炸药爆轰热力学数据非线性拟合方法研究
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摘要
利用最小二乘法拟合得到炸药爆轰产物热力学数据的非线性拟合方程。为了验证此方程的准确性,分别采用Kast平均热容法和非线性拟合法计算物质的焓变(H~T-H~(298)),并与理论值比较。结果显示:非线性拟合法计算值最大误差为0.5%;Kast平均热容法的计算最小误差为3.1%,最大误差为12.5%。为实现爆轰参数的编程计算和验证非线性拟合法计算爆轰参数的可行性,根据前期研究成果,选取BKW状态方程作为爆轰产物的状态方程,利用最小自由能原理和Hugoniot关系,建立求解数学模型,分别结合Kast平均热容法和非线性拟合法,计算密度为1.80 g/cm~3的RDX和密度为1.14 g/cm~3的硝基甲烷的爆轰参数和爆轰产物组成,计算过程由自编程序完成。计算结果显示,非线性拟合法比Kast平均热容法计算的爆轰参数值更接近实验值;非线性拟合法计算RDX的爆温、爆压和爆速与实验值的误差分别为3.3%、0.4%和0.3%。
Least squares method was used to establish nonlinear fitting equations about thermodynamic data of detonation products. In order to verify the accuracy of these equations, Kast average heat capacity and nonlinear fitting equations were applied to calculate the enthalpy change(H~T-H~(298)). Compared with the theoretical value, Results show that the maximum error of nonlinear fitting equations is 0.5%, the minimum and the maximum error of Kast average heat capacity are 3.1% and 12.5%, respectively. In order to accomplish the programming calculation of detonation parameters and verify the feasibility of nonlinear fitting equations, BKW equation of state was selected as the equation of state for detonation products, the principle of minimum free energy and the equation of Hugoniot were utilized, Kast average heat capacity and nonlinear fitting equations were used to obtain detonation temperature, respectively. Detonation parameters of RDX and nitromethane were calculated by self-made program, where the density of RDX is 1.80 g/cm~3, the density of nitromethane is 1.14 g/cm~3. Calculation results show that detonation parameters calculated by the nonlinear fitting equations are more close to the experimental values than Kast average heat capacity. The error of detonation temperature, pressure and velocity of RDX for nonlinear fitting equations is 3.3%, 0.4% and 0.3%, respectively.
Least squares method was used to establish nonlinear fitting equations about thermodynamic data of detonation products. In order to verify the accuracy of these equations, Kast average heat capacity and nonlinear fitting equations were applied to calculate the enthalpy change(H~T-H~(298)). Compared with the theoretical value, Results show that the maximum error of nonlinear fitting equations is 0.5%, the minimum and the maximum error of Kast average heat capacity are 3.1% and 12.5%, respectively. In order to accomplish the programming calculation of detonation parameters and verify the feasibility of nonlinear fitting equations, BKW equation of state was selected as the equation of state for detonation products, the principle of minimum free energy and the equation of Hugoniot were utilized, Kast average heat capacity and nonlinear fitting equations were used to obtain detonation temperature, respectively. Detonation parameters of RDX and nitromethane were calculated by self-made program, where the density of RDX is 1.80 g/cm~3, the density of nitromethane is 1.14 g/cm~3. Calculation results show that detonation parameters calculated by the nonlinear fitting equations are more close to the experimental values than Kast average heat capacity. The error of detonation temperature, pressure and velocity of RDX for nonlinear fitting equations is 3.3%, 0.4% and 0.3%, respectively.
引文
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[17] GOKIEN N A,CHANG E T,POSTON T M.Determination of graphite/liquid/vapor triple point by laser hea-ting[J].High Temperature Science,1976,8:89-91.
[18] TOGAYA M,SUGIGAMA S,MIZUBARA E.Melting of graphite [C]// High Pressure Science and Technology.New York:AIP Press,1993.
[19] 杜明燃,汪旭光,郭子如,等.爆轰产物组成和爆轰参数计算方法的理论研究[J].爆炸与冲击,2015,35(4):449-453.DU M R,WANG X G,GUO Z R,et al.Theoretical studies for calculating the detonation products and pro-perties of explosives [J].Explosion and Shock Waves,2015,35(4):449-453.
[20] 欧育湘.炸药学[M].北京:北京理工大学出版社,2006.OU Y X.Explosive [M].Beijing:Beijing Institute of Technology Press,2006.
[21] 张立.爆破器材性能与爆炸效应测试[M].合肥:中国科学技术大学出版社,2006.ZHANG L.Blasting equipment performance and explosion effect test [M].Hefei:University of Science and Technology of China Press,2006.
[2] CHIRAT R,PITTION-ROSSILLON G.A new equation of state for detonation products [J].Journal of Chemical Physics,1981,74(8):4634-4645.
