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基于理想磁流体动力学方程组, 采用CTU (corner transport upwind) + CT (constrained transport)算法, 数值研究了磁场控制下R22气柱界面Richtmyer-Meshkov不稳定性的演化过程. 结果描述了平面激波冲击气柱界面过程中激波结构和界面不稳定性的发展; 无磁场时, 流场结构与Haas和Sturtevant (Hass J F, Sturtevant B 1987 J. Fluid Mech. 181 41)的实验结果相符; 施加纵向磁场后, 激波结构的演化基本无影响, 但明显抑制了气柱界面的不稳定性. 进一步研究表明, 激波与界面的作用, 使磁感线在界面上发生折射, 改变流场的磁场梯度, 在内外涡量层上形成磁张力. 磁张力的形成, 对界面流体产生一个与速度剪切相反的力矩, 抑制了界面的失稳及主涡的卷起. 另外, 磁张力沿界面分布的不均匀, 改变磁感线在界面上的聚集程度, 放大磁能量, 最终增强磁场对气柱界面不稳定性的抑制作用.
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关键词:
- Richtmyer-Meshkov不稳定性 /
- 磁流体 /
- 激波 /
- 圆形气柱
Based on the ideal magneto-hydro-dynamic equations (MHD) and adopting the CTU (Corner Transport Upwind) + CT (Constrained Transport) algorithm, the Richtmyer-Meshkov (RM) instability of the Gaussian distribution R22 gas column generated by the interaction of a planar shock wave with the gas column in the presence of magnetic field is investigated numerically. The numerical results show that the evolution of shock wave structure and interface instability during the interaction between shock wave and gas column are consistent with the experimental results of Haas and Sturtevant (Hass J F, Sturtevant B 1987 J. Fluid Mech. 181 41) in the absence of a magnetic field. In the presence of a longitudinal magnetic field, the evolution of the shock structures is almost unaffected, while the density interface appears very smooth and interfacial vortex sequences vanish, which is a clear indication of the RMI suppresion. Moreover, as the shock wave impinges on the interface, the magnetic field lines refract on the interface, resulting in the generation of magnetic field gradient in the flow field, which is not consistent with the scenario in the above case. As a result, a stronger magnetic tension is produced on the inner and outer vorticity layer. Simultaneously, the magnetic tension produces a moment on the interface fluid, which is opposite to the rolling direction of the velocity shear. Therefore, the interface instability and the main vortex rolling-up are effectively suppressed. In addition, the non-uniform distribution of magnetic tensions along the interface changes the aggregation degree of the magnetic lines, amplifying the magnetic strength, and finally enhancing the suppression effect of the magnetic field on the interface instability.-
Keywords:
- Richtmyer-Meshkov instability /
- magneto-hydro-dynamic /
- shock wave /
- gas column
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图 1 (a)计算模型; (b)界面组分沿对称轴的分布
Fig. 1. (a) Schematic of the computational model; (b) the distribution of R22 mole fraction along the symmetry axis of column.
图 2 激波与气柱作用过程的计算阴影结果(上)与实验结果(下)[25]的对比 (a) t = 0.09 ms; (b) t = 0.215 ms; (c) t = 0.25 ms; (d) t = 1.20 ms
Fig. 2. Comparison of our numerical (up) and experimental[25] (down) shadowgraph images of the interactions between shock wave and gas column: (a) t = 0.09 ms; (b) t = 0.215 ms; (c) t = 0.25 ms; (d) t = 1.20 ms.
图 3 施加磁场后流场的计算阴影图 (a) t = 0.12 ms; (b) t = 0.2 ms; (c) t = 0.25 ms; (d) t = 0.29 ms; (e) t = 0.425 ms; (f) t = 0.85 ms; (g) t = 1.20 ms; (h) t = 1.55 ms
Fig. 3. Numerical shadowgraph images of the case in the presence of a magnetic field: (a) t = 0.12 ms; (b) t = 0.2 ms; (c) t = 0.25 ms; (d) t = 0.29 ms; (e) t = 0.425 ms; (f) t = 0.85 ms; (g) t = 1.20 ms; (h) t = 1.55 ms.
图 4 无磁场时流场涡量分布 (a) t = 0.3 ms; (b) t = 1.2 ms
Fig. 4. Vorticity distribution in the absence of a magnetic field: (a) t = 0.3 ms; (b) t = 1.2 ms.
图 5 施加磁场后流场涡量分布 (a) t = 0.12 ms; (b) t = 0.2 ms; (c) t = 0.29 ms; (d) t = 0.425 ms; (e) t = 0.85 ms; (f) t = 1.2 ms
Fig. 5. Vorticity distribution in the presence of a magnetic field: (a) t = 0.12 ms; (b) t = 0.2 ms; (c) t = 0.29 ms; (d) t = 0.425 ms; (e) t = 0.85 ms; (f) t = 1.2 ms.
