Aiding and Opposing Mixed Convection Flow in Melting From a Vertical Flat Plate Embedded in a Porous Medium

The problem of melting from a vertical flat plate embedded in a porous medium is studied. The main focus is to determine the effect of mixed convection flow in the liquid phase on the melting phenomenon. Both aiding and opposing flows are considered. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The governing equations are solved numerically. Numerical results are obtained for the temperature and flow fields in the melting region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface.     

Calculation of the flow of a two-phase mixture in a Laval nozzle,allowing for the turbulent diffusion of the particles

The flow of a mixture of gas and condensed particles in an axisymmetric Laval nozzle is considered. The motion of the particles is calculated in a specified field of gas flow, with due allowance for their turbulent diffusion. The results of calculations indicating the necessity of allowing for this phenomenon when considering the motion of particles toward the wall of a profiled nozzle are presented.Translated from Izvestiya Akademii Nauk SSSR, No. 2, pp. 161–165, March–April, 1973.     

Radiation of a shock layer during hypersonic flow of air about a spherical segment

The problem on the flow of radiating air about a spherical segment is solved. A comparison of results obtained with investigations of the flow of a radiating gas about a sphere and the flow of gas about a spherical segment, with radiation left out of account, is made. The influence of radiation in the neighborhood of the rim of the segment on the flow in the shock layer is considered, and it is shown that it does not exert a significant influence on the fields of the gas-dynamical parameters because the latter are determined by processes occurring near the axis of symmetry, due to the phenomenon of radiation freezing.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–106, January–February, 1972.     

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.     

Propagation of a flush wave in a prismatic channel

By a water flush there is generally understood an unsteady-state flow of water, arising in millraces, with the breaching (rupture) of a dam. The special characteristics of a flush wave are also possessed by a flow in a lower millrace at some distance from the dam, with the overflow of water arising in the reservoir over the crest of the dam. Usually, the necessary information on the parameters of a flush wave with its motion in natural channels is obtained by numerical solution, in a digital computer, of the equations of not fully established one-dimensional flow [1–3]. These calculations are very labor-consuming and require rather detailed information on the channel. Therefore, it is of practical importance to clarify the overall laws governing the propagation of flush waves in schematized, in particular, in prismatic channels. In some cases, on the basis of such laws, it is possible to make a preliminary diagnosis of the expected scales of the phenomenon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–44, January–February, 1975.     

Flow and heat transfer of a viscous fluid when there is a phase transition

A study is made of the problem of the flow and heat transfer of a fluid formed by the phase transition (melting or sublimation) when the end of a rod touches a heated surface. Problems of this kind arise, in particular, when a heated surface is cooled by means of the heats of the phase transitions of materials with an energy content. A solution is obtained to a simplified system of heat and mass transfer equations obtained by estimating the order of magnitude of the various terms in the Navier-Stokes equations in a manner similar to that in [1–3]. The parameters that govern the process are identified, and an approximate analytic solution is found for the quasi-stationary case. The analytic solution is compared with a numerical solution obtained iteratively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–131, May–June, 1931.     

High-velocity penetration of a melting solid by a slender body

The high-velocity penetration of a melting solid by a thermally insulated slender body is considered. Under certain constraints on the dimensionless melting parameters the flow in the molten layer can be described within the framework of lubrication theory. The local angle of inclination of the body and the surfaces of the molten layer with respect to the velocity is assumed to be small and is taken into account in the linear approximation. The heat flow into the solid is found by simulating the body and the molten layer by means of a segment with distributed heat sources. Within the framework of this simple formulation a closed solution of the problem of the fusion zone around a moving slender body is constructed. The dependence of the shape of the molten layer and the structure of the temperature and longitudinal velocity fields in the layer on the shape of the body and the other governing parameters of the problem is investigated. The results obtained also give a solution of the problem of the melting of a solid rubbing at high velocity against a thermally insulated rough substrate, when the characteristic height of the roughness is of the order of the thickness of the layer and the characteristic length of the order of the contact length.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 43–48, November–December, 1992.     

