考虑非傅立叶效应的火药等离子体点火模拟
摘要
电热化学炮等离子体点火较常规点火有很多优点，为进一步完善电热化学推进技术，有必要对含能材料(火药)等离子体点火进行更深入的研究。本文的研究工作在于更深入地了解电热化学炮等离子体点火过程中的含能材料的温度分布规律。首先给出了在极高、低温度下，考虑热量传播速度的非傅立叶热传导理论，并对球坐标下一维热传导微分方程的解析解进行了探讨，认识到颗粒的松弛时间、尺度、导热系数以及热作用时间对是否需要考虑非傅立叶效应很重要；然后通过等离子体对固体颗粒热传导行为的更深入的分析，以及对已有学者建立的等离子体点火模型的介绍，发展了针对电热化学炮等离子体点火特点的，考虑有限热传播速度的非傅立叶效应的等离子体点火模型。对单个药粒在等离子体环境下的相互作用，分别建立了接近电热化学炮实际点火边界条件下，含能材料等离子体点火的一维和二维数学模型，模型的主控方程是考虑非傅立叶导热的双曲型偏微分方程，并在适当的简化条件下对模型进行了数值求解，通过对所得的数值解的分析讨论，认识到等离子体能量对点火性能有较大影响，等离子体能量增大，点火延迟缩短；考虑径向和轴向温度均变化的二维圆柱模型，比只考虑径向温度变化的球模型更符合实际情况；并且通过普通火药和包覆层火药分别考虑经典傅立叶导热和非傅立叶导热时得到的结果比较，发现考虑等离子体点火时的非傅立叶导热效应更加合理，与实际情况更加符合。
There are many excellences in plasma ignition for Electrothermal-Chemical Gun (ETCG)
when compared with the normal ignition. In order to improve the ETC launch technique, it
is necessary to study the propellant with plasma ignition thoroughly. The investigation of
this thesis is to find out the temperature distribution of propellant in ETCG with plasma
ignition. Firstly, at the surroundings of fearfully high or low temperature, Non-Fourier heat
transfer whose heat transmission speed is a finite value is introduced, and analytical
solutions of hyperbolic heat conduction model for a one-dimension sphere has been
discussed, it is realized that whether the Non-Fourier heat transfer be considered is
determined by the relaxation time, size, thermal conductivity of the particle and thermal
effect time. Then, the Non-Fourier conduction heat transfer model which attention to the
characteristics of ETCG is developed, which base on the characteristic of solid grains with
plasma conduction and conventional ignition theory and some plasma ignition models
established by scholars before. The one-dimension sphere and two-dimension cylinder
plasma ignition model of propellant are established which are different from the
conventional ignition models. The govern equation of this new model is hyperbolic partial
differential equation of Non-Fourier heat conduction. Lastly, the numerical simulation of
the model is used to rich the analysis under the suitable simple. The result show that: the
ignition delay will be shortened while the energy of plasma increase; the two-dimension
cylinder model with consideration of radial and axis temperature change is more feasibility
when compared with the one-dimension sphere model with consideration of radial
temperature changes; the comparisons of the results of classical Fourier heat conduction
and Non-Fourier heat conduction model with considering of normal propellant and the
propellant with protective films respectively, show that it is more feasibility to considering
Non-Fourier heat conduction, and it agree with the practical situation better.
