Numerical Simulation of Near-Field Explosion

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1 Journal of Applied Science and Engineering, Vol. 16, No. 1, pp (2013) 61 Numerical Simulation of Near-Field Explosion Ding-Shing Cheng 1, Cheng-Wei Hung 2 and Sheng-Jung Pi 2 * 1 Department of Environmental Information and Engineering, Chung Cheng Institute of Technology, National Defense University, Tauyuan County, Taiwan, R.O.C. 2 School of Defense Science, Chung Cheng Institute of Technology, National Defense University, Tauyuan County, Taiwan, R.O.C. Abstract The objective of this study is to simulate shock wave due to near-field explosion by using Arbitrary-Lagargian-Eulerian (ALE) fluid-structure interaction algorithm in the LS-DYNA finite element analysis software. Overpressure from near-field burst simulation was compared to the U. S. Army Technical Manual TM5-1300, with relative difference of 5%, for a scaled distance from 0.09 to 0.29 m kg 1/3. The results showed that LS-DYNA can predict near-field explosion. Furthermore, using LS-DYNA Mapping 2D to 2D technology can effectively increase the numerical model size of which scaled distance can be extended from 0.09 to 0.61 m kg 1/3. Key Words: ALE, LS-DYNA, Overpressure, Mapping 1. Introduction Explosives were widely applied in military and studied for many years. Initiation of the detonation train in a conventional weapons explosive begins with an extremely rapid chemical reaction. The sudden release of energy from an explosion in the air produces an instantaneous high-temperature, high-pressure detonation wave in the atmosphere. The energy carried by the blast pressure wave will decrease as the propagation distance and time increases. The pressure behind the shock wave front can instantly reduce to below the air pressure of the surrounding atmosphere. A typical explosion pressure time history curve was shown in Figure 1 [1]. As the reaction progresses, the explosive material are converted to a very hot, dense, high-pressure gas. Pressures immediately behind the detonation front, called Chapman-Jouget pressures, range from 18,620 to 38,620 MPa, while temperatures range from about 3,800 K to 5,700 K. According to the reaction, the impact of an explosion is sufficient to constitute great threat to facility and personnel, and even lead to equipment damages and personnel casualties. *Corresponding author. sampeetw@gmail.com In the explosions analysis, ideal explosions are defined as being produced by bare (uncased) charges with either a spherical or hemispherical geometry. Trinitrotoluene (TNT) is one of the most commonly used explosives, the historically accepted standard reference explosive, since the preponderance of effects data used for analyses and prediction are based on this explosive. As well-known U.S. TM [2] and TM handbook are via a large number of experimental data to establish empirical formula for design. However, the explosion of near-field burst measurement is not easy to implement, mainly because of its Figure 1. Typical pressure-time history of an airblast in free air.

2 62 Ding-Shing Cheng et al. complex behaviour and great variation measurement. The rapid development in recent years due to the popularization of the PC and the finite element analysis software, such as ANSYS, LS-DYNA, AUTODYN, DY- TRAN, ABAQUS, PAM-CRASH, ZAPOTEC etc. Under the premise of saving a lot of human and financial resources, engaged in numerical simulation study using computer-aided analysis software has become a trend [3 11]. 2. Theoretical Background This study aims at investigating the airblast propagation of near-field burst by using LS-DYNA software. Arbitrary-Lagrangian-Eulerian (ALE) algorithm for Fluid- Structure-Interaction model of the LS-DYNA software was adopted. Results of the fluid-structure-interaction model using the ALE algorithm were compared with TM The results can serve as reference for future analysis and design. 2.1 Arbitrary-Lagrangian-Eulerian (ALE) Algorithm In general, there are two classical algorithms often used with finite element meshes for continuum: the Lagrangian and the Eulerian algorithm. In the Lagrangian algorithm, nodes on meshes can be moved with material points, and element meshes can be deformed. In the Eulerian algorithm, element meshes are fixed in space, and the material points move in pre-planned meshes. Element meshes do not deform during the movement of an object, so that large fluid meshes are to be planned appropriately [12]. The ALE algorithm has been developed to combine the advantages of the Lagrangian and the Eulerian algorithms. In the ALE algorithm, the nodes of meshes for solids use the Lagrangian algorithm, and the nodes then move with the deformation of the solids. On the other hand, meshes for fluids use the Eulerian algorithm, in which the nodes of meshes are fixed in space. The ALE algorithm simultaneously describes the motion of fluids and also shows the dynamic response of solids, In the ALE algorithm, the Eulerian and Lagrangian meshes must be overlapped to produce better accuracy, but the two meshes do not need to be consistent [13]. An appropriate constitutive material model and equation of state (EOS) model for each material need to be considered. The ALE models the explosion and calculates the pressure throughout the mesh. The ALE model is computationally more expensive than the Lagrangian model, and is only appropriate for small standoff distances. The constitutive models and material parameters used in this paper were shown in Table 1 and described below [14,15] Air MAT-NULL (Material Type 9) is adopted for air and is combined with a linear polynomial equation of state shown in Eqs. (1) and (2). E 0 and indicate the initial internal energy and dynamic viscosity coefficient, respectively [16]. P = C 0 + C C 3 3 +(C 4 + C 5 + C 6 2 )E 0 (1) E 0 = initial C vt (2) Since air is assumed to be an ideal gas, C 1,C 2,C 3, and C 6 are set to zero. C 4 = C 5 when = 1.4, is the ratio of specific heats. P is air pressure, initial is the initial air density, C v is the specific heat of air at constant volume, and T is the initial temperature of air. The equation of state is further simplified as follows. P =( -1) current initial E 0 + C 0 (3) where current is the current air density, C 0 is the adjustable coefficient Explosive For explosive material, Mat-High-Explosive-Burn (Material Type 8) is used. The JWL equation of state is Figure 2. Lagrangian, Eulerian and ALE meshes and particle motion.

