Numerical simulation of influence of different initial magnetic fields on process of shock wave shocking R22 heavy gas column
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摘要: 基于磁流体动力(magneto-hydrodynamic，MHD)方程，采用CTU+CT方法，对在不同初始磁场作用下的平面入射激波与磁化R22重质气柱作用过程进行了数值研究。数值结果清晰地描述了不同初始磁场条件时激波诱导R22气柱界面不稳定性的过程，揭示了磁场控制界面不稳定性的机理。另外，还分析了磁感应强度对界面不稳定性的影响，发现在磁场较小时，涡层附着于界面，但随着磁感应强度的增大，平均涡量随之增大，涡层与界面逐渐分离，最终更好地抑制了界面不稳定性。同时，还发现平均涡度拟能随着磁感应强度的增大而减小，而垂直磁场比平行磁场更能降低平均涡度拟能，因而平均涡度拟能可较好地反映磁场对不稳定性的影响效果。Abstract: In this paper, the process of the plane incident shock wave shocking a magnetized R22 heavy circular gas column with different initial magnetic field was numerically studied based on the magneto-hydrodynamic (MHD) equation and CTU+CT method. The numerical results clearly describe the development of the instabilities induced by the shock waves on the interface of the R22 gas column with different initial magnetic field, and reveal the mechanism of the magnetic field governing the instabilities. In addition, the influence of different magnetic field strengths on the instabilities was analyzed, and it was found that when the magnetic field strength is small, the vortex layer attaches to the interface; that, with the increase of the magnetic field strength, the vortex layer gradually separates from the interface and the mean vorticity increases; and, finally, that the instabilities on the interface are brought under control. Meanwhile, with the increase of the magnetic field, the average enstrophy decreases, and the vertical magnetic field exerts a better inhibition effect on the average enstrophy than the parallel magnetic field. Thus the average enstrophy can fairly well reflect the effect of the magnetic field on the instabilities.
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Key words:
- magneto-hydrodynamic equation /
- vorticity /
- magnetic field /
- instability /
- shock wave
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图 2 激波与R22气柱作用过程中涡量分布及密度纹影图
Figure 2. Vorticity distribution and schlieren images of interaction of shock wave and R22 column
图 3 当B=0.01 T时激波与R22气柱作用过程的涡量分布图
Figure 3. Vorticity distribution of interaction of shock wave and R22 column at B=0.01 T
图 4 当B=0.05 T时激波与R22气柱作用过程的涡量分布图
Figure 4. Vorticity distribution of interaction of shock wave and R22 column at B=0.05 T
图 5 当t=945 μs时不同初始磁场情况下的密度纹影图
Figure 5. Density schlieren images with different initial magnetic field at t=945 μs
图 6 当B=0.05 T垂直磁场时磁压力及磁能量分布
Figure 6. Graph of magnetic pressure and magnetic energy at B=0.05 T and θ=90°
图 7 当B=0.05 T水平磁场时磁压力及磁能量分布
Figure 7. Graph of magnetic pressure and magnetic energy at B=0.05 T and θ=0°
表 1 流场平均涡量
Table 1. Average vorticity
初始条件 Ω/s-1 B/T θ/(°) 85 μs 165 μs 200 μs 250 μs 450 μs 945 μs 0 - 55.79 121.1 145.5 142.1 190.7 255.1 0.01 90 56.21 117.0 140.3 131.8 155.5 205.3 0.01 0 56.14 116.9 139.9 132.8 169.9 270.0 0.05 90 68.44 132.5 156.5 169.8 216.4 289.9 0.05 0 60.65 123.2 147.0 169.5 247.4 354.5 
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表 2 流场平均涡度拟能
Table 2. Average enstrophy
初始条件 Ω2/s-2 B/T θ/(°) 85 μs 165 μs 200 μs 250 μs 450 μs 945 μs 0 - 6.604×106 1.332×107 1.557×107 1.116×107 1.153×107 1.135×107 0.01 90 1.899×106 3.527×106 4.694×106 3.144×106 3.334×106 4.533×106 0.01 0 4.275×106 7.098×106 7.332×106 6.285×106 7.132×106 9.524×106 0.05 90 1.714×106 2.679×106 3.586×106 2.932×106 3.268×106 4.572×106 0.05 0 3.343×106 4.817×106 5.036×106 5.413×106 6.965×106 9.723×106
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