There are many excellences in plasma ignition for Electrothermal-Chemical Gun (ETCG)
when compared with the normal ignition. In order to improve the ETC launch technique, it
is necessary to study the propellant with plasma ignition thoroughly. The investigation of
this thesis is to find out the temperature distribution of propellant in ETCG with plasma
ignition. Firstly, at the surroundings of fearfully high or low temperature, Non-Fourier heat
transfer whose heat transmission speed is a finite value is introduced, and analytical
solutions of hyperbolic heat conduction model for a one-dimension sphere has been
discussed, it is realized that whether the Non-Fourier heat transfer be considered is
determined by the relaxation time, size, thermal conductivity of the particle and thermal
effect time. Then, the Non-Fourier conduction heat transfer model which attention to the
characteristics of ETCG is developed, which base on the characteristic of solid grains with
plasma conduction and conventional ignition theory and some plasma ignition models
established by scholars before. The one-dimension sphere and two-dimension cylinder
plasma ignition model of propellant are established which are different from the
conventional ignition models. The govern equation of this new model is hyperbolic partial
differential equation of Non-Fourier heat conduction. Lastly, the numerical simulation of
the model is used to rich the analysis under the suitable simple. The result show that: the
ignition delay will be shortened while the energy of plasma increase; the two-dimension
cylinder model with consideration of radial and axis temperature change is more feasibility
when compared with the one-dimension sphere model with consideration of radial
temperature changes; the comparisons of the results of classical Fourier heat conduction
and Non-Fourier heat conduction model with considering of normal propellant and the
propellant with protective films respectively, show that it is more feasibility to considering
Non-Fourier heat conduction, and it agree with the practical situation better.
引文
1 陶其恒．国外电热发射技术研究综述．弹道学报．1998，10(3)：91-96
2 欧阳立新．电热化学反射技术的应用前景．弹道学报．1995，7(2)：92-96
3 Wildegger-Gaissmaier. Modeling Flame Spread in Plasma Ignited Gun Charges. Proceedings of the 16th International Symposium on Ballistics, U.S.A, 1996:387-396
4 金志明，袁亚雄，宋明．现代内弹道．北京：北京理工大学出版社，1992
5 金志明，翁春生．高等内弹道学．北京：高等教育出版社，2003，12
6 戴荣，栗保明，卢顺祥．固体发射药等离子态点火过程及弹道效应分析．爆炸与冲击．1999，19(1)：84-89
7 张小兵，袁亚雄，谢玉树．等离子体点火密闭爆发器实验研究．火炸药学报．2003，26(2)：24-31
8 C.M.Edwards, M.A.Bourham, J.G.Gilligan. Experimental Studies of the Plasma-Propellant Interface for Electrothermal-Chemical Launchers. IEEE TRANSACTIONS ON MAGNETICS. 1995,31(1):404-409
9 Baoming Li, Hongzhi Li. Energetic Particle Ignition Exposed to Thermal Plasma. 17th International Symposium on Ballistics, South Africa, Vol.1, 1998:347-358
10 南京理工在学机械学院101教研室．电热—电磁发射技术译文选辑．1994，4
11 White K J. Katulka G L. Electrothermal Chemical Plasma Interaction with Propellants. Proceedings of the 16th International Symposium on Ballistics, U.S.A, 1996:387-396
