搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

高超声速飞行器磁控热防护霍尔电场数值方法研究

李开 柳军 刘伟强

引用本文:
Citation:

高超声速飞行器磁控热防护霍尔电场数值方法研究

李开, 柳军, 刘伟强

Numerical solution procedure for Hall electric field of the hypersonic magnetohydrodynamic heat shield system

Li Kai, Liu Jun, Liu Wei-Qiang
PDF
导出引用
  • 作为一种新概念高超声速热防护手段,磁控热防护系统在实际应用中往往需要考虑霍尔效应的影响. 为了在真实气体环境下求解霍尔电场,采用交替隐式近似因子分解法建立并验证了热化学非平衡流体域电场数值求解方法. 分析了电场虚拟步进因子和收敛性的关系以及影响步进因子取值的因素,提出了当地变步进因子加速电场收敛方法. 研究表明,存在一个最优的步进因子ap使得霍尔电场收敛速度最快,并且随网格尺度的减小和霍尔系数的增加,最优步进因子ap变大,电势场收敛速率变慢. 对于局部加密网格而言,当地变步进因子法的电势收敛性明显优于常规的定步进因子法.
    Magnetohydrodynamic (MHD) heat shield system is a novel-concept thermal protection technique for hypersonic vehicles, which has been proved by lots of researchers with both numerical and experimental methods. Most of researchers neglect the Hall effect in their researches. However, in the hypersonic reentry process, the Hall effect is sometimes so significant that the electric current distribution in the shock layer can be changed by the induced electric field. Consequently, the Lorentz force as well as the Joule heat is varied, and thus the efficiency of the MHD heat shield system is affected.In order to analyze the influence of Hall effect, the induced electric field must be taken into consideration. According to the weakly-ionized characteristics of hypersonic flow post bow shock, the magneto-Reynolds number is assumed to be small. Therefore, the Maxwell equations are simplified with the generalized Ohm's law, and the induced electric field is governed by the potential Possion equation. Numerical methods are hence established to solve the Hall electric field equations in the thermochemical nonequilibrium flow field. The electric potential Poisson equation is of significant rigidity and difficult to solve for two reasons. One is that the coefficient matrix may not be diagonally dominant when the Hall parameter is large in the shock layer, and the other is that this matrix including the electric conductivity is discontinuous across the shock. In this paper, a virtual stepping factor is included to strengthen the diagonal dominance and improve the computational stability. Moreover, approximate factor and alternating direction implicit method are employed for further improving the stability. With these methods, a FORTRAN code is written and validated by comparing the numerical results with the analytical ones as well as results available from previous references. After that, relation between the convergence property and the virtual stepping factor is revealed by theoretical analysis and numerical simulations. Based on these work, a local variable stepping factor method is proposed to accelerate the iterating process. Results show that the convergence property is closely related to the mesh density and Hall parameter, and there exists a best stepping factor for a particular mesh as well as a particular Hall parameter. Since the best stepping factor varies a lot for different meshes and different Hall parameter, its appropriate value is hard to choose. The best value of stepping factor coefficient still exists in the local step factor method, but its value range is relatively smaller. More importantly, the local stepping factor method yields better convergence property than the regular constant one when employing a locally refined mesh.
      通信作者: 李开, LiKai898989@126.com
    • 基金项目: 湖南省自然科学基金(批准号:13JJ2002)和国家自然科学基金(批准号:90916018)资助的课题.
      Corresponding author: Li Kai, LiKai898989@126.com
    • Funds: Project supported by the Natural Science Foundation of Hunan Province, China (Grant No. 13JJ2002) and the National Natural Science Foundation of China (Grant No. 90916018).
    [1]

    Zhu Y J, Jiang Y S, Hua H Q, Zhang C H, Xin C W 2014 Acta Phys. Sin. 63 244101 (in Chinese) [朱艳菊, 江月松, 华厚强, 张崇辉, 辛灿伟 2014 物理学报 63 244101]

    [2]

    Yin J F, You Y X, Li W, Hu T Q 2014 Acta Phys. Sin. 63 044701 (in Chinese) [尹纪富, 尤云祥, 李巍, 胡天群 2014 物理学报 63 044701]

    [3]

    Zhao G Y, Li Y H, Liang H, Hua W Z, Han M H 2015 Acta Phys. Sin. 64 015101 (in Chinese) [赵光银, 李应红, 梁华, 化为卓, 韩孟虎 2015 物理学报 64 015101]

    [4]

    Yu H Y 2014 Acta Phys. Sin. 63 047502 (in Chinese) [于红云 2014 物理学报 63 047502]

    [5]

    Bityurin V A, Bocharov A N 2014 52nd Aerospace Sciences Meeting National Harbor, Maryland, January 13-17, 2014

    [6]

    Bisek N J, Gosse R, Poggie J 2013 J. Spacecraft Rockets 50 927

    [7]

    Cristofolini A, Borghi C A, Neretti G, Battista F, Schettino A, Trifoni E, Filippis F D, Passaro A, Baccarella D 2012 18th AIAA/3AF International Space Planes and Hypersonic Systems and Technologies Conference Tours, France, September 24-28, 2012

    [8]

    Lv H Y, Lee C H 2010 Chin. Sci. Bull. 55 1182 (in Chinese) [吕浩宇, 李椿萱 2010 科学通报 55 1182]

    [9]

    Li K, Liu W Q 2016 Acta Phys. Sin. 65 064701 (in Chinese) [李开, 刘伟强 2016 物理学报 65 064701]

    [10]

    Hu H Y, Yang Y J, Zhou W J 2011 Chin. J. Theo. App. Mechan. 43 453 (in Chinese) [胡海洋, 杨云军, 周伟江 2011 力学学报 43 453]

    [11]

    Gaitonde D V, Poggie J 2002 40th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 14-17, 2002

    [12]

    Wan T, Candler G V, Macheret S O, Shneider M N 2009 AIAA J. 47 1327

    [13]

    Bisek N J 2010 Ph. D. Dissertation (Michigan: University of Michigan)

    [14]

    Lv H Y, Lee C H, Dong H T 2009 Sci. Sin. Phys. Mechan. Astron. 39 435 (in Chinese) [吕浩宇, 李椿萱, 董海涛 2009 中国科学 G辑 39 435]

    [15]

    Peng W, He Y G, Fang G F, Fan X T 2013 Acta Phys. Sin. 62 020301 (in Chinese) [彭武, 何怡刚, 方葛丰, 樊晓腾 2013 物理学报 62 020301]

    [16]

    Fujino T, Matsumoto Y, Kasahara J, Ishikawa M 2000 Progress in Aerospace Sci. 36 1

    [17]

    Zhang K P, Ding G H, Tian Z Y, Pan S, Li H 2009 J. National Univ. Defense Tech. 31 39 (in Chinese) [张康平, 丁国昊, 田正雨, 潘沙, 李桦 2009 国防科技大学学报 31 39]

    [18]

    Tian Z Y, Zhang K P, Pan S, Li H 2008 Chin. Quar. Mechan. 29 72 (in Chinese) [田正雨, 张康平, 潘沙, 李桦 2008 力学季刊 29 72]

    [19]

    Gnoffo P A, Gupta R N, Shinn J L 1989 NASA TP2867

  • [1]

    Zhu Y J, Jiang Y S, Hua H Q, Zhang C H, Xin C W 2014 Acta Phys. Sin. 63 244101 (in Chinese) [朱艳菊, 江月松, 华厚强, 张崇辉, 辛灿伟 2014 物理学报 63 244101]

    [2]

    Yin J F, You Y X, Li W, Hu T Q 2014 Acta Phys. Sin. 63 044701 (in Chinese) [尹纪富, 尤云祥, 李巍, 胡天群 2014 物理学报 63 044701]

    [3]

    Zhao G Y, Li Y H, Liang H, Hua W Z, Han M H 2015 Acta Phys. Sin. 64 015101 (in Chinese) [赵光银, 李应红, 梁华, 化为卓, 韩孟虎 2015 物理学报 64 015101]

    [4]

    Yu H Y 2014 Acta Phys. Sin. 63 047502 (in Chinese) [于红云 2014 物理学报 63 047502]

    [5]

    Bityurin V A, Bocharov A N 2014 52nd Aerospace Sciences Meeting National Harbor, Maryland, January 13-17, 2014

    [6]

    Bisek N J, Gosse R, Poggie J 2013 J. Spacecraft Rockets 50 927

    [7]

    Cristofolini A, Borghi C A, Neretti G, Battista F, Schettino A, Trifoni E, Filippis F D, Passaro A, Baccarella D 2012 18th AIAA/3AF International Space Planes and Hypersonic Systems and Technologies Conference Tours, France, September 24-28, 2012

    [8]

    Lv H Y, Lee C H 2010 Chin. Sci. Bull. 55 1182 (in Chinese) [吕浩宇, 李椿萱 2010 科学通报 55 1182]

    [9]

    Li K, Liu W Q 2016 Acta Phys. Sin. 65 064701 (in Chinese) [李开, 刘伟强 2016 物理学报 65 064701]

    [10]

    Hu H Y, Yang Y J, Zhou W J 2011 Chin. J. Theo. App. Mechan. 43 453 (in Chinese) [胡海洋, 杨云军, 周伟江 2011 力学学报 43 453]

    [11]

    Gaitonde D V, Poggie J 2002 40th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 14-17, 2002

    [12]

    Wan T, Candler G V, Macheret S O, Shneider M N 2009 AIAA J. 47 1327

    [13]

    Bisek N J 2010 Ph. D. Dissertation (Michigan: University of Michigan)

    [14]

    Lv H Y, Lee C H, Dong H T 2009 Sci. Sin. Phys. Mechan. Astron. 39 435 (in Chinese) [吕浩宇, 李椿萱, 董海涛 2009 中国科学 G辑 39 435]

    [15]

    Peng W, He Y G, Fang G F, Fan X T 2013 Acta Phys. Sin. 62 020301 (in Chinese) [彭武, 何怡刚, 方葛丰, 樊晓腾 2013 物理学报 62 020301]

    [16]

    Fujino T, Matsumoto Y, Kasahara J, Ishikawa M 2000 Progress in Aerospace Sci. 36 1

    [17]

    Zhang K P, Ding G H, Tian Z Y, Pan S, Li H 2009 J. National Univ. Defense Tech. 31 39 (in Chinese) [张康平, 丁国昊, 田正雨, 潘沙, 李桦 2009 国防科技大学学报 31 39]

    [18]

    Tian Z Y, Zhang K P, Pan S, Li H 2008 Chin. Quar. Mechan. 29 72 (in Chinese) [田正雨, 张康平, 潘沙, 李桦 2008 力学季刊 29 72]

    [19]

