Structure of detonation waves,ionizing a gas,in the presence of an electromagnetic field. Cases of low magnetic viscosity

If behind a detonation wave, ionizing a gas, the magnetic Reynolds number is much greater than unity, then in order to describe such waves (just as for ionizing shock waves) complementary relations [1, 2] are necessary. These complementary relations are not the consequence of the basic integral laws, but can be found from a consideration of the wave structure. In [2], the structure of detonation waves, ionizing a gas, was investigated in an oblique magnetic field. It was supposed that the flow in a layer representing the structure is determined by the finite rate of the chemical reaction and the finite electrical conductivity. In the case when the characteristic length of the chemical reaction is much less than the characteristic dissipation length of the magnetic field, the complementary relations which ensure the existence of the structure are obtained in explicit form. The case is considered below when the characteristic length of the chemical reaction is much greater than the dissipation length of the magnetic field. In this case, the complementary relations are obtained in the explicit form.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 95–101, May–June, 1976.     

Stability of a radiation-absorbing ionizing shock wave in an electromagnetic field

The linear stability of a radiation-absorbing ionizing shock wave (light detonation waves) in the presence of a uniform electromagnetic field is investigated. The applied electric field is considered to be normal to the wave front and the magnetic field to be parallel to the front and perpendicular to the plane in which perturbations propagate. The medium satisfies a two-parameter equation of state. Analytic stability criteria are obtained. For a perfect gas the effect of the electromagnetic field and radiation on shock wave stability is determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–30, January–February, 1996.     

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.     

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.     

Simple stationary waves in an inclined magnetic field

One component of the solution to the problem of flow around a corner within the scope of magnetohydrodynamics, with the interception or stationary reflection of magnetohydrodynamic shock waves, and also steady-state problems comprising an ionizing shock wave, is the steady-state solution of the equations of magnetohydrodynamics, independent of length but depending on a combination of space variables, for example, on the angle. The flows described by these solutions are called stationary simple waves; they were considered for the first time in [1], where the behavior of the flow was investigated in stationary rotary simple waves, in which no change of density occurs. For a magnetic wave, of parallel velocity, the first integrals were found and the solution was reduced to a quadrature. The investigations and the applications of the solutions obtained for a qualitative construction of the problems of streamline flow were continued in [2–8]. In particular, problems were solved concerning flow around thin bodies of a conducting ideal gas. The general solution of the problem of streamline flow or the intersection of shock waves was not found because stationary simple waves with the magnetic field not parallel to the flow velocity were not investigated. The necessity for the calculation of such a flow may arise during the interpretation of the experimental results [9] in relation to the flow of an ionized gas. In the present paper, we consider stationary simple waves with the magnetic field not parallel to the flow velocity. A system of three nonlinear differential equations, describing fast and slow simple waves, is investigated qualitatively. On the basis of the pattern constructed of the behavior of the integral curves, the change of density, magnetic field, and velocity are found and a classification of the waves is undertaken, according to the nature of the change in their physical quantities. The relation between waves with outgoing and incoming characteristics is explained. A qualitative difference is discovered for the flow investigated from the flow in a magnetic field parallel to the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 130–138, September–October, 1976.The author thanks A. A. Barmin and A. G. Kulikovskii for constant interest in the work and for valuable advice.     

Solitary wave trains in a cold plasma

The existence of traveling solitary waves, the products of modulation instability in a cold quasi-neutral plasma, is considered. Solitary waves of this type (solitary wave trains) are formed as a result of bifurcation from a nonzero wave number of the linear wave spectrum. It is shown that the complete system of equations describing the wave process in a cold plasma has solutions of the solitary wave train type, at least when the undisturbed magnetic field is perpendicular to the wave front. Sufficient conditions of existence of solitary wave trains in weakly dispersive media are also formulated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–161, September–October, 1996.     

Waves in an inhomogeneous plasma with Hall dispersion

The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1976.The author is grateful to V. B. Baranov for constant interest in the work and valuable comments.     

Regular reflection of a magnetohydrodynamic shock wave from a conducting wall

In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1977.The author thanks A. A. Barmin, A. G. Kulikovskii, and G. A. Lyubimov for useful discussion of the results obtained.     

