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.     

On the origin and part played by pulsations of a detonation front

Arguments are given which show that the occurrence of pulsations is independent of the part they play in self-sustained detonation. It is shown that the perturbations which generate kinks in the detonation front are not formed in the region of shock compression but in the burning gas. It is suggested that the primary cause of the perturbations could be strong fluctuations associated with intense chemical transformations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 190–194, September–October, 1979.I am grateful to V. A. Levin and G. G. Chernii for discussions and valuable comments and to Ya. K. Troshin for support.     

Population inversion behind a detonation wave propagating in a variable-density medium

The creation of an active medium by means of detonation has been investigated on a number of occasions. It was suggested that one could use the expansion of the detonation products of an acetylene-air mixture in vacuum [1] or the cooling of the detonation products of a mixture of hydrocarbons and air through a nozzle [2, 3]. In [4], the detonation of a solid high explosive was used to produce population inversion in the gas mixture CO₂-N₂-He(H₂O). Stimulated emission from HF molecules was observed in [5] behind the front of an overdriven detonation wave propagating in an F₂-H₂-Ar mixture in a shock tube. Population inversion behind a detonation wave was studied in H₂-F₂-He mixtures in [6–8] and in H₂-Cl₂-He mixtures in [9] with energy release on a plane and on a straight line in a medium with constant density. Similar problems were solved for shock waves propagating in both a homogeneous gaseous medium [7, 10] and in the supersonic part of an expanding nozzle. In the present paper, we study theoretically population inversion behind an overdriven detonation wave propagating in a mixture (fine carbon particles + acetylene + air) which flows through a hypersonic nozzle. The propagation of detonation in media with variable density and initial velocity was considered, for example, in [11, 12]. Analysis of the gas parameters behind a detonation wave propagating in a medium with constant density (for a given fuel) showed that the temperature difference across the detonation front is insufficient to produce population inversion of the vibrational levels of the CO₂ molecule.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–71, January–February, 1980.I am grateful to V. P. Korobeinikov for a helpful discussion of the results.     

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.     

Detonation Wave Propagation in Rotational Gas Flows

This paper studies the propagation of detonation and shock waves in vortex gas flows, in which the initial pressure, density, and velocity are generally functions of the coordinate — the distance from the symmetry axis. Rotational axisymmetric flow having a transverse velocity component in addition to a nonuniform longitudinal velocity is considered. The possibility of propagation of Chapman–Jouguet detonation waves in rotating flows is analyzed. A necessary conditions for the existence of a Chapman–Jouguet wave is obtained.     

On regular reflection of detonation waves

The boundaries of regular reflection of detonation waves by a rigid wall are calculated. It is assumed that detonation is initiated at the point of reflection when a shock wave is incident on the wall at a finite angle in a gas fuel mixture, the detonation propagating instantaneously along the reflected front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–180, March–April, 1983.     

Errors in stress measurements in soils under short-term loads

The results of experimental investigations of systemic errors in stress measurements in sandy soils by strain gauges under short-term loads produced by detonation of a plane charge are presented. The effect of rigidity of sensitive elements of the gauges and the effects of stress concentrations around the gauge body on the stress field measured are analyzed. A comparison of the experimental results with the theoretical calculations of [1, 2] is offered. It is shown that the systemic errors will not exceed ± 3–7% if certain easily achieved requirements with respect to the gauges are fulfilled. The question of evaluating systemic error in stress measurement in soils under low intensity static loads has been examined in [3–6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 146–154, July–August, 1972.In conclusion, the authors thank N. V. Zvolinskii and A. M. Skobeev for their valuable advice and evaluation of the study, and A. I. Kotov, V. P. Sutyrin, and L. G. Romanov for participation in the conduct of the experiments and processing of the results.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

Structure of detonation waves in gas suspensions of fuel containing the oxidant

The structure of detonation waves in air suspensions of unitary fuels (fuels containing an oxidant such as gunpowder and high explosives) is investigated. In such systems, complete combustion of the particles is possible at a high mass concentration of the fuel. As a result, the structure of detonation differs from that in gas-drop [1–3] and gas [4, 5] mixtures. The shock adiabats characteristic for air suspensions [6, 7] are used to investigate the field of integral curves which describe the structure of detonation waves in disperse media. Calculated distributions of the parameters which characterize the gas and particles in the detonation front are given. The influence of the rate of combustion of the particles and the intensity of interphase friction on the structure of the detonation is investigated. Results of the calculation of the structure of relaxation shock waves in gas suspensions of the solid fuel of rockets are given in [8]. Unsteady problems of convective combustion and the transition of combustion of air suspensions into detonation are analyzed in [9, 10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–53, September–October, 1981.     

