Pressure waves in a separated gas-liquid layer in a horizontal duct with a step

Pressure wave propagation into a separated gas-liquid layer in a horizontal duct with a step is investigated analytically. The linear solution is derived assuming a large density ratio of liquid to gas. The solution can be found first for the gas layer and then for the liquid layer. The linear wave in a liquid layer is valid even for fairly large initial pressure ratios, and clearly exhibits the dispersive characteristics of the pressure wave in a liquid layer. As the initial pressure ratio is increased, the pressure wave in the gas layer becomes a shock wave. Thus, its effect on the wave in a liquid layer can be found analytically by modifying the boundary condition in part. The wave in a liquid layer consists of a main wave, which propagates with the shock speed in gas, and a precursor wave, whose front propagates with the speed of sound in liquid. The precursor wave has an oscillatory structure; its amplitude increases with increasing shock strength and also with liquid layer thickness.     

Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a laval nozzle

Within the framework of a two-liquid (two-velocity and two-temperature) model of a continuous medium, the article considers the flow of a mixture of a gas and foreign particles in the subsonic, transonic, and supersonic parts of a Laval nozzle. In the case of a thin layer of pure gas near the wall, the problem is solved in two stages. First, the method of establishment is used to calculate the core of the flow, where the gas with the particles is flowing; under these circumstances, the parameters in the layer of pure gas are determined approximately; then simplified equations (of the type of the equations of the boundary layer) are used to find the distribution of the parameters in the zone of pure gas, and the flow in the core of the stream is refined. Examples of the calculation are given. Use of the method developed permitted establishing some of the special characteristics of the flow of a mixture of gas with particles in a Laval nozzle in the case of Stokes flow around the foreign particles.     

Influence of the wall boundary layer thickness on a gas jet injected into a liquid crossflow

The effects of the wall boundary layer thickness on the development of an axisymmetric gas jet injected into a confined vertical water flow were investigated. The variations in the wall boundary layer were made by using suction at the wall through rectangular profiled slots. The water velocity around the two-phase jet was studied for several boundary layer thickness values by laser Doppler velocimetry. The gas jet outline was extracted by image processing applied on visualisations for a wide variety of water, gas and suction conditions. These comparisons showed that the boundary layer has no influence on jet development. The data showed that the interactions between flows near the injection do not develop downstream, which accounts for the absence of the two classical contrarotating vortices in the medium field of the jet. The influence of the gas pocket, and then of buoyancy, is predominant over other phenomena. Received: 15 December 1999 / Accepted: 29 August 2000     

The distribution of particles in a shock-induced boundary layer of a dusty gas over a solid surface

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied. The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account. A method for calculating the density profile of dispersed phase near the wall is proposed and some numerical results are given. It is shown that behind the shock wave, there exists a curved thin layer where the density of particles is many times higher than the original one. This dust collection effect may be of essential importance to the problem of dust explosion in industry.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

Effect of a space-time source structure simulating a dielectric barrier discharge on the laminar boundary layer

The time-dependent pulse-periodic action of a surface electric discharge on a flat-plate laminar boundary layer is simulated theoretically. The effect of the discharge is estimated within the framework of the numerical solution of the boundary value problem for the time-dependent two-dimensional compressible boundary layer with additional terms in the momentum and energy conservation equations simulating the force and thermal action of the discharge on the gas flow with allowance for the pressure gradient across the boundary layer induced by the corresponding body force component. The effect of certain parameters of the problem formulated above on the gas velocity induced by the discharge in the boundary layer is also estimated.     

Travelling performance of a wheel on a finite thickness ground

Off-road terrain can often be regarded as a finite thickness ground consisting of a soft soil layer on a rigid base. Experiments for the traveling performance of a wheel in a dense sand layer on a rigid base revealed that as the soil layer thickness decreases under the condition of high constant slip, the drawbar pull does not increase monotonically but increases gradually to a maximal value, then decreases to a minimal value, and thereafter again increases rapidly to the highest value at zero soil layer thickness. The mechanical interpretation of the relationship between the drawbar pull and the soil layer thickness is given qualitatively from the aspects of the shear characteristics of dense sand and the rigid-body friction between the wheel and the rigid base of the soil layer. It is indicated that the relationship takes the same form as van der Waals' state equation for the pressure and the volume of an imperfect gas with a phase transition between gas and liquid. The equation representing the relationship of the drawbar pull to the soil layer thickness is proposed in accordance with van der Waals' equation.     

