Modeling spherical explosions with aluminized energetic materials. (English) Zbl 1195.76239

Summary: This paper deals with the numerical solution and validation of a reactive flow model dedicated to the study of spherical explosions with an aluminized energetic material. Situations related to air blast as well as underwater explosions are examined. Such situations involve multiscale phenomena associated with the detonation reaction zone, the aluminium reaction zone, the shock propagation distance and the bubble oscillation period. A detonation tracking method is developed in order to avoid the detonation structure computation. An ALE formulation is combined to the detonation tracking method in order to solve the material interface between detonation products and the environment as well as shock propagation. The model and the algorithm are then validated over a wide range of spherical explosions involving several types of explosives, both in air and liquid water environment. Large-scale experiments have been done in order to determine the blast wave effects with explosive compositions of variable aluminium content. In all situations the agreement between computed and experimental results is very good.


76L05 Shock waves and blast waves in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
Full Text: DOI


[1] Baer M.R., Nunziato J.W. (1986) A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flows 12, 861–889 · Zbl 0609.76114
[2] Baudin, G., Bergues, D.: A reaction model for aluminized PBX applied to underwater explosion calculations. In: The 10th Symposium on Detonation, Boston, USA (1993)
[3] Baudin, G.: QUERCY, Un code thermochimique adapté au calcul des caractéristiques de détonation des explosifs aluminisés. In: Europyro 93, 5 th International Congres on Pyrotechnics, 6–11 June 1993, Tours, France (1993)
[4] Bergues, D., Baudin, G.: Prédiction des performances sous-marines dexplosifs aluminisés partir dinformations recueillies lors de tests balistiques aériens (coopération Franco-Britannique WG7-SG2). Note technique T94-24, DGA/DRET/CEG (in French)(1994)
[5] Bdzil J.B., Stewart P.S. (1989) Modeling two-dimensional detonations with detonation shock dynamics. Phys. Fluids A1(7): 1261–1267 · Zbl 0673.76082
[6] Brun, L.: Un nouveau modèle macroscopique de la détonation non soutenue dans les explosifs condensés. In: 3eme Symp. Int. Hautes Pressions Dynamiques, La Grande Motte, pp. 103–107 (1989)
[7] Chinnayya A., Daniel E., Saurel R. (2004) Modelling detonation waves in heterogeneous energetic materials. J. Comput. Phys. 196(2): 490–538 · Zbl 1109.76335
[8] Cole R.H. (1965) Underwater Explosions. Dover, New York
[9] Davis S.F. (1988) Simplified second order Godunov type methods. SIAM J. Sci. Stat. Comput. 9 (N3): 445–473 · Zbl 0645.65050
[10] Fickett W., Davis W.C. (1979) Detonation. University of California Press, Berkeley
[11] Fried, E.: CHEETAH 1.39 user’s manual. UCRL-MA-117541 Rev 3, Energetic Material Center. Lawrence Livermore National Laboratory (1996)
[12] Godunov S.K. (1959) A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Math. Sb. 47: 375 · Zbl 0171.46204
[13] Godunov S.K. (1979) Résolution numérique des problèmes multidimensionnels de la dynamique des gaz. Editions Mir, Moscou, USSR
[14] Harlow, F.H., Amsden, A.A.: Fluid dynamics. Los Alamos Scientific Laboratory, LA-4700, UC 34 (1971) · Zbl 0221.76011
[15] Heuzé O. (1986) Equation of state of detonation products: influence in the repulsive intermolecular potential. Phys. Rev. A 34(1): 428–433
[16] Lee, E.L., Horning, H.C., Kury, J.W.: Adiabatic expansion of high Explosives detonation products. Lawrence Radiation Lab., Un. of Cal., Livermore, TID 4500 – UCRL 50422 (1968)
[17] Kingery, C.N., Pannill, B.F.: Peak overspressure vs scaled distance for TNT surface bursts (hemispherical charges). Ballistic Research Laboratories n518, Maryland (1964)
[18] Kingery, C.N.: Air blast parameters vs distance for hemispherical TNT surface bursts. Ballistic Research Laboratories n 1544, Maryland (1966)
[19] Kingery, C.N., Bulmash, G.: Air blast parameters from TNT air burst and hemispherical surface burst. Technical ARBRL-TR-02555, U.S. Army ARDC-BRL, Aberdeen Proving Ground, Maryland (1984)
[20] Menikoff R., Plohr B. (1989) The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61, 75–130 · Zbl 1129.35439
[21] Persson P.A., Holmberg R., Lee J. (1996) Rock blasting and explosive engineering. CRC Press, Boca Raton
[22] Rayleigh L. (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Phys. Mag. 34, 94–98 · JFM 46.1274.01
[23] Saurel, R.: DPEX: Un outil numérique pour la détermination des cinétiques réactionnelles des explosifs fortement non idéaux. IUSTI Report under Centre d’Etude de Gramat contract (1996)
[24] Saurel R., Massoni J. (1998) On Riemann-problem-based methods for detonations in solid energetic materials. Int. J. Num. Meth. Fluids 26, 101–121 · Zbl 0906.76057
[25] Saurel R., Le Metayer O. (2001) A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431, 239–271 · Zbl 1039.76069
[26] Toro E.F., Spruce M., Spearce W. (1994) Restauration of the contact surface in the HLL-type Riemann solver. Shock Waves 4, 25–34 · Zbl 0811.76053
[27] Wood W.W., Kirkwood J.C. (1954) Diameter effect in condensed explosives.The relationship between velocity and radius of curvature of the detonation wave. J. Chem. Phys. 22, 1920–1924
[28] Zhang F., Frost D.L., Thibault P.A., Murray S.B. (2001) Explosive dispersal of solid particles. Shock Waves 10, 431–443 · Zbl 0967.76523
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.