Simulation of detonation wave interaction using an ignition and growth model

A kinetics based detonation model has been integrated with an existing object oriented hydrocode. The model has been demonstrated to correctly predict the shock initiation of explosives and captures key features such as the von Neumann pressure spike and reaction zone. Comparisons to experimental flyer plate data for both primary and secondary class explosives have been performed and key features such as detonation wave form and resulting target disk velocities are reproduced. Simulations have also been performed representing the interaction of various mechanical waves. First, the interaction of detonation waves, a key process in energetic systems, is simulated. Next, the response of an established detonation wave to an explosive that has been preconditioned by a weak compression wave is modeled. These have been carried out to determine the utility of the existing kinetic schemes for such problems.     

反向起爆模型下的冲击波加载

为了实现对大尺寸材料试件的动态加载,得到与轻气炮加载应力波相同的爆炸加载冲击波,基于叠加原理,提出了利用炸药反向起爆模型完成对可压缩固体材料的冲击波加载。通过联立爆炸产物和可压缩流体的速度-压力曲线以及综合考虑炸药和材料试件各自由边所受稀疏波干扰的情况,从理论上给出了冲击波压力和冲击波加载平台宽度的计算方法。并结合数值模拟,对理论分析结果进行了验证,两者基本一致。

     

2021-08期封面

铝粉反应模型是对悬浮铝粉尘气-固两相爆轰进行数值模拟研究的关键。通过考虑铝粉燃烧产物氧化铝（Al₂O₃）在高温下的分解吸热反应,改进了铝粉的扩散燃烧模型。将该模型嵌入到三维的气-固两相爆轰数值计算程序中,分别对铝粉/空气混合物以及铝粉/氧气混合物的爆轰进行了数值模拟,计算得到的稳定爆轰波速度与实验结果、文献值均吻合较好,误差小于5.5%,表明改进的铝粉反应模型适用于不同氧化气体氛围中铝粉尘爆轰的模拟计算。此外,对两相爆轰参数及爆轰流场的物理量分布进行分析,获得了铝粉反应模型对爆轰波结构的影响规律。     

Energy of an asymptotically equivalent point detonation for the detonation of a charge of finite volume in an ideal gas

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–51, November–December, 1988.     

One-dimensional diffusional model of heterogeneous (gas-film) detonation

The detonation process in a tube filled with a gaseous oxidant (oxygen) and which has a thick layer of fuel (carbon with a low vapor pressure) deposited over its entire perimeter is examined; the weight ratio of fuel to oxidant considerably exceeds the stoichiometric ratio. It is assumed that the rate of heat release is determined by the diffusional (noninstantaneous) process of mixing of the vaporizing fuel and the oxidant. An estimate is made of the effect on the detonation parameters of heterogeneity in the composition over the cross section of the tube and of friction and heat losses. Dependences of the detonation parameters (propagation velocity, pressure profile in the front, distance to the Chapman—Jouquet plane) on the thermophysical properties of the fuel and oxidant are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoe Fiziki, No. 3, pp. 86–95, May–June, 1974.     

Experimental study of an air-breathing pulse detonation engine ejector

Experimental studies were performed in order to improve the understanding of the performance of ejector driven by an air-breathing pulse detonation engine (PDE) with a convergent nozzle. This research utilized a gasoline-air PDE at four different operating frequencies of 8 Hz, 10 Hz, 12 Hz and 15 Hz. The performance of PDE-ejector was quantified by thrust measurements. The effects of single ejector length and axial location on thrust augmentation were investigated. It was found that the single ejector with L/D of 2 showed the best performance and the maximum thrust augmentation occurred at a downstream placement of +1 tube diameter. The performances of two-stage and three-stage ejectors were also investigated. The results indicated that both the overlap ratio and the flow area between two stages should not be too large. The performance of the two-stage ejector was not as sensitive as single-stage ejector to axial position in current conditions. The three-stage ejector behaved better than the two-stage ejector but worse than the single-stage ejector in this work. A maximum thrust augmentation of 1.8 was obtained with an L/D of 2 at a downstream placement of +1 position and 15 Hz operating frequency.     