[3] MADER C L.Numerical modeling of detonation [M].Berkeley,Los Angels:University of California Press,1979.
[4] THIEL M V,REE F H.Nonequilibrium effects of slow diffusion controlled reactions on the properties of explosives [C]//Ninth Symposium(International) on Detonation.Portland,Oregon,1991:743-750.
[5] WU X.BKW equation of state for detonation products[C]//Eighth Symposium (International) on Detonation.Portland,Oregon,1985:438.
[6] 赵艳红,刘海风,张弓木.PETN炸药爆轰产物状态方程的理论研究[J].高压物理学报,2009,23(2):143-149.ZHAO Y H,LIU H F,ZHANG G M.Equation of state of detonation products for PETN explosive [J].Chinese Journal of High Pressure Physics,2009,23(2):143-149.
[7] 赵铮,陶钢,杜长星.爆轰产物JWL状态方程应用研究[J].高压物理学报,2009,23(4):277-282.ZHAO Z,TAO G,DU C X.Application research on JWL equation of state of detonation products [J].Chinese Journal of High Pressure Physics,2009,23(4):277-282.
[8] 王军,景梅,张晓玉,等.硝基二唑炸药爆炸参数的经验计算(Ⅱ)[J].含能材料,2013,21(5):609-611.WANG J,JING M,ZHANG X Y,et al.Empirical calculation of the explosion parameters of nitrodiazole explosives(Ⅱ) [J].Chinese Journal of Energetic Materials,2013,21(5):609-611.
[9] 欧育湘.炸药分析[M].北京:兵器工业出版社,1994.OU Y X.Explosive analysis [M].Beijing:Ordnance Industry Press,1994.
[10] 李德华,程新路,杨向东,等.PETN、RDX和HMX炸药爆轰参数的数值模拟[J].爆炸与冲击,2005,25(4):325-328.LI D H,CHENG X L,YANG X D,et al.Numerical simulation of detonation parameters for PETN,RDX and HMX explosives [J].Explosion and Shock Waves,2005,25(4):325-328.
[11] BARIN I.Thermochemical date of pure substances[M].3rd ed.New York:VCR,1995.
[12] 赵艳红,刘海风,张弓木.基于统计物理的爆轰产物物态方程研究[J].物理学报,2007,56(8):4791-4797.ZHAO Y H,LIU H F,ZHANG G M.Equation of state of detonation products based on statistical mechanical theory[J].Acta Physica Sinica,2007,56(8):4791-4797.
[13] FRIED L E,HOWARD W M.Explicit Gibbs free energy equation of state applied to the carbon phase diagram [J].Physical Review B,2000,61(13):8734-8743.
[14] 龙新平,何碧,蒋小华,等.论VLW状态方程[J].高压物理学报,2003,17(4):247-254.LONG X P,HE B,JIANG X H,et al.Discussions on the VLW equation of state [J].Chinese Journal of High Pressure Physics,2003,17(4):247-254.
[15] 吴雄.新型爆轰产物物态方程[J].高压物理学报,1991,5(2):98-103.WU X.A new equation of state for detonation products [J].Chinese Journal of High Pressure Physics,1991,5(2):98-103.
[16] 魏贤凤,龙新平,韩勇.VLWR程序计算CHNO炸药爆轰性能碳相态的选择[J].含能材料,2013,21(5):604-608.WEI X F,LONG X P,HAN Y.Selection of carbon phase in calculation of detonation performance by VLWR program for CHNO explosives [J].Chinese Journal of Energetic Materials,2013,21(5):604-608.
[17] GOKIEN N A,CHANG E T,POSTON T M.Determination of graphite/liquid/vapor triple point by laser hea-ting[J].High Temperature Science,1976,8:89-91.
[18] TOGAYA M,SUGIGAMA S,MIZUBARA E.Melting of graphite [C]// High Pressure Science and Technology.New York:AIP Press,1993.
[19] 杜明燃,汪旭光,郭子如,等.爆轰产物组成和爆轰参数计算方法的理论研究[J].爆炸与冲击,2015,35(4):449-453.DU M R,WANG X G,GUO Z R,et al.Theoretical studies for calculating the detonation products and pro-perties of explosives [J].Explosion and Shock Waves,2015,35(4):449-453.
[20] 欧育湘.炸药学[M].北京:北京理工大学出版社,2006.OU Y X.Explosive [M].Beijing:Beijing Institute of Technology Press,2006.
[21] 张立.爆破器材性能与爆炸效应测试[M].合肥:中国科学技术大学出版社,2006.ZHANG L.Blasting equipment performance and explosion effect test [M].Hefei:University of Science and Technology of China Press,2006.