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针对霍尔效应对高超声速磁流体力学控制的影响问题, 考虑高超声速流动过程中高温化学反应、气体分子热力学温度激发(即平动、转动、振动以及电子温度能量模态之间的激发与松弛过程)及多电离组分等离子体霍尔系数分布, 通过耦合求解各向异性霍尔电场泊松方程和带电磁源项的高温热化学非平衡流动控制方程组, 建立了高超声速流动磁流体力学控制霍尔效应数值模拟方法, 开展了多种条件下高超声速流动磁流体力学控制数值模拟, 分析了霍尔效应“漏电”与“聚集”现象原理及其对气动力/热特性的影响机制, 详细探讨了不同空域、速域和飞行器特征尺度条件下霍尔效应的作用机理和影响规律. 研究表明: 1)霍尔效应改变了流场等离子体洛伦兹力分布, 削弱了整体的力学效果, 使整体的磁阻特性降低; 2)霍尔效应对高超声速磁流体力学控制的影响, 与壁面导电性和壁面附近漏电层的“漏电”现象紧密相关, 要增强磁控效果, 必须抑制壁面附近的“漏电”现象; 3)霍尔效应对磁控热防护效果的影响较为复杂, 受“漏电”现象和电流“聚集”现象共同作用; 4)基于本文基准状态, 当高度高于67 km或速度高于5.7 km/s或特征尺度大于0.5 m时, 霍尔效应使磁控热防护效果增强, 电流“聚集”现象对气动热环境的影响占主导; 反之, 则霍尔效应使磁控热防护效果减弱, “漏电”现象对气动热环境的影响占主导.In this paper, the influence of Hall effect on hypersonic magnetohydrodynamic control is studied. By considering high temperature thermo-chemical reactions, the excitation of thermodynamic temperature of gas molecules, Hall coefficient distribution of various ionized components, and by solving the coupled anisotropic Possion’s equation of Hall electric field and the high temperature thermo-chemical non-equilibrium flow governing equations with electromagnetic source term, the numerical simulation method of the Hall effect on hypersonic magnetohydrodynamic (MHD) control is established, and the numerical simulation of hypersonic MHD control under various conditions is conducted, the mechanism of “leakage” and “gathering” phenomenon of Hall effect and its influence on aerodynamic force and aerothermal environment are analyzed, the mechanism and its influences of Hall effect under various flight altitudes, flight speeds and characteristic lengths are discussed in detail. The result shows that 1) Hall effect changes the Lorentz force distribution of plasma, weakens the total mechanical effect, thus lowering the total magneto-resistance effect. 2) The influence of Hall effect on hypersonic MHD control is closely related to the wall conductivity and the “leakage” phenomenon of the leakage layer near the wall. The “leakage” phenomenon must be restrained in order to enhance the magnetic control effect. 3) The influence of Hall effect on magnetic control thermal protection is complicated, which is the combined result of the “leakage” and “gathering” phenomenon. 4) Based on the normal state in this paper, when the flight altitude is higher than 67 km or the flight speed higher than 5.7 km/s or the characteristic length is bigger than 0.5 m, Hall effect can enhance the magnetic control thermal protection, and the current “gathering” phenomenon dominates the influence on aerothermal environment. On the contrary, Hall effect can weaken the effect of magnetic control thermal protection, and the “leakage” phenomenon dominates the influence on aerothermal environment.
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Keywords:
- magnetohydrodynamic /
- Hall effect /
- plasma /
- numerical simulation
[1] 田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)
Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[2] 胡友秋, 程福臻, 刘之景 1995 电磁学 (北京: 高等教育出版社) 第288−289, 397页
Hu Y Q, Cheng F Z, Liu Z J 1995 Electromagnetism (Beijing: Higher Education Press) pp288−289, 397 (in Chinese)
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[21] 董维中 1996 博士学位论文 (北京: 北京航空航天大学)
Dong W Z 1996 Ph. D. Dissertation (Beijing: Beihang University) (in Chinese)
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Google Scholar
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图 1 磁场配置示意图和网格无关性分析 (a)磁场配置; (b)表面压力; (c)表面热流
Fig. 1. Magnetic field configuration and anlysis of indepence of grids: (a) Magnetic field configuration; (b) surface pressure; (c) surface heat flux.
