Real-time calculation of fragment velocity for cylindrical warheads
|
摘要
To simulate explosion fragments, it is necessary to predict many variables such as fragment velocity, size distribution and projection angle. For active protection systems these predictions need to be made very quickly, before the weapon hits the target. Fast predictions also need to be made in real time simulations when the impact of many different computer models need to be assessed. The research presented in this paper focuses on creating a fast and accurate estimate of one of these variables-the initial fragment velocity. The Gurney equation was the first equation to calculate initial fragment velocity. This equation,sometimes with modifications, is still used today where finite element analysis or complex mathematical approaches are considered too computationally expensive. This paper enhances and improves Breech's two-dimensional Gurney equation using available empirical data and the principals of conservation of momentum and energy. The results are computationally quick, providing improved accuracy for estimating initial fragment velocity. This will allow the developed model to be available for real-time simulation and fast computation, with improved accuracy when compared to existing approaches.
To simulate explosion fragments, it is necessary to predict many variables such as fragment velocity, size distribution and projection angle. For active protection systems these predictions need to be made very quickly, before the weapon hits the target. Fast predictions also need to be made in real time simulations when the impact of many different computer models need to be assessed. The research presented in this paper focuses on creating a fast and accurate estimate of one of these variables-the initial fragment velocity. The Gurney equation was the first equation to calculate initial fragment velocity. This equation,sometimes with modifications, is still used today where finite element analysis or complex mathematical approaches are considered too computationally expensive. This paper enhances and improves Breech's two-dimensional Gurney equation using available empirical data and the principals of conservation of momentum and energy. The results are computationally quick, providing improved accuracy for estimating initial fragment velocity. This will allow the developed model to be available for real-time simulation and fast computation, with improved accuracy when compared to existing approaches.
To simulate explosion fragments, it is necessary to predict many variables such as fragment velocity, size distribution and projection angle. For active protection systems these predictions need to be made very quickly, before the weapon hits the target. Fast predictions also need to be made in real time simulations when the impact of many different computer models need to be assessed. The research presented in this paper focuses on creating a fast and accurate estimate of one of these variables-the initial fragment velocity. The Gurney equation was the first equation to calculate initial fragment velocity. This equation,sometimes with modifications, is still used today where finite element analysis or complex mathematical approaches are considered too computationally expensive. This paper enhances and improves Breech's two-dimensional Gurney equation using available empirical data and the principals of conservation of momentum and energy. The results are computationally quick, providing improved accuracy for estimating initial fragment velocity. This will allow the developed model to be available for real-time simulation and fast computation, with improved accuracy when compared to existing approaches.
引文
[1] Gabrovsek S, Colwill I, Stipidis E. Agent-based simulation of improvised explosive device fragment damage on individual components. JDefModelSimulat:Appl, Methodol, Technol 2016;13(4):399e413.
[2] Gabrovsek S. Agent-based modelling of fragment damage for platform combat utility prediction. 2017.
[3] Gurney RW. The initial velocities of fragments from bombs, shell and grenades. DTIC Document; 1943.
[4] Taylor G. Analysis of the explosion of a long cylindrical bomb detonated at one end. Mechanics of Fluids. Sci Papers GI Taylor 1941;2:277e86.
[5] Mott. A theory of the fragmentation of shells and bombs. 1943.
[6] Huang G-y, Li W, Feng S-s. Axial distribution of Fragment Velocities from cylindrical casing under explosive loading. Int J Impact Eng 2015;76:20e7.
[7] Charron YJ. Estimation of velocity distribution of fragmenting warheads using a modified gurney method. DTIC Document; 1979.
[8] Szmelter J, Davies N, Lee CK. Simulation and measurement of fragment velocity in exploding shells. 2007.
[9] Choi CH, et al. Modification of the gurney equation for explosive bonding by slanted elevation angle. 2014.
[10] Liu M, et al. Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology. Comput Fluids 2003;32(3):305e22.
[11] Ma S, et al. Simulation of high explosive explosion using adaptive material point method. Comput Model Eng Sci 2009;39(2):101.
[12] Spranghers K, et al. Numerical simulation and experimental validation of the dynamic response of aluminum plates under free air explosions. Int J Impact Eng 2013;54:83e95.
[13] Pearson J. A fragmentation model for cylindrical warheads. DTIC Document;1990.
[14] Karpp R, Predebon W. Calculations of fragment velocities from naturally fragmenting munitions. DTIC Document; 1975.
[15] Grisaro H, Dancygier AN. Numerical study of velocity distribution of fragments caused by explosion of a cylindrical cased charge. Int J Impact Eng2015;86:1e12.
[16] Victor AC. Warhead performance calculations for threat hazard assessment.DTIC Document; 1996.
[17] Kennedy J. Explosive output for driving metal. Albuquerque, N. Mex:Sandia Labs.; 1972.
[18] Kennedy J. Gurney energy of explosives:estimation of the velocity and impulse imparted to driven metal. 1970.
[19] Gardner S. Analysis of fragmentation and resulting shrapnel penetration of naturally fragmenting cylindrical bombs. California:Lawrence Livermore National Laboratory; 2000.
[20] Ko€nig P. A correction for ejection angles of fragments from cylindrical wareheads. Propellants, Explos Pyrotech 1987;12(5):154e7.
[21] Zulkoski T. Development of optimum theoretical warhead design criteria.Naval Weapons Center China Lake CA; 1976.
