Lai H L, Li W, Sun G L, Succi S 2022 J. Fluid Mech. 951 A8 Google Scholar
[36]	Zhang D J, Xu A G, Zhang Y D, Gan Y B, Li Y J 2022 Phys. Fluids 34 086104 Google Scholar
[37]	Zhang Y D, Xu A G, Chen F, Lin C D, Wei Z H 2022 AIP Adv. 12 035347 Google Scholar
[38]	Song J H, Xu A G, Miao l, Chen F, Liu Z P, Wang L F, Wang N F, Hou X 2024 Phys. Fluids 36 016107 Google Scholar
[39]	沙莎, 张焕好, 陈志华, 郑纯, 吴威涛, 石启陈 2020 物理学报 69 184701 Google Scholar Sha S, Zhang H H, Chen Z H, Zheng C, Wu W T, Shi Q C 2020 Acta Phys. Sin. 69 184701 Google Scholar
[40]	Zhang H H, Zheng C, Aubry N, Wu W T, Chen Z H 2020 Phys. Fluids 32 116104 Google Scholar
[41]	Colella P 1990 J. Comput. Phys. 87 171 Google Scholar
[42]	Londrillo P, Zanna L D 2004 J. Comput. Phys. 195 17 Google Scholar
[43]	Shin M, Stone J M, Snyder G F 2008 Astrophys. J. 680 336 Google Scholar
[44]	Saltzman J 1994 J. Comput. Phys. 115 153 Google Scholar
[45]	Colella P, Woodward P 1984 J. Comput. Phys. 54 17
[46]	Evans C, Hawley J 1988 Astrophys J. 322 659
[47]	Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21 Google Scholar
[48]	Giordano J, Burtschell Y 2006 Phys. Fluids. 18 036102 Google Scholar

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