雷击金属结构物时雷电流分布的研究
摘要
针对雷击金属结构物雷电分布,本文推导了数值有限差分计算方法,分别对雷击规则和不规则的金属结构物的雷电分布进行了建模仿真,得到了雷电分布的数值计算结果。主要的研究内容包括以下方面。
在飞行器防雷方面,阐述了飞行器的雷电效应,分析了飞行器的雷电机械效应,热效应和电效应,描述了雷击飞行器的主要特征,提出了飞行器雷电的防护措施。
在雷电流模型的认识方面,首先探讨了自然雷电的形成,雷电压的本质。列出了雷电闪击的类型、五种雷电的模型和雷电的参数。其中,对霍得勒(Heidler)函数模型和脉冲函数模型分别在时域和频域进行仿真,着重讨论和分析比较了两者之间的优劣和作为研究所适用的场合。
在推导数值有限差分计算方法方面,首先介绍了差分计算的原理,分别采用了正方形网格划分和三角形网格划分的方法。运用这两种划分方法,分别得到各划分方法的差分格式公式。在研究不同的雷击金属结构物雷电分布的场域,为减小计算误差,达到所需要的计算精度,在考虑尽量让网格节点和雷电分布场域边界尽量重合的前提下,有选择性的运用所推导的网格划分对雷电分布进行计算分析。
在雷击金属结构物雷电分布的数值计算方面,对规则的金属结构物,采用了正方形网格划分的方法在MATLAB上编程迭代出计算结果并仿真了分布图。同时,在MATLAB平台上构建了结构物的模型,采用了同样的参数,运用自动生成的三角形网格划分方法对该规则金属结构物进行了雷电分布的模拟,得到的结果与正方形划分方法完全一致。对于不规则金属结构物,构建的模型是容易遭受雷击的飞机的机头部分,仿真出了雷电分布的图形,得到了每一个节点的计算结果。分析可知,雷电分布仿真的结果与实际的雷电分布相一致。这正说明了该计算方法对于雷电分布的研究具有一定的参考价值。
最后,对本文的研究工作进行了总结,指出了本文研究的主要内容。找到了一种数值计算方法,利用该方法可以求解雷击金属结构物任意点的雷电分布。此外,本文还提出了进一步研究中亟待解决的问题。
In this paper, a Method of Finite Difference(FDM) calculation to analyze the lightning distribution when it strikes to the metallic structure is deduced. The Modeling Simulations of the regular and irregular metallic structure that lightning distributes on them are built and achieve the results of the lightning distribution. The main contents include the following aspects
About lightning prevention of aircraft, expatiate on aircraft lightning effects, the mechanical effects and thermal effects of lightning are also analyzed. The main character of lightning strikes to aircraft is depicted and putting forward the measures of lightning prevention.
About the knowledge of lightning models, the form of nature lightning and the character of lightning voltage are described at first. The type of lightning, five different lightning models and lightning parameters are given. Especially, according to Heidler and Pulse function models, detailedly discussed the advantage and disadvantage between theses two models by means of simulating respectively in time field and frequency field.
About the numerical FDM, firstly reciting its principle, adopting foursquare and triangular cell-grid partition, then the FDM formula based on those two kinds of partition are achieved. In the different field in which studying lightning distributes, it should take account into making the grid note coincide with the field boundary and take the right grid partition method to analyze the lightning distribute so that it can reduce errors and get needed calculation precision.
About the numerical calculation of lightning distribution when it strikes to metallic structure, achieving the simulation result of regular metallic structure by choosing the square cell-grid partition method and programming on Matlab platform. According to the same models with the same parameters, it also acquires the completely coincident simulation result by means of constructing models on Matlab platform with triangle cell-grid partition. In allusion to irregular metallic structure, the model constructed in this paper is a part of fighter plane's head which is vulnerable by lightning. The result of lightning distribution simulation and every note are achieved. By analyzing the result, it can make conclusion that the simulation result is coincident with the practical lightning distribution. Thus, the result shows the numerical FDM has certain reference value to study the lightning distribution.
Finally, the work in this paper is summarized and main contents about the subject are indicated. Finding a numerical, and it can figure out the lightning distribution on arbitrary point. Besides, the further research problems are indicated.