3 Numerical Simulation of Near-Field Explosion 63 Table 1. The material parameters for near-field burst analysis. Unit (g, cm, second, Mbar) *MAT NULL (Air) RO PC MU TEROD CEROD YM PR *EOS LINEAR POLYNOMIAL (Air) C 0 C 1 C 2 C 3 C 4 C 5 C 6 E 0 V *MAT HIGH EXPLOSIVE BURN (TNT) RO D PCJ BETA K G SIGY *EOS JWL (TNT) A B R 1 R 2 E 0 V necessary to simulate the behaviour of an explosive [16], and it is expressed as follows: (4) wherea,b,r1,r2,and are coefficients for a specific explosive, P is pressure, V r is the relative volume, and E 0 is the initial internal energy. If A and B are set to zero and is -1, Eq. 4 represents the equation of state for an ideal gas TNT Near-Field Explosion Model Numerical simulations of near-field burst were conducted using LS-DYNA software. Arbitrary-Lagrangian- Eulerian (ALE) algorithm of the LS-DYNA software was adopted. The structure model was discretized into finite number of sections over which the conservation and constitutive equations are solved. There are two materials in this study: air and explosive, shown in Figure 3, both the explosive and air are modelled with Eulerian meshes. A sphere of TNT explosive weighing 30 g, radius cm, detonated in a central location to simulate the near-field burst. The analysis with 2D simplified axisymmetric computations is performed on near-field burst Model, which are modelled with shell elements. In this study, Air model side length is 10 cm 10 cm. Mesh convergence is addressed with a series of calculations in which the size of the ALE elements is increasingly reduced with a refinement ratio of 0.5. The sizes of the elements are , , and cm, respectively. Air and explosives are defined multi-material ALE element, calculations using the 1 Point ALE multi material element and axisymmetric solid of area weighted. The control of mass of charges is realized by defining initial volume fraction of different materials in multi-material ALE. In addition, DATA- 2.2 Near-Field Explosion Model Figure 3. Near-field burst model.

