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.     

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.     

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.     

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.     

Equations of hydromechanics and compression shock in two-velocity and two-temperature continuum with phase transformations

The equations of motion of multiphase mixtures have been considered in [1–10] and several other studies. In [1] it is proposed that the mixture motion be considered as an interpenetrating motion of several continua when velocity, pressure, mean density, concentration, etc., fields for each phase are introduced in the flowfield. The equations of motion are written separately for each phase, and the force effect of the other components is considered by introducing the interaction forces, which for the entire system are internal. The assumption of component barotropy is used to close the system.The energy equations are used in [2, 3] in place of the component barotropy assumption. Moreover, mixtures without phase transformations are considered. In [4] an analysis is made of the equations of turbulent motion with account for viscous forces for a two-velocity, but single-temperature medium in which equilibrium phase transformations are assumed, i. e., a two-phase medium is considered in which the phase temperatures are the same, the composition is equilibrium, but the phase velocities are different. In [5] the equations are written on the interface in a multicomponent medium consisting of barotropic fluids. A discontinuity classification is also presented here. In the aforementioned work [3] the equations on the shock are written for a continuum with particles without the use of the property of barotropy of the carrier fluid. Various different aspects of the motion of multiphase mixtures are considered in [6–11], for example, the effect of particle collisions with one another, the effect of the volume occupied by the particles on the parameters stream, shock waves, etc. In [7] a study is made of the force effect of an agitated medium on a particle on the basis of the Basset-Boussinesq-Oseen equation.In the following we derive the equations of motion of a two-velocity and two-temperature continuum with drops or particles with nonequilibrium phase transformations, i. e., a medium in which the phase velocities and temperatures are different and the composition may be nonequilibrium. In addition, we study the effect of the presence of particles or drops on the gas parameters behind a shock. Further, the equations obtained here are used to study compression waves, and in particular shock waves.The author wishes to thank Kh. A. Rakhmatulin, S. S. Grigoryan, and Yu. A. Buevich for helpful discussions and valuable comments.     

Nonlinear magnetoacoustic waves in a conducting liquid containing gas bubbles

The propagation of long waves in an incompressible conducting liquid saturated with nonconducting gas bubbles is considered on the basis of the equations of magnetohydrodynamics of a homogeneous gas-liquid medium. It is shown that the propagation of weakly nonlinear MHD waves in such a medium is described by the Burgers-Korteweg-de Vries (BKdV) equation. The influence of MHD interaction effects on the parameters of fast and slow weak magnetoacoustic shock waves is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–147, March–April, 1991.     

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.     

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.     

Shock wave in a gas-liquid medium

The propagation of weak shock waves and the conditions for their existence in a gas-liquid medium are studied in [1]. The article [2] is devoted to an examination of powerful shock waves in liquids containing gas bubbles. The possibility of the existence in such a medium of a shock wave having an oscillatory pressure profile at the front is demonstrated in [3] based on the general results of nonlinear wave dynamics. It is shown in [4, 5] that a shock wave in a gas-liquid mixture actually has a profile having an oscillating pressure. The drawback of [3–5] is the necessity of postulating the existence of the shock waves. This is connected with the absence of a direct calculation of the dissipative effects in the fundamental equations. The present article is devoted to the theoretical and experimental study of the structure of a shock wave in a gas-liquid medium. It is shown, within the framework of a homogeneous biphasic model, that the structure of the shock wave can be studied on the basis of the Burgers-Korteweg-de Vries equation. The results of piezoelectric measurements of the pressure profile along the shock wave front agree qualitatively with the theoretical representations of the structure of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–69, May–June, 1973.     

Motion of shock waves in an inhomogeneous gas

Whitham [1] has proposed a method of approximate calculation of the motion of shock fronts giving results in fairly good agreement with the experiments when one considers various nonstationary problems of the interaction of shock waves with one another and solid surfaces. However, the method gives rise to fundmental difficulties when one considers the propagation of shock waves in a moving medium [1, 2]. In the present paper, the method is generalized to the case of a gas which is moving nonuniformly in front of the shock wave, no restrictions being made on the nature of the motion or the variation of its parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 175–178, January–February, 1981.I thank M. D. Gerasimov for interest and assistance in the work.     

