Plane nonstationary gas flow with a strong discontinuity

The problem of plane, nonstationary gas motion under the effect of a piston in the shape of a dihedral angle moving at constant velocity in the gas is considered. In contrast to one-dimensional motion under the effect of a flat piston, a curvilinear shockwave originates here, and the flow becomes nonisentropic and vortical. This problem is examined herein in a linear formulation when the angle of the piston breakpoint is assumed small. The linear problem reduces to an inhomogeneous Riemann—Hilbert problem whose solution is found explicitly. The problem under consideration adjoins a circle of problems associated with shockwave diffraction and reflection studied by Lighthill [1], Smyrl [2], Ter-Minassiants [3], etc.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–50, May–June, 1971.The author is grateful to L. V. Ovsyannikov for interest in the research and useful comments.     

Autowave flows of weakly conducting gas in rough channels in the presence of strong electromagnetic fields

The steady-state flow of a gas in a rough channel in the presence of strong transverse magnetic and electric fields is considered. It is shown that in this case there also exists a periodic regime consisting of a sequence of deceleration waves [5–7]. The periodic regime results from the action of the forces of resistance to the motion of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–158, January–February, 1989.The authors wish to thank A. A. Barmin and A. G. Kulikovskii for valuable discussions.     

Steady-state wave flows of a weakly conducting gas in transverse electromagnetic fields

Gas flow in a MHD channel in transverse magnetic and electric fields is considered. The steady-state flows associated with the establishment of equilibrium between the hydraulic resistence and ponderomotive forces are investigated. The conditions of existence and the properties of such a steady-state flow regime are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 123–129, July–August, 1990.     

Motion of an incompressible conducting liquid in a strong self-consistent magnetic field

One of the common regimes of operation of many laboratory and industrial magnetohydrodynamic (MHD) devices using liquid metals as working medium is the regime for which the Alfvén number A, the ratio of the magnetic and kinetic energy densities, appreciably exceeds unity. For example, for a typical MHD device [1] with characteristic length 0.1 m of the working region, velocity 1 m/sec of the medium, and magnetic induction 1 T (the medium is molten sodium at temperature 330°C) the Alfvén number is A - 900. To simplify the investigation of the processes in such devices, one can use the approximation of a strong magnetic field proposed by Somov and Syrovatskii [2] to describe certain types of hydrodynamic flows of a dissipationless plasma in a magnetic field. In the present paper, the approach to the analysis of the self-consistent magnetohydrodynamic problem in this asymptotic approximation is extended to the case of an incompressible liquid with finite conductivity. A study is made of the closed reduced system of MHD equations obtained from the complete model in the zeroth order in the small parameter A^–1, in which the magnetic field is a force-free field. An investigation is made of the free diffusion of force-free magnetic field with constant coefficient a of proportionality between the current density and the magnetic induction in a spatially unbounded liquid, and the kinematic properties of a velocity field of the liquid in which the force-free nature of the magnetic field is maintained during the damping process are determined. It is shown that the complete class of such velocity fields is represented by the group of rigid-body motions of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1991.     

Dynamics of a nonuniformly conducting gas flow in a magnetic field

The dynamics of a nonuniformly conducting gas flow in the channel of a MHD generator are investigated on the basis of numerical modeling. The initial shape of the plasmoids periodically entering the MHD channel qualitatively correspond to that noted in [6, 7]. The alkali metal seed is uniformly distributed over the entire flow. The mechanism of dynamic interaction of the plasmoids and the low-conductivity gas flowing over them, the variation of the shape of the plasmoids and the evolution of the gas dynamic structure of the flow are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 135–145, September–October, 1989.     

Electromagnetic field generated in air by a nonstationary gamma-ray source in an ideally conducting plane

We consider a model problem on the generation of a radio signal by a nonstationary gamma-ray source. The problem is essentially two-dimensional in space but is reduced to a number of one-dimensional nonstationary problems. The results of a numerical solution of the problem are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 18–26, May–June, 1975.In conclusion, the authors wish to thank A. A. Milyutin and I. E. Dinaburg for working out the numerical methods used for the solution of this problem, and also thank I. N. Mikhailov and G. M. Gandel'man for their participation in the development of the problem.     

Calculation of the free surface of a conducting liquid in a strong electric field

A study is made of the static shape of a conducting liquid in a strong inhomogeneous electric field at the end of a capillary. Numerical solution of a self-consistent problem is used.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 165–167, November–December, 1983.     

Shape of an incompressible,weakly conducting jet in a strong electric field

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 20–25, March–April, 1991.     

Dynamic strain of a conducting half space with a cavity in a strong magnetic field

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 16–20, November–December, 1991.     

Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field

A general solution is obtained describing the flow of a conducting liquid in an arbitrary region, which is bounded by nonconducting walls, in the case when it is possible to neglect inertial and viscous forces in comparison with the magnetic field, as well as the induced magnetic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 144–150, May–June, 1973.     

Stabilization of the unstable steady states of a conducting fluid in an electromagnetic field

The linear disturbance spectrum is determined for the solution with the fluid at rest and its unstable region identified. It is shown that an electric field has a destabilizing effect, while a magnetic field and viscosity affect only the rate of damping of the disturbances and not the actual existence of instability. An example of a feedback regulator that stabilizes two unstable modes is constructed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 138–142, November–December, 1993.     

Two-dimensional spreading of a cloud of conducting gas in a magnetic field self-similar solution

A self-similar solution of the problem on the spreading in a magnetic field of a cloud of conducting gas, having the shape of a cylinder of noncircular cross section, is constructed. The cylindrical surface of the gas is restrained by a nonconducting sheath that spreads according to a prescribed law. The shape of the transverse cross section of the cylindrical cloud is determined from the solution. Cross sections obtained for a concrete case are represented in graphic form.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 29–36, March–April, 1973.In conclusion the author thanks V. I. Khonichev for assistance with the numerical calculations.     

Flow of a conducting gas jet beyond the nozzle outlet of an electromagnetic accelerator

A solution is given for the problem of the motion of a conducting gas beyond the outlet of an accelerator. The form of the jet is found as well as the distribution of all jet parameters. The problem is solved assuming that the flow is plane, that there are no Hall currents, and that the velocity increase in the jet is small compared with the magnitude of the velocity at the exit of the accelerator channel.     

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.