Theory of one-dimensional unsteady transport of heavy particles by a flow of fluid

A study is made of the one-dimensional unsteady transport of heavy particles of rock by a flow of flushing fluid in a bore hole. The proposed theory of this process leads to a quasilinear Monge—Ampere equation of parabolic type. A well-posed boundary-value problem is formulated and a method indicated for its solution. A typical problem is solved, and this illustrates the qualitative picture of the physical process. The investigated process of flushing the end of a bore hole is the main process that limits the drilling rate in a superdeep bore hole.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 73–79, March–April, 1984.     

Effect of the translatory motion of a vapor bubble on its condensational collapse

Vapor condensation and the effect on this process of two factors: relative motion and the external influence of the carrier flow (pressure perturbation) are investigated. A mathematical model describing all the stages of the phenomenon is constructed. The model includes the mass, momentum and energy balance equations (both for the vapor and for the liquid) or their first integrals.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 85–91, November–December, 1989.     

Asymptotic analysis of the unsteady problem of waves in a two-layer flow

The problem investigated is the unsteady problem of the internal waves generated in a two-layer flow by a certain periodic perturbation which leads to small deviations from the basic flow. A method of constructing an approximate solution uniformly valid throughout the region of variation of the variables and the parameters of the problem is indicated. It is confirmed that for large times and near-resonance parameters the motion of the fluid is described by the mixed problem for a cubic Schrödinger equation. Certain qualitative properties of the solution of this nonlinear problem are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 82–90, November–December, 1987.The author is grateful to V. I. Bukreev and to I. V. Sturova for their interest in his work.     

Asymptotic behavior of the neutral curves of the linear stability problem for a laminar boundary layer

Asymptotic flow schemes corresponding to two branches of the solution for the neutral stability curve of a laminar boundary layer in an incompressible fluid are constructed. Two-term asymptotic solutions are obtained in the limit when the Reynolds number tends to infinity. The linear formulation of the problem is used and the flow is assumed to be two dimensional.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 39–46, September–October, 1981.I should like to thank O. V. Denisenko for making the numerical calculations.     

Investigation of the starting process in the shaped nozzle of a large-diameter shock tube

The characteristics of flow formation in the shock-wave starting process of a shaped nozzle with a developed subsonic section are analyzed on the basis of numerical calculations in the inviscid two-dimensional formulation. It is shown that in this case the use of steady-state boundary conditions in the throat section can lead to a significant error in determining the startup time. The results of the calculations are compared with experimental data obtained over a broad interval of the leading parameters. The results of the comparison help to explain the part played in the starting process by flow separation from the nozzle walls, which was not taken into account in the numerical investigation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 88–95, September–October, 1986.The authors wish to express their thanks to R. I. Serikov and V. M. Khailov for the wind tunnel nozzle blowdown data and to V. P. Stulov for useful advice and discussions.     

Ignition of hydrogen in a turbulent boundary layer on a plate

The ignition of hydrogen blown into a turbulent supersonic boundary layer on a flat plate is investigated numerically. It is assumed that the mixture consists of six chemically active components H, O, OH, H₂O, O₂, H₂ and inert nitrogen N₂. The boundary layer is divided into outer and inner regions, for which different expressions for the coefficients of turbulent transport are used. The influence of pulsations on the rates of the chemical reactions, and also the back reaction of the chemical processes on the mechanism of turbulent transfer are not taken into account. The surface of the plate is assumed to be absolutely catalytic with respect to the recombination reactions of the H and O atoms. The influence of the blowing intensity, the Mach number in the outer flow, and the pressure on the ignition delay is analyzed. The possibility of effective porous cooling of the surface when there is combustion in the boundary layer is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 33–40, November–December, 1979.I thank V. G. Gromov and V. A. Levin for their interest in the work.     

Charging of perfectly conducting and nonconducting particles in a suspension by collisions with walls

The change in the electric charge of perfectly conducting and nonconducting particles of a suspension as a result of their collision with walls in a flow of the suspension is found. Criteria for the applicability of the obtained expressions to real particles are given. For the density of the electric current in rarefied suspensions consisting of a nonconducting gas and charged particles a condition is obtained that is satisfied for flow of a suspension at impermeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–87, July–August, 1980.I thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the work.     

Unsteady effects in weakly perturbed pulsatile channel flows

Pulsatile incompressible laminar flow in a plane channel with slight asymmetric deformation of the walls is considered on the basis of an asymptotic approach to the solution of the Navier-Stokes equations at large Reynolds numbers. It is shown that for extended deformations the change in the direction of the undisturbed flow in the wall regions is accompanied by a sharp increase in the amplitude of the perturbations; this is an essentially unsteady process. For flows with a small positive friction stress two classes of eigensolutions are obtained in the quasisteady approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 96–104, March–April, 1987.The author is grateful to V. V. Sychev and A. I. Ruban for a number of useful consultations in the course of the work.     

