Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Motion of shock waves in a channel of variable cross section in the presence of a steady flow regime

The motion of shock waves against a steady flow in a channel of variable cross section is considered. Situations for which Chisnell's hypothesis [1] or a quasistationary flow model are valid are considered. The problem is of interest, in particular, in connection with the investigation of the starting of shock wind tunnels.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 103–110, July–August, 1981.I am very grateful to A. N. Kraiko and V. T. Grin' for valuable advice and support during the work.     

Large irreversible local slips of a loose free–flowing material under hard sign–variable quasistationary loading

The theory of slip for the case of large strains is considered. Irreversible distortion by slippage is represented as a Truesdell transformation of simple shear and is specified with respect to the unstrained configuration. It is proved that a small local slip leads decreases tangential stresses on the slip area and changes the strained stress over the entire region. The calculated orientations of the local slip systems are compared to results of classical experiments on sign–variable quasistationary deformation of loose free–flowing materials.     

Flow processes with change of regime in fractured reservoirs

Experimental and industrial observations indicate a strong nonlinear dependence of the parameters of the flow processes in a fractured reservoir on its state of stress. Two problems with change of boundary condition at the well — pressure recovery and transition from constant flow to fixed bottom pressure — are analyzed for such a reservoir. The latter problem may be formulated, for example, so as not to permit closure of the fractures in the bottom zone. For comparison, the cases of linear [1] and nonlinear [2] fractured porous media and a fractured medium [3] are considered, and solutions are obtained in a unified manner using the integral method described in [1]. Nonlinear elastic flow regimes were previously considered in [3–6], where the pressure recovery process was investigated in the linearized formulation. Problems involving a change of well operating regime were examined for a porous reservoir in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–73, May–June, 1991.     

Some problems of centrally symmetrical percolation of a gas

A solution is considered for the centrally symmetrical problem of unsteady inflow of gas to a stratum sampler on a logging cable in a thick stratum with constant pressure at the discharge and variable pressure when filling the closed cylinder of the sampler with gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 117–121, November–December, 1971.     

Development of the temperature fields in an electric arc struck on a point electrode in a homogeneous gas stream

A study is made of the problem of a point electric source in a homogeneous gas stream and operating in the arc discharge regime. The development of an electric arc struck on a point cathode in a medium which moves without deformation is studied. The stationary problem of a two-dimensional electric arc that develops in a medium with piecewise constant electrical conductivity is solved. Expressions are obtained for the temperature fields, the thickness of the arc, the current-voltage characteristics, and the power in the arc. The stability of this stationary state with respect to short-wavelength perturbations is investigated. The critical electrical current at which instability commences is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 91–99, March–April, 1981.I thank O. N. Sinkevich and I. M. Rutkevich for discussing the work, and also V. I. Grabovskii and V. A. Mareev for making some calculations.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

The distribution function of atomic level populations in a plasma

An analytic form is obtained for the population distribution function in an atomic plasma as a series in successive time derivatives of the population of the first level. The first approximation includes the well-known method of a stationary sink. The quasistationary distribution obtained for hydrogen agrees well with numerical calculations of recombination and ionization, and for lithium, helium, and argon the quasistationary distribution gives qualitative agreement with numerical calculations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 18–26, July–August, 1972.We should like to thank B. F. Gordiets for a helpful discussion.     

Plasma generation using a large V-groove cathode discharge

The results of an investigation of the plasma parameters generated by a large V-groove cathode discharge are presented. The cathode consists of a twelve inch aluminum plate into which V-grooves of 1/8th inch spacing and 60 deg angle are milled. With this cathode, a negative glow discharge is produced which yields a stable, steady-state plasma. Electron densities up to 2×10¹² cm^–3 have been obtained in the 12 inch diameter chamber. The electron temperature is about 1200 K and is independent of discharge current and gas pressure over the range, 0.3 to 0.9 Torr.The discharge operates in the same fashion as a conventional brush cathode discharge but with lower operating voltage for equal current densities. The lower operating voltage which reduces the arcing problems at the cathode-glass junction and the relative ease in fabricating the V-groove cathode make it an attractive alternative to the brush cathode for many applications. It is shown that the plasma is beam generated and the dominant electron loss mechanism in the steady state is electron-ion recombination. However, although most electrons are lost by recombination, diffusion losses still play a strong role in determining the electron density profile.     