Theoretical investigation of ignition and detonation of coal-particle gas mixtures

A mathematical model of ignition of a coal-particle gas suspension is developed within the framework of mechanics of reacting heterogeneous media. Some qualitative features are studied, which reveal different typical variants of heat dynamics of the mixture: heterogeneous ignition caused by the coke residue ignition reaction, homogeneous ignition induced by volatile oxidation in the gas phase, and hybrid ignition due to the simultaneous effect of surface and volume reactions. Verification of the model is performed using available experimental data on ignition delay times for coal-particle suspensions in air and oxygen behind reflected shock waves. The model is extended to detonation processes in the suspension, verified by experimental data on the relation between the propagation velocity and initial particle concentration. Stationary detonation regimes are studied, and specific features of detonation structures are discussed.This paper was presented at the 18th International Colloquium on the Dynamics of Explosions and Reactive System, Seattle, Washington, USA, August, 2001     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Chapman-Jouguet waves in a dusty gas

An analytic solution is obtained of the problem of flow of a two-phase medium, representing a mixture of gas and solid or liquid particles behind plane, cylindrical, and spherical Chapman-Jouguet detonation waves. It is assumed that all the particles are the same, are chemically inert, have a true density much greater than the density of the gas, and that their volume concentration a is low. The interaction of the particles and the influence of Brownian motion on them are disregarded. The gas is assumed to be perfect. On the detonation wave, the particle parameters are assumed to be continuous, and the usual gas-dynamical relations on the detonation wave have been applied for the gas parameters because is low. Behind the detonation front, the phases interact through interphase forces and heat transfer. It has been found that the dust content of the combustible gas qualitatively changes the character of flows with Chapman-Jouguet (C-J) waves. It is shown that a plane C-J wave is an envelope of one of the acoustic families of characteristics, and not a characteristic, as occurs in a pure gas [1]. In view of this, only two solutions of the problem of flow behind a plane C-J wave are possible: one solution corresponds to a rarefaction flow and the other to a compression flow. In a pure gas such a problem has a nondenumerable set of solutions: an arbitrary Riemann rarefaction wave can adjoin the plane C-J wave. It is found that in a dusty gas there are converging cylindrical and spherical C-J waves. In a pure gas, there are no converging C-J waves [2, 3]. An expression is found for the distance r_* from the axis (center) of symmetry on which the converging cylindrical (spherical) C-J wave changes into a supercompressed detonation wave. It has been found that r_* d/₀, = 1, 2 for the cylindrical and spherical waves, respectively, d is the particle diameter, ₀ is their initial volume concentration, and the proportionality factor decreases together with d. For the detonating mixture 2H₂ + O₂ the calculations of r_* are given in a number of cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–118, July–August, 1985.The author wishes to thank V. A. Levin for his interest in the work and his useful discussion of the results.     

Numerical study of the dynamics of a vapor envelope round a heated solid particle in a liquid

A study is made of the radial motion of a vapor envelope surrounding an isolated spherical particle in an unbounded mass of liquid. It is assumed that the liquid is viscous and incompressible and that the temperature is distributed uniformly in the solid particle. A model of a calorifically perfect gas is used for the vapor phase. The same assumptions are made as in Rayleigh's formulation for the problem of the dynamics of a single bubble: that the process is spherically symmetric and that the pressure P₂ (t) in the vapor phase is homogeneous. The justification for making these assumptions in problems of the dynamics of gas, vapor, and vaporgas bubbles is discussed in [1–5]. In this paper, the collapse of the vapor layer and the boiling of the liquid on the surface of the heated particle are not considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 154–157, July–August, 1985.     

Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas

Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture \(K_p\) , and the ratio of the density of solid particles to the initial density of the gas \(G_a\) are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.     

Self-similar solution of cylindrical shock wave propagation in a rotational axisymmetric mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has a variable azimuthal fluid velocity together with a variable axial fluid velocity. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. The shock Mach number is not infinite, but has a finite value. The azimuthal and axial component of the fluid velocity in the ambient medium are assumed to be vary and obey power laws, and the density of the ambient medium is taken to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of the variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of the density of solid particles to the initial density of the gas are investigated.     

Shock and detonation wave diffraction at a sudden expansion in gas–particle mixtures

Numerical modeling of the propagation of shock and detonation waves is carried out in a duct with an abrupt expansion for a heterogeneous mixture of fine particles of aluminum and oxygen. A considerable difference from corresponding flows in pure gas is found. The influence of the size and mass loading of particles on the flow and shock wave structure behind the backward-facing step is determined. As in gaseous detonations, three types of scenarios of detonation development are obtained. Specific features of the flow structure are revealed such as deformation of the combustion front due to interaction between the relaxation zone and the vortex structure. The influence of particle size and channel width on detonation propagation is analyzed. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.