[22] Fairlie G. The numerical simulation of high explosives using AUTODYN-2D&3D. In:Institute of explosive engineers 4th biannual symposium; 1998.
[23] Snyman I, Mostert F. Computation of fragment velocities and projection angles of an anti-aircraft round. 2014.
[24] Odintsov V. Expansion of a cylinder with bottoms under the effect of detonation products. Combust Explos Shock Waves 1991;27(1):94e7.
[25] Breech BA. Extension of the gurney equations to two dimensions for a cylindrical charge. DTIC Document; 2011.
[26] Lloyd RM. Conventional warhead systems physics and engineering design,vol. 179. AIAA; 1998.
[27] Goto D, et al. Investigation of the fracture and fragmentation of explosively driven rings and cylinders. Int J Impact Eng 2008;35(12):1547e56.
[28] Taylor G. The fragmentation of tubular bombs. 1944.
[29] Waggener S. The performance of axially initiated cylindrical warheads. In:Fourth international symposium on ballistics; 1978.
[30] Lee Rodgers J, Nicewander WA. Thirteen ways to look at the correlation coefficient. Am Statistician 1988;42(1):59e66.
[31] Massey FJ. The Kolmogorov-smirnov test for goodness of fit. J Am Stat Assoc1951;46(253):68e78.
[32] Kong X, et al. A numerical investigation on explosive fragmentation of metal casing using Smoothed Particle Hydrodynamic method. Mater Des 2013;51:729e41.
[2] Gabrovsek S. Agent-based modelling of fragment damage for platform combat utility prediction. 2017.
[3] Gurney RW. The initial velocities of fragments from bombs, shell and grenades. DTIC Document; 1943.
[4] Taylor G. Analysis of the explosion of a long cylindrical bomb detonated at one end. Mechanics of Fluids. Sci Papers GI Taylor 1941;2:277e86.
[5] Mott. A theory of the fragmentation of shells and bombs. 1943.
[6] Huang G-y, Li W, Feng S-s. Axial distribution of Fragment Velocities from cylindrical casing under explosive loading. Int J Impact Eng 2015;76:20e7.
[7] Charron YJ. Estimation of velocity distribution of fragmenting warheads using a modified gurney method. DTIC Document; 1979.
[8] Szmelter J, Davies N, Lee CK. Simulation and measurement of fragment velocity in exploding shells. 2007.
[9] Choi CH, et al. Modification of the gurney equation for explosive bonding by slanted elevation angle. 2014.
[10] Liu M, et al. Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology. Comput Fluids 2003;32(3):305e22.
[11] Ma S, et al. Simulation of high explosive explosion using adaptive material point method. Comput Model Eng Sci 2009;39(2):101.
[12] Spranghers K, et al. Numerical simulation and experimental validation of the dynamic response of aluminum plates under free air explosions. Int J Impact Eng 2013;54:83e95.
[13] Pearson J. A fragmentation model for cylindrical warheads. DTIC Document;1990.
[14] Karpp R, Predebon W. Calculations of fragment velocities from naturally fragmenting munitions. DTIC Document; 1975.
[15] Grisaro H, Dancygier AN. Numerical study of velocity distribution of fragments caused by explosion of a cylindrical cased charge. Int J Impact Eng2015;86:1e12.
[16] Victor AC. Warhead performance calculations for threat hazard assessment.DTIC Document; 1996.
[17] Kennedy J. Explosive output for driving metal. Albuquerque, N. Mex:Sandia Labs.; 1972.
[18] Kennedy J. Gurney energy of explosives:estimation of the velocity and impulse imparted to driven metal. 1970.
[19] Gardner S. Analysis of fragmentation and resulting shrapnel penetration of naturally fragmenting cylindrical bombs. California:Lawrence Livermore National Laboratory; 2000.
[20] Ko€nig P. A correction for ejection angles of fragments from cylindrical wareheads. Propellants, Explos Pyrotech 1987;12(5):154e7.
[21] Zulkoski T. Development of optimum theoretical warhead design criteria.Naval Weapons Center China Lake CA; 1976.
[22] Fairlie G. The numerical simulation of high explosives using AUTODYN-2D&3D. In:Institute of explosive engineers 4th biannual symposium; 1998.
[23] Snyman I, Mostert F. Computation of fragment velocities and projection angles of an anti-aircraft round. 2014.
[24] Odintsov V. Expansion of a cylinder with bottoms under the effect of detonation products. Combust Explos Shock Waves 1991;27(1):94e7.
[25] Breech BA. Extension of the gurney equations to two dimensions for a cylindrical charge. DTIC Document; 2011.
[26] Lloyd RM. Conventional warhead systems physics and engineering design,vol. 179. AIAA; 1998.
[27] Goto D, et al. Investigation of the fracture and fragmentation of explosively driven rings and cylinders. Int J Impact Eng 2008;35(12):1547e56.
[28] Taylor G. The fragmentation of tubular bombs. 1944.
[29] Waggener S. The performance of axially initiated cylindrical warheads. In:Fourth international symposium on ballistics; 1978.
[30] Lee Rodgers J, Nicewander WA. Thirteen ways to look at the correlation coefficient. Am Statistician 1988;42(1):59e66.
[31] Massey FJ. The Kolmogorov-smirnov test for goodness of fit. J Am Stat Assoc1951;46(253):68e78.
[32] Kong X, et al. A numerical investigation on explosive fragmentation of metal casing using Smoothed Particle Hydrodynamic method. Mater Des 2013;51:729e41.