Numerical solution of the two-dimensional unsteady-state problem of the motion of a shell under the action of the products of an axial detonation

A numerical solution is obtained to the problem of the motion of an incompressible cylindrical shell with a charge of explosive, with excitation of the detonation simultaneously along the whole axis of the charge. The strength of the shell is not taken into consideration. A three-term equation of state is adopted for the products of the detonation. In [1] a numerical solution is obtained to the problem of the one-dimensional motion of a shell with the axial detonation of a charge of explosive.     

Numerical solution of the two-dimensional nonstationary problem of the motion of a shell under the action of detonation products

The problem of the motion of an incompressible cylindrical shell with an explosive charge is solved numerically for the propagation of a plane detonation wave from the end of the charge. The strength of the shell is not taken into account. A three-term equation of state [1] is assumed for the detonation products. A comparison is made with the one-dimensional case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 76–79, July–August, 1972.The authors thank G. S. Roslyakov and V. M. Paskonov for assistance in the work and for helpful advice.     

Motion of the detonation products of a point-ignited charge in a cylindrical shell

A numerical solution is obtained for the two-dimensional nonsteady problem of the motion of detonation products from a cylindrical high-explosive charge enclosed in a shell with the initiation of detonation at a central point in the end of the charge. The detonation products propagate in vacuum. The strength of the shell is not considered. A three-term equation of state is used for the detonation products.     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

Container for Localization of an Explosion of a Compact High–Explosive Charge with an Inert Shell

Results of an experimental study of fragmentation effects in the explosion and the piercing power of the fragments of inert masses in the form of hemispherical aluminum and soft–steel shells enclosing the spherical charge of a high explosive under their action on flat steel, aluminum, steel–net, and claydite—concrete barriers are given. A design of the lightest spherical explosion–proof container with a load–carrying steel or glass–reinforced plastic shell protected by a splinter–proof layer capable of withstanding an explosion of a high–explosive charge (with a twofold safety factor) with an inert steel shell is proposed.     

内部爆炸作用下钢筒变形过程的电探针测量技术

为了研究圆柱形爆炸容器在炸药爆炸作用下的变形过程,设计了电探针测量内部爆炸作用下钢筒变形的方法。采用数值模拟方法进行预估,在钢筒的中心进行了120g TNT和180g TNT当量球形装药下的爆炸加载实验,获得了爆炸不同时刻钢筒径向位移随时间的变化关系,电探针测量钢筒最大变形与实验后钢筒变形测量结果较好吻合。

     

Solution of certain variational problems of thermal resilience for thin shells considering the selection of optimum conditions for localized heat treatment

One of the possible ways of stating and solving the selection problem for optimum temperature fields for localized axisymmetric heating of shells is investigated. The minimum of shell elastic energy is taken as the optimization criterion. An infinite cylindrical shell was considered in a similar formulation in [1], The corresponding variational problem is formulated for the functional of elastic energy with additional limitations imposed on the function of twist angle at specified shell sections. The variational problem is reduced to an isoperimetric by the use of singular functionals of the -function kind. The related Euler equation is obtained, and this together with the problem resolvent equation constitute a complete set of equations for determining the extremum temperature field with related stress-strain state of the shell. Cylindrical, conical, and spherical shells are considered separately. A numerical analysis is made for the simplest conditions of localized heating of cylindrical and conical shells.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 4, pp. 47–54, July–August, 1968.     

Gasdynamics of the scattering of the detonation products of a cylindrical explosive charge with inert metal particles

A mathematical model of the scattering of the detonation products of a condensed explosive with inert metal particles when the wave travels along the axis of a cylindrical charge is proposed and numerical calculations are carried out. Detonation product scattering is simulated by a two-phase nonequilibrium axisymmetric jet flow in a supersonic external airstream. A technique for calculating the product gas-suspension behind the detonation wave is developed. The optimal values of the difference scheme parameters ensuring the required calculation accuracy are found. The gasdynamic properties of the process associated with the particles and the lateral spread are investigated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–111, September–October, 1995.     

