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磁控条件下激波冲击三角形气柱过程的数值研究

董国丹 张焕好 林震亚 秦建华 陈志华 郭则庆 沙莎

引用本文:
Citation:

磁控条件下激波冲击三角形气柱过程的数值研究

董国丹, 张焕好, 林震亚, 秦建华, 陈志华, 郭则庆, 沙莎

Numerical investigations of interactions between shock waves and triangular cylinders in magnetic field

Dong Guo-Dan, Zhang Huan-Hao, Lin Zhen-Ya, Qin Jian-Hua, Chen Zhi-Hua, Guo Ze-Qing, Sha Sha
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  • 本文基于磁流体动力学方程组,在保证磁场散度为零的条件下,采用CTU+CT(corner transport upwind+constrained transport)算法,对有无磁场控制下激波与重质或轻质三角形气柱相互作用过程进行数值研究.结果表明:无论有无磁场,两气柱在激波冲击下均具有完全不同的波系结构和射流现象.其中,入射激波与重气柱发生常规折射,形成介质射流,而与轻气柱作用则发生非常规折射,形成反相空气射流.无磁场时,气柱在激波冲击下,产生Richtmyer-Meshkov和Kelvin-Helmholtz不稳定性,界面出现次级涡序列,重气柱上下角卷起形成主涡对,轻气柱空气射流穿过下游界面后形成偶极子涡.施加横向磁场后,次级涡序列、主涡对以及偶极子涡均消失.进一步研究表明,在磁场作用下,洛伦兹力将不稳定性诱导产生的涡量向界面两侧的Alfvn波上输运,减少界面涡量沉积,抑制界面卷起失稳.最终,涡量沿界面两侧形成相互远离的涡层,界面不稳定性得到控制.此外,定量分析表明磁场能加快两气柱上游界面的运动,抑制下游界面的运动,且对轻气柱的控制效果更好.
    Magnetohydrodynamic (MHD) equations are solved by using the CTU+CT (corner transport upwind + constrained transport) algorithm which guarantees the divergence-free constraint on the magnetic field. The interactions between shock wave and heavy or light triangular cylinder are investigated in detail in the cases with and without magnetic field. In the cases of hydrodynamic (B=0 T) and MHD (B=0.01 T), the numerical results indicate that heavy and light triangular cylinders have quite different wave patterns and jet structures after being impacted by a planar incident shock wave. Specifically, a regular refraction and downstream R22 jet are formed in the heavy case, whereas an irregular refraction and upstream air jet are generated in the light case. In the hydrodynamic case, the Richtmyer-Meshkov (R-M) instability and Kelvin-Helmholtz (K-H) instability are induced by the incident shock wave. Hereafter, both heavy and light density interfaces begin to roll up with a series of interfacial vortex sequences. In addition, a main vortex ring is formed in the heavy case, while a vortex dipole passing through the downstream interface is generated in the light case. In the MHD case, both heavy and light density interfaces remain smooth and interfacial vortex sequences vanish. Furthermore, the main vortex ring formed in the heavy cases and the vortex dipole generated in the light cases disappear. Moreover, in the presence of a magnetic field, a detailed investigation demonstrates that Lorentz forces give rise to the transport of baroclinic vorticities to the Alfvn waves. As a consequence, the deposition of interfacial vorticities decreases and the rolling-up of interfaces is suppressed. In the end, the vorticities are transformed into two vortex sheets travelling away from the density interfaces, and the R-M instability and K-H instability are well controlled. The quantitative investigations reveal that for both heavy and light triangular cylinders, magnetic field can accelerate the upstream interface and decelerate the downstream interface, especially for the light triangular cylinder.
      Corresponding author: Dong Guo-Dan, Dongguodan9@163.com;zhanghuanhao@njust.edu.cn ; Zhang Huan-Hao, Dongguodan9@163.com;zhanghuanhao@njust.edu.cn
    • Funds: Project supported by the Young Scientists Fund of National Natural Science Foundation of China (Grant Nos. 11502117, 11702005).
    [1]