Influence of acoustic perturbations on the flow structure in a boundary layer with adverse pressure gradient

An experimental Investigation was made of the flow in a laminar boundary layer in a region of adverse pressure gradient in the presence of an acoustic field. There is a significant rearrangement of the laminar flow under the influence of the sound. The strong influence of the sound on the average flow is due to the excitation of vorticity perturbations, but this does not completely explain the phenomenon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 48–52, March–April, 1983.     

The structure of the supersonic turbulent boundary layer in its interaction with a shock wave

An experimental study is made of the turbulent boundary layer in its interaction with a shock wave, the purpose being to clarify questions connected with the increase in the fullness of the velocity profiles. New systematic data are obtained on the development of the boundary layer, and its structure and asymptotic behavior beyond the interaction region. These results are for axisymmetric flow in the range of Mach numbers M=2–4 and angles of rotation of the flow 10–25°. Conditions of developed separation are included. Extensive information about the general properties of flows with separation has been obtained in a number of studies. A survey of these may be found, for example, in [1, 2]. Certain questions about the separation and reattachment of the boundary layer are clarified. The dimensions of the separation region are determined and its structure studied in detail for various shapes of the surface around which the flow takes place. Nevertheless it has not yet proved possible to reach a complete understanding of this complex phenomenon. Usually plane models have been used for the investigations, but in this case it is evidently impossible to exclude completely the influence of end effects on the flow in the interaction zone. Therefore it is preferable to study such flows in axisymmetric models; this considerably eases the task of analyzing and interpreting the results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 75–82, September–October, 1985.     

Theory of thermal instability of the flow of a viscoelastic fluid

The problem of the stability of the flow of viscoelastic fluids has fundamental importance for the technology of the production of polymer products and viscosimetry. This problem is not reduced only to classical inertial turbulence. A number of other mechanisms leading to flow instability are known [1, 2]. A thermal mechanism based on the allowance for dissipative heating and elastic properties within the framework of a linear model of a viscoelastic fluid was drawn upon to explain this phenomenon in [1]. The possibility of a self-oscillatory mode of flow was demonstrated on the basis of a qualitative analysis of the theological equation and the equation of heat balance in application to simple shear flow and uniform stretching. A theoretical analysis of the self-heating of flowing systems possessing viscoelastic properties is carried out in the present report. The main laws of the thermal instability of viscoelastic fluids discovered in [1] are described.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 115–122, May–June, 1979.     

Asymptotic analysis of the equations of a three-dimensional boundary layer

The asymptotic solutions of the self-similar equations of two- and three-dimensional boundary layers have been investigated by many authors (see, for example, [1–3]). In [4, 5], asymptotic solutions were found for non-self-similar equations for two-dimensional flow, and the propagation of perturbations near the external edge of the boundary layer was analyzed. In the present paper, asymptotic solutions are obtained for the non-self-similar equations of a three-dimensional laminar boundary layer of an incompressible fluid. It is shown that the conclusion drawn in [5] — that the boundary conditions can be transferred from infinity to a finite distance from the wall — is also true for three-dimensional flow. The obtained solutions explain the experimentally well-known phenomenon of the conservativeness of the secondary currents. The essence of this phenomenon is that a change in the sign of the transverse (along the normal to a streamline of the external flow) pressure gradient is accompanied by a very rapid change in the direction of the secondary flow near the wall, whereas in the upper layers of the boundary layer the direction remains unchanged for a substantial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 155–157, September–October, 1979.     

Numerical study of the behavior of a uniform “spot” in an ideal density-stratified liquid

A numerical analysis of the flow arising as a result of the collapse of a uniform spot in a heavy ideal liquid linearly stratified with respect to density is presented. The nonlinear model of the phenomenon is employed. The numerical results are compared with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 120–126, May–June, 1973.     