Transient dynamic behavior of a closed gas-filled shell subjected to internal blast loading

The paper concerns the numerical solution of a problem on the forced vibration of a shell system under a blast load. The mathematical model of the transient dynamic process in the given multicomponent system is based on the use of a system of hydrodynamic equations to describe the motion of the detonation products and air and equations from shell theory to determine the stress-strain state of the shell system. The hydrodynamic equations are integrated in moving grids by the method developed by S. K. Godunov. The shell-theory equations are integrated by the integro-interpolation method. The distribution of the loads on the shells, the distribution of the maximum strains along the generatrix of the shell system, and the transformations of the detonation products at characteristic points are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 34, No. 3, pp. 76–82, March, 1999.     

Breakdown of a discontinuity,taking account of the real equation of state of the detonation products from a condensed explosive

The problem is considered concerning the breakdown of an arbitrary discontinuity, due to the emergence of a detonation wave at the boundary of a condensed explosive charge. The real equation of state of the detonation products of Hexogen was used in the numerical calculations. A u vs p diagram is constructed, which allows graphical calculations to be carried out of the discontinuity breakdown for different media. A comparison is carried out of the calculated values of the initial shock-wave velocities with the experimental data obtained at a certain distance from the explosive charge. It is shown that an increase of the pressure of the gas in which dispersion of the explosion products occurs leads to a reduction of the initial shock wave velocity and to an enhancement of its attenuation during its further motion in the shock tube.     

Numerical simulation of flow during compression of cylindrical samples by a glancing detonation wave

The parameters of shock waves created in cylindrical samples of various materials during detonation of explosive charges surrounding them have been determined experimentally [1–3]. It was established that in a number of materials the reflection of a conical shock wave from the symmetry axis of a sample leads to the formation of a Mach triple shock-wave configuration which gives rise to a complex flow pattern in the region beyond the shock waves. Analytic study of irregular reflection is a complex problem. Solutions obtained under various assumptions about the nature of the flow are presented in papers reviewed in [4]. In the present paper, axisymmetric flow of detonation products (DP) and sample material in the region adjacent to the detonation front is determined from the solution of a two-dimensional, time-dependent problem in gasdynamics by the finite-difference method [5].     

Fracture behavior of explosively loaded spherical molded steel shells

Experimental and numerical works are made to study the fracture of explosively loaded spherical molded steel shells. The first series of experiments included three sawdust recovery shots to save fragments for examination. In this series, detonation was initiated from the center of the sphere. Results of the experiments show that two types of fractures are observed in spherical shells: radial and shear as in cylindrical shells. Spall fracture is also observed in spherical shells. To assist understanding of the experimental results, a computer simulation of expanding shells is performed to provide information on the stress, strain, strain rate and position of each element of the shell wall as a function of time after detonation. For t=7.5 μs after detonation, triaxial non-uniform strain prevails in the middle of the thickness of the wall. The peak of the stress equals to 6.5 GPa and exceeds the spall strength of carbon steel. In the second series of experiments, spall fracture is suppressed by displacing the point of detonation initiation from the center to periphery of HE charge.     

The nature of the electrical impulse in an explosion

The mechanism for the formation of an electric impulse on the explosion of ordinary explosive substances is analyzed. A double electrical layer with voltage of the order kT 0.2–0.6 V is formed in the detonation wave. When the detonation wave passes to the outer surface of the charge, electrons adhere to molecules of air and explosion products. As the charged explosion products fly apart, the distance between the positive and negative charge s increases and the voltage increases to a magnitude of the order of a kilovolt. The asymmetric separation of the charged explosion products is the cause of the impulse. Theoretical estimates are compared with experiments [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 2, pp. 72–75, March–April, 1970.The authors are grateful to Ya. B. Zel'dovich and Yu. P. Raizer for useful discussions.     

Effect of the casing on the initial parameters of the underwater explosion of a cylindrical charge of explosive

An experimental determination was made of the initial parameters of shock waves in water with the explosion of cylindrical charges of TNT in casings. It is shown that these parameters depend mainly on the dynamic rigidity of the material and the relative weight of the shell. It is established that during the process of the expansion of the casing of the charge with an explosion in limited volumes of water there is formed a region of extremely rapid expansion, whose boundary can be identified with the boundary between the detonation products and the water after destruction of the casing, coinciding in time with the arrival of the cavitation front.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 165–168, January–February, 1973.     