12 M.A.Bourham, J.G.Gilligan. Augmentation and Control of Bum Rate in Plasma-Devices. APL Progress Report, 1997
13 K.J.White, lrvin Stobie, W.Oberle, Gary Katulka, Simon Driesen. Combustion Control Requirements in High Loading Density, Solid Propellant ETC Gun Firings. IEEE Transactions on Magnetics, Vol.33,1997:350-355
14 G.P.Wren, W.F.Oberle. Ballistic Analysis of Electrothermal-Chemical (ETC) Propellant. ARL-TR-1245, Dec. 1996
15 G.L.Katulka, et al. Experimental Characterization of Plasma Effects on Energetic Materials for Electrothermal-Chemical Launch Applications. IEEE Transactions on Magnetics, Vol.35,No.1,Jan.1999:197-200
16 Kaste P, et al. Plasma Ignition of Consolidated Propellant in A 60mm ETC Gun. ISL, French-German Research institutes of Saint-Louis.19th International Symposium on Ballistics, 2001 (1): 187-194
17 Kaste P, et al. Analysis of Burning Rate Phenomena and Extinguished Solid Propellant from an Interrupted Closed Bomb with Plasma Igniter. IEEE Transactions on Magnetics, Vol.37,No.1,Jan.2001:173-177
18 Bourham M A, Gilligan J G, Oberle W F. Analysis of Solid Propellant Combustion Behavior under Electrothermal Plasma Injection for ETC Launchers. IEEE Transaction on Magnetics, Vol.33,No1, Jan. 1997:278-284
19 Tran M P, et al. Relationship between Plasma and Gas Generation in an Electrothermal-Chemical Gun. ARL-TR-327,Jan. 1994
20 White K J et al. Combustion Control Requirements in High Loading Density, Solid Propellant ETC Gun Firings. IEEE Transaction on Magnetics, Vol.33, No.1, Jan. 1997:350-355
21 Fifer R A, et al. Chemical Effects in Plasma Ignition. IEEE Transactions on Magnetics, Vol.39,No.1, Jan.2003
22 Beyer R A. Pesce-Rodriguez R A. Experiments to Define Plasma-Propellant Interactions. IEEE Transaction on Magnetics, Vol.39,No.1,Jan.2003:207-211
23 D.E.Kooker. A Mechanism for ETC-Augmented Burning Rate of Solid Propellant consistent with Closed Chamber Experiment. 18th international symposium on ballistics, 1999:236-243
24 Michael A. Schroeder, Richard A. Beyer, Rose A. Pesce-Rodriguez. Scanning Electron Microscope Examination of JA2 Propellant Samples Exposed to Plasma Radiation. IEEE TRANSACTIONS ON MAGNETICS. 2005,41(1):350-354
25 OBERLEW, et al. Summary of Experimental Effects to Determines Plasma-Augmented Burn Rates. ARL-TR-782. 1995
26 戴荣，栗保明．电热化学炮等离子体增强燃烧过程研究．兵工学报．2003，24(3)：396-398
27 Alimi R, Perelmutter L, Onn U. Modeling an Internal injection Process for the Solid Propellant Electro-thermal Chemical Gun. 16th International Symposium on Ballistic. 1996
28 程代模．美国电热化学炮技术成就的综述与分析．弹箭技术．1995，(1)：1-10
29 梁昆淼．数学物理方法．北京：人民教育出版社，1979，2
30 姜任秋．热传导、质扩散与动量传递中的瞬态冲击效应．北京：科学出版社，1997，2
31 高正阳，阎维平，刘忠．煤颗粒在快速升温过程中非傅立叶导热效应的计算研究．中国电机工程学报．2002，22(9)：141-145
32 蒋方明，刘登瀛．非傅立叶导热的最新研究进展．力学进展．2002，32(1)：128-140
33 Kiwan S, Al-Nimr M, Al-Sharo'a M. Trial solution method to solve the hyperbolic heat conduction equation. International Committee Heat Mass Transfer. 2000, 27(6):865-876