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    [2]

    Lindl J, Landen O, Edwards J, Moses E 2014 Phys. Plasmas 21 339

    [3]

    Sano T, Nishihara K, Matsuoka C, Inoue T 2012 ApJ. 758 12

    [4]

    Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297

    [5]

    Meshkov E E 1969 Fluid Dyn. 4 101

    [6]

    Rudinger G, Somers L M 1960 J. Fluid Mech. 7 161

    [7]

    Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41

    [8]

    Layes G, Jourdan G, Houas L 2003 Phys. Rev. Lett. 91 174502

    [9]

    Layes G, Jourdan G, Houas L 2009 Phys. Fluids 21 074102

    [10]

    Ranjan D, Oakley J, Bonazza R 2011 Annu Rev. Fluid Mech. 43 117

    [11]

    Ranjan D, Niederhaus J H J, Oakley J G, Anderson M H 2008 Phys. Fluids 20 24

    [12]

    Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800

    [13]

    Luo X S, Wang M H, Si T, Zhai Z G 2015 J. Fluid Mech. 773 366

    [14]

    Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186

    [15]

    Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese)[沙莎, 陈志华, 薛大文 2013 物理学报 62 144701]

    [16]

    Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese)[沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]

    [17]

    Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese)[沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]

    [18]

    Mininni P D 2010 Annu. Rev. Fluid Mech. 43 377

    [19]

    Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese)[陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]

    [20]

    Li Y, Luo X S 2014 Acta Phys. Sin. 63 085230 (in Chinese)[李源, 罗喜胜 2014 物理学报 63 085230]

    [21]

    Wu C C 2000 J. Geophys. Res-Space 105 7533

    [22]

    Samtaney R 2003 Phys. Fluids 15 L53

    [23]

    Wheatley V, Pullin D I, Samtaney R 2005 Phys. Rev. Lett. 95 125002

    [24]

    Wheatley V, Samtaney R, Pullin D I 2009 Phys. Fluids 21 082102

    [25]

    Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 238

    [26]

    Sano T, Inoue T, Nishihara K 2013 Phys. Rev. Lett. 111 20500

    [27]

    Cao J T, Wu Z W, Ren H J, Dong L 2008 Phys. Plasmas 15 445

    [28]

    Mostert W, Wheatley V, Samtaney R, Pullin D I 2015 Phys. Fluids 27 104102

    [29]

    Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21

    [30]

    Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explosion and Shock Waves 37 748 (in Chinese)[林震亚, 张焕好, 陈志华, 刘迎 2017 爆炸与冲击 37 748]

    [31]

    Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123

    [32]

    Londrillo P, Zanna L D 2003 J. Comput. Phys. 195 17

    [33]

    Qin J H, Jiang X H, Dong G D, Guo Z Q, Chen Z H 2018 Fluid Dyn. Res. 50 045508

    [34]

    Henderson L F, Colella P, Puckett E G 2006 J. Fluid Mech. 224 1

    [35]

    Landau L D, Lifshitz E M 1960 Electrodynamics of Continuous Media (Oxford: Pergamon) pp241-243

  • [1]

    Brouillette M 2002 Annu. Rev. Fluid Mech. 34 445

    [2]

    Lindl J, Landen O, Edwards J, Moses E 2014 Phys. Plasmas 21 339

    [3]

    Sano T, Nishihara K, Matsuoka C, Inoue T 2012 ApJ. 758 12

    [4]

    Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297

    [5]

    Meshkov E E 1969 Fluid Dyn. 4 101

    [6]

    Rudinger G, Somers L M 1960 J. Fluid Mech. 7 161

    [7]

    Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41

    [8]

    Layes G, Jourdan G, Houas L 2003 Phys. Rev. Lett. 91 174502

    [9]

    Layes G, Jourdan G, Houas L 2009 Phys. Fluids 21 074102

    [10]

