Slender profiles in flowing two-phase disperse media

The two-dimensional problem of steady flow of a homogeneous two-phase medium consisting of gas and solid particles past a slender profile is considered in the linear formulation at a low volume concentration of the solid phase. The flow regimes with low supersonic velocity and negligible compressibility of the carrier phase and with supersonic velocity are investigated. The aim of the paper is, in the framework of the model of interpenetrating continua [1, 2], to determine the aerodynamic characteristics of slender profiles at small angles of attack.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, 147–154, September–October, 1981.I thank V. P. Stulov for interest in the work and a helpful discussion.     

Finite-particle-size effects in disperse two-phase flows

Three aspects of the finite radius of spherical particles in disperse two-phase flows are described. The first one is the relation between the exact volume fraction and the widely used approximation nv (n is the particle number density and v is the particle volume). The approximation affects the behavior of the effective equations at short wavelengths with possible consequences on stability and hyperbolicity. Secondly, the dilute theory of inviscid suspensions is corrected retaining the next leading order in the particle size and an application of this result to the linear problem is described. Thirdly, it is shown how several important properties of suspensions such as effective thermal conductivity and viscosity depend on the subtle effect of translation of the average fields over distances of the order of the particle size.This work has been supported by DOE and NSF under Grants DE-FG02-89ER14043 and CBT-8918144, respectively.     

Buoyancy of bodies in disperse media

The question of the forces acting on bodies immersed in disperse media is investigated and the hydrostatics of such media are discussed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–174, January–February, 1992.The author is grateful to Yu. L. Yakimov for his comments relating to the role of the apparent mass effect when 1.     

Determination of the parameters of particles suspended in two-phase media by means of penetrating radiation

Determination of the concentration, size, and internal structure of microscopic particles suspended in two-phase media by means of contactless methods constitutes an important technological problem. If the particle sizes are on the order of the wavelength of light, methods based on light scattering by particles are widely used for this purpose. The most direct method consists in observing the optical signal scattered by an individual particle [1]. There are also several methods where the total signal from a large number of particles is recorded, but, in this case, multiple rescattering of light on particles must be negligible [2, 3]. At the same time, the complex relationship between the scattering amplitude and the refraction index, the shape of particles, etc., as well as the increasing background of multiply scattered light with greater thickness of the scattering layer, restrict the scope of application of such methods and make other measurement methods desirable, e.g., in the case of instrument calibration. Our aim is to point out the advisability of investigating two-phase media by means of penetrating radiation, which has been used successfully for radiation flaw detection [4] and for inspecting the composition and density of matter [5], We shall mention the most important advantages of the proposed method. First, the interaction between individual particles and nonrefracted radiation is described by simple expressions, which makes the interpretation of results much easier. Second, in using the most informative scheme whereby scattering media are investigated by transillumination, the background of multiply scattered radiation with a low information content (or, to borrow a term from radiation protection physics, the build-up factor [6]) increases with an increase in the scattering layer thickness much more slowly than it does for light. This makes it possible to use radiation methods for investigating optically dense two-phase media. We shall consider below the possibility of determining the distribution function of particle sizes by measuring the radiation attenuation as a function of the linear coefficient of attenuation inside the particles.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 11–14, May–June, 1979.     

Nonspherical particles in two-phase flow

We bave examined the trio-phase fiow of a gas with dispersed, nonspherical, rigid particles. We describe a model for the motion of a single ellipsoid in the fiuid, including the degrees of freedom associated with translation, lift, orientation and angular velocity. We assume there is no interaction between the particles, and give the Liouville equation for the distribution function of the particles. A computer code bas been developed to simulate the two-dimensional behavior of such a fiow. We demonstrate, in the case of a high-speed jet impinging on an obstacle, that the force exerted on the obstacle by the particles depends strongly on the eccentricity.     

Velocity of sound in two-phase media

A theory is developed for calculating the velocity of sound in solid-gas and liquid-gas systems. Using mass and momentum balances, an equation is obtained which shows that the velocity of sound depends on the relative velocity between the two phases, on the ratio of densities, on the porosity, on the particle diameter, on the drag coefficient, and on the frequency of sound.

The theory can be applied only if the one phase is distributed in the other homogeneously in the form of particles, droplets or bubbles of equal size. The experimental results agree very well with the theory.