34 张浙，刘登瀛．超急速传热时球体内非稳态热传导的非傅立叶效应．工程热物理学报．1998，19(5)：601-605
35 C.S.Tsai, Y.C.Lin, C.I.Hung. A study on the non-Fourier effects in spherical media due to sudden temperature changes on the surfaces. Heat Mass Transfer. 2005,41:709-716
36 张建奇．热等离子体环境下含能颗粒点火与燃烧特性研究．南京理工大学硕士学位论文，1999
37 李宝奇．等离子体点火模型的理论分析和研究．南京理工大学硕士学位论文，2004
38 张柏生．火药燃烧导论．南京：华东工学院，1988
39 王伯羲，冯增国．火药燃烧理论．北京：北京理工大学出版社，1997
40 陈熙．高温电离气体的传热与流动．北京：科学出版社，1993
41 Proulx. Plasma-Particle Interaction Effects Induction Plasma Modeling under Dense Loading Conditions. Int J. Heat Mass Transfer, Vol.28, No.7, 1985:1327-1336
42 Wei.D, Y.C.Farouk. Melting Powder Particles in a Low-Pressure Plasma Jet. ASME Journal of Heat Transfer, Vol.109,1987:971-976
43 Andreas Koleczko, Walter Ehrhard, et al. Plasma Ignition and Combustion. Propellant, Explosives, Pyrotechnics, Vol.26, 2001:75-83
44 Woodlet C R. Modeling Heat Transfer from Conventional and Plasma Igniters to Solid propellant. 20th International Symposium on Ballistics, Orlandol. September,2002:276-282
45 张小兵，袁亚雄，陈健，陈涛．含能材料等离子体点火过程的数值模拟．南京理工大学学报．第28卷，第3期，2004，6
46 谢玉树，张小兵等．含能材料等离子体点火过程的强瞬态二维热传导分析．兵工学报．第26卷，第6期，2005，11
47 Glass D E, et al. Hyperbolic heat conduction with surface radiation. Int J Heat Mass Transfer, 1982,28(10): 1823-1830
48 Carey G F, Tsai M. Hyperbolic heat transfer with reflection. Numerical Heat Transfer, 1982,5:309-327
49 陈材侃．一种用差分算子变换求过渡矩阵的新方法．华中理工大学学报．第18卷，第5期，1990，10
50 陈材侃．计算流体力学．重庆：重庆出版社，1992，12
51 张广海．火炮火药点火的实验和理论研究．华东工学院硕士学位论文，1987
52 杨世铭，陶文铨．传热学．高等教育出版社，1998
53 W.Shen, S.Han. A numerical solution of two-dimensional hyperbolic heat conduction with non-linear boundary conditions. Heat and Mass Transfer.2003,(39):499-507
54 钟涛，王中伟，张为华．固体推进剂热松弛时间分析与测定．推进技术．2005，26(6)：573-576
55 K.K.Kuo, M.Summerfield.固体推进剂燃烧基础(中译本)．北京：宇航出版社，1988
56 D.J.Chen, S.C.Wu. Simulation of three-dimensional transient temperature field during laser bending of sheet metal. Materials Science and Technology, Vol.18, 2002:215-218
57 Y.P.Wan, V.Pradad, et al. Model and Powder Particle Heating, Melting, Resolidification, and Evaporation in Plasma Spraying Processes. Journal of Heat Transfer,Vol.121, 1999:691-699
58 Kaminski W. Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. ASME Journal of Heat Transfer, 1990:555-560
59 J.Gembarovic. Non-Fourier Heat Conducting Modeling in a Finite Medium. International Journal of Thermophusics.2004,25(4): 1261-1268
60 R.J.Lieb, C.J.Gillich. Morphology of Extinguished Monolithic JA2 Grains Fired in a 30mm Solid Propellant Electrothermal-Chemical(SPETC)Gun. Army Research Laboratory, ART-TR-606. 1994
2 欧阳立新．电热化学反射技术的应用前景．弹道学报．1995，7(2)：92-96
3 Wildegger-Gaissmaier. Modeling Flame Spread in Plasma Ignited Gun Charges. Proceedings of the 16th International Symposium on Ballistics, U.S.A, 1996:387-396
4 金志明，袁亚雄，宋明．现代内弹道．北京：北京理工大学出版社，1992
5 金志明，翁春生．高等内弹道学．北京：高等教育出版社，2003，12
6 戴荣，栗保明，卢顺祥．固体发射药等离子态点火过程及弹道效应分析．爆炸与冲击．1999，19(1)：84-89
7 张小兵，袁亚雄，谢玉树．等离子体点火密闭爆发器实验研究．火炸药学报．2003，26(2)：24-31