    Ranjan D, Oakley J, Bonazza R 2011 Annu Rev. Fluid Mech. 43 117

    [11]

    Ranjan D, Niederhaus J H J, Oakley J G, Anderson M H 2008 Phys. Fluids 20 24

    [12]

    Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800

    [13]

    Luo X S, Wang M H, Si T, Zhai Z G 2015 J. Fluid Mech. 773 366

    [14]

    Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186

    [15]

    Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese)[沙莎, 陈志华, 薛大文 2013 物理学报 62 144701]

    [16]

    Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese)[沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]

    [17]

    Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese)[沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]

    [18]

    Mininni P D 2010 Annu. Rev. Fluid Mech. 43 377

    [19]

    Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese)[陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]

    [20]

    Li Y, Luo X S 2014 Acta Phys. Sin. 63 085230 (in Chinese)[李源, 罗喜胜 2014 物理学报 63 085230]

    [21]

    Wu C C 2000 J. Geophys. Res-Space 105 7533

    [22]

    Samtaney R 2003 Phys. Fluids 15 L53

    [23]

    Wheatley V, Pullin D I, Samtaney R 2005 Phys. Rev. Lett. 95 125002

    [24]

    Wheatley V, Samtaney R, Pullin D I 2009 Phys. Fluids 21 082102

    [25]

    Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 238

    [26]

    Sano T, Inoue T, Nishihara K 2013 Phys. Rev. Lett. 111 20500

    [27]

    Cao J T, Wu Z W, Ren H J, Dong L 2008 Phys. Plasmas 15 445

    [28]

    Mostert W, Wheatley V, Samtaney R, Pullin D I 2015 Phys. Fluids 27 104102

    [29]

    Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21

    [30]

    Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explosion and Shock Waves 37 748 (in Chinese)[林震亚, 张焕好, 陈志华, 刘迎 2017 爆炸与冲击 37 748]

    [31]

    Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123

    [32]

    Londrillo P, Zanna L D 2003 J. Comput. Phys. 195 17

    [33]

    Qin J H, Jiang X H, Dong G D, Guo Z Q, Chen Z H 2018 Fluid Dyn. Res. 50 045508

    [34]

    Henderson L F, Colella P, Puckett E G 2006 J. Fluid Mech. 224 1

    [35]

    Landau L D, Lifshitz E M 1960 Electrodynamics of Continuous Media (Oxford: Pergamon) pp241-243

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出版历程
  • 收稿日期:  2018-06-09
  • 修回日期:  2018-07-11
  • 刊出日期:  2019-10-20

磁控条件下激波冲击三角形气柱过程的数值研究

    基金项目: 国家自然科学青年科学基金(批准号:11502117,11702005)资助的课题.

摘要: 本文基于磁流体动力学方程组,在保证磁场散度为零的条件下,采用CTU+CT(corner transport upwind+constrained transport)算法,对有无磁场控制下激波与重质或轻质三角形气柱相互作用过程进行数值研究.结果表明:无论有无磁场,两气柱在激波冲击下均具有完全不同的波系结构和射流现象.其中,入射激波与重气柱发生常规折射,形成介质射流,而与轻气柱作用则发生非常规折射,形成反相空气射流.无磁场时,气柱在激波冲击下,产生Richtmyer-Meshkov和Kelvin-Helmholtz不稳定性,界面出现次级涡序列,重气柱上下角卷起形成主涡对,轻气柱空气射流穿过下游界面后形成偶极子涡.施加横向磁场后,次级涡序列、主涡对以及偶极子涡均消失.进一步研究表明,在磁场作用下,洛伦兹力将不稳定性诱导产生的涡量向界面两侧的Alfvn波上输运,减少界面涡量沉积,抑制界面卷起失稳.最终,涡量沿界面两侧形成相互远离的涡层,界面不稳定性得到控制.此外,定量分析表明磁场能加快两气柱上游界面的运动,抑制下游界面的运动,且对轻气柱的控制效果更好.

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