飞行器雷击过程的数值仿真方法

doi:10.7527/S1000-6893.2025.31899

Abstract

Abstract:

To meet the design requirements for lightning protection coatings on hypersonic vehicles， a numerical simulation method for lightning strike processes was developed. Under local thermodynamic equilibrium conditions， the thermodynamic and transport properties of air were calculated using the free energy minimization method. The effects of Joule heating， viscous radiation， short-wavelength thermal radiation， and the Lorentz force on the magnetic confinement of the lightning channel were considered. The development of the lightning channel， variations in the thermodynamic parameters of the channel， and the shock wave development process were investigated. The results show that the shock wave development process obtained from the numerical method aligns with experimental measurements. The shock wave velocity decay rate and overpressure decay rate match the theoretical predictions， with clear distinctions in shock wave attenuation characteristics before and after the transition point between strong and weak shocks. Additionally， this method is used to analyze the effects of thermal radiation， magnetic confinement， lightning discharge power， and discharge time on the lightning strike process.

Key words: lightning, lightning protection coating, shock wave, hypersonic, thermal radiation

CLC Number:

V411.3

Yicheng QIU, Chaokai YUAN, Guilai HAN. Numerical simulation methods for aircraft exposed to lightning strikes[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(18): 131899.

Figures/Tables 17

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Table 2

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References 51

[1]	段泽民. 飞机雷电防护概述［J］. 高电压技术， 2017， 43（5）： 1393-1399.
	DUAN Z M. Review of aircraft lightning protection［J］. High Voltage Engineering， 2017， 43（5）： 1393-1399 （in Chinese）.
[2]	HEIDLER F， CVETIC J M， STANIC B V. Calculation of lightning current parameters［J］. IEEE Transactions on Power Delivery， 1999， 14（2）： 399-404.
[3]	周萍，吕英华，陈志红，等. 航天系统雷电防护技术发展综述及展望［J］. 宇航学报， 2018， 39（8）： 827-837.
	ZHOU P， LV Y H， CHEN Z H， et al. Review and prospect of lightning protection technology for an astronautic system［J］. Journal of Astronautics， 2018， 39（8）： 827-837 （in Chinese）.
[4]	HIRANO Y， KATSUMATA S， IWAHORI Y， et al. Artificial lightning testing on graphite/epoxy composite laminate［J］. Composites Part A： Applied Science and Manufacturing， 2010， 41（10）： 1461-1470.
[5]	段泽民，司晓亮，孙安宏. 航空器雷电防护技术［M］. 北京：航空工业出版社， 2013.
	DUAN Z M， SI X L， SUN A H. Aircraft lightning protection technology［M］. Beijing： Aviation Industry Press， 2013 （in Chinese）.
[6]	刘贺楠，郭俊，伊同强，等. 飞行器雷电直接效应与间接效应防护综述［J］. 宇航总体技术， 2019， 3（4）： 56-62.
	LIU H N， GUO J， YI T Q， et al. Protection of direct and indirect effects of lightning on aircraft［J］. Astronautical Systems Engineering Technology， 2019， 3（4）： 56-62 （in Chinese）.
[7]	苑朝凯，王春，姜宗林. 电子发汗冷却技术及其研究进展［J］. 力学学报， 2024， 56（3）： 507-520.
	YUAN C K， WANG C， JIANG Z L. Electron transpiration cooling technology and its research progress［J］. Chinese Journal of Theoretical and Applied Mechanics， 2024， 56（3）： 507-520 （in Chinese）.
[8]	苑朝凯，李进平，陈宏，等. 高超声速溢流冷却实验研究［J］. 力学学报， 2018， 50（1）： 1-8.
	YUAN C K， LI J P， CHEN H， et al. Experimental study of hypersonic overflow cooling［J］. Chinese Journal of Theoretical and Applied Mechanics， 2018， 50（1）： 1-8 （in Chinese）.
[9]	苑朝凯，李进平，陈宏，等. 高超声速条件下溢流液膜厚度测量方法［J］. 中国科学：技术科学， 2018， 48（6）： 629-638.
	YUAN C K， LI J P， CHEN H， et al. Measuring method of overflow liquid film thickness in hypersonic flow［J］. Scientia Sinica （Technologica）， 2018， 48（6）： 629-638 （in Chinese）.
