Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Motion of a piston under the influence of gas pressure in the presence of an initial temperature gradient

A study is made of the motion of a piston without initial velocity under the influence of gas pressure. Under the assumption that the temperature gradient is constant and fairly small, expressions are obtained for the distributions of the gas-dynamic parameters in the disturbed region between the piston and the leading edge of the sound wave propagating through the gas at rest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1984.     

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.     

Effect of friction on motion of a piston driven by combustion products

In recent years the two-stage light gas ballistic apparatus with deformable plastic pistons has become widely used in experimental aerodynamics. The existing methods of calculating such devices either completely neglect friction of the piston on the channel wall [1–3] or use a schematization of the frictional forces [4–6], which does not have a satisfactory physical basis. In a number of studies [7, 8] the friction force was considered constant, and its value was specified not from physical considerations, but to produce the best agreement between calculated and experimental values of object velocity or driving gas pressure. Since friction is such a significant factor, its proper consideration in calculating piston motion parameters requires special study. In this connection, it is useful to consider the operation of only the first stage of the ballistic apparatus, which sets the piston in motion. Below we will consider the problem of the internal ballistics of a one-stage powder-driven apparatus in the column channel of which a piston made of polymer material moves, experiencing friction. The friction model is constructed on the basis of a series of experiments on the slow forcing of polymer specimens compressed in the longitudinal direction through a steel channel. An experimental study was made of the relationship between the gunpowder gas pressure and time within a constant volume chamber, allowing establishment of the true powder-burning law, and its deviation from the geometric law of [9]. Calculated and experimental values of maximum gas pressure and muzzle velocity of a polyethylene piston are compared.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 73–80, September–October, 1978.The authors express their gratitude to S. S. Grigoryan for his interest in the study and valuable advice, and to G. N. Suntsov for aid in performing the experimental studies.     

The evolution of a finite rate periodic oscillation

Finite rate oscillations of a gas in a closed tube arise when the amplitude of the applied periodic piston velocity is small while its acceleration is unrestricted. The asymptotic form of the periodic motion for large acceleration is given. The evolution to the final periodic motion from the initial state of rest is constructed for a finite rate oscillation. Exact results for a piecewise linear piston velocity are used to illustrate the solutions.     

Stability of one-dimensional gas flows in expanding regions

The stability of gas flows produced by the motion of a flat piston or the decay of an arbitrary discontinuity is considered. The boundaries of the region (or regions) in which the development of perturbations is considered are planes (shock wave, contact discontinuity, piston, etc.) which move away from each other.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 112–119, March–April, 1981.     

Approximate solution to nonself-similar problem of motion of a piston after an impact

An approximate solution is obtained to the problem of the motion of a piston after an impact and under the influence of gas pressure under the assumption that the parameter = u_o/a _o, where u_o is the initial velocity of the piston anda _o is the velocity of sound in the gas at rest, is small. Functions that determine the law of motion of the piston and the shock wave, and also the gas flow in the disturbed region are found explicitly to terms of order ³ Translated from Izvestiya Akadeinii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–171, November–December, 1982.     

Waves in a liquid mixture with gas bubbles

The one-dimensional nonstationary motion of a mixture of an ideal incompressible liquid with gas bubbles in a tube behind a moving piston is considered. An exact solution is obtained. Shock-wave propagation is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 143–145, July–August, 1976.The author thanks L. I. Sedov for his evaluation of the study and advice.     

A variational problem in one-dimensional unsteady gas dynamics

The problem of finding the optimal motion of a piston that confines a certain volume of gas at the initial time is solved. The motion with which the piston performs the maximum work subject to constraints on its motion and the duration of this motion is found. Cases of plane, cylindrical, and spherical symmetry are considered. Numerical examples are given. It is noted that there is some analogy between the solution obtained and the known solutions for two-dimensional supersonic optimal nozzles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 171–175, July–August, 1984.I thank A. N. Kraiko for helpful discussions of the work.     

The problem of a dihedral piston

The problem of the plane nonstationary motion of a gas behind a dihedral piston is considered. The problem is linearized on the assumption that the piston angle is small. The mixed problems and the Goursat problem are solved for the linearized double-wave equation in the region of hyperbolicity and then the mixed boundary value problem is solved in the region of ellipticity. The solutions are obtained in elementary functions and quadratures.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 74–81, May–June, 1969.The author thanks L. V. Ovsyannikov for his interest and helpful advice.     

Gas-dynamic calculation of pulsating flow in pipelines

A numerical solution is examined for a system of equations of one-dimensional isothermal flow of a perfect gas in a horizontal pipe with a periodically varying function of the flow rate at the boundary. The numerical solution is compared with the solution of the linearized problem. The results can be used to calculate the pulsating motion of gas in the pipeline systems of piston compressors [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 85–88, July–August, 1972.     

