Motion of a viscoplastic liquid in a porous inhomogeneous medium

Equations of motion are derived for a viscoplastic liquid in a nonuniform medium of type 2 (piecewise uniform) or type 3 (with a variable filtration coefficient) [1] on the assumption that the motion is of steady-state type. Solutions are presented for a parallel flow and a flow with axial symmetry.     

Transonic outflow of an imperfect gas from a vessel with plane walls

Transonic isentropic imperfect gas flows^* were investigated in the one-dimensional formulation in [2–5]. The problem of the transonic outflow of a jet of thermally perfect gas with equilibrium excitation of the vibrational degrees of freedom of the molecules (calorically imperfect gas) was investigated in the two-dimensional formulation in [6]. Below the problem of the transonic outflow of a real (thermally and calorically imperfect) gas from a vessel with plane walls is considered. A method of solution is proposed. Calculation results characterizing the effect of the angle between the walls and the stagnation parameters on the transonic outflow of air are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 88–95, November–December, 1993.The authors are grateful to G. Yu. Stepanov for his interest in their work.     

Motion of gas due to a point explosion in an inhomogeneous atmosphere

The problem of a strong point explosion in an atmosphere with exponential dependence of the density on the altitude was considered in detail in the monograph [1]. As the blast wave becomes weaker, it is necessary to take into account the counterpressure and the gravitational force. Then in the central hot region of the explosion the gas-dynamic processes are intensified, and the method of calculating the flow parameters in the neighborhood of the point of energy release becomes important. The singularity at this point can be eliminated by including dissipative factors in the treatment; it is then possible to use standard difference methods in the hot central region. In the present paper, the qualitative and quantitative effects of the counterpressure and gravitation are analyzed. A model of the explosion with a simple mechanism of energy dissipation — heat transfer by radiation — is considered. The calculations of the explosion are continued until the formation of the mushroom cloud. The results are compared with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zfaidkosti i Gaza, No. 6, pp. 144–151, October–December, 1981.     

Motion analysis of a spinning satellite system with off-centre tanks partially filled with liquid

The sloshing problem for, a spherical tank partially filled with liquid is analysed in this paper. The study is based on the goveming, equations of fluid dynamics and the Euler's equations of systems with the influences of tank off-centering, fluid vortices and the Coriolis' acceleration on the motion states of the systems taken into consideration. In the study, we adopt the concept of uniform vortex motion of fluid generalized by Pfeiffer and apply the boundary element method (BEM) to the calculation of the natural frequence and the velocity field of the liquid sloshing. The motion characteristics of the flow-solid spinning system is then analysed. The project is supported by the National Natural Science Foundation of China and Ministry of Astronautics.     

Electrization and liquid glow in a coaxial channel with dielectric walls

Dielectric-liquid flows in narrow channels with walls composed of different dielectrics are investigated experimentally. It is revealed that at a certain flow velocity, as a result of electrization, on the interface between the dielectrics the liquid begins to glow. The glow is discrete in the form of frequent pulses and is accompanied by electromagnetic noise on the radio-frequency range. It is shown that with decrease in the channel thickness the glow appears at smaller flow velocities. The glow is accompanied by heating of the liquid in the wall region to temperatures that may reach several tens of degrees. The electrization potential reaches more than 100 kV. The mechanisms of electrization and liquid glow are discussed.     

Motion of a tracer particle surface in strata of finite length

We consider some characteristic features that occur in the solution of problems of unsteady motion of tracer fluid particles in strata of finite dimensions and in strata consisting of portions of different permeability. The behavior of a water-copper sulfate solution interface at the boundary of two media of different permeability was investigated experimentally in [1]. In that study, depending on the conditions, either breaks or discontinuities of the exudation interval type were observed in the fluid interface line at this boundary of the media. It appears that certain of the observed effects may be described by techniques similar to those presented in the following.     

Control of the motion of a vessel with a heavy inhomogeneous liquid

The problem of controlling the internal waves inside a closed rectangular cavity filled with a heavy two-layer fluid is considered in the linear approximation. The fluid is assumed to be stably stratified, ideal, and incompressible. The controlling horizontal force is applied to the body containing the cavity. It is assumed that at the initial moment there are no oscillations of the fluid and the interface is horizontal. The problem is to bring the vessel as a whole into a prescribed state of linear motion without relative wave motion of the fluid. The Cauchy-Poisson problem and the self-consistent integro-differential equation of the vessel motion are solved using the Fourier method and taking into account the reaction of the internal waves. On the basis of an analysis of the corresponding generalized momentum problem, approaches are proposed for solving the problem of control. It is shown that a control action with a sufficiently high order of Steklov smoothness ensures the approximate solution of the control problem with the required accuracy for all the characteristics of the motion of the hybrid oscillating system under consideration.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–22, May–June, 1995.The study was performed with financial support from the Russian Foundation for Fundamental Research (project No. 94-01-01368).     

Motion and filling of cavities in a boundless liquid and close to a plane

The motion of bubbles in liquids has been studied in many earlier papers [1–8]. In this paper methods of the projection type are applied to the problem of a cavity in an ideal, incompressible liquid in the absence of vortices. The collapse of a bubble having a finite initial velocity in a boundless liquid is considered; also considered is the collapse of a stationary bubble close to a solid wall. Using the small-parameter method the generation of a jet is examined analytically. A numerical computing method not involving small parameters is developed; it is based on calculating the projection by numerical computation of the corresponding integrals. The method combines economy and simplicity of application with a high accuracy in the region in which the representation of the velocity potential by a series of spherical functions remains effective.     

Motion of a bubble in a viscous liquid

The discussion concerns steady-state flow of a viscous fluid around a spherical bubble at small Reynolds number R. Asymptotic matching [1] provides a way of calculating the resistance force, which agrees well with the measured force for R < 5. The rate of growth or dissolution of the bubble is calculated on the assumption that the Péclet number is large.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 107–111, January–February, 1971.We are indebted to V. G. Levich for a discussion.     

Motion of a liquid droplet in a vibrating fluid

The motion of a liquid droplet in a liquid with density different from that of the liquid composing the droplet and subjected to harmonic excitations is investigated. Nonlinear equations are obtained that describe the translational motion of the droplet and its oscillations. It is shown by numerical means that, under the essential resonance conditions, the droplet ascends by a cascade method if the value of the load coefficient is small.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 78–83, July, 1995.     

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.