Experimental investigation of the anomalous aerodynamic heating of bodies with a deep cavity

This paper analyzes the results of experiments using hollow models of different form, located in a steady-state subsonic or supersonic flow at different angles of attack. Concepts of the physical conditions of the appearance of an effect of heating the gas inside the cavity above the stagnation temperature of the oncoming flow are refined.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 113–119, January–February, 1978.In conclusion, the authors thank O. Yu. Pivovarov and V. A. Shilov for their aid in carrying out the experiments.     

Oscillatory rotationally symmetric loss of stability of nonisothermal couette flow

A study is made of the stability of nonisothermal Couette flow — steady flow of a viscous heat conducting fluid between two rotating concentric cylinders heated to different temperatures. The methods of perturbation theory are used to establish conditions sufficient for bifurcation of a neutral curve of oscillatory instability from the neutral curve of monotonic instability. Computer calculations show that for certain values of the parameters of the problem these conditions are realized and there is an oscillatory loss of stability of the nonisothermal Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–80, January–February, 1984.I thank V. I. Yudovich for constant interest in the work.     

Combined method of calculating supersonic ideal-gas flow over a wing with a supersonic blunt leading edge

A combined numerical method, based on the successive calculation of the flow regions near the blunt leading edge and center of a wing, is proposed on the assumption that the angle of attack and the relative thickness and bluntness radius of the leading edge are small. The flow in the neighborhood of the leading edge of the wing is assumed to be identical to that on the windward surface of a slender body coinciding in shape with the surface of the blunt nose of the wing and is numerically determined in accordance with [1]. The flow parameters near the center of the wing are calculated within the framework of the law of plane sections [2]. In both regions the equations of motion of the gas are integrated by the Godunov method. The flow fields around elliptic cones are obtained within the framework of the combined method and the method of [3], A comparative analysis of the results of the calculations makes it possible to estimate the region of applicability of the method proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–164, January–February, 1989.The authors wish to express their gratitude to A. A. Gladkov for discussing their work, and to G. P. Voskresenskii, O. V. Ivanov, and V. A. Stebunov for making available a program for calculating supersonic flow over a wing with a detached shock.     

Flow with heat transfer in the presence of phase transitions on the wall of an annular channel

A solution is presented to the problem of the laminar flow of a heat-transfer vapor in an annular channel of constant cross section in the presence of a liquid film on the outer wall and heating through the inner wall of the channel. The results of test calculations for water vapor are given. The obtained results are analyzed, and it is shown that they make it possible to establish a number of characteristic features of the process, in particular, the possible existence of a self-similar solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–146, May–June, 1981.     

Unsteady processes in the neighborhood of a well in the case of a nonlinear flow law and determination of stratum parameters

A study is made of the propagation of disturbances in the neighborhood of a well in the case of a linear elastic regime for a flow law with limiting gradient, and also for a nonlinear elastic regime for different forms of the flow law. The obtained results are used to investigate the difference between two forms of flow anomaly — nonlinearity of the flow law associated with non-Newtonian behavior of the fluid and a pressure dependence of the parameters of the nonlinear flow law due to nonlinear elastic deformations of strata [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–70, July–August, 1983.I thank V. M. Entov and L. A. Chudov for helpful advice and discussion.     

Calculation of flow of highly attenuated gas around a body,taking into account interactions with the surface

The results of Monte Carlo calculations are given for the aerodynamic characteristics of different bodies in free-molecular and near-free-molecular conditions. The calculations are made for different models of the interaction between the attenuated-gas flow and the surface of the body. Analysis and comparison of the results obtained with available experimental and natural data serves as the basis for a discussion of the applicability of individual parameters of these models in practical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 117–123, September–October, 1978.It remains to thank M. N. Kogan, V. A. Perepukhov, A. I. Erofeev, A. I. Bunimovich, L. L. Zvorykin, A. A. Pyarnpuu, and V. F. Kameko for discussions of the results and for valuable comments.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

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.     

Collapse of vapor bubbles in a liquid

The effect of nonequilibrium phase transitions on the vibrations of a vapor bubble in a liquid caused by a suddenly applied pressure drop is considered. This problem is of interest in the study of mixed liquid and vapor flows with a discrete vapor phase. Results are presented of a numerical solution of this problem in the form of dimensionless radius-time curves for various values of the parameter which characterizes the kinetics of the phase transitions. The case of equilibrium phase transitions has been considered in [1, 2]. The thermal and dynamic interactions of a gaseous bubble with the surrounding fluid are the subject of [3, 4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 50–54, November–December, 1973.The author thanks R. I. Nigmatulin for advice and interest in this work and V. Sh. Shagapov for useful discussions.     

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.     

Nonlinear regimes of current flow through a weakly ionized boundary layer and their stability

The problem of steady states and stability of current flow in low-temperature plasma with allowance for the Joule heat release have been considered repeatedly for the case of confined stationary plasma (see, for example, [1]). The present paper is devoted to the asymptotic solution of this problem for the case of a laminar boundary layer of weakly ionized plasma. A similar problem was previously considered in [2] in a zero-dimensional approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–163, July–August. 1986.The author thanks G. A. Lyubimov and the participants in the seminar he directs, I. M. Rutkevich and V. D. Khait for their discussion of the work and their useful observations.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow