Drag of a flat wedge in a two-phase flow

The drag of a flat wedge in a subsonic two-phase flow is investigated. In contrast to earlier work of Balanin and Zlobin [1] particular attention is devoted to the influence of the particle size. Detailed investigations are made of the dependences of the forces and aerodynamic coefficients on the concentration of the solid phase, the opening angle of the wedge, and the particle size. It is established that the drag coefficients depend on the particle size only for particles with diameters less than 30 um.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1982.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Particle fluctuation intensities in sediment-laden flows

By employing the kinetic theory of solid–liquid two-phase flow, the velocity distribution of sediment was discussed and the theoretical results of the mean square value of the particle peculiar velocity in axis direction and vertical direction were obtained. The comparison of the experimental results of particle motion in horizontal pipe and the calculated results showed satisfactory agreement. The present study is unique not only in simulation of particle fluctuation characteristics in sediment-laden flows, but also in examination of the relationship between the fluid fluctuation intensities and particle fluctuation intensities, which reveals the coherence characteristics of particle and fluid fluctuations in dilute solid–liquid two-phase flows with fine sediments.     

Charging of disperse particles in two-phase media with unipolar charge

Charging of disperse particles with good conduction in two-phase media with unipolar charge is considered in the case when the volume concentration of the particles is low. For this, in the framework of electrohydro-dynamics [1, 2], a study is made of the charge of one perfectly conducting liquid particle in a gas (or liquid) with unipolar charge in a fairly strong electric field. The influence of the inertial and electric forces on the motion of the gas is ignored, and the velocities are found by solving the Hadamard—Rybczynski problem. We consider the axisymmetric case when the gas velocity and electric field intensity far from the particle are parallel to a straight line. The analogous problem for a solid spherical particle was solved in [3–6] (in [3], the relative motion of the gas was ignored, while in [4–6] Stokes flow around the particle was considered). The two-dimensional problem of the charge of a solid circular, perfectly conducting cylinder in an irrotational flow of gas with unipolar charge was studied in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 108–115, November–December, 1980.We thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the present work.     

Radiative and convective heat transfer during blowing into a compressed hypersonic layer of two-phase products from the ablation of a covering

The study examines the screening of the radiative heat flux in conditions of hypersonic flow around blunt bodies with ablated carbon-based coverings. In contrast to the studies already known [1–3], allowance is made for the presence of condensed microscopic particles in the products of ablation. In [4] the problem of radiative transfer is considered in a layer of two-phase ablation products with parametrically prescribed dimensions, particle temperature, and layer thickness. The present study uses a closed system of equations which describes the processes of heat and mass transfer. This gives rise to considerable differences in the numerical results, according to the degree of screening.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–166, November–December 1985.deceased     

Quasihomogeneous model of cavitation flows in diffuser channels

Starting with the experiments carried out by Reynolds in 1894, the flow in Venturi tubes has traditionally been used to study and demonstrate various forms of cavitation. Numerous authors have carried out experimental research on the various flow regimes in diffuser channels [1–7] or have investigated theoretical models of such flows [6, 8]. The occurrence and development of cavitation is closely associated with the phenomenon of turbulent separation complicated by the presence of two-phase flow in the dissipation zone. For a long time these effects were considered separately, until Gogish and Stepanov [9] proposed a single model of cavitation and separation based on the theory of intense interaction of an incompressible potential flow and a turbulent cavitation layer of variable density and embracing the various stages of cavitation. The object of this study is to demonstrate the possibilities of this model with reference to the simple example of flows accompanied by cavitation and separation in plane and axisymmetric diffuser channels of the Venturi tube type with straight and curved walls. The dissipative flow near the walls is described by a quasihomogeneous model of turbulent two-phase flow, in which the presence of two phases is taken into account only by varying the mean density. The potential core of the flow is considered in the one-dimensional formulation. The displacement thickness serves as the flow interaction parameter. The conditions of ocurrence and development of circulatory flows are determined. Examples of symmetrical and nonsymmetrical flows are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–54, September–October, 1986.     

Modeling of the thermoerosive action of two-phase media

The action of a supersonic two-phase flow on the surface of a solid is considered. Various methods of modeling the particle concentration, the dynamic head, and the temperature and velocity disequilibria of the phases in connection with the investigation of the thermoerosive action of atmospheric formations in gas dynamic installations are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 92–98, July–August, 1986.     

Skin effect in two-phase flow over a wing

The author proposes a mathematical model of the skin effect — the flow in the thin film formed on the surface of a wing in a two-phase stream and consisting of the particle component [1–6]. The possible regimes are classified and the influence of the skin effect on the overall aerodynamic characteristics of a wing moving through heavy rain is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–55, January–February, 1990.The author is grateful to A. N. Kraiko for discussing the topic and for his valuable comments.     

Supersonic two-phase flow around a wedge

Supersonic two-phase flow around bodies is encountered in calculating the flow around the last stages of blades of condensing turbines, in studying the motion of airplanes under cloudy conditions, etc. In the latter case, there is, along with erosion of the forward edges of the wing profiles, a change in the wave structure and interference situation in the flow about the airplane, leading to off-design regimes of motion. Supersonic flow of a two-phase mixture around a wedge, without taking account of the influence of the particles on the flow, was investigated in [1–3]. In [4], also in this kind of simplified setting, a study was made of the interaction of particles with the surface of a wedge in which reflection of the particles from the wall was taken into account. Morganthaler [5] made an experimental study of the flow of a mixture of air and aluminum oxide particles around a wedge. In [6] a theoretical study was made of a supersonic two-phase flow around thin flat axially-symmetric bodies. In particular, for the flow around a wedge, closed form solutions were obtained for the form of the shock wave, the gas streamlines and particle paths, and the distribution of all the parameters along the surface of the wedge. On the basis of the equations given in [7] and the method of characteristics, which were developed for flows consisting of a mixture of a gas and heterogeneous particles in nozzles [8,9], we present below a study of a supersonic two-phase flow around a wedge.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–88, March–April, 1972.     

Experimental investigation of the drag of simple bodies in a two-phase flow

In connection with their increasing use in technology, two-phase flows are being widely studied at the present time. However, computational methods for determining the parameters and influence of two-phase flows on constructional elements of machines, etc., are as yet inadequately developed. In addition, their further development in rational directions requires a large body of experimental data. It is therefore very important to extend the experimental investigations into two-phase flows. The present paper reports an experimental investigation into the aerodynamic drag of simple bodies in a two-phase flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–162, May–June, 1979.     

Dependence of the stagnation temperature of a jet of gas containing solid particles on the concentration of particles and their velocity

This article gives the results of experiments on the measurement of the stagnation temperature of a two-phase jet, issuing from a nozzle. The experiments were made using a mixture of air and aluminum oxide (particle diameter 50) with a ratio of the mass flow rate of the solid phase to the mass flow rate of the gas equal to 0.3–2.5, and at initial temperatures of the mixture of 150–450°C. It follows from the results of the experiments that the stagnation temperature of a two-phase flow considerably exceeds the temperature of the mixture at the inlet of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–176, July–August, 1970.     

Resistance matrix for a particle in a nonuniform gas flow

The slow (relative to the medium) motion of a heat-conducting particle in a gas flow described by the Navier-Stokes equations is examined. The particle is small as compared with the macroscopic scale of the flow and the Local perturbation it creates is therefore described by a Linear Boltzmann equation. A system of thermodynamic fluxes corresponding to the thermodynamic forces is established, and the transport coefficients forming the resistance matrix are shown to be symmetric.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–108, January–February, 1988.     

Percolation model of equilibrium three-phase flow through porous media

Percolation models of one-phase and two-phase flow through porous media are extended to the three-phase case. The characteristic regions of realization of one-phase, two-phase and three-phase flow are determined, Relative phase permeability calculations are presented for a model capillary radial density function. The theory is compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 109–114, January–February, 1989.     