8 C.M.Edwards, M.A.Bourham, J.G.Gilligan. Experimental Studies of the Plasma-Propellant Interface for Electrothermal-Chemical Launchers. IEEE TRANSACTIONS ON MAGNETICS. 1995,31(1):404-409
9 Baoming Li, Hongzhi Li. Energetic Particle Ignition Exposed to Thermal Plasma. 17th International Symposium on Ballistics, South Africa, Vol.1, 1998:347-358
10 南京理工在学机械学院101教研室．电热—电磁发射技术译文选辑．1994，4
11 White K J. Katulka G L. Electrothermal Chemical Plasma Interaction with Propellants. Proceedings of the 16th International Symposium on Ballistics, U.S.A, 1996:387-396
12 M.A.Bourham, J.G.Gilligan. Augmentation and Control of Bum Rate in Plasma-Devices. APL Progress Report, 1997
13 K.J.White, lrvin Stobie, W.Oberle, Gary Katulka, Simon Driesen. Combustion Control Requirements in High Loading Density, Solid Propellant ETC Gun Firings. IEEE Transactions on Magnetics, Vol.33,1997:350-355
14 G.P.Wren, W.F.Oberle. Ballistic Analysis of Electrothermal-Chemical (ETC) Propellant. ARL-TR-1245, Dec. 1996
15 G.L.Katulka, et al. Experimental Characterization of Plasma Effects on Energetic Materials for Electrothermal-Chemical Launch Applications. IEEE Transactions on Magnetics, Vol.35,No.1,Jan.1999:197-200
16 Kaste P, et al. Plasma Ignition of Consolidated Propellant in A 60mm ETC Gun. ISL, French-German Research institutes of Saint-Louis.19th International Symposium on Ballistics, 2001 (1): 187-194
17 Kaste P, et al. Analysis of Burning Rate Phenomena and Extinguished Solid Propellant from an Interrupted Closed Bomb with Plasma Igniter. IEEE Transactions on Magnetics, Vol.37,No.1,Jan.2001:173-177
18 Bourham M A, Gilligan J G, Oberle W F. Analysis of Solid Propellant Combustion Behavior under Electrothermal Plasma Injection for ETC Launchers. IEEE Transaction on Magnetics, Vol.33,No1, Jan. 1997:278-284
19 Tran M P, et al. Relationship between Plasma and Gas Generation in an Electrothermal-Chemical Gun. ARL-TR-327,Jan. 1994
20 White K J et al. Combustion Control Requirements in High Loading Density, Solid Propellant ETC Gun Firings. IEEE Transaction on Magnetics, Vol.33, No.1, Jan. 1997:350-355
21 Fifer R A, et al. Chemical Effects in Plasma Ignition. IEEE Transactions on Magnetics, Vol.39,No.1, Jan.2003
22 Beyer R A. Pesce-Rodriguez R A. Experiments to Define Plasma-Propellant Interactions. IEEE Transaction on Magnetics, Vol.39,No.1,Jan.2003:207-211
23 D.E.Kooker. A Mechanism for ETC-Augmented Burning Rate of Solid Propellant consistent with Closed Chamber Experiment. 18th international symposium on ballistics, 1999:236-243
24 Michael A. Schroeder, Richard A. Beyer, Rose A. Pesce-Rodriguez. Scanning Electron Microscope Examination of JA2 Propellant Samples Exposed to Plasma Radiation. IEEE TRANSACTIONS ON MAGNETICS. 2005,41(1):350-354
25 OBERLEW, et al. Summary of Experimental Effects to Determines Plasma-Augmented Burn Rates. ARL-TR-782. 1995
26 戴荣，栗保明．电热化学炮等离子体增强燃烧过程研究．兵工学报．2003，24(3)：396-398
27 Alimi R, Perelmutter L, Onn U. Modeling an Internal injection Process for the Solid Propellant Electro-thermal Chemical Gun. 16th International Symposium on Ballistic. 1996