[10]	RAKOV V A， UMAN M A. Lightning： Physics and effects［M］. Cambridge： Cambridge University Press， 2003.
[11]	CHEMARTIN L， LALANDE P， MONTREUIL E， et al. Three dimensional simulation of a DC free burning arc. Application to lightning physics［J］. Atmospheric Research， 2009， 91（2-4）： 371-380.
[12]	李婷，叶辉，董琪，等. 柔性防热层外用雷击防护涂层的制备及其性能研究［J］. 涂料工业， 2022， 52（7）： 27-33.
	LI T， YE H， DONG Q， et al. Preparation and properties of lightning protection coating on flexible thermal insulation coating［J］. Paint & Coatings Industry， 2022， 52（7）： 27-33 （in Chinese）.
[13]	宋树培. GJB1804《运载火箭雷电防护》简介［J］. 航天标准化， 1997（2）： 9-11.
	SONG S P. Brief introduction of GJB1804 lightning protection for launch vehicles［J］. Aerospace Standardization， 1997（2）： 9-11 （in Chinese）.
[14]	COUNCIL N R. The earth‘s electrical environment［M］. Washington， D.C.： NASA， 1986.
[15]	AE-2 LIGHTNING COMMITTEE. Aircraft lightning test methods ［S］. Warrendale： SAE International， 2005.
[16]	PLOOSTER M N. Shock waves from line sources. numerical solutions and experimental measurements［J］. The Physics of Fluids， 1970， 13（11）： 2665-2675.
[17]	PLOOSTER M N. Numerical model of the return stroke of the lightning discharge［J］. Physics of Fluids， 1971， 14（10）： 2124-2133.
[18]	PLOOSTER M N. Numerical simulation of spark discharges in air［J］. The Physics of Fluids， 1971， 14（10）： 2111-2123.
[19]	AKRAM M. Two-dimensional model for spark discharge simulation in air［J］. AIAA Journal， 1996， 34（9）： 1835-1842.
[20]	AKRAM M. The evolution of spark discharges in gases： II. Numerical solution of one-dimensional models［J］. Journal of Physics D： Applied Physics， 1996， 29（8）： 2137-2147.
[21]	孙景群. 闪电通道的径向扩展［J］. 大气科学， 1979， 3（1）： 69-77.
	SUN J Q. Radial expansion of lightning channels［J］. Chinese Journal of Atmospheric Sciences， 1979， 3（1）： 69-77 （in Chinese）.
[22]	XIONG J M， LI L E， DAI H Y， et al. The development of shock wave overpressure driven by channel expansion of high current impulse discharge arc［J］. Physics of Plasmas， 2018， 25（3）： 032115.
[23]	LIAO Y Q， MAHARDIKA N， ZHAO X G， et al. Shock wave propagation in long laboratory Sparks under negative switching impulses［J］. Journal of Physics D： Applied Physics， 2021， 54（1）： 015205.
[24]	CAPITELLI M， COLONNA G， GORSE C， et al. Transport properties of high temperature air in local thermodynamic equilibrium［J］. The European Physical Journal D-Atomic， Molecular， Optical and Plasma Physics， 2000， 11（2）： 279-289.
[25]	KARCH C， SCHREINER M， HONKE R， et al. Shock waves from a lightning discharge［C］∥2018 34th International Conference on Lightning Protection （ICLP）. Piscataway： IEEE Press， 2018： 1-6.
[26]	BOCHAROV A N， MAREEV E A， POPOV N A. Numerical simulation of the main stage of a lightning［J］. Plasma Physics Reports， 2024， 50（3）： 380-387.
[27]	LUO S C， WU L Y， CHANG Y. Mechanism analysis of magnetohydrodynamic control in hypersonic turbulent flow［J］. Acta Physica Sinica， 2022， 71（21）（in Chinese）.
[28]	罗凯，汪球，李进平，等. 基于高温真实气体效应的双锥磁流体流动控制［J］. 航空学报， 2022， 43（S2）： 79-91.
	LUO K， WANG Q， LI J P， et al. Magnetohydrodynamic flow control of double-cone under high temperature real gas effect［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（Sup 2）： 79-91.
[29]	WRIGHT J K. Shock tubes［M］. London： Methuen， 1961： 131.
[30]	PAI S I. Radiation gas dynamics［M］. New York： Springer Verlag， 1966： 8-24.
[31]	OLSEN H N. Thermal and electrical properties of an argon plasma［J］. The Physics of Fluids， 1959， 2（6）： 614-623.
[32]	SPITZER L， HÄRM R. Transport phenomena in a completely ionized gas［J］. Physical Review， 1953， 89（5）： 977-981.
[33]	SHER E， BEN-YA’ISH J， KRAVCHIK T. On the birth of spark channels［J］. Combustion and Flame， 1992， 89（2）： 186-194.