Stability of a steady-state discontinuity of a fluid layer on the surface of an immiscible fluid

A new stable structure of the three-phase system formed by a gas, a horizontal liquid layer with a free upper surface and an underlying immiscible liquid substrate is investigated experimentally and theoretically. When the upper layer has a greater surface tension than the lower layer and its thickness is fairly small, a local deformation of its surface can lead to the development of a steady-state concentric discontinuity within whose limits the lower layer os in contact with the gas. The conditions of stability of such a phase system with a steady-state discontinuity are studied and the dependences of the discontinuity parameters on the vessel diameter, the upper layer thickness, and the liquid surface tensions are obtained for various pairs of liquids. The formulation of the analytic problem of the layer discontinuity is discussed. The experimental data are compared with the results of calculations carried out for a model of a discontinuity in an infinite layer.     

Radiative-convective heat transfer in a plane layer of a selectively absorbing mist

This paper deals with the thermal field in a plane layer of selectively absorbing gas which has been injected into a steady turbulent stream of high-temperature gas flowing around a porous plate. The boundary-value problem in terms of the energy equation reduces to a nonlinear integral equation in terms of a dimensionless temperature, and this equation is solved numerically by the Newton-Kantorovich method. The results are presented on graphs of temperature and thermal flux in the absorbing gas layer as functions of the space coordinate. Such a problem has been analyzed in [1] for the case of an injected gray gas.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 3, pp. 179–182, May–June, 1972.     

Sublimation of a crystal slowed by sorption of foreign molecules from a gaseous medium

Numerical simulation of the sublimation of the surface of an ice crystal has shown that the presence of a non-condensable gas substantially reduces the sublimation rate. It has been found that the slowing of the sublimation due to the adsorption of gas molecules on the crystal surface that fill the vacancies during sublimation prevents the formation of vacancy islands on the surface of the crystal required for evaporation of the surface molecular layer. The available results of studies that explain the slowing of the sublimation by the presence of a diffusion layer formed in the vapor medium near the sublimating surface are supplemented with new data showing that molecular processes on the crystal surface play an equally important role as the diffusion layer. Cases have been found where crystal sublimation is accelerated by the sorption of gas molecules. The obtained results refining the theory of sublimation can be used to develop methods for controlling sublimation.     

One-dimensional compression of bounded volumes of a self-gravitating gas

Unsteady plane and spherically-symmetric self-gravitating gas flows are analytically and numerically studied. It is assumed that the gas is enclosed in a plane layer of finite thickness or in a bounded spherical volume. Two characteristic compression patterns are established, namely, a quasiperiodic regime in which gravitational equilibrium is attained and a fast compression regime with a many orders increase in the density. The quasiperiodic regime is realized when the layer thickness is fairly small as compared with the Jeans length. The fast compression occurs when the layer thickness is greater than the Jeans length.     

Stability of a liquid layer with bubbling

The article discusses a new type of instability of a horizontal layer of a motionless liquid, due to the motion of bubbles of gas or of particles of a suspension through the layer. It is shown that, when a certain critical mass flow rate of the gas or the suspension is attained, due to the essential inhomogeneity of the velocity of the gas bubbles, the layer becomes unstable and convective flow develops in a Bénard cell. With the motion of bubbles in the field of gravity, the criterion of instability is found to be independent of the size of the bubbles and the kinematic viscosity of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, July–August, 1974.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Interaction between slip and the high-frequency vibrations of a shaped surface in the working gap of a gas-lubricated bearing with inclined grooves

The article discusses a flat bearing with a gas lubricant, one of whose surfaces is shaped by inclined grooves and vibrates in accordance with a given harmonic law with a high frequency. The reaction of a thin layer of viscous compressible gas is formed as a result of interaction between the effects of slip and high-frequency vibrations. Asymptotic methods are used in the investigation of the reactions of the gaseous layer; the thermodynamic process in the lubricating layer is assumed to be isothermal, and in the equation of motion of the gas the effect of inertial and mass forces is not taken into consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 43–50, March–April, 1976.     