4 64 Ding-Shing Cheng et al. BASE TRACER was used to obtain overpressure history from LS-DYNA model. Tracer particles can be retrieved within 3 to 9 cm from the centre of charge along the x-axis. The scaled distance Z of overpressure was between 0.09 to 0.29 m kg 1 3. Results of overpressure from the ALE model were compared with TM The scaled distance Z is expressed as follows: (5) where R is the standoff distance (m), and W is the mass of explosive (kg) TNT Near-Field Burst Mapping Model The SECTION ALE2D method is available for two types of shells (axisymmetric and plane strain elements) and two types of ALE formulations (single and multi-materials). 2D ALE code provides the same functionalities as 3D such as pure Euler, ALE with grid motion and Fluid-Structure Interaction (FSI). LS-DYNA new technique named Mapping has been developed to allow the decomposition of a calculation in several steps. The last cycle of a 2D or 3D ALE model can be mapped into another 2D or 3D ALE model. This technique offers very large possibilities since it enables to change the mesh length or the model size, to add Lagrangian or Eulerian parts. Due to its properties, Mapping technique is a perfect method to study such problems where the quality of initiation is a determining parameter. Indeed, starting with a very fine mesh is the crucial point, because having the right initial energy guarantees a good final % Error with experimental data. Mapping enables to combine a good accuracy in a first very fine mesh with areasonablecputimewithasecondlargermesh [17,18]. Numerical simulations of near-field burst model are divided into air and explosive. A sphere of TNT explosive weighing 30 g, radius cm, detonated in a central location to simulate the near-field burst. The 2D simplified axisymmetric computations are performed analysis on near-field burst Model, which are modelled with shell elements. The air models mapping side lengths are 10 cm 10 cm, 20 cm 20 cm and 40 cm 40 cm. The sizes of the air and explosive elements are , and cm. The data of overpressure histories capture ranges are 3 to 5cm, 6 to 14 cm, 15 to 19 cm, as shown in Figure 4. Air and explosives are defined multi-material ALE element, calculations using the 1 Point ALE multi material element and axisymmetric solid of area weighted. The numerical simulation results were through INITIAL ALE MAPPING setting, that a very fine mesh result mapping to a second larger mesh. The DATABASE TRACER retrieve location along the x-axis 3 to 19 cm from the centre of charge, the overpressure can be obtained from the air. The scaled distance Z of overpressure was between 0.09 to m/kg 1/3. Results of overpressure from the mapping model were compared with TM Result 3.1 TNT Near-Field Burst Model To investigate the model convergence, Near-field burst models with the element sizes , , and cm were set up with the ratio of 0.5. The results shown in Figure 5 indicated that when scale distance Z greater than 0.1 m kg 1 3 the relative differences of elements overpressure were less than 5 had reached convergence, which the elements sizes in , and cm. The relative difference ( ) = (coarse mesh overpressure value - fine mesh overpressure value) fine mesh overpressure value 100. The Figure 4. Near-field burst mapping model.

5 Numerical Simulation of Near-Field Explosion 65 relative overpressure of four mesh size are greater than 5 when the scale distance between 0.09 to 0.1 m kg 1 3. However, element size in cm the relative overpressure was less than 8. In addition, the numerical simulation results of overpressure compared with TM5-1300, as shown in Figure 6. With the scale distance Z increased, the peak overpressure shows a decreasing trend. For comparing the relative overpressure relation between numerical simulation and TM5-1300, element size in cm shows agreement with relative difference ranges from 4.25 to %, as shown in Figure 7. The outcomes show consistent results can be obtained with numerical simulation for near-field explosion and empirical formula that conducive to the peak incident pressure predicted, but mesh size must be very fine. 3.2 TNT Near-Field Explosion Mapping Model Figure 8 shows numerical simulation overpressure of air compared with TM With the scale distance Z increased, the peak overpressure shows a decreasing trend. This figure confirms the very good results given by mapping technique in simulating air blast problems. Since relative overpressure between simulation and TM are 3.30 to -0.29% when the scale distances Z from to m kg 1 3, as shown in Figure 9. The relative difference ( ) = (coarse mesh overpressure value - fine mesh overpressure value) fine Figure 7. Numerical results vs. relative difference from TM Figure 5. Mesh convergence analysis results. Figure 8. Numerical Mapping results vs. overpressure from TM Figure 6. Numerical results vs. overpressure from TM Figure 9. Numerical Mapping results vs. relative difference from TM