Stability of moving soliton lattices

A quasistationary dynamic state of such systems as a long Josephson junction, a superconducting film of periodically modulated thickness and some others is known to be a sequence of regularly spaced solitons moving with a constant velocity. Corresponding self-similar solutions of the nonconservative sine-Gordon equation are investigated. Their stability and a small oscillation spectrum are analyzed. Current-voltage characteristics are obtained for the case of coherent oscillations.     

Distribution function of isotropically scattered particles in anisotropic structures

A study is made of the properties of solutions for a one-dimensional single-velocity transport equation for particles in a medium in which the probabilities of the elementary processes depend on the direction, and the scattering indicatrix (phase function) is spherical. It is shown that the linear parameter of the asymptotic exponential reduction in the global particle density when orientational inhomogeneity is allowed for can differ strongly from the value found by averaging the probabilities of the elementary processes over the directions. The role played by the structure of the orientational inhomogeneity is considered. The results are generalized to the case of anisotropy of the scattering.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 46–50, September–October, 1971.I should like to thank N. A. Khizhnyak for his constant interest.     

Breakdown of the near-electrode layer in a flow of ionized gas

An electric discharge in a flow of ionized gas is widely used in many physics and engineering problems. Among them are problems associated with current flow in various magnetohydrodynamic devices (generators, accelerators), arc shunting in a plasmatron, physical experiments in shock tubes, etc. It is known that with cold electrodes providing the contact between the plasma and the external circuit and relatively high pressures, two modes of current flow occur: at low current, the discharge is of a distributed nature; as the applied voltage increases, the discharge abruptly shifts into a discharge with a clearly developed cathode spot at some critical current density (we call this form of discharge an arc discharge). Existing experimental data [1–20] refers to varying experimental conditions. Furthermore, the critical voltage (or current) at which the transition of the discharge from a distributed discharge to an arc discharge occurs varies within very broad limits. From an analysis of the experimental data, a condition is formulated which the discharge parameters satisfy at the time of transition from a distributed discharge to an arc discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–23, May–June, 1973.The author thanks Yu. A. Nikuev for invaluable help in the analysis of experimental data.     

Low-density jets beyond a sonic nozzle at large pressure drops

The gas-dynamical structure of jets of a low-density diatomic gas beyond a sonic nozzle at large pressure drops under conditions of a transition from continuous medium processes to rarefied gas processes is examined on the basis of experimental data obtained in low-density gas-dynamical tubes using electron-beam diagnostics and the Pitot tube method. Isomorphism is shown in the density distribution and total pressure in all cross sections of the jet with respect to pressures at a constant value of the complex R_L=R_*/N^1/2(R_* is the Reynolds number in the critical cross section of the nozzle, and N is the ratio of the Pitot pressure and the pressure in the discharge chamber). It is shown on the basis of a comparison of local Reynolds numbers for all zones of the jet that this is an analog complex. The experimental data on the variation in the jet structure are presented as a function of the number R_L in the range of 5–600. For R_L> 100 the flow in the jet can be considered as continuous; for R_L< 5–10 the flow corresponds to a scattering process; the range of 5–10< R_L< 100 corresponds to a transitional state. Ranges of isomorphism of the jet with respect to R_* and N are indicated. Based on the results of the measurements, it is shown that the flow behind a Mach disk for R_L> 200 remains subsonic on the axis to a distance of several lengths of the primary cycle. A transition to supersonic velocity on the jet axis can occur with a decrease in the numbers R_L owing to ejection acceleration by the supersonic ring-shaped compressed layer.This word is apparently interchangeable with self-similarity-Translator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–73, March–April, 1973.     

Experimental investigation of the development of motion of liquid in conduits

Only a few studies have been devoted to the experimental study of the initial stage of the motion of a liquid from the state of rest in a closed delivery conduit [1]. It can be concluded on the basis of the results of these studies that at the beginning of the process the mechanical energy losses are smaller than in quasistationary flow. These studies also suggest that the laminar nature of the flow persists in the nonstationary flow. However, investigations are of an integral nature and therefore in them the flow structure is not determined. In the present study the development of the motion of the liquid in a delivery conduit from the state of rest is investigated. The tangential frictional stresses at the wall of the conduit, measured by the thermal anemometric method, show that the transitional Reynolds number, at which the laminar flow regime changes into turbulent, depends on the acceleration of the flow and far exceeds the critical value for the case of the stationary flow. At maximum acceleration of the flow equal to 11.78 m/sec² the transition of the laminar regime to the turbulent at the wall of the conduit occurs at Re = 234, 500. The loss coefficients of mechanical energy have been computed from experimental results, which show that the use of the corresponding coefficient of quasistationary turbulent flow in the computation leads to appreciable errors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–85, November–December, 1977.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