Boundary layer flows behind constant speed shock waves moving into a dusty gas

Laminar boundary layer flows behind constant speed shock waves moving into a dusty gas are analyzed numerically. The basic equations of two-phase flows are derived in shock fixed coordinates and solved by an implicit finite-difference method for the side wall boundary layer in a dusty gas shock tube. The development of the boundary layer and resulting velocity and temperature profiles, respectively, for the gas and particles are given from the shock front to far downstream. The effects of diaphragm pressure ratio, mass loading ratio of particles and particle size upon the flow properties are discussed in detail.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Quasiequilibrium Knudsen boundary layer on a nonisothermal porous body

The state of a gas near a permeable nonisothermal body with ultrathin pores, that is, pores in which the motion of molecules is not accompanied by intermolecular collisions, is studied. A boundary layer of a new type, namely, the quasiequilibrium Knudsen boundary layer on the porous body surface, is investigated. It is formed on condition that within the body there is a heat flux, even when the body is in an equilibrium gas. The statistical methods for solving the Boltzmann equation are used to determine the temperature and pressure jumps across the Knudsen layer near thin perforated and porous membranes.     

Effect of Gas Injection from the Surface of a Body on Its Interaction with a Temperature Inhomogeneity in a Supersonic Flow

The flow pattern in the shock layer and the aerodynamic characteristics of a hemisphere in unsteady axisymmetric interaction with a closed spherical hot-gas region embedded in the oncoming supersonic flow in the presence of intense injection of gas from the body surface into the shock layer are studied on the basis of the inviscid perfect gas model. Two cases are considered, namely, (1) when the radius of the permeable surface is greater than that of the temperature inhomogeneity and (2) when the injection is localized in the vicinity of the forward stagnation point and the permeable region is smaller the inhomogeneity.     

Blowing into a supersonic stream through a permeable surface

Distributed blowing of gas into a supersonic stream from flat surfaces using an inviscid flow model was studied in [1–9]. A characteristic feature of flows of this type is the influence of the conditions specified on the trailing edge of the body on the complete upstream flow field [3–5]. This occurs because the pressure gradient that arises on the flat surface is induced by a blowing layer whose thickness in turn depends on the pressure distribution on the surface. The assumption of a thin blowing layer makes it possible to ignore the transverse pressure gradient in the layer and describe the flow of the blown gas by the approximate thin-layer equations [1–5]. In addition, at moderate Mach numbers of the exterior stream the flow in the blowing layer can be assumed to be incompressible [3]. In [7, 8] a solution was found to the problem of strong blowing of gas into a supersonic stream from the surface of a flat plate when the blowing velocity is constant along the length of the plate. In the present paper, a different blowing law is considered, in accordance with which the flow rate of the blown gas depends on the difference between the pressures on the surface over which the flow occurs and in the reservoir from which the gas is supplied. As in [8, 9], the solution is obtained analytically in the form of universal formulas applicable for any pressure specified on the trailing edge of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 108–114, September–October, 1980.I thank V. A. Levin for suggesting the problem and assistance in the work.     

Boundary layer laminarization on a thermally insulated surface with energy supply to the flow

A subsonic stream of gas flowing over a thermally insulated plate and having an elevated temperature in a thin layer adjacent to the surface is considered. This temperature distribution in the flow can be obtained by providing a volume energy supply near the leading edge of the plate. The results of calculating the position of the line of laminar-turbulent transition on the basis of linear stability theory and the e^N method are presented. It is shown that the presence of a heated layer of gas near the surface of the plate leads to an increase in the stability of the laminar flow and an extension of the laminar interval of the boundary layer. A nonmonotonic dependence of the length of the laminar interval on the thickness of the heated layer of gas is detected. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 58–61, September–October, 1988.