Experimental investigation of the motion of cylindrical shells under the action of the products of an explosion in a cavity

An investigation was made of the motion of a cylindrical shell under the action of the products of an explosion in a cavity. An incompressible, nonviscous shell without strength was considered. The method of pulsed x-ray photography, with recording by the shadow method in a streak camera, was used to investigate the motion of shells made of alloy D16, brass, copper, and lead, with different degrees of filling of the cavity of the shells by the charge of explosive. The experimental and calculated results are compared. The agreement between the experimental results and calculation is satisfactory.     

聚奥-9C装药的传爆管殉爆

为了研究冲击波作用下引信传爆装置的响应规律,进行了以主发炸药为RDX-8701、被发装置为聚奥-9C（JO-9C）装药的传爆管（含导爆药柱）的殉爆实验。通过观测残留传爆药、壳体和见证块变形,判断传爆管的爆炸程度,分析了殉爆过程中JO-9C爆轰波的成长历程及传播规律。采用AUTODYN软件建立了殉爆实验有限元模型,计算模型中主要考虑了主发炸药产生的爆炸冲击波对传爆管的冲击响应。基于流固耦合方法,通过调整距离模拟计算得到了传爆管的临界殉爆距离和殉爆安全距离。结果表明,传爆管上端的侧角受到爆炸冲击后产生的爆轰波沿斜下方传播,使传爆药柱完全爆轰,并引起导爆药柱发生殉爆;数值模拟结果显示,JO-9C装药的传爆管临界殉爆距离为5.7 mm,殉爆安全距离为8.8 mm。     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, May–June, 2009.     

On the motion of flying plate under explosive attack

The one-dimensional problem of the motion of a rigid flying plate under explosive attack has an analytic solution only when the polytropic index of detonation products equals to three. In general, a numerical analysis is required. In this paper, however, by utilizing the weak shock behavior of the reflection shock in the explosive products, and applying the small parameter purterbation method, an analytic, first-order approximate solution is obtained for the problem of flying plate driven by various high explosives with polytropic indices other than but nearly equal to three. Final velocities of flying plate obtained agree very well with numerical results by computers. Thus an analytic formula with two parameters of high explosive (i.e. detonation velocity and polytropic index) for estimation of the velocity of flying plate is established.     

内爆加载下金属柱壳的冻结回收方法

针对内爆炸载荷下膨胀态金属柱壳的回收问题,设计了冻结回收试验方法,实现了起爆后不同时刻金属柱壳的冻结回收。基于一体式壳体提出了3种改进结构,并分别对4种柱壳结构在内爆载荷下的膨胀断裂过程进行数值模拟。结果表明,两段式结构最有利于减小非起爆端对预期回收中间段壳体的影响。根据选定的最优壳体结构和金属柱壳在起爆后不同时刻的膨胀外形特征,设计与之匹配的冻结回收装置并进行冻结回收试验。试验结果表明,设计的冻结回收试验方法可以实现膨胀态金属柱壳的回收,回收壳体的轴向和径向尺寸与设计理想值符合较好,整体误差可控制在10%以内。

     

锥形长药柱水下爆炸冲击波参数计算方法

为了计算锥形长药柱水下爆炸冲击波压力,以及研究长脉宽冲击波的传输特性,基于叠加原理建立了冲击波压力-时间曲线的计算方法,通过实验验证了该方法的有效性,在此基础上分析了锥形长药柱不同方位冲击波压力的分布规律。研究结果表明:锥形长药柱产生的冲击波压力具有各向异性,在起爆端一侧形成的是具有厚波头特征的低幅值长脉宽冲击波,在装药径向形成的是接近指数衰减的高幅值冲击波,而在远离起爆端的冲击波压力幅值和脉宽则介于前两者之间。锥形长药柱与球形装药冲击波分布的差异是由于装药形状和起爆方式的改变所导致的,由于装药不同部位起爆的时间差,导致水下爆炸冲击波在不同位置的叠加效果存在明显差异,药柱周围流场中形成的冲击波压力具有方向性。利用提出的计算方法得到的计算结果与实验结果和数值模拟结果吻合较好,研究结果可为锥形长药柱水下爆炸冲击波威力场和毁伤评估提供参考和依据。