图 2 不同霍尔系数条件下钝柱体气动特性 (a)轴向力系数; (b)侧向力系数
Fig. 2. Aerodynamic coefficent using different Hall parameter: (a) Axial force coefficent; (b) side force coefficent.
图 5 基准状态部分流场参数分布 (a)驻点线温度; (b)表面热流
Fig. 5. Partical flow field parameters of refference state: (a) Temperatrue along stagnation line; (b) surface heat flux.
图 6 基准状态环形电流和洛伦兹力矢量分布 (a) Case 2; (b) Case 3
Fig. 6. Annular electric current and Lorentz force: (a) Case 2; (b) Case 3
图 7 基准状态电导率和相对霍尔系数分布 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 7. Distribution of electronic conductivity and Hall parameter: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 8 不同飞行高度下驻点热流及其磁控效率 (a)驻点热流; (b)磁控热防护效率
Fig. 8. Heat flux at stagnation point and its control efficiency at different altitudes: (a) Heat flux; (b) control efficiency.
图 9 不同飞行高度下阻力系数及其磁控效率 (a)阻力系数; (b)磁控增阻效率
Fig. 9. Darg coefficient and its control efficiency at different altitudes: (a) Darg coefficient; (b) control efficiency.
图 10 不同高度下流场驻点线电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 10. Electronic conductivity and Hall parameter along stagnation line at different altitudes: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 11 不同飞行高度下流场最大电势差和激波后较大区域的相对霍尔系数
Fig. 11. Potential difference maximum and Hall parameter after shock wave at different altitudes.
图 12 不同高度下流场壁面附近电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 12. Electronic conductivity and Hall parameter near wall at different altitudes: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 14 不同飞行速度下驻点热流及其磁控效率 (a)驻点热流; (b)磁控热防护效率
Fig. 14. Heat flux at stagnation point and its control efficiency at different velocities: (a) Heat flux; (b) control efficiency.
图 15 不同飞行速度下阻力系数及其磁控效率 (a)阻力系数; (b)磁控增阻效率
Fig. 15. Darg coefficient and its control efficiency at different velocities: (a) Darg coefficient; (b) control efficiency.
图 16 不同速度下流场驻点线电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 16. Electronic conductivity and Hall parameter along stagnation line at different velocities: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 17 不同速度下流场壁面附近电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 17. Electronic conductivity and Hall parameter near wall at different velocities: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 18 不同尺度下驻点热流及其磁控效率 (a)驻点热流; (b)磁控热防护效率
Fig. 18. Heat flux at stagnation point and its control efficiency using different scales: (a) Heat flux; (b) control efficiency.
图 19 不同尺度阻力系数及其磁控效率 (a)阻力系数; (b)磁控增阻效率
Fig. 19. Darg coefficient and its control efficiency using different scales: (a) Darg coefficient; (b) control efficiency.
图 20 不同尺度下流场驻点线电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 20. Electronic conductivity and Hall parameter along stagnation line using different scales: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .
图 21 不同尺度下壁面附近电导率和相对霍尔系数 (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ Fig. 21. Electronic conductivity and Hall parameter near wall using different scales: (a)
$\sigma $ ; (b)${\beta _{\rm{e}}}$ .表 1 基准状态的阻力系数
Table 1. Drag coefficient of refference state.