6 66 Ding-Shing Cheng et al. mesh overpressure value 100. For comparing the near-field burst model and near-field burst mapping model that shows mapping technique can effectively increase the numerical model range. Doing the charge ignition in a fine 2D model ensures a very important accuracy for the first part of calculation. Using Mapping to increase mesh size leads to a very small Error between simulation and TM with a reasonable CPU time. 4. Conclusion This study used LS-DYNA 2D ALE model and 2D ALE mapping model, and numerical results were compared with TM The results of numerical simulation were analytically compared, and the correctness of results was checked by verifying numerical simulation. The outcomes are applied as basis for establishing empirical equations and numerical models for near-field explosion to provide reference for evaluating protective designs. The results are as follows: (1) Near-field explosion model: A comparison between the numerical results and the TM empirical formulas for the overpressure shows that scale distance between 0.09 to 0.29 m kg 1 3 the relative overpressure are between 4.25 to The outcomes show consistent results can be obtained with numerical simulation for near-field explosion and empirical formula that conducive to the peak incident pressure predicted, but mesh size must be very fine and need more CPU time. (2) Near-field explosion mapping model: A comparison between the numerical mapping results and the TM empirical formulas for the overpressure shows that scale distance Z from 0.09 to m kg 1 3 the relative overpressure are between 3.30 to These confirm the very good results given by mapping technique in simulating near-field explosion problems and effectively increase the numerical model range. Doing the near-field explosion in a fine 2D ALE mapping model ensures a very important accuracy for the first part of calculation. Using Mapping to increase mesh size leads to a very small Error between simulation and TM with a reasonable CPU time. References [1] Department of the Army, Fundamental of Protective Design for Conventional Weapons, Technical Manual TM , U.S.A., pp (1998). [2] Department of the Army, Structures to Resist the Effects of Accidental Explosions, TM5-1300, U.S.A., pp (1990). [3] Cheng, D. S., Chiu, S. C. and Hung, C. W., Validation of Fluid Structure Interaction Models of Reinforced Concrete Structures Subjected to Internal Explosion, 3rd Int. Conf. Design and Analysis of Protective Structures, Singapore, May 10-12, pp (2010). [4] Cheng, D. S., Chang, J. L., Chung C. N. and Hung, C. W., Effect of Erosion Value of Strain on Crater Size of Reinforced Concrete Plates Subjected to Shaped Charge, 3rd Int. Conf. Design and Analysis of Protective Structures, Singapore, May 10-12, pp (2010). [5] Chen, H. C., Hung, C. W. and Yu, W. F., Validation of Fluid Structure Interaction Models of Magazines Subjected to Internal Explosion, 8th Int. Conf. Shock Impact Loads on Structures, Adelaide, Australia, Dec 2-7, pp (2009). [6] Lai, H. H., Chiu, S. C., Cheng, D. S. and Hung, C. W., Effect of Steel, CFRP and GFRP-Retrofitted Plate on Crater of Reinforced Concrete Subjected to Contact Explosion, 8th Int. Conf. Shock Impact Loads on Structures, Adelaide, Australia, Dec 2-7, pp (2009). [7] Hung, C. W., Yu, W. F. and Cheng, D. S., A Parametric Study of Explosion Simulation for Reinforced Concrete Slab Subjected to a Rectangular Explosive, International Symposium on Interaction of the Effects of Munitions with Structures 12.1, Orlando, U.S.A., Sept (2007). [8] Yu, W. f., Hung, C. W. and Cheng, D. S., Effect of Subdividing Stacks on Blast Overpressure from Explosion Inside Ammunition Storage Magazine, J. Explosives and Propellants, Vol. 24, No. 2, pp (2008). [9] Yu, W. f., Hung, C. W. and Cheng, D. S., Effect of Blast wall on Safety Distance of Ammunition Storage Magazine Subjected to Internal Explosion, J. Chung Cheng Institute of Technology, Vol. 39, No. 2, pp , 2010.

7 Numerical Simulation of Near-Field Explosion 67 [10] Cheng, D. S. and Hung, C. W., Experiment and Numerical Simulation of Peak Overpressure of C4 Explosives in the Airblast, J. Explosives and Propellants, Vol. 26, No. 2, pp (2010). [11] Pi, S. J., Cheng, D. S., Cheng, H. L., Li, W. C. and Hung, C. W., Fluid-Structure-Interaction for a Steel Plate subjected to Non-Contact Explosion, Theoretical and Applied Fracture Mechanics, Vol. 59, pp. 1 7 (2012). [12] Haufe, A., Weimar, K., and Göhner, U., Advanced Airbag Simulation Using Fluid-Structure-Interaction And The Eulerian Method in LS-DYNA, Proceedings of the third LS-DYNA forum, Bamberg, Germany, Oct (2004). [13] Gebbeken, N. and Ruppert, M., On the Safety and Reliability of High Dynamic Hydrocode Simulations, Int. J. for Numerical Methods in Engineering, Vol. 46, No. 6, pp (1999). [14] Dobratz, B. M., Crawford, P. C., LLNL Explosives Handbook - Properties of Chemical Explosives and Explosives Simulates, Lawrence Livermore National Laboratory, UCRL Change 2, University of California, pp (1985). [15] Mullin, J. M. and O Toole, J. B., Simulation of Energy Absorbing Materials in Blast Loaded Structures, The 8th International LS-DYNA Users Conference, Michigan, U.S.A., May 2-4, pp (2004). [16] LS-DYNA Version 971 Rev 5 User s Manual, Livermore Software Technology Corporation, U.S.A., pp (2010). [17] Aquelet, N., 2D to 3D ALE mapping, The 10th International LS-DYNA Users Conference, Michigan, U.S.A., Jun. 8-10, pp (2008). [18] Lapoujade, V., Van Dorsselaer, N., Kevorkian, S. and Cheval, K., A Study of Mapping Technique for Air Blast Modeling, The 11th International LS-DYNA Users Conference, Michigan, U.S.A., Jun. 6-8, pp (2010). Manuscript Received: Nov. 20, 2012 Accepted: Feb. 20, 2013

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