Nonregular interaction of shock waves in magnetohydrodynamics

The nonregular quasisteady interaction of plane-polarized shock waves in a magnetic field is considered. Within the framework of the magnetohydrodynamic approximation, a Mach interaction pattern is proposed and investigated. This pattern contains the Mach shock wave moving between the initial shocks and connecting their branch points. Unlike the gasdynamic case, in the vicinity of both branch points the flow contains, in addition to the Mach shock, up to five waves whose qualitative structure cannot be predicted in advance. Numerical methods of solving the problem are elaborated. The numerical simulations of the phenomenon under consideration were carried out by means of a specially designed software package with the entire range of all the upstream parameters being covered. It was found that the velocity and inclination of the Mach shock depend significantly on the vector of the magnetic induction in the initial state. The wave pattern of the developing flow is a function of all the key parameters, being particularly sensitive to the inclination of the magnetic field. The values of the parameters for which catastrophic restructurings of the wave pattern occur are determined. Sudden changes in the flow and the magnetic field occur in a zone behind the colliding shock waves. The interaction of the shock waves at different angles and for different magnetic fields are analyzed in detail.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 184–198, May–June, 1993.The authors wish to thank G. G. Chernyi, A. B. Vatazhin, A. G. Kulikovskii, and G. A. Lyubimov for helpful discussions of their results.     

Experimental investigation of the interaction of a shock wave with a magnetic field

We present certain results of an experimental investigation of the propagation of a shock wave S through a magnetohydrodynamic channel of the Faraday type. Under conditions of short circuiting of the induced currents in the supersonic stream that follows the shock wave, we registered the occurrence of a shock front T. The x-t diagrams of the motion of the S and T shock waves in the channel and behind it are determined. For a number of fixed sections in the channel, we have measured the density and degree of ionization of the gas and determined their time dependence. The investigations were performed in argon, and the ionizing shock wave propagated with Mach numbers 12–13. The magnetic field intensity was 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 153–183, May–June, 1971.     

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.     

Investigation of the properties of a shock wave arising in a supersonic flow of plasma,passing through a transverse magnetic field

In a flow of plasma, set up by an ionizing shock wave and moving through a transverse magnetic field, under definite conditions there arises a gasdynamic shock wave. The appearance of such shock waves has been observed in experimental [1–4] and theoretical [5–7] work, where an investigation was made of the interaction between a plasma and electrical and magnetic fields. The aim of the present work was a determination of the effect of the intensity of the interaction between the plasma and the magnetic field on the velocity of the motion of this shock wave. The investigation was carried out in a magnetohydrogasdynamic unit, described in [8]. The process was recorded by the Töpler method (IAB-451 instrument) through a slit along the axis of the channel, on a film moving in a direction perpendicular to the slit. The calculation of the flow is based on the one-dimensional unsteady-state equations of magnetic gasdynamics. Using a model of the process described in [9], calculations were made for conditions close to those realized experimentally. In addition, a simplified calculation is made of the velocity of the motion of the above shock wave, under the assumption that its front moves at a constant velocity ahead of the region of interaction, while in the region of interaction itself the flow is steady-state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–91, January–February, 1975.     

Strong explosion in a combustible gas mixture

Assume that a planar, cylindrical, or spherical point explosion takes place in a combustible mixture of gases. As a result of the explosion a strong shock wave develops and triggers chemical reactions with the release of heat. The solution of the problem for the case in which the thickness of the heat release zone is neglected (the infinitely thin detonation wave model) was obtained in [1–3].It was emphasized in [4] that these solutions can be considered only as asymptotic solutions for time and distance scales which are large in comparison with the scales which are characteristic for the chemical reactions, and under the assumption that as the overdriven detonation wave which is formed in the explosion is weakened by the rarefaction waves it does not degenerate into an ordinary compression shock. Here the question remains open of the possibility of obtaining such asymptotic solutions with account for finite chemical-reaction rates.In conclusion the authors wish to thank E. Bishimov for carrying out most of the computations for this study.     

Propagation of detonation waves in electric and magnetic fields appearing as a result of concentrated energy input

The propagation of detonation waves in an electromagnetic field is investigated. The effect of a constant external electromagnetic field on the motion of the detonation wave and the combustion products behind the wave is analyzed for small magnetic Reynolds numbers. The detonation is initiated by a plane point explosion.     

Propagation of shock waves in nonuniform plasma

Results of numerical simulation of the propagation of one-dimensional magnetohydrodynamic shock waves in a nonuniform plasma containing a magnetic field are discussed. Possible uses for the production of high velocities and temperatures and astrophysical applications are considered. The essential effect of the magnetic field is shown; acceleration of a shock wave is intensified in a medium with decreasing density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 22–26, March–April, 1976.In conclusion, the authors are grateful to S. K. Godunov for a detailed discussion of the computational aspects and of the results, and to A. E. Voitenko for a discussion of experimental possibilities and of the results.     

Method of narrow strips for nonlinear problems of a stratified fluid

Plane steady flow is considered for an ideal incompressible stratified fluid in a gravitational field of force. It is a characteristic feature of these flows that the density is constant and Bernoulli's constant remains the same along a streamline. Internal waves arise because of ponderability in the stratified fluid; they are not due to the presence of a free surface. These wave motions are studied in detail in the linear formulation, but flows of the solitary wave type can be described only by nonlinear equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–178, March–April, 1986.     

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.     

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.     

Roll waves in a gas–liquid medium

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interactio...