[34]	PLOOSTER M N. Shock waves from line sources［M］. Boulder： National Center for Atmospheric Research， 1968.
[35]	Мандельштан С Л， Суходрев Н К. Элементарные процессы в канале искрового разряда［J］. ЖЭТФ， 1953， 24（6）： 701-7.
[36]	EDWARDS J R. A low-diffusion flux-splitting scheme for Navier-Stokes calculations［J］. Computers & Fluids， 1997， 26（6）： 635-659.
[37]	WADA Y， LIOU M S. A flux splitting scheme with high-resolution and robustness for discontinuities： AIAA-1994-83［R］. Reston： AIAA， 1994.
[38]	GOTTLIEB S， SHU C-W. Total variation diminishing Runge-Kutta schemes［J］. Mathematics of Computation， 1998， 67（221）： 73-85.
[39]	BRUCE C E R， GOLDE R H. The lightning discharge［J］. Journal of the Institution of Electrical Engineers-Part Ⅱ： Power Engineering， 1941， 88（6）： 487-505.
[40]	DENNIS A S， PIERCE E T. The return stroke of the lightning flash to earth as a source of VLF atmospherics［J］. Journal of Research of the National Bureau of Standards， Section D： Radio Science， 1964， 68D（7）： 777.
[41]	CHEMARTIN L， LALANDE P， PEYROU B， et al. Direct effects of lightning on aircraft structure： Analysis of the thermal， electrical and mechanical constraints［J］. Aerospace Lab， 2012 （5）： 1-15.
[42]	ORVILLE R E， UMAN M A， SLETTEN A M. Temperature and electron density in long air Sparks［J］. Journal of Applied Physics， 1967， 38（2）： 895-896.
[43]	HIGHAM J B， MEEK J M. The expansion of gaseous spark channels［J］. Proceedings of the Physical Society Section B， 1950， 63（9）： 649.
[44]	NORINDER H， KARSTEN O. Investigation of resistance and power in experimental lightning discharges［J］. Journal of the Franklin Institute， 1952， 253（3）： 225-233.
[45]	滕宏辉，姜宗林，韩肇元. 环形激波绕射、反射和聚焦的数值模拟研究［J］. 力学学报， 2004， 36（1）： 9-15.
	TENG H H， JIANG Z L， HAN Z Y. Numerical investigation of diffraction， focusing and reflection of toroidal shock waves［J］. Chinese Journal of Theoretical and Applied Mechanics， 2004， 36（1）： 9-15 （in Chinese）.
[46]	JONES D L， GOYER G G， PLOOSTER M N. Shock wave from a lightning discharge［J］. Journal of Geophysical Research （1896-1977）， 1968， 73（10）： 3121-3127.
[47]	胡宗民，姜宗林. 气体动力学［M］. 北京：科学出版社， 2023.
	HU Z M， JIANG Z L. Gas dynamics［M］. Beijing： Science Press， 2023 （in Chinese）.
[48]	ZHOU H B， ZHANG Y M， HAN R Y， et al. Signal analysis and waveform reconstruction of shock waves generated by underwater electrical wire explosions with piezoelectric pressure probes［J］. Sensors， 2016， 16（4）： 573.
[49]	WANG Y， ZHUPANSKA O I. Lightning strike thermal damage model for glass fiber reinforced polymer matrix composites and its application to wind turbine blades［J］. Composite Structures， 2015， 132： 1182-1191.
[50]	王道洪，郄秀书，郭昌明. 雷电与人工引雷［M］. 上海：上海交通大学出版社， 2000.
	WANG D H， QIE X S， GUO C M. Lightning and artificial lightning induction［M］. Shanghai： Shanghai Jiao Tong University Press， 2000 （in Chinese）.
[51]	WANG R Y， YUAN P， CEN J Y， et al. Influence of the observation distance on the lightning channel temperature studied by means of spectroscopic diagnosis［J］. Acta Physica Sinica， 2014， 63（9）： 099203.

参数	数值
气体常数R/（J·K^-1·kg^-1）	2.880 946×10²
比解离能E₀/（J·kg^-1）	2.930 557×10⁷
一次电离比能E₁/（J·kg^-1）	9.591 766×10⁷
二次电离比能E₂/（J·kg^-1）	2.0620 56×10⁸
解离常数C₀/（m³·K^1.5kg^-1）	4.817 588×10^-4
一次电离常数C₁/（m³·K^1.5kg^-1）	11 014.16
二次电离常数C₂/（m³·K^1.5kg^-1）	10 339.65
振动温度T_v/K	3 150.0
标准空气密度ρ₀/（kg·m^-3）	1.172 358
标准温度T₀/K	300.0
标准压强p₀/Pa	101 325

序号	I₀/kA	t_m/μs	k_n/μs	对比试验
1	7	1.5	8	Orville等^［42］
2	20	5	50	Plooster^［17］
3	0.5	0.25	15	Higham， Meek^［43］
4	10	4	12	Norinder， Karsten^［44］
5	2	2	2	Liao等^［23］

Numerical simulation methods for aircraft exposed to lightning strikes

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