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基于固体炸药爆轰过程中化学反应混合区内的固相反应物与气相生成物处于力学平衡状态及热学非平衡状态的事实，提出一种考虑热学非平衡效应的反应流动模型来描述固体炸药的爆轰流动现象.该爆轰流动模型的主要特点是，在反应混合物Euler方程和固相反应物质量守恒方程的基础上，通过附加一套关于固相反应物的组分物理量的流动控制方程来表达固相反应物与气相生成物之间的热学非平衡效应.根据反应混合区内固相反应物与气相生成物这两种化学组分保持各自内能守恒的混合规则，并借助它们具有压力相等的性质以及满足体积分数总和为1的条件，推导获得的附加方程有：固相反应物的内能演化方程、体积分数演化方程及反应混合物的压力演化方程.这样，建立的爆轰模型包括：反应混合物的质量守恒方程、动量守恒方程、总能量守恒方程、压力演化方程，以及固相反应物的质量守恒方程、内能演化方程、体积分数演化方程.对所获得的爆轰模型方程组采用一个时空二阶精度的有限体积法进行数值求解，典型爆轰问题算例结果表明本文提出的固体炸药爆轰模型是合理的.A thermal nonequilibrium reactive flow model is proposed to deal with the detonation dynamics of solid explosive. For the detonation in solid explosive, the solid-phase reactant and gas-phase product in the chemically reactive mixture zone do not have molecular collisions as in the case of gaseous detonation, so the solid-phase reactant and gas-phase product can arrive at a mechanical equilibrium but cannot reach a thermal equilibrium when the detonation happens. The main properties of the present detonation model are as follows. The Euler equations for chemical mixture and the mass conservation equation for solid-phase reactant are used to express the chemically reactive flows in solid explosive detonation as a traditional way, and an additional set of governing equations of the species physical variables for solidphase reactant is derived to give an expression to the thermal nonequilibrium between the solid-phase reactant and gas-phase product. The chemical mixture within a control volume is defined as a collection of species which possess distinct internal energy or temperature, and the same pressure and velocity. For the explosive detonation, the species include solid-phase reactant and gas-phase product. Based on the mixing rule that every species can preserve the conservation of its internal energy in the reactive mixture zone, the evolution equation of internal energy for solid-phase reactant may be obtained, meanwhile, based on the property of mechanical equilibrium in the reactive mixture zone, the total volume fraction is equal to one, and the equation of state of every species, the evolution equation of volume fraction for solid-phase reactant and the evolution equation of pressure for chemical mixture can be derived. Thus, the theoretical model of solid explosive detonation includes the conservation equation of mass, momentum, total energy and the evolution equation of pressure for the chemical mixture, and the conservation equation of mass and the evolution equation of internal energy and volume fraction for the solid-phase reactant. The partially differential equations of the detonation model are numerically solved by a finite volume scheme with two-order spatiotemporal precision, through using a wave propagation algorithm by means of Strang splitting operator. The validation of the proposed detonation model is checked by the propagation of planar one-dimensional detonation, the propagation of cylindrically divergent detonation and the interaction between two cylindrically divergent detonations, and the typical examples demonstrate that the proposed theoretical model of solid explosive detonation is reasonable.
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Keywords:
- solid explosive detonation /
- thermal nonequilibrium /
- reactive flow model /
- total energy conservation of chemical mixture
[1] Chapman D L 1899 Philos. Mag. 47 90
[2] Jouguet E J 1905 de Math. Pures et Appl. 1 347
[3] von Neumann J 1956 Theory of Detonation Waves in John von Neumann's Collected Works (New York: Macmilann) pp18-28
[4] Zel'dovich Y B, Kompaneets A S 1960 Theory of Detonation (New York: Academic) pp234-245
[5] Davis W C, Fickett W 1979 Detonation (Berkeley: University of California Press) pp23-29
[6] Zhang F 2012 Detonation Dynamics, Shock Wave Science and Technology Reference Library (Vol. 6) (Berlin, Heidelberg: Springer) pp33-100
[7] Lee J H S 2008 The Detonation Phenomenon (Cambridge: Cambridge University Press) pp43-48
[8] Ershov A P, Satonkina N P, Ivanov G M 2006 Proceedings of the 13rd International Detonation Symposium Norfolk, USA, July 23-28, 2006 p79
[9] Nichols Ⅲ A L 2005 Shock Compression of Condensed Matter-2005, AIP Conference Proceedings Baltimore, USA, July 31-August 5, 2005 p03113-1
[10] Kay J J 2015 Shock Compression of Condensed Matter-2015, AIP Conference Proceedings Baltimore, USA, July 23-29, 2015 p03002-1