Flow of a viscous fluid in a closed cavity in the presence of slip effects

Slip at the wall is observed in the flow of non-Newtonian fluids [1–4] and rarefied gases [5]. The most complete information on the phenomenon is obtained in capillary viscosimetry. For small radii of the capillaries and in porous media the slip effect is manifested even for Newtonian fluids (water, kerosene, for example) [6]. Experiments [2, 4] show that the influence of the entrance section can be ignored if the length of the capillary exceeds its radius by about 100 times. For the measurement of the rheological characteristics of high-viscosity fluids the use of long capillaries is difficult, and it is necessary to calculate the two-dimensional flow at the entrance section with allowance for slip. The need for such calculations also arises, for example, when one is choosing the optimal parameters of the screw devices employed in the processing of polymers [7]. Two-dimensional flows of a viscous incompressible fluid are frequently calculated with the flow function and vorticity =– used as variables [8–14]. The expressions for the vorticity on the boundary are usually obtained from the viscous no-slip condition [8, 9]. In the present paper, expressions are obtained for the vorticity on a wall in the presence of slip. The obtained expressions are used to solve a test problem on the flow of a viscous incompressible fluid in a cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–16, January–February, 1980.     

Characteristics of the pressure fluctuation spectra ahead of a step in supersonic transitional flow

The results of an experimental investigation of the boundary pressure fluctuations ahead of an axisymmetric step on an ogival cylinder are presented. The experiments were carried out at supersonic flow velocities on the low Reynolds number range. The results made it possible to detect a new phenomenon, previously unobserved in flows with a free separation line — the generation, development and decay of sharply expressed high-intensity peaks in the pressure fluctuation spectra with variation of the Reynolds numbers corresponding to separtion of the transitional boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–173, May–June, 1989.     

Unsteady flow of a two-phase disperse medium from a cylindrical channel of finite dimensions into the atmosphere

Within the framework of the mechanics of heterogenous media, the flow of a mixture of high-pressure gas and an initially close-packed disperse phase from a cylindrical channel of finite dimensions into the atmosphere is investigated numerically. The physical picture is analyzed and the characteristic stages of the process are established. Experimental data indicating satisfactory agreement between the mathematical model and the phenomenon investigated are presented.St.-Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–66, May–June, 1996.     

Instability and nonuniqueness of quasisteady flows of a viscoelastic liquid

Within the framework of the 4-constant Oldroyd model unidirectional steady-state and quasisteady flow of a viscoelastic liquid is considered. A new explanation, not based on the assumption of slip, is given for the well-known effect of a sharp increase in the fluid flow rates at shear velocities higher than a certain critical value. It is shown, analytically and numerically, that the phenomenon of hysteresis is closely related to this effect. The relation between the problem of stability of the flow in question and the problems of nonuniqueness of the steady-state solution is also noted. A modification of the standard Oldroyd model is proposed and the corresponding integral conditions removing the singularities related with the nonexistence and nonuniqueness of the steady-state solution are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 29–39, November–December, 1996.     

Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

On “vortex breakdown”

The well-known investigations of vortex breakdown are supplemented with an exact analytic representation of this phenomenon on the basis of the complete Navier-Stokes equations for the case of a potential swirl of the input flow about the axis of symmetry.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 167–169, May–June, 1995.     

Boundary conditions of gas dynamic slip on a rough surface

The phenomenon of gas dynamic slip associated with the flow of a monatomic, slightly rarefied gas over a rough surface is investigated. It is assumed that the characteristic dimensions of the roughness are comparable with the molecular mean free path. It is shown that if there is anisotropy of the surface shape the relation between the slip velocity and the friction stress vector becomes tensorial. In this case for almost any orientation of the gas dynamic flow the so-called cross slip effect is observed. The symmetry of the slip coefficient matrix is proved for fairly general assumptions concerning the type of roughness, the law of reflection of molecules from the surface, and the law of intermolecular interaction. The components of the slip coefficient matrix are calculated by a variational method for a corrugated model of the roughness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–184, January–February, 1987.