End effects in magnetohydrodynamic channels at finite magnetic reynolds numbers

The effects of the magnetic Reynolds number have been examined via the distribution of the magnetic fields induced by the motion of a medium in a rectangular channel with conducting walls in the presence of an inhomogeneous magnetic field; the effects of wall conductivity and geometry of the external field are also examined as regards the distribution of the induced currents, the Joule loss, and the electric and magnetic fields over the cross section. The problem has previously been considered for a channel with insulating walls [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 19–27, May–June, 1971.We are indebted to A. B. Vatazhin for his interest.     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Kinetic model of the electron plasma component in plasma accelerators with closed drift

The dynamics of the electron plasma component in plasma accelerators with closed drift and a long acceleration zone are considered under certain simplifying assumptions (strong uniform magnetic field, elastic diffuse electron scattering by the channel walls, etc.). Exact solutions of the kinetic equation for electrons in different limiting cases are found. The results are generalized to include the case of a weakly nonuniform magnetic field.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 187–193, November–December, 1994.     

Influence of magnetic reynolds number on the current distribution in a magnetohydrodynamic channel with allowance for the Hall effect

Stationary plane flow of a conducting gas across a magnetic field in a magnetohydrodynamic channel of constant cross section made up of electrodes of finite length and insulators is considered in the linear approximation. It is assumed that the electromagnetic forces are small. It is shown that the current density increases near the exit from the interelectrode gap with increasing magnetic Reynolds number. The mutual influence of the Hall parameter and of the magnetic Reynolds number on the distribution of the currents in the channel is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 148–152, May–June, 1971.     

Stationary flow of a conducting liquid in a rectangular channel with two nonconducting walls and two walls having an arbitrary conductivity parallel to an external magnetic field

The flow of a conducting liquid in a channel of rectangular cross section with two walls (parallel to the external magnetic field) having an arbitrary conductivity, the other two being insulators, is considered. The solution of the problem is presented in the form of infinite series. The relationships obtained are used for numerical calculations of the velocity distribution and the distribution of the induced magnetic field over the cross section for several modes of flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostt i Gaza, No. 5, pp. 46–52, September–October, 1970.     

Plasma flow accompanied by blowing and pumping of plasma across electrodes

The article discusses plane stationary slowly varying flows of a nonviscous plasma with good conductivity in a channel in a transverse magnetic field; the flows are accompanied by blowing in and pumping plasma across solid metallic electrodes. The Hall effect is taken into consideration. It is shown that the potential jump near the anode, which appears in an accelerated plasma flow in an ordinary channel with solid electrodes, can be eliminated in flows accompanied by blowing in (pumping) of plasma. It is also shown that flows are possible in which the velocity, density, and the transverse electric field increase in the direction of the accelerator cathode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 26–34, November–December, 1970.     

Stationary supersonic conducting gas flow in a channel with nonconducting walls under weak magnetohydrodynamic interaction

A solution of the problem of flow in a channel with nonconducting walls for a small magnetohydrodynamic interaction parameter N is obtained by numerical methods. In the 0–10 range of variation of the Hall and magnetic Reynolds number parameters the distributions of the electrical parameters and the average (over the cross section) and local gasdynamic flow parameters are computed for two different geometries of the applied magnetic field. It is shown that an increase in the Hall and magnetic Reynolds number parameters is accompanied by a diminution in the Joule dissipation and the perturbation of the average (over the cross section) gasdynamic flow characteristics. It is disclosed that the distribution of the gasdynamic parameters over the channel cross section is extremely nonmonotonic in the end current zones.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 20–29, July–August, 1970.In conclusion, the author is grateful to A. B. Vatazhin for useful comments and constant attention to the research and to I. U. Tolmach for valuable comments.     

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.     

Joule loss due to compressibility of gas in a channel of variable section

It is known that closed electric currents arise in a conducting medium moving in a non-uniform magnetic field. These currents lead to additional energy loss and adversely affect the characteristics of magnetohydrodynamic channels. (The numerous investigations of these effects are dealt with in the review [2, 3].) Eddy electric currents are also formed, however, when a medium flows in a uniform magnetic field perpendicular to the to the plane of motion if the channel has a variable cross section and the medium is compressible [1], This paper is devoted to an investigation of some features of these flows. It is assumed in the analysis that the gas flows in channels whose geometry varies slightly.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 4, pp. 3–9, July–August, 1968.     

Nonstationary conducting free flow in a transverse magnetic field

In magnetohydrodynamic flow the viscous friction at the walls can be substantial. The role of viscous friction can be considerably reduced by using a free or a semirestricted flow of the conducting fluid. Nonstationary phenomena in one-dimensional motion of a free plane incompressible fluid flow in a transverse magnetic field are examined. The narrow sides of the flow come into contact with the sectional electrodes connected through external circuits with an active-inductive load. The magnetic Reynolds number and the magnetody-dynamic interaction parameter are assumed to be large. When the electric field due to electromagnetic induction in the channel is much smaller than the field due to the external circuits, the problem can be reduced to the characteristic Cauchy problem for a quasilinear hyperbolic system of first-order equations which can be solved by the method of characteristics using a computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 34–39, July–August, 1970.     