Ignition and detonation of solid explosives: a micromechanical burn model

This paper describes a new computational framework for modeling splid explosives and proof-of-concept calculations. Our goal is to expand predictive model capability through the inclusion of various micro-mechanical burn processes. We propose a model which is complicated enough to represent underlying physics, but simple enough for engineering scale computations. Key components of the model include energy localization, the growth of hot spots, micro-mechanics in/around hot spots, and a phase-averaged mixture equation of state. The nucleation and growth of locally heated regions is treated by a statistical model based on an exponential size distribution. Proof-of-concept calculations are limited to shock loading, but show the capability of simulating Pop-plots, initial temperature effect, detonation waves in 2D, detonation shock confinement test, and multi-dimensional effects in a unified fashion based on micro-physics.

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地下爆炸气体输运的一种双孔隙度数学模型

考虑气体在压力驱动下的渗透、气体和岩体的热传导以及气体的扩散,建立了用于模拟地下爆炸气体输运的二维轴对称双孔隙度双渗透率数学模型,并编制了数值模拟程序;研究了参数在取值范围内变化对计算结果的影响。结果显示：泄漏到地表的气体随着裂隙区域圆心角的增大而先增大后减小,随裂隙渗透率的增大而增大,随介质孔隙度和孔隙渗透率的增大而减小。用该模型对一次砂砾岩中地下爆炸实验气体的泄漏行为进行了数值模拟。将数值模拟结果与气体泄漏实测结果进行对比,反推出当地介质的裂隙渗透率在4×10^-11 m2～5×10^-11 m2之间。利用反推得到的介质参数,可以对同类介质中地下爆炸气体泄漏行为进行预测。     

Regular reflection of plane detonation waves from an elastic half-space

An effective method for the approximate solution of the Eq. [1] for the intensity of a reflected shock wave in the case of oblique incidence of a detonation wave on an elastic half-space is described; the elastic half-space is described by a certain specific form of the equation of state. Formulas relating the front and particle velocities behind the transmitted wave front to physical parameters are derived. Values of the wave intensity and other quantities determined with the aid of a Ural-2 computer are cited.The author of [1, 2] investigated the regular reflection of shock waves from the boundary between two bodies. In the present paper we solve the analogous problem in the case of oblique incidence of a detonation wave on an elastic half-space. The detonation wave deforms the elastic half-space, which assumes the position OK₁ (Fig. 1) forming the angle to the initial direction KO of the halfspace boundary. We assume that the acoustic stiffness of the halfspace is larger than the acoustic stiffness of the explosive. In this case, both reflected wave 2 and transmitted wave 3 are shock waves [3]. Let us denote the velocities of propagation of the detonation, reflected, and transmitted waves by U_i(i=1, 2, 3), respectively; let the pressure be p_i and let the density bep _i(i=0, 1, 2, 3, 4). The quantities U₁, ₁, ₀, and ₄ are given. We determine the intensities of waves 2 and 3, their velocities of propagation, and the angles ₂, ₃ and . The parameters are constant within each of the domains a, b, c, d, and e. In domains a and e the medium is stationary, i.e., u₀=u₄ =0. The basic equations of the problem express the conditions at the wave fronts and the dynamic and kinematic relationships.     

Structure of an oblique detonation wave induced by a wedge

The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.     

含铝炸药爆轰驱动的非线性特征线模型

针对含铝炸药爆轰的非理想特性,提出了含铝炸药爆轰产物膨胀的局部等熵假设,建立含铝炸药爆轰驱动的非线性特征线模型,为研究含铝炸药爆轰产物的非等熵流动和膨胀做功提供了一种新的理论分析方法。设计了5、50 μm含铝炸药和含LiF炸药驱动0.5、1 mm厚金属板实验,通过激光位移干涉仪测试金属板运动的速度历程,再通过实验结果计算得到铝粉在爆轰产物中的反应度变化规律,结合含铝炸药爆轰产物的非线性特征线模型,理论计算了含铝炸药驱动金属板的速度历程。对比理论与实验结果,理论方法能够很好地描述铝粉二次反应对炸药做功能力的贡献,同时验证了含铝炸药爆轰驱动的非线性特征线模型的正确性。     

Liquid-gas coexistence equilibrium in a relaxation model

Stability of liquid-gas coexistence equilibrium in a relaxation model for isothermal phase transition in a sealed one-dimensional tube was discussed. With matched asymptotic expansion, a linear system for first order perturbations was derived formally. By solving this system analytically, it is shown that small initial perturbations are damped out in general; yet they may maintain at certain level for special cases. Numerical evidence is presented. This manifests the regularization effects of relaxation.     