Hydrodynamics op underground gas storage vaults

The problem of determining the change of the volume and pressure of a gas cavity with time in a mildly sloping seam of the dome type, used as an underground gas storage vault, is solved by the method of combined asymptotic expansions; the gas storage vault has an arbitrary law of variation of discharge with time. A comparison is carried out with the existing exact solution for the case of a seam with constant thickness; good agreement is revealed. Calculations are carried out on the dynamics of a gas cavity in an actual seam. The case of a seam with a steep dome and a strong anisotropic permeability is also considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 56–63, May–June, 1976.The authors thank V. D. Epishin for the calculations performed by him.     

Nonstationary laminar heat convection in a closed domain for a given heat flux

Characteristic modes of the time development of nonstationary heat convection in a closed planar domain upon a sudden supply of heat from the lateral surface are considered for Rayleigh numbers 10³–10⁷. Estimates of the boundaries of the beginning of the influence of convection on the temperature field and the buildup of a quasistationary convection mode in the range of Rayleigh and Fourier numbers are given. Characteristics of the circulation flow, the singularities of the temperature-field configuration and of the heat transfer from the wall to the fluid, are investigated. The mechanism for the origination and disappearance of vertical temperature differences, caused by convection, and the dependence of the vertical temperature differences on the Rayleigh and Fourier numbers, on the thermal mode of the boundary, and the domain geometry, are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 109–117, July–August, 1970.The author is grateful to T. D. Pirumov and T. V. Volokitin for assistance in performing the computations.     

Self-similar problem of the motion of a plane layer of heated material with an arbitrary equation of state

The self-similar problem of the nonstationary motion of a plane layer of material in which energy from an external source is released for values of the flux density q₀ on the boundary which are constant in time is considered. The self-similar variable is = m/t, where m is the Lagrangian mass coordinate and t is the time. The characteristic values of the velocity, density, and pressure do not vary with time. For a self-similar problem the energy flux density q must also depend only on the self-similar variable. In this case q() can be an arbitrary function of its argument and can be given by a table. Examples are presented of actual physical processes in which the mass of the energy-release zone increases linearly with time. The equation of state can have an arbitrary form, including specification by a table. The gaseous state of matter for an arbitrary variable adiabatic exponent, the condensed state, and a two-phase state can be described. A solution of the self-similar problem is presented for the heating of a half-space bounded by a vacuum for a certain specific equation of state and various flux densities q₀ and velocities M of the advance of the energy-release zone.Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 5, pp. 136–145, September–October, 1975.     

Stability of a high-frequency glow discharge in the normal combustion regime

A high frequency glow discharge in its high current form differs from a dc discharge in that there is a significant decrease in the role of the pre-anode region in plasma generation [1], thus leading to greater stability [2]. In a dc discharge the pre-anode current-voltage characteristic (CVC) is falling [3], which causes electrodynamic instability of the plasma column and leads to its contraction over times much shorter than the thermal times [4]. It is characteristic that conductivity in the volume of a dc discharge at moderate pressures is caused by drift of ions from the pre-anode region. In an hf discharge the plasma distribution is symmetric about the midpoint of the interelectrode gap and the space charge zones near the electrodes are separated from the volume by narrow zones with high conductivity. Under such conditions, together with volume ionization processes a noticeable contribution to maintenance of conductivity can be produced by ambipolar diffusion and plasma drift due to disruption of quasineutrality [5, 6]. In order to study the stability of an hf discharge plasma column it is of interest to find the current-voltage characteristic of this part of the discharge under conditions of high longitudinal inhomogeneity and low values of E/p. In connection with the experimentally observed weak current form of the discharge [1, 2], which is characterized by a unique value of the normal current density and lacks a proper theoretical explanation, there has been increased interest in the properties of the hf discharge which are produced by phenomena in the pre-electrode regions. In particular, it is necessary to theoretically confirm the similar properties of the dc discharge and the hf discharge in the normal current density regime. The present study will present results of a numerical calculation of an hf discharge in nitrogen with consideration of space charge effects within the framework of a two-dimensional model and calculated the CVC of a plasma column with the diffusion-drift mechanism for maintenance of conductivity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 16–26, November–December, 1986.The authors express their gratitude to N. A. Yatsenko for information provided during the course of the study, and to L. G. Gryukanov for performing the numerical calculations and assistance in formulating the results.