在飞行器防雷方面,阐述了飞行器的雷电效应,分析了飞行器的雷电机械效应,热效应和电效应,描述了雷击飞行器的主要特征,提出了飞行器雷电的防护措施。
在雷电流模型的认识方面,首先探讨了自然雷电的形成,雷电压的本质。列出了雷电闪击的类型、五种雷电的模型和雷电的参数。其中,对霍得勒(Heidler)函数模型和脉冲函数模型分别在时域和频域进行仿真,着重讨论和分析比较了两者之间的优劣和作为研究所适用的场合。
在推导数值有限差分计算方法方面,首先介绍了差分计算的原理,分别采用了正方形网格划分和三角形网格划分的方法。运用这两种划分方法,分别得到各划分方法的差分格式公式。在研究不同的雷击金属结构物雷电分布的场域,为减小计算误差,达到所需要的计算精度,在考虑尽量让网格节点和雷电分布场域边界尽量重合的前提下,有选择性的运用所推导的网格划分对雷电分布进行计算分析。
在雷击金属结构物雷电分布的数值计算方面,对规则的金属结构物,采用了正方形网格划分的方法在MATLAB上编程迭代出计算结果并仿真了分布图。同时,在MATLAB平台上构建了结构物的模型,采用了同样的参数,运用自动生成的三角形网格划分方法对该规则金属结构物进行了雷电分布的模拟,得到的结果与正方形划分方法完全一致。对于不规则金属结构物,构建的模型是容易遭受雷击的飞机的机头部分,仿真出了雷电分布的图形,得到了每一个节点的计算结果。分析可知,雷电分布仿真的结果与实际的雷电分布相一致。这正说明了该计算方法对于雷电分布的研究具有一定的参考价值。
最后,对本文的研究工作进行了总结,指出了本文研究的主要内容。找到了一种数值计算方法,利用该方法可以求解雷击金属结构物任意点的雷电分布。此外,本文还提出了进一步研究中亟待解决的问题。
In this paper, a Method of Finite Difference(FDM) calculation to analyze the lightning distribution when it strikes to the metallic structure is deduced. The Modeling Simulations of the regular and irregular metallic structure that lightning distributes on them are built and achieve the results of the lightning distribution. The main contents include the following aspects
About lightning prevention of aircraft, expatiate on aircraft lightning effects, the mechanical effects and thermal effects of lightning are also analyzed. The main character of lightning strikes to aircraft is depicted and putting forward the measures of lightning prevention.
About the knowledge of lightning models, the form of nature lightning and the character of lightning voltage are described at first. The type of lightning, five different lightning models and lightning parameters are given. Especially, according to Heidler and Pulse function models, detailedly discussed the advantage and disadvantage between theses two models by means of simulating respectively in time field and frequency field.
About the numerical FDM, firstly reciting its principle, adopting foursquare and triangular cell-grid partition, then the FDM formula based on those two kinds of partition are achieved. In the different field in which studying lightning distributes, it should take account into making the grid note coincide with the field boundary and take the right grid partition method to analyze the lightning distribute so that it can reduce errors and get needed calculation precision.
About the numerical calculation of lightning distribution when it strikes to metallic structure, achieving the simulation result of regular metallic structure by choosing the square cell-grid partition method and programming on Matlab platform. According to the same models with the same parameters, it also acquires the completely coincident simulation result by means of constructing models on Matlab platform with triangle cell-grid partition. In allusion to irregular metallic structure, the model constructed in this paper is a part of fighter plane's head which is vulnerable by lightning. The result of lightning distribution simulation and every note are achieved. By analyzing the result, it can make conclusion that the simulation result is coincident with the practical lightning distribution. Thus, the result shows the numerical FDM has certain reference value to study the lightning distribution.
Finally, the work in this paper is summarized and main contents about the subject are indicated. Finding a numerical, and it can figure out the lightning distribution on arbitrary point. Besides, the further research problems are indicated.
引文
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[2]K.Beger.Novel observations on lightning discharges:results of research on Mount San Salvatore[J].J.Franklin Inst,1967(28):478-525.
[3]F.Heidler and J.M.Cvetic and B.V.Stanic,Calculation of Lightning Current Parameters[J]. IEEE Transactions on Power Delivery, Vol.14, No.2, pp399-404, 1999.
[4]Heidler F Trvaling current source model for LEMP calculation.6th Int Sym EM C. Zurich.1985,157.
[5]A.S.Podgorski,J.A.Landt. Three dimensional time domain modeling of lightning.IEEE Trans.Power Del.,1987,PWRD-2:931-938
[6]Chandima Gomes, Vernon cooray. Concepts of Lightning Return Stroke Models. IEEE Transactions on Electromagnetic Compatibility,2000,42(1): 82-96.
[7]A. Andreotti, U.De Martinis,L.Verolino.Comparison of electromagnetic field for two different lightning pulse current models[J]. European Transactions on Electrical Power, Volume 11 Issue 4, Pages 221-225,2007.
[8]Chunshan Yang and Bihua Zhou" Calculation methods of electromagnetic fields very close to lightning", IEEE Trans. on Electromagn.Compa.,2004,Vol.46,No.1,pp.133-141.