Case ${C_{\rm{D}}}$ ${C_{{\rm{D1}}}}$ ${C_{{\rm{D2}}}}$ 磁控增阻百分比 Case1 0.9239 0.9239 — — Case2 1.1679 0.9462 0.2217 26.4% Case3 1.1167 0.9375 0.1792 20.9% 
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[1] 田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)
Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[2] 胡友秋, 程福臻, 刘之景 1995 电磁学 (北京: 高等教育出版社) 第288−289, 397页
Hu Y Q, Cheng F Z, Liu Z J 1995 Electromagnetism (Beijing: Higher Education Press) pp288−289, 397 (in Chinese)
[3] 胡海洋, 杨云军, 周伟江 2011 力学学报 43 453
Google Scholar
Hu H Y, Yang Y J, Zhou W J 2011 Chin. J. Theor. Appl. Mech. 43 453
Google Scholar
[4] Borghi C A, Carraro M R, Cristofolini A 2003 34th AIAA Plasmadynamics and Lasers Conference Orlando, Florida, June 23−26, 2003 p3761
[5] Otsu H 2005 36th AIAA Plasmadynamics and Lasers Conference Toronto, Ontario, Canada, June 6−9, 2005 p5049
[6] Fujino T, Matsumoto Y, Kasahara J 2007 J. Spacecraft Rockets 44 626
Google Scholar
[7] Fujino T, Sugita H, Mizuno M 2006 J. Spacecraft Rockets 43 63
Google Scholar
[8] [9] Nagata Y, Otsu H, Yamada K 2012 43rd AIAA Plasmadynamics and Lasers Conference NewOrleans, Louisiana, June 25−28, 2012 p2734
[10] Fujino T, Ishikawa M 2013 44th AIAA Plasmadynamics and Lasers Conference SanDiego, California, June 24−27, 2013 p3000
[11] Takahashi T, Shimosawa Y, Masuda K, Fujino T 2015 46th AIAA Plasma Dynamics and Lasers Conference Dallas, Texas, June 22−26, 2015 p3365
[12] Masuda K 2015 46th AIAA Plasma Dynamics and Lasers Conference Dallas, Texas, June 22—26 2015, p3366
[13] 吕浩宇, 李椿萱 2010 科学通报 55 1182
Google Scholar
Lü H Y, Lee C H 2010 Chin. Sci. Bull. 55 1182
Google Scholar
[14] 李开, 柳军, 刘伟强 2017 物理学报 66 084702
Google Scholar
Li K, Liu J, Liu W Q 2017 Acta Phys. Sin. 66 084702
Google Scholar
[15] 李开, 柳军, 刘伟强 2017 物理学报 66 054701
Google Scholar
Li K, Liu J, Liu W Q 2017 Acta Phys. Sin. 66 054701
Google Scholar
[16] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗 2017 航空学报 38 121030
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z 2017 Acta Aeronaut. Astronaut. Sin. 38 121030
Google Scholar
[17] 丁明松, 江涛, 刘庆宗, 董维中, 高铁锁 2019 航空学报 40 123009
Google Scholar
Ding M S, Jiang T, Liu Q Z, Dong W Z, Gao T S 2019 Acta Aeronaut. Astronaut. Sin. 40 123009
Google Scholar
[18] 丁明松, 江涛, 董维中, 高铁锁, 刘庆宗 2019 物理学报 68 174702
Google Scholar
Ding M S, Jiang T, Dong W Z, Gao T S, Liu Q Z 2019 Acta Phys. Sin. 68 174702
Google Scholar
[19] 丁明松, 刘庆宗, 江涛, 董维中, 高铁锁 2020 航空学报 41 123278
Google Scholar
Ding M S, Liu Q Z, Jiang T, Dong W Z, Gao T S 2020 Acta Aeronaut. Astronaut. Sin. 41 123278
Google Scholar
[20] Park C 1993 J. Thermophys. Heat Transfer 7 385
Google Scholar
[21] 董维中 1996 博士学位论文 (北京: 北京航空航天大学)
Dong W Z 1996 Ph. D. Dissertation (Beijing: Beihang University) (in Chinese)
[22] 丁明松, 董维中, 高铁锁 2018 航空学报 39 121588
Google Scholar
Ding M S, Dong W Z, Gao T S 2018 Acta Aeronaut. Astronaut. Sin. 39 121588
Google Scholar
[23] 丁明松, 董维中, 高铁锁 2017 宇航学报 38 1361
Google Scholar
Ding M S, Dong W Z, Gao T S 2017 J. Astronaut. 38 1361
Google Scholar
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