Unsteady-state periodic jet structure created by the pulsed motion of a piston jet generator

The results of an experimental and theoretical investigation of the process of formation of an unsteady-state water jet by the pulsed motion of the piston of a piston jet generator are given. An approximate mathematical model of the generator dynamics which can explain the mechanism of formation of the experimentally obtained periodic transverse thickening structure is considered.Nikolaev. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–178, July–August, 1996.     

Self-similar solution of the Navier-Stokes equations for a completely ionized hydrogen plasma (the plane piston problem)

The self-similar motion of a completely ionized hydrogen plasma is considered in the two-temperature hydrodynamic approximation, i.e., we consider the plane piston problem and the problem on energy release at a fixed wall. Results obtained by numerical integration of the relevant system of ordinary differential equations are quoted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 34–39, May–June, 1969.     

Effect of the friction of a thrown piston on the internal ballistics of a one-stage unit

The present article gives a method for the direct measurement of the friction force of cylindrical samples strongly compressed along the axis at the wall of the bore of a gun with a small velocity of the motion, modelling the behavior of a piston in a ballistic unit. As an example, the article gives the results of measurements with a polymer material, i.e., caprolon. On the basis of an experimental investigation, a new friction model is constructed, which is used for the solution of the problem of the internal ballistics of a single stage powder unit with a piston made of caprolon. The laws of similarity of the processes under consideration are investigated. It is established that the value of the maximal pressure of the powder gases and velocity of the piston depend essentially on the value of the friction coefficient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–83, May–June, 1978.     

Nonlinear gas oscillations in a closed tube driven by the aperiodic motion of a piston

Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation law in place of the entropy conservation laws. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484).     

Problem concerning a spherical piston in a compressible medium with “dry” friction

We study the self-similar problem concerning the motion of a spherical piston in a medium with dry friction. The piston moves with constant velocity in a nonideal medium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 136–140, January–February, 1973.The authors thanks T. F. Kryukov for performing the major part of the calculations.     

Interaction between slip and the high-frequency vibrations of a shaped surface in the working gap of a gas-lubricated bearing with inclined grooves

The article discusses a flat bearing with a gas lubricant, one of whose surfaces is shaped by inclined grooves and vibrates in accordance with a given harmonic law with a high frequency. The reaction of a thin layer of viscous compressible gas is formed as a result of interaction between the effects of slip and high-frequency vibrations. Asymptotic methods are used in the investigation of the reactions of the gaseous layer; the thermodynamic process in the lubricating layer is assumed to be isothermal, and in the equation of motion of the gas the effect of inertial and mass forces is not taken into consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 43–50, March–April, 1976.     

Shape of an axisymmetric liquid film on the surface of a rotating cylinder

The steady axisymmetric motion of a viscous film together with a cylinder is investigated. The shape of an axisymmetric film of constant mass depends not only on the physical properties of the liquid, the rate of rotation and the radius of the cylinder but also on the pressure difference between the liquid and the ambient medium. By calculation and by means of a qualitative investigation of the first integral of the basic equation it is shown that for different values of the parameters the free surface of the film may be cylindrical or wavy, intersect itself or consist of periodically distributed isolated annular layers. The calculation results correspond with the experimental data the more closely the thinner the film and the greater its transverse velocity. This is attributable to the absence of gravitational acceleration from the model of the steady axisymmetric motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 23–27, July–August, 1989.     

Flow regimes with temperature extrema is the motion of a gas through a porous medium

Self-similar solutions are obtained for the problem of the motion of a heated gas through a porous medium with allowance for heat transfer between the gas and the solid phase in accordance with Newton's law. It is shown that there exist flow regimes in which the gas temperature increases with distance in the direction of motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–77, July–August, 1987.     

Axisymmetric motion of a viscous fluid in the finite annular cavity of a rotating cylindrical vessel

The method of nets is used to investigate unsteady axisymmetric viscous flow in a cylindrical gap of finite height. This situation is characterized by vortex motion in a plane passing through the axis of the coaxial cylinders. These flows have previously been studied in relation to the case of stepwise variation of the angular velocity of the cylinders [1]. In the present case the angular velocity is varied linearly in the acceleration stage and the acceleration interval is a parameter of the problem. After acceleration the rotation rate is determined from the ordinary differential equation describing the process of deceleration of the system as a whole.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 37–42, March–April, 1988.The authors are grateful to E. M. Zhukhovitskii for his interest and valuable comments.