28 程代模．美国电热化学炮技术成就的综述与分析．弹箭技术．1995，(1)：1-10
29 梁昆淼．数学物理方法．北京：人民教育出版社，1979，2
30 姜任秋．热传导、质扩散与动量传递中的瞬态冲击效应．北京：科学出版社，1997，2
31 高正阳，阎维平，刘忠．煤颗粒在快速升温过程中非傅立叶导热效应的计算研究．中国电机工程学报．2002，22(9)：141-145
32 蒋方明，刘登瀛．非傅立叶导热的最新研究进展．力学进展．2002，32(1)：128-140
33 Kiwan S, Al-Nimr M, Al-Sharo'a M. Trial solution method to solve the hyperbolic heat conduction equation. International Committee Heat Mass Transfer. 2000, 27(6):865-876
34 张浙，刘登瀛．超急速传热时球体内非稳态热传导的非傅立叶效应．工程热物理学报．1998，19(5)：601-605
35 C.S.Tsai, Y.C.Lin, C.I.Hung. A study on the non-Fourier effects in spherical media due to sudden temperature changes on the surfaces. Heat Mass Transfer. 2005,41:709-716
36 张建奇．热等离子体环境下含能颗粒点火与燃烧特性研究．南京理工大学硕士学位论文，1999
37 李宝奇．等离子体点火模型的理论分析和研究．南京理工大学硕士学位论文，2004
38 张柏生．火药燃烧导论．南京：华东工学院，1988
39 王伯羲，冯增国．火药燃烧理论．北京：北京理工大学出版社，1997
40 陈熙．高温电离气体的传热与流动．北京：科学出版社，1993
41 Proulx. Plasma-Particle Interaction Effects Induction Plasma Modeling under Dense Loading Conditions. Int J. Heat Mass Transfer, Vol.28, No.7, 1985:1327-1336
42 Wei.D, Y.C.Farouk. Melting Powder Particles in a Low-Pressure Plasma Jet. ASME Journal of Heat Transfer, Vol.109,1987:971-976
43 Andreas Koleczko, Walter Ehrhard, et al. Plasma Ignition and Combustion. Propellant, Explosives, Pyrotechnics, Vol.26, 2001:75-83
44 Woodlet C R. Modeling Heat Transfer from Conventional and Plasma Igniters to Solid propellant. 20th International Symposium on Ballistics, Orlandol. September,2002:276-282
45 张小兵，袁亚雄，陈健，陈涛．含能材料等离子体点火过程的数值模拟．南京理工大学学报．第28卷，第3期，2004，6
46 谢玉树，张小兵等．含能材料等离子体点火过程的强瞬态二维热传导分析．兵工学报．第26卷，第6期，2005，11
47 Glass D E, et al. Hyperbolic heat conduction with surface radiation. Int J Heat Mass Transfer, 1982,28(10): 1823-1830
48 Carey G F, Tsai M. Hyperbolic heat transfer with reflection. Numerical Heat Transfer, 1982,5:309-327
49 陈材侃．一种用差分算子变换求过渡矩阵的新方法．华中理工大学学报．第18卷，第5期，1990，10
50 陈材侃．计算流体力学．重庆：重庆出版社，1992，12
51 张广海．火炮火药点火的实验和理论研究．华东工学院硕士学位论文，1987
52 杨世铭，陶文铨．传热学．高等教育出版社，1998
53 W.Shen, S.Han. A numerical solution of two-dimensional hyperbolic heat conduction with non-linear boundary conditions. Heat and Mass Transfer.2003,(39):499-507
54 钟涛，王中伟，张为华．固体推进剂热松弛时间分析与测定．推进技术．2005，26(6)：573-576
55 K.K.Kuo, M.Summerfield.固体推进剂燃烧基础(中译本)．北京：宇航出版社，1988
56 D.J.Chen, S.C.Wu. Simulation of three-dimensional transient temperature field during laser bending of sheet metal. Materials Science and Technology, Vol.18, 2002:215-218
57 Y.P.Wan, V.Pradad, et al. Model and Powder Particle Heating, Melting, Resolidification, and Evaporation in Plasma Spraying Processes. Journal of Heat Transfer,Vol.121, 1999:691-699
58 Kaminski W. Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. ASME Journal of Heat Transfer, 1990:555-560
59 J.Gembarovic. Non-Fourier Heat Conducting Modeling in a Finite Medium. International Journal of Thermophusics.2004,25(4): 1261-1268
60 R.J.Lieb, C.J.Gillich. Morphology of Extinguished Monolithic JA2 Grains Fired in a 30mm Solid Propellant Electrothermal-Chemical(SPETC)Gun. Army Research Laboratory, ART-TR-606. 1994