[11] Harier D 2015 Modeling ‘Hot-Spot’ Contributions in Shocked High Explosives at the Mesoscale (Los Alamos: Los Alamos National Lab.) LA-UR-15-26389
[12] Kapila A K, Menikoff R, Bdzil J B, Son S F, Stewart D S 2001 Phys. Fluids 13 3002
[13] Petitpas F, Richard Saurel, Franquet E, Chinnayya A 2009 Shock Waves 19 377
[14] Conley P A, Benson D J 1998 Proceedings of the 11th International Detonation Symposium Snowmass, CO, USA, July 15-20, 1998 p768
[15] Baer M R, Kipp M E, van Swol F 1998 Proceedings of the 11th International Detonation Symposium Snowmass, CO, USA, July 15-20, 1998 p788
[16] Nichols Ⅲ A L 2010 Proceedings of the 14th International Detonation Symposium Coeur d'Alane, USA, April 11-16, 2010 p1549
[17] Tarasov M D, Karpenko I I, Sudovtsov V A, Tolshmyakov A I 2007 Combust. Explo. Shock Waves 43 465
[18] Gerard B, Fabien P, Richard S 2010 Proceedings of the 14th International Detonation Symposium Coeur d'Alene Idaho, USA, April 11-16, 2010 p509
[19] Tarver C M 2005 Shock Compression of Condensed Matter-2005, AIP Conference Proceedings Baltimore, USA, July 31-August 5, 2005 p03113-1
[20] Ton V T 1996 J. Comp. Phys. 128 237
[21] Schoch S, Nordin-Bates K, Nikiforakis N 2013 J. Comp. Phys. 252 163
[22] Strang G 1968 SIAM J. Num. Anal. 5 506
[23] Leveque R J 1997 J. Comp. Phys. 131 327
[24] Zhong X L 1996 J. Comp. Phys. 128 19
[25] Lee E F, Tarver C M 1980 Phys. Fluids 23 2362
[26] Ralph M 2015 JWL Equation of State (Los Alamos: Los Alamos National Laboratory) LA-UR-15-29536
[27] Mader C L 1998 Numerical Modeling of Explosives and Propellants (2nd Ed.) New York: CRC Press) pp271-272
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[1] Chapman D L 1899 Philos. Mag. 47 90
[2] Jouguet E J 1905 de Math. Pures et Appl. 1 347
[3] von Neumann J 1956 Theory of Detonation Waves in John von Neumann's Collected Works (New York: Macmilann) pp18-28
[4] Zel'dovich Y B, Kompaneets A S 1960 Theory of Detonation (New York: Academic) pp234-245
[5] Davis W C, Fickett W 1979 Detonation (Berkeley: University of California Press) pp23-29
[6] Zhang F 2012 Detonation Dynamics, Shock Wave Science and Technology Reference Library (Vol. 6) (Berlin, Heidelberg: Springer) pp33-100
[7] Lee J H S 2008 The Detonation Phenomenon (Cambridge: Cambridge University Press) pp43-48
[8] Ershov A P, Satonkina N P, Ivanov G M 2006 Proceedings of the 13rd International Detonation Symposium Norfolk, USA, July 23-28, 2006 p79
[9] Nichols Ⅲ A L 2005 Shock Compression of Condensed Matter-2005, AIP Conference Proceedings Baltimore, USA, July 31-August 5, 2005 p03113-1
[10] Kay J J 2015 Shock Compression of Condensed Matter-2015, AIP Conference Proceedings Baltimore, USA, July 23-29, 2015 p03002-1
[11] Harier D 2015 Modeling ‘Hot-Spot’ Contributions in Shocked High Explosives at the Mesoscale (Los Alamos: Los Alamos National Lab.) LA-UR-15-26389
[12] Kapila A K, Menikoff R, Bdzil J B, Son S F, Stewart D S 2001 Phys. Fluids 13 3002
[13] Petitpas F, Richard Saurel, Franquet E, Chinnayya A 2009 Shock Waves 19 377
[14] Conley P A, Benson D J 1998 Proceedings of the 11th International Detonation Symposium Snowmass, CO, USA, July 15-20, 1998 p768
[15] Baer M R, Kipp M E, van Swol F 1998 Proceedings of the 11th International Detonation Symposium Snowmass, CO, USA, July 15-20, 1998 p788
[16] Nichols Ⅲ A L 2010 Proceedings of the 14th International Detonation Symposium Coeur d'Alane, USA, April 11-16, 2010 p1549
[17] Tarasov M D, Karpenko I I, Sudovtsov V A, Tolshmyakov A I 2007 Combust. Explo. Shock Waves 43 465
[18] Gerard B, Fabien P, Richard S 2010 Proceedings of the 14th International Detonation Symposium Coeur d'Alene Idaho, USA, April 11-16, 2010 p509
[19] Tarver C M 2005 Shock Compression of Condensed Matter-2005, AIP Conference Proceedings Baltimore, USA, July 31-August 5, 2005 p03113-1
[20] Ton V T 1996 J. Comp. Phys. 128 237
[21] Schoch S, Nordin-Bates K, Nikiforakis N 2013 J. Comp. Phys. 252 163
[22] Strang G 1968 SIAM J. Num. Anal. 5 506
[23] Leveque R J 1997 J. Comp. Phys. 131 327
[24] Zhong X L 1996 J. Comp. Phys. 128 19
[25] Lee E F, Tarver C M 1980 Phys. Fluids 23 2362
[26] Ralph M 2015 JWL Equation of State (Los Alamos: Los Alamos National Laboratory) LA-UR-15-29536
[27] Mader C L 1998 Numerical Modeling of Explosives and Propellants (2nd Ed.) New York: CRC Press) pp271-272
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