[9]Martin A.Uman.Natural lightning. IEEE Transactions on Industry Applications,1994,30(3):785-790
[10]IEC 1312-1, Protection against lightning electromagnetic impulse-Part Ⅰ[S]. General priciples,1995.
[11]ManeckJ.Master.Martin A.Uman.Lighting induced voltages on power lines:theory. IEEE Transactions on power apparatus and systems,19824,PAS-103(9):2502-2515
[12]R.Moini,V.A.Rakov,M.A.Uman et al.An antenna theory model for the lightning return stroke In:Proc.12th Int.Zurich Symp. Electromagnetic Compat.Zurich,Switzerland,Feb.1997.149-152
[13]Yoshihiro Baba, Masaru Ishii. Lightning Return-Stroke Model Incorporating Current Distortion [J]. IEEE Trans. Electromagn. Compat.,2002, 44(3):476-477.
[14]Miyakes S K, Shindo T. Discharge path model in model test of lightning strokes to tall mast [J]. IEEE Trans. on Power Apparatus and Systems, 1981,100(7):3553-3564.
[15]Mazur V. Triggered lightning strikes to aircraft and natural intra-cloud discharges[J]. J Geophys.Res.,1989,94:3311-3325.
[16]V.A.Rakov.Characterization Of Lightning Electromagnetic.In:Proc.13th Int.Zurich Symp. On Electromagnetic Compatibility.Zurich,Switzerland,1999.561-566
[17]Dellera L, Garbagnati E. Lightning strokes simulation by means of the leader progression model[J]. IEEE Trans. on Power Delivery,1990,5(4):2009-2017.
[18]Carlo Alberto Nucci, Farhad Rachidi. On the contribution of the electromagnetic field components in field-to-transmisssion line interaction. IEEE transactions on Electromagnetic Compatibility,1995,37(4):505-508.
[19]Martin A. Uman, Marcos Rubinstein. Methods for calculating the electromagnetic fields from a known source distribution:application to lightning IEEE Transactions on Electromagnetic Compatibility,1989,31(2): 183-189
[20]Demkowicz L. On some convergence results for FDM with irregular mesh. Computer Methods in Applied Mechanics and Engineering,1984; 42(3):344-356
[21]Childers, L., Disz, T., Olson et al. Access Grid:Immersive Group-to-Group Collaborative Visualization. In:Proc.4th International Immersive Projection Technology Workshop,2000.
[22]Sabrina. M and Innovative S. Absorbing boundary conditions for the efficient FDTD analysis of lightning-interaction problems[J]. IEEE Transaction on Electromagnetic Compatibility,2001,43(3):368-381.
[23]Zhang Jun, Pan Zu-Liang. Symmetries and Exact Solutions of Some Classes of Nonlinear Difference Equations[J].Appl Math J ChineseUniv,2001,16A(2):143-146.
[24]Blacker T D, Stephenson M B. Paving:A new approach to automated quadrilateral mesh generation[J]. International Journal for Numerical Methods in Engineering.1991,32(4):811-847.
[25]Rubinstein M, Uman M A. Methods for calculating the electromagnetic fields from a known source distribution:application to lightning. IEEE Trans on EMC,1989,31(20):183.
[26]Noda. T. and Numerical A. Simulation of transient electromagnetic fields for obtaining the step response of a transmission tower using the FDTD method[J]. IEEE Transaction on Power Delivery,2003,26(2):1262-1266.
[27]Li Qian, Zhao Zhi-bin, and Cui Xiang. Calculation and research of electromagnetic field in space aroud lightning path with finite difference time domain method[C]. International Symposium on Electromagnetic Compatibility, Qingdao, Oct,2007:424-427.
[28]Zhang, Z.T., Atluri, S.N., A local boundary integral equation(LBIE) method in computational mechanics, and a mesh-less discretization approach[J]. Comput. Mech.1998,21:223-235
[29]Winslow A M. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. Journal of Computational Physics, 1967;1(2):149-172
[30]Belytschko, T., Krongauz, T., Organ, D., Fleming, M., Krysl, P., Mesh-less methods:An overview and recent developments[J]. Comput. Methods Appl. Mech. Engrg.1996,139:3-4
[31]Saber Elaydi. An Introduction to Difference Equations[M]. New York:Springer-Verlag,2005.
[32]柯恒,张为民译.富兰克林的实验[M].北京：电子工业出版社,198.924-28.
[33]徐学基,诸定昌,气体放电物理[M].上海：复旦大学出版社,1996：21-31.
[34]王道洪,郡秀书,郭昌明.雷电与人工引雷[M].上海：上海交通大学出版社,2000.
[35]苏邦礼等.雷电与避雷工程[M].广州：中山大学出版社,1996.66-70.
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