图 6 t = 0.2 ms时, 流场中各物理量的分布 (a)横向磁场强度; (b)纵向磁场强度; (c)磁能量; (d)横向磁张力; (e)纵向磁张力; (f)涡量
Fig. 6. Spatial distribution of various physical quantities at t = 0.2 ms: (a) Transverse magnetic field; (b) longitudinal magnetic field; (c) magnetic energy; (d) transverse magnetic tension; (e) longitudinal magnetic tension; (f) vorticity.
图 8 t = 0.2 ms时, 涡量层上磁张力矢量分布 (a)下半流场; (b)局部放大图
Fig. 8. Distribution of magnetic tension vector on the vorticity layer at t = 0.2 ms: (a) Lower half flow field; (b) local enlarged drawing.
图 9 气柱发展过程中流场磁能量和磁感线分布 (a) t = 0.2 ms; (b) t = 0.425 ms; (c) t = 0.85 ms
Fig. 9. Distribution of the magnetic energy and the magnetic field lines during the evolution of gas column: (a) t = 0.2 ms; (b) t = 0.425 ms; (c) t = 0.85 ms.
图 10 磁张力对界面不稳定性的作用 (a)横向磁张力; (b)纵向磁张力; (c)磁张力矢量.
Fig. 10. Effect of magnetic tension on interface instability: (a) Transverse magnetic tension; (b) longitudinal magnetic tension; (c) magnetic tension vector.
图 11 流场最大磁强度 (a)与平均磁能密度(b)随时间的变化(红色虚线为基准线)
Fig. 11. Time evolution of the maximum (a) and average (b) magnetic field strength (the red dotted line is the reference line).
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[1] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
Google Scholar
[2] Meshkov E E 1969 Fluid Dyn. 4 101
Google Scholar
[3] Lindl J D, McCrory R L, Campbell E M 1992 Phys. Today 45 32
Google Scholar
[4] Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Steven W, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
Google Scholar
[5] Lindl J D, Otto Landen O, Edwards J, Moses E 2014 Phys. Plasmas 21 020501
Google Scholar
[6] Yang J D, Kubota T, and Zukoski E E 1993 AIAA J. 31 854
Google Scholar
[7] Samtaney R 2003 Phys. Fluids 15 53
Google Scholar
[8] Hawley J F, Zabusky N J 1989 Phys. Rev. Lett. 63 1241
Google Scholar
[9] Wheatley V, Pullin D I, Samtaney R 2005 Phys. Rev. Lett. 95 125002
Google Scholar
[10] Wheatley V, Samtaney R, Pullin D I 2009 Phys. Fluids 21 082102
Google Scholar
[11] Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 016102
Google Scholar
[12] Cao J, Wu Z, Ren H, Li D 2008 Phys. Plasmas 15 042102
Google Scholar
[13] Sano T, Nishihara K, Matsuoka C, Inoue T 2012 The Astrophys. J. 758 126
Google Scholar
[14] Mac Low M M, McKee C F, Klein R I 1994 The Astrophys. J. 433 757
Google Scholar
[15] Fragile P C, Anninos P, Gustafson K 2005 The Astrophys. J. 619 327
Google Scholar
[16] 李源, 罗喜胜 2014 计算物理 31 659
Google Scholar
Li Y, Luo X S 2014 Chinese J. Comput. Phys. 31 659
Google Scholar
[17] 董国丹, 张焕好, 林震亚, 秦建华, 陈志华, 郭则庆, 沙莎 2018 67 204701
Google Scholar
Dong G D, Zhang H H, Lin Z Y, Qin J H, Chen Z H, Guo Z Q, Sha S 2018 Acta Phys. Sin. 67 204701
Google Scholar
[18] 董国丹, 郭则庆, 秦建华, 张焕好, 姜孝海, 陈志华, 沙莎 2019 68 165201
Google Scholar
Dong G D, Guo Z Q, Qin J H, Zhang H H, Jiang X H, Chen Z H, Sha S 2019 Acta Phys. Sin. 68 165201
Google Scholar
[19] 沙莎, 陈志华, 薛大文 2013 62 144701
Google Scholar
Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701
Google Scholar
[20] 沙莎, 陈志华, 张庆兵 2015 64 015201
Google Scholar
Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201
Google Scholar
[21] Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21
Google Scholar
[22] 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 Explosion and Shock Waves 37 748
Google Scholar
[23] Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123
Google Scholar
[24] Londrillo P, Zanna L D 2003 J. Comput. Phys. 195 17
Google Scholar
[25] Hass J F, Sturtevant B 1987 J. Fluid Mech. 181 41
Google Scholar
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