Long waves in two superposed layers of magnetic fluid

The equations and boundary conditions describing plane-parallel potential motions of two superposed layers of stably stratified magnetic fluid are formulated. The fluid is assumed to fill entirely a horizontal plane channel in the presence of a uniform longitudinal magnetic field induced by external sources. With reference to the case of long waves propagating over the interface between the upper and lower layers, it is shown that the action of the field may be interpreted as the result of an increase in the nondimensional surface tension by an amount proportional to the square of the undisturbed field. In the linear formulation the effect of the field on the evolution of a long-wave perturbation of the initially plane interface is investigated. Korteweg-de Vries equations with quadratic and cubic nonlinearities are derived and the action of the field on the internal solitary waves is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–133, May–June, 1993.     

Effect of an inhomogeneous magnetic field on the structure of an ionized gas flow

Results of an experimental study of the flow of an ionized gas produced by a shock wave through an inhomogeneous magnetic field are presented. Braking of the gas flow produced by the end currents is determined at two fixed sections of the magnetogasdynamic channel from the value of the isolated shock wave formed in the vicinity of the hemispherical model over which the flow passes. Maximum recorded reduction in Mach number was 30%, and with a magnetogasdynamic interaction parameter greater than 1.5, a transition of supersonic flow to infrasonic at the exit of the magnetic zone was observed. Experimental results were compared with a solution of a model problem which assumed one-dimensional flow in the flow core. The gas used was argon, with a maximum magnetic field induction of 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–178, September–October, 1976.     

Shock stability in magnetogasdynamic channel flows

The question of shock stability in a perfect-gas channel flow was examined in [1] in the onedimensional approximation under various assumptions: the disturbances are not reflected from the channel exit section, weak shock, etc. The results were found to coincide for two specific forms of the boundary conditions at the channel exit, from which it was concluded that the shock was not sensitive to the exit boundary condition. In [2] the question of shock stability was studied numerically in relation to a conducting-gas flow in a flat channel of constant cross section in the presence of a magnetic field (zero electric field intensity). It was established that the shock stability is significantly affected by the form of the conductivity law. A condition for the limiting regime between the stable and unstable regions was also given for flow with a shock wave. It was assumed that the pressure in the channel exit section is given. In this paper the effect of the exit boundary condition on shock stability in gasdynamic and magnetogasdynamic flows is demonstrated for small magnetic Reynolds numbers. Stability criteria are obtained for shocks near the channel exit for a specific exit condition. The influence of electromagnetic effects (conductivity law, electric load factor) on shock stability is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 16–23, January–February, 1970.The author is grateful to A. G. Kulikovskii for discussing his work.     

Similarity parameter of processes near the electrode

The nature of the layers near the electrode, which occur in the case of dissipative flow of plasma in the channel of a powerful flow accelerator with a natural magnetic field, depends basically on the extent of the manifestation of the Hall effect [1, 2]. The nature of the layers nearthe electrode can be assessed according to the magnitude of the similarity parameter given below.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 117–118, January–February, 1972.     

Flow of a conductive gas in a circular tube in a strong axiosymmetric magnetic field

The flow of a conductive gas along a channel in an external axiosymmetric magnetic field with a finite value of the magnetogasodynamic parameter N is examined. Numerical flow calculations are performed for a circular tube in such a field. Gas dynamic parameter fields, total pressure losses, and electric current intensities with the presence of transsonic zones and highly compressed regions are determined. Through comparison of the results obtained with linear theory data, the range of applicability of the latter is determined. Of the works dedicated to study of flow in external magnetic fields with N1, we should take note of [1], in which the process of entry of the gas into a transverse magnetic field was examined; [2], which studied one-dimensional transient motion with shock waves; and [3], where mixed flow in a Laval nozzle with an axiosymmetric homogeneous magnetic field was studied. Flow in a circular tube was examined in [4]; but the analysis performed by the characteristic method permitted calculation of only the initial supersonic flow zone. Motion in circular tubes in the presence of an axiosymmetric, magnetic field was studied in the linear formulation in [4, 5].Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–155, September–October, 1972.     

A Magnetoelastic Field in a Ferromagnetic with an Elliptic Inclusion

A stress–strain problem is solved for an infinite isotropic magnetically soft body containing an elliptic inclusion. It is assumed that the body is in an external magnetic field. The basic characteristics of the stress–strain state and the induced magnetic field are determined and their features at the inclusion are analyzed. Graphs are drawn for the total magnetoelastic and Maxwell stresses versus the ratio of the ellipse axes and the angle of dip, and tabular maximum stresses versus the magnetic induction and the magnetic properties of the material.     

A Magnetoelastic Field in a Ferromagnetic Medium with a Spherical Cavity

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing a spherical cavity is considered. It is assumed that the body is under an external magnetic field. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the cavity are studied. Graphs are presented for the total magnitoelastic and Maxwell stresses as functions of the magnetic induction, the angle of dip, and the mechanical and magnetic properties of the material     

The Stress State of a Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing an elliptic crack is considered. It is assumed that the body is under an external magnetic field perpendicular to the crack plane. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the elliptic crack are studied. Formulas are given for the stress intensity factors for the force and magnetic fields near the crack tip     

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.     

Stress Concentration in a Soft Ferromagnetic with an Elliptic Inclusion in a Homogeneous Magnetic Field

The paper addresses a stress–strain problem for an infinite soft ferromagnetic body with an elliptic inclusion. The body is in a homogeneous magnetic field B ₀₁. The basic stress–strain characteristics and induced magnetic field in the body and inclusion are determined and their features in the neighborhood of the inclusion are studied. The magnetoelastic and Maxwell stresses are plotted against the ratio of ellipse axes and the latitude angle. Maximum stresses versus magnetic induction and mechanical and magnetic properties of the material are tabulated