    Gnoffo P A, Gupta R N, Shinn J L 1989 NASA TP2867

  • [1] 金哲珺雨, 曾钊卓, 曹云姗, 严鹏. 磁子霍尔效应. 物理学报, 2024, 73(1): 017501. doi: 10.7498/aps.73.20231589
    [2] 苗钰钊, 唐桂华. 非封闭式热斗篷热防护特性. 物理学报, 2024, 73(3): 034401. doi: 10.7498/aps.73.20231262
    [3] 强晓斌, 卢海舟. 磁场中拓扑物态的量子输运. 物理学报, 2021, 70(2): 027201. doi: 10.7498/aps.70.20200914
    [4] 丁明松, 傅杨奥骁, 高铁锁, 董维中, 江涛, 刘庆宗. 高超声速磁流体力学控制霍尔效应影响. 物理学报, 2020, 69(21): 214703. doi: 10.7498/aps.69.20200630
    [5] 姚霄, 刘伟强, 谭建国. 高速飞行器磁控阻力特性. 物理学报, 2018, 67(17): 174702. doi: 10.7498/aps.67.20180478
    [6] 李开, 柳军, 刘伟强. 基于变均布霍尔系数的磁控热防护系统霍尔效应影响. 物理学报, 2017, 66(5): 054701. doi: 10.7498/aps.66.054701
    [7] 李开, 刘伟强. 高超声速飞行器磁控热防护系统建模分析. 物理学报, 2016, 65(6): 064701. doi: 10.7498/aps.65.064701
    [8] 李少峰, 杨联贵, 宋健. 层结流体中在热外源和效应地形效应作用下的非线性Rossby孤立波和非齐次Schrdinger方程. 物理学报, 2015, 64(19): 199201. doi: 10.7498/aps.64.199201
    [9] 苏青峰, 刘长柱, 王林军, 夏义本. 不同织构CVD金刚石膜的Hall效应特性. 物理学报, 2015, 64(11): 117301. doi: 10.7498/aps.64.117301
    [10] 韦庞, 李康, 冯硝, 欧云波, 张立果, 王立莉, 何珂, 马旭村, 薛其坤. 在预刻蚀的衬底上通过分子束外延直接生长出拓扑绝缘体薄膜的微器件. 物理学报, 2014, 63(2): 027303. doi: 10.7498/aps.63.027303
    [11] 吴宝嘉, 李燕, 彭刚, 高春晓. InSe的高压电输运性质研究. 物理学报, 2013, 62(14): 140702. doi: 10.7498/aps.62.140702
    [12] 彭武, 何怡刚, 方葛丰, 樊晓腾. 二维泊松方程的遗传PSOR改进算法. 物理学报, 2013, 62(2): 020301. doi: 10.7498/aps.62.020301
    [13] 侯碧辉, 刘凤艳, 焦彬, 岳明. 纳米金属Tm的电子浓度研究. 物理学报, 2012, 61(7): 077302. doi: 10.7498/aps.61.077302
    [14] 王经纬, 边继明, 孙景昌, 梁红伟, 赵涧泽, 杜国同. Ag掺杂p型ZnO薄膜及其光电性能研究. 物理学报, 2008, 57(8): 5212-5216. doi: 10.7498/aps.57.5212
    [15] 刘 奎, 丁宏林, 张贤高, 余林蔚, 黄信凡, 陈坤基. 量子点浮置栅量子线沟道三栅结构单电子场效应管存储特性的数值模拟. 物理学报, 2008, 57(11): 7052-7056. doi: 10.7498/aps.57.7052
    [16] 罗成林, 杨兵初, 戎茂华. 磁场对滤纸上Zn电解沉积物形貌的影响. 物理学报, 2006, 55(7): 3778-3784. doi: 10.7498/aps.55.3778
    [17] 陈卫平, 冯尚申, 焦正宽. Fe15.16Ag84.84金属颗粒膜自旋极化相关的霍尔效应研究. 物理学报, 2003, 52(12): 3176-3180. doi: 10.7498/aps.52.3176
    [18] 李慧玲, 阮可青, 李世燕, 莫维勤, 樊荣, 罗习刚, 陈仙辉, 曹烈兆. MgB2和Mg0.93Li0.07B2的电阻率与霍尔效应研究. 物理学报, 2001, 50(10): 2044-2048. doi: 10.7498/aps.50.2044
    [19] 胡响明, 彭金生. 量子拍激光:双模亚泊松光. 物理学报, 1998, 47(8): 1296-1303. doi: 10.7498/aps.47.1296
    [20] 庆承瑞, 周玉美. 环形非圆截面等离子体自由界面的磁流体平衡方程解. 物理学报, 1980, 29(1): 106-110. doi: 10.7498/aps.29.106
计量
  • 文章访问数:  5264
  • PDF下载量:  211
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-09-16
  • 修回日期:  2017-01-22
  • 刊出日期:  2017-04-05

/

返回文章
返回