基于非平衡多相模型的含铝炸药爆速研究

通过对爆轰反应区中铝粉压力、温度弛豫时间的计算,发现爆轰产物压力是平衡的,温度是不平衡 的。对传统CJ模型进行了改进,考虑爆轰产物的多相性和产物温度间的非平衡性,提出了一种新的计算含 铝炸药爆速的模型。采用该模型对几种含铝炸药的爆速进行了计算,并与已有的实验数据进行了对比,计算 结果优于传统CJ模型,与实验的误差在2%以内。     

破片撞击起爆柱面带壳装药的临界速度修正判据

为获得适用于柱面带壳装药的冲击起爆修正判据,以Picatinny工程判据为基础加入修正项进行修正。采用AUTODYN-3D软件对破片撞击柱面带钢壳的B炸药进行数值计算,获得了破片入射角、装药曲率半径对炸药临界起爆速度的影响规律;通过拟合得到修正项表达式,建立了考虑破片入射角、柱壳装药形状函数的炸药起爆临界速度修正判据。判据计算值与实验数据和数值计算值吻合较好,该判据能较好的预测柱形带壳装药的冲击起爆条件。     

Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model

This paper mainly addressed the stability analysis and the estimation of domain of attraction for the endemic equilibrium of a class of susceptible-exposed-infected-quarantine epidemic models. Firstly, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region D of the epidemic model, respectively. Secondly, we use a geometric approach to investigate the global stability of the endemic equilibrium in a positive invariant region \(D_s(\subset D)\). Furthermore, we estimates the domain of attraction for the endemic equilibrium via sum of squares optimization method, and obtain the optimal estimation by solving an semidefinite programming problem with sum of squares polynomial constraints. Finally, numerical simulation is examined to demonstrate the feasibility and effectiveness of the research results.     

On equilibrium stability of an elastic-viscoplastic medium

We consider the stability of an elastic-plastic medium when one part of the body is in an elastic state and the other part in a plastic state.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1970.     

Effect of inhomogeneities in an explosive on the critical detonation diameter

The effect of inhomogeneities in an explosive on the critical detonation diameter is theoretically analyzed. On the assumption that the inhomogeneities are centers of the reaction behind the detonation front, a formula is obtained for determining the critical diameter as a function of the concentration and size of the inhomogeneities. It is shown that when the inhomogeneities are particles of an inert substance added to the explosive, the dependence of the critical diameter on the mass fraction and size of the inert particles may have a minimum. The results of the theoretical analysis are in qualitative agreement with the experimental data.In conclusion the author thanks R. Kh. Kurbangalina for formulating and discussing'the problem and L. N. Stesik for his useful remarks.     

氢氧爆轰波在变截面扩张管道中传播的数值模拟

采用二阶精度频散控制耗散格式(DCD)和8组分20个方程的基元反应模型,对轴对称变截面管道中氢氧爆轰波传播进行数值模拟。结果表明,爆轰波传播至突变截面扩张管道时,由于稀疏波的作用可能会使爆轰波局部熄爆甚至完全熄爆,对于某些敏感度高的反应气体爆轰波可以二次起爆。而在渐变截面扩张管道爆轰波相对不易熄爆。     

Percolation model of equilibrium three-phase flow through porous media

Percolation models of one-phase and two-phase flow through porous media are extended to the three-phase case. The characteristic regions of realization of one-phase, two-phase and three-phase flow are determined, Relative phase permeability calculations are presented for a model capillary radial density function. The theory is compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 109–114, January–February, 1989.