Based on Hert'z equation for the deformation of spheres, a further theory is described which enables calculation of the velocity of sound in gas-solid systems of low porosity, such as packings or porous bodies.     

Modeling of two-phase flow in porous media with heat generation

The main purpose of this work is investigation of coolability of a boiling debris bed. The main governing equations are derived using volume averaging technique. From this technique some specific interfacial areas between phases are appeared and proper relations for modeling these areas are proposed. Using these specific areas, a modification for the Tung/Dhir model in the annular flow regime is proposed. The proposed modification is validated and the agreements with experimental data are good. Finally, governing equations and relations are implemented in the THERMOUS program to model two-phase flow in the debris bed in the axisymmetric cylindrical coordinate. Two typical configurations including flat and mounted beds are considered and the main physical phenomena during boiling of water in the debris bed are studied. Comparing the results with the one-dimensional analysis shows higher specific power of the bed.     

Vertical two-phase flow in porous media

New concepts are introduced to describe single-component two-phase flow under gravity. The phases can flow simultaneously in opposite directions (counterflow), but information travels either up or down, depending on the sign of the wavespeedC. Wavespeed, saturation and other quantities are defined on a two-sheeted surface over the mass-energy flow plane, the sheets overlapping in the counterflow region. A saturation shock is represented as an instantaneous displacement along a line of constant volume fluxJ _Q in the flow plane. Most shocks are of the wetting type, that is, they leave the environment more saturated after their passage. When flow is horizontal all shocks are wetting, but it is a feature of vertical two-phase flow that for sufficiently small mass and energy flows there also exist drying shocks associated with lower final saturations.     

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.     

Interfacial drag of two-phase flow in porous media

In this paper, the influence of the interfacial drag on the pressure loss of combined liquid and vapour flow through particulate porous media is investigated. Motivation for this is the coolability of fragmented corium which may be expected during a severe accident in a nuclear power plant. Cooling water is evaporated due to the particles decay heat. To reach coolability, the outflowing steam has to be replaced by inflowing water.     

Thermodynamic instability of disperse media isolated from external actions

The evolution of the structure of a medium containing disperse elements (the drops in a weakly viscous fluid, rigid spheres in glycerin, and air pores in a gel) is studied experimentally in the case where the gradient temperature and the concentration fields are absent in the system, and the medium is isolated from the influence of an external force field (including gravity forces). It is shown that these systems are nonequilibrium: if the initial distance between disperse particles is of the order of their sizes, the particles approach until they come in contact (coagulation) irrespective of the scale of the system. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 53–58, May–June, 1999.     

Shock-induced two-phase flows in an aligned baffle system filled with suspended particles

This paper describes the shock propagation through a dilute gas-particle suspension in an aligned baffle system. Numerical solution to two-phase flows induced by a planar shock wave is given based on the two-continuum model with interphase coupling. The governing equations are numerically solved by using high-resolution schemes. The computational results show the shock reflection and diffraction patterns, and the shock-induced flow fields in the 4-baffle system filled with the dusty gas.     

Anisotropy effects in two-phase flows through porous media

Effects manifested in two-phase flows through anisotropic porous reservoirs with monoclinic and triclinic characteristics are analyzed. It is shown that in two-phase flows through media with monoclinic and triclinic symmetries of flow characteristics the position of the principal axes of the phase permeability tensors depends on the saturation and does not coincide with the position of the principal axes of the absolute permeability tensor in single-phase flows and that going over from single-to two-phase flow may lead to a change in the symmetry group of the flow characteristics. A general representation of the phase permeability tensor components is presented and formulas are given for the diagonal and nondiagonal components of the relative phase permeabilities, which are universal and can be used for anisotropic media with any type of anisotropy (symmetry) of flow characteristics. A complex of laboratory tests for finding the nondiagonal components of the phase and relative phase permeability tensors is discussed.     

Influence of particles on the drag of bodies in a disperse flow

A study is made of the motion of a disperse medium with a low volume but high mass concentration of very inert particles. It is shown that in the framework of linearization of the equations the motion of such a medium will be irrotational if the oncoming flow is undisturbed at infinity. Simple expressions are proposed for estimating the influence of the particles on the drag of a body of arbitrary shape moving in the medium and also for the determination of the flow velocity by means of a Pitot-Prandtl tube.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 164–167, May–June, 1982.