Similarity motions of a gas in the case of local supply of mass and energy in a fuel mixture

One-dimensional nonstationary similarity motions of a gas with exothermic reactions behind shock waves are analyzed. The thickness of the region of chemical reactions is ignored. New solutions are obtained for the problems of flows of a chemically active gas with the formation of shock and detonation waves. In particular, it is shown that in the framework of the adopted schemes of the combustion process a solution with five strong-discontinuity surfaces can be constructed. The results are given of numerical solutions for supercompression detonation and Chapman-Jouguet detonation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–77, July–August, 1979.     

Numerical calculation of the magnetic cumulation process

A numerical calculation is made of the process in the MK-1 magnetocumulative generator under the assumption that the magnetic flux is constant and the tube contraction process is one-dimensional. The instantaneous detonation scheme is adopted. The effect of initial magnetic field intensity and relative size of the cavity on the magnitude of the maximal magnetic field intensity obtained inside the tube is studied.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 51–55, May–June, 1970.The authors wish to thank L. A. Chudov for his continued interest in the study and valuable advice, and also Yu. V. Korovin for assistance in the calculations.     

The detonation burning of a fuel mixture resulting from a double explosion

A study is made of the propagation of a multifront detonation burning in a fuel mixture consisting of a gaseous fuel and an oxidant with additions of combustible solid or liquid particles arising as a result of a double point explosion. In such combustible media it is possible for there to be propagation of several detonation or burning fronts following one after the other. The easily igniting gaseous fuel burns in the first detonation wave, which propagates in the gaseous mixture with particles which are heated by the products of the explosion, ignite and burn in the second detonation wave or in the flame front. Self-similar regimes of propagation of such waves in an idealized formulation were studied in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–131, March–April, 1985.     

Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Flow of a gas behind a Chapman-Jouguet detonation wave in the vicinity of a line of discontinuity of a surface wave curvature

This paper discusses questions of constructing a solution of the gasdynamic equations near a line of curvature discontinuity at the surface of a detonation wave, propagating under Chapman—Jouguet conditions. It describes the construction of the solution in two cases: in a flow arising with the initiation of a detonation along a half-plane in a quiescent homogeneous combustible gas and in a flow arising with the initiation of a detonation along a half-line under these same conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 120–126, January–February, 1978.     

Existence of Solutions for Steady Detonation of Gas Suspensions

The existence of solutions of the traveling–wave type is studied for a system of equations that describes a one–dimensional motion of a suspension of evaporating particles in a viscous and heat–conducting chemically reacting gas. Using topological methods, it is shown that solutions corresponding to weak, strong, and Chapman—Jouguet detonation exist under certain restrictions on energy release and mass transfer.     

Spatially polarized structure of detonation waves ionizing a gas

Additional relationships must be used [1–3], in addition to those following from the main integral laws, in describing ionizing detonation waves, exactly as for ionizing shocks. These additional relationships are obtained from the requirement for the existence of wave structure. The structure of detonation waves ionizing a gas in an oblique magnetic field was investigated in [1, 2]. The case of a plane-polarized structure was considered, when the velocity vector and the magnetic field lie in a plane passing through the normal to the front. The structure of ionizing detonation waves is studied in this paper for the case when the wave is spatially polarized and both transverse magnetic field components vary in the structure. It is considered that the magnetic viscosity and a quantity reciprocal to the chemical reaction rate are much greater than the remaining dissipative coefficients in the layer representing the structure. Conditions for the existence of such a spatial structure are clarified. Plane-polarized ionizing detonation waves whose structure is not planar are also considered. When the characteristic length of magnetic field dissipation is much greater or much less than the characteristic length of the chemical reaction, the additional relationships assuring the existence of structure are written down explicitly or are investigated qualitatively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–169, November–December, 1976.     

Calculating the structure of detonation waves

Some results of calculations are shown which have been obtained for detonation waves with the fission of the explosive material occurring at a finite rate.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 73–80, May–June, 1971.     

Gas dynamic aspects of the interaction between a centered compression wave and an incompressible plate

The interaction regime of a centered compression wave and an incompressible plate projected by the detonation products of a condensed explosive is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–168, July–August, 1990.     

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.     

Study of the attenuation of a detonation wave with a two-front structure by the boundary (shock) layer method

The possibility that a plane overcompressed detonation wave may undergo a transition to the Chapman-Jouguet mode during its attenuation is considered on the basis of the two-front model, allowing for the change in flow parameters in the interval between the fronts. G. G. Chernyi's approximate method of boundary (shock) layer is used in order to describe the flow of the gas in this interval. The use of this method is justified by the fact that the velocity of propagation of the detonation wave is extremely great (order of several km/sec), and the gas between the compression jump and the combustion front is strongly compressed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp. 59–65, May–June, 1971.