Nonstationary quasi-one-dimensional filtration in an inhomogeneous stratum

We consider the quasi-one-dimensional flow of a fluid (gas) in a porous stratum with conductivity and cross section varying along a stream tube. A special form of the differential equation (1.4) for nonstationary quasi-one-dimensional filtration is proposed. We obtain and study some sets of special solutions of this equation including specific solutions of known one-dimensional problems. We establish a relation between the stationary and nonstationary potential and flux distributions in a given filtration region. The laws we find are used as the basis for a method of hydrodynamic probing in inhomogeneous porous media.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–147, May–June, 1971.     

Vortex Scattering of Monatomic Gas Along Plane Curves

An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral curves constructed for it. For a separatrix of a saddle, an approximate solution is studied. Such solutions describe the vortex scattering of gas along plane curves placed on the surface of revolution.     

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.     

Self-similar solutions for energy liberation in a gas stream

By using dimensional analysis some possible kinds of nonstationary and stationary gas flows with energy liberation which result in self-similar problems are investigated. The cases of energy liberation in a gas at rest and in uniform supersonic and hypersonic streams are examined. The gas is assumed inviscid and perfect. Results of a computation of some hypersonic self-similar gas motions are presented. Three classes of self-similar gas motions have been well studied at this time: the strong explosion, the power-law flow caused by the expansion of a plane, cylindrical, or spherical piston [1], and conical flow (including combustion and detonation waves [2–4]). Some new self-similar motions caused by energy liberation on certain lines, surfaces, or in volumes will be examined below.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–113, November–December, 1974.     

On a gas source in a constant force field

The nonbarochronic regular partially invariant submodel of the equations of gas dynamics is studied. The submodel reduces to an implicit ordinary differential equation of the first order for an auxiliary function X = X(x). The physical quantities (velocity, density, and pressure) are expressed in terms of the function X. The properties of the solutions of the equation are investigated and interpreted physically in terms of gas motion. The existence of a shock-wave solution is proved. The properties of the shock adiabat are studied. It is shown that the results obtained are new and differ significantly from the results for the case of no constant force. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 3–16, November–December, 2006.     

Galilean-invariant axisymmetric self-similar submodel of gas dynamics without swirling

This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics. It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over axisymmetric bodies with possible strong discontinuities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009.     

Viscoelastoplastic Deformation of Reinforced Shells of Revolution Under Nonstationary Loading

The elastoviscoplastic behavior of a discretely reinforced shell under axisymmetric nonstationary loading is considered within the framework of the geometrically and physically nonlinear Timoshenko-type theory of shells. The stress–strain state of the structure is studied in terms of the incremental plasticity with kinematic hardening and dynamic yielding condition, which allows for the dynamic viscosity of the structure. The nonstationary behavior of a rigidly fastened reinforced shell under axisymmetric pulse loading normal to the shell surface is considered as an example. The deflection–time and deflection–space relationships are found     

Nonstationary processes in starting strongly underexpanded jets

Results of the investigation of nonstationary efflux of argon by the electron-beam-sounding method are presented in [1]. Comparing the regularities obtained in that paper for the front motion of material during efflux from a nozzle with computations [2] for nonstationary expansion from a spherical source and the experimental results in [3] permitted clarification of the singularities of the influence of counter pressure and the temperature factor in jet expansion. The density distribution in nonstationary nitrogen and argon jets is obtained in this paper and study of the regularities of the front motion of the escaping gas is continued.Translated from Zhurnal Prikladnoi Mekhiniki i Tekhnicheskoi Fiziki, No. 1, pp. 34–40, January–February, 1978.     

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.     

Two-dimensional nonstationary gas dissipation into a vacuum from a plane or axisymmetric channel

The nonstationary escape of an ideal polytropic gas from a plane or axisymmetric channel is investigated. It is hence assumed that the gas is initially at rest, and the diaphragm separating it from the vacuum can be at any section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–83, January–February, 1976.     

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.     

Deceleration and deformation of a liquid drop in a gas stream

An analytic method is developed for calculating the nonstationary motion and spreading of two-dimensional and axisymmetric liquid drops in a gas stream. The method is based on an expansion of the Navier-Stokes equations in a small parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–69, March–April, 1981.     

Nonstationary (transient) radiative-conductive heat transfer in a plane layer of gray absorbing medium

The kinetics of the heating of a plane layer of gray absorbing medium by radiative-conductive heat transfer are considered. The nonstationary energy equation is reduced to a nonlinear integral equation by means of a Green's function, and this is solved numerically by the Newton method. The results of the solution are presented in the form of the temperature fields in the layer for various values of the defining parameters (optical thickness, radiative-conductive heat-transfer criterion, heat-transfer criterion at the boundaries).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 156–159, January–February, 1972.     

Resonance Vibrations and Dissipative Heating of Thin-Walled Laminated Elements Made of Physically Nonlinear Materials

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations     

Similarity motions of a gas in the case of local supply of mass and energy in a fuel mixture

One-dimensional nonstationary similarity motions of a gas with exothermic reactions behind shock waves are analyzed. The thickness of the region of chemical reactions is ignored. New solutions are obtained for the problems of flows of a chemically active gas with the formation of shock and detonation waves. In particular, it is shown that in the framework of the adopted schemes of the combustion process a solution with five strong-discontinuity surfaces can be constructed. The results are given of numerical solutions for supercompression detonation and Chapman-Jouguet detonation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–77, July–August, 1979.     

Weakly nonlinear magnetosonic waves and structure of low-intensity discontinuities in magnetohydrodynamics

Mathematical techniques are proposed which make it possible to reduce the system of magnetohydrodynamic equations for a viscous heat-conducting gas with finite electric conductivity and a general equation of state to the model Burgers equation. On the basis of this equation the structure of weakly nonlinear magnetohydrodynamic shock waves is studied. In particular, the width of the shock wave is estimated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 43–48, May–June, 1993.     

Spherical expansion of vapor during evaporation of a droplet

The problem of the evaporation of a spherical particle is solved by a numerical finnite-difference method for the stationary and nonstationary cases on the basis of the generalized Krook kinetic equation [1]. Evaporation into a vacuum and into a flooded space are considered taking into account the reduction in size and cooling of the droplet. The minimum mass outflow is determined for stationary evaporation into a vacuum at small Knudsen numbers. The results are compared with those of other authors for both the spherical and plane problems. Most previous studies have used different approximations which reduce either to linearizing the problem [2, 3] or to use of the Hertz-Knudsen equation [4]. The inaccurate procedure of matching free molecular and diffusive flows at some distance from the surface of the droplet [5] is completely unsuitable in the absence of a neutral gas. Equations for the rate of growth of a droplet in a slightly supercooled vapor were obtained in [6] from a solution of the ellipsoidal kinetic model by the method of (expansion of) moments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 97–102, March–April, 1976.     

Study of three-dimensional wave structure of nonstationary gas outflow from a planar sonic nozzle

Results are reported of an experimental study of the three-dimensional structure of nonstationary gas outflow from a planar nozzle. Outflow of a heated shock wave in a nitrogen tube at different moments of time from the start of outflow (0–1 msec) in two mutually perpendicular directions is considered. A scheme for reconstructing the flow at different outflow stages is proposed. The dimensions of the Riemann wave are found to oscillate.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 41–45, January–February, 1976.     

A plane-parallel nonstationary motion of gas

A solution is found to the system of equations that describe plane-parallel nonstationary irrotational flows of an ideal gas under the condition that the velocity components of the gas depend on the polar angle and the time t.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 156–157, November–December, 1979.     

Nonstationary Gas Filtration Caused by an Intense Thermal Action on a Damp Porous Medium

A mathematical model and an algorithm are proposed for evaluating nonstationary heat and mass transfer in a porous medium that contains a mechanically absorbed liquid and a two–component gas (vapor—inert gas mixture). The case of an intense thermal action on a damp porous mixture caused by an external heat flux and convective heat transfer is considered. Typical flow regions and typical regions of the interaction between the phases are described.