Unsteady flow through a porous medium in the presence of chemical reactions

The underground leaching of uranium ores and nonferrous and precious metals under natural conditions is one of the latest methods of mineral extraction [1]. It consists of pumping into isolated formations through reaction wells an acid solution which upon reacting with the rock yields a readily soluble salt that can be brought to the surface with water through extraction wells. Together with the acid solution, it is also possible to pump in other reactants to participate in the chemical reaction, for example, gases such as oxygen. Moreover, secondary gases may be formed as a result of the chemical reaction. Thus, the chemical reaction proceeds in the presence of a one or two-phase flow in the porous medium. The mathematical modeling of these processes is usually based on the approximation of one-phase flow without allowance for the changes in the porosity and permeability of the medium as a result of the reaction [2]. In this paper we solve the problem of unsteady flow in the presence of a chemical reaction for a two-phase system taking into account the changes in the flow parameters of the porous medium. The condition of stability of the plane reaction front is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–87, January–February, 1987.The author is grateful to R. I. Nigmatulin for his useful comments and interest in the work.     

Numerical simulation and experimental validation of gas–solid flow in the riser of a dense fluidized bed reactor

Gas–solid flow in the riser of a dense fluidized bed using Geldart B particles (sand), at high gas velocity (7.6–15.5 m/s) and with comparatively high solid flux (140–333.8 kg/m² s), was investigated experimentally and simulated by computational fluid dynamics (CFD), both two- and three-dimensional and using the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd and EMMS drag models. The results predicted by EMMS drag model showed the best agreement with experimental results. Calculated axial solids hold-up profiles, in particular, are well consistent with experimental data. The flow structure in the riser was well represented by the CFD results, which also indicated the cause of cluster formation. Complex hydrodynamical behaviors of particle cluster were observed. The relative motion between gas and solid phases and axial heterogeneity in the three subzones of the riser were also investigated, and were found to be consistent with predicted flow structure. The model could well depict the difference between the two exit configurations used, viz., semi-bend smooth exit and T-shaped abrupt exit. The numerical results indicate that the proposed EMMS method gives better agreement with the experimental results as compared with the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd models. As a result, the proposed drag force model can be used as an efficient approach for the dense gas–solid two-phase flow.     

Steady two-phase flow in a vertical tube subject to combined free and forced convection

Using the two-velocity, two-temperature model of a continuous medium, the viscousgravitational flow of a mixture of incompressible liquid and solid particles in a vertical round tube is considered. The free-convection equations are written down on the basis of the general equation of motion and the energy equation of a two-phase medium [1, 2]. Using a finite Hankel integral transformation, a solution is constructed for the case of a linear wall-temperature distribution along the tube. The results of some practical calculations of the velocity and temperature fields over the cross section of the tube are presented, together with the dimensionless heat-transfer coefficient expressed as a function of the Rayleigh number and phase concentration. Here it is assumed that the dynamic and thermal-interaction coefficients between the phases correspond to the Stokes mode of flow for each particle, as a result of which the velocity and thermal phase lag is very small [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1975.     

Order and disorder in particle–liquid flows in a pipe

The spherical expanded polystyrene particle–oil two-phase flow in a vertical pipe was used to simulate the dispersed phase distribution in laminar bubbly flows. A three-dimensional particle image tracking technique was used to track the particles in the flow to study the ordered structure of dispersed phase distribution and its transition to disorder. The ordered structures behaved as particle strings aligned in the flow direction as induced by the flow shear. The structures were quite durable in high liquid velocity flows and dispersed gradually as the liquid velocity decreased. In lower velocity flows, the particles tended to form clusters in the horizontal direction, as predicted by potential theory for spherical bubbles rising in a quiescent inviscid liquid and as observed in experiments on non-shear bubbly water flows.     

Numerical study of the structure of a finely disperse unsteady two-phase jet

The structure of an unsteady two-phase jet is numerically studied within the framework of the model of a heterogeneous medium with nonequilibrium velocities and temperatures with allowance for particle collisions and intergranular pressure.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 91–97, March–April, 2005.     

Asymptotic form of the solution to the problem of multicomponent mixture flow through a porous medium with a boundary layer

In problems of two-phase mixture flow through a porous medium in a subterranean stratum a boundary layer phenomenon arises caused by the fact that relative phase motion exists in the system, and so having no analogy with the single-phase case. The physical nature of boundary layer phenomena is explained, and an asymptotic solution is constructed for the self-similar problem with an arbitrary number of components in the system, by using the method of matched asymptotic forms. The conditions are established for the motions of a multicomponent and a binary mixture to be equivalent, and a study is made of the role of convective factors in the formation of averaged working indices for the stratum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–100, July–August, 1985.