Pulsed discharge of a two-phase medium from a bounded duct capable of longitudinal motion

The regularities of the initial stage of discharge of a two-phase disperse medium from a bounded duct capable of longitudinal motion are established. Numerical results obtained within the framework of a medium with nonequilibrium for velocities and temperatures are compared with analytical solutions of the equilibrium mechanics of disperse systems for the case where the characteristic time of the process is of the order of the characteristic times of velocity and thermal relaxation or smaller. Mozhaiskii Military Space Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 84–91, January–February, 2000.     

Shock-wave-initiated lifting of particles from a cavity

The dynamics of particles of the disperse phase in a turbulent gas flow in planar shock waves sliding along a solid surface with a trapezoid cavity is examined numerically. Lifting of particles from the cavity walls is calculated in the approximation of a rarefied gas suspension. It is shown that the intensity of the transient shock wave and the initial positions of particles have a significant effect on the particle-lifting properties. The height of particle lifting is found to nonmonotonically depend on the initial streamwise coordinate and shock-wave Mach number. It is shown that zones of aggregation and subtraction of particles may be formed at the cavity bottom. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 24–34, January–February, 2007.     

Kinetic equations for a finely dispersed rarefied gas suspension

Starting from the Liouville equation, the kinetic equations for a finely dispersed rarefied gas-particle medium are derived. The size of the suspension particles is assumed to be much less than the free path of the gas molecules, while their density is so small that interaction between the particles can be neglected. It is shown that in general the dynamics of this gas suspension can be described by a system of two kinetic equations, which differ radically from the Boltzmann equations. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 165–171, March–April, 1994.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

Numerical study of initial pulsed motion of a powder layer in a duct under the action of a compressed gas

One-dimensional plane pulsed joint motion of a gas phase and a disperse phase in the presence of friction of the latter against the duct walls are studied numerically using the model of a heterogeneous medium. It is established that two qualitatively different regimes of motion are possible, depending on the initial conditions in a high-pressure chamber and the value of the friction factor. It is found that the powder exit velocity is self-similar with respect to friction. Mozhaiskii Military Space Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 122–127, November–December, 1999.     

Mechanism of coagulation of disperse elements in media isolated from external actions

A physical model of the experimentally observed coagulation (the mutual approach) of spherical liquid, solid, and gaseous disperse elements (of diameter of up to1 cm) in polar liquid and viscoelastic thixotropic matrices when the system is completely isolated from the external forces and the gradient temperature and concentration fields is proposed. It is shown that a weak stress-field gradient is formed in a polar liquid or viscoelastic matrix in the presence of interphase at the matrix-spherical disperse element interface, i.e., when the capillary pressure is negative at the convex boundary of the matrix. If the second disperse particle enters into this field, the resulting force acts on it in the direction of the first particle, thus ensuring their coagulation over large time lapses. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 156–161, July–August, 1999.     

Sediment-discharge vector in a turbulent flow above an eroded bottom

The problem of determination of sediment discharge by a turbulent flow of a fluid above an eroded surface of an arbitrary relief with a finite slope of the bottom is considered. The surface of the bottom separates a stationary granular medium (sand) from a moving two-phase mixture of a fluid and solid particles. The medium is set into motion under the action of shear stress of the fluid. The medium obeys Coulomb's friction law for a granular medium and Prandtl's law of turbulent friction of the fluid. As a result of solving the boundary-value problem for the motion of a two-phase mixture of a fluid and solid particles, a generic formula for sediment discharges is derived. The sediment-discharge vector is expressed through the vector of shear stress on the bottom, the vector of the slope of the bottom, and the distribution function of the solid particles in the bottom layer for an arbitrary relief of the bottom with a finite slope. It is shown that the sediment discharge depends weakly on the detailed distribution of particles in the bottom layer. Conditions of failure of the bottom surface are obtained. The sediment-discharge formula allows one to derive a closed system of equations that determines the process of bottom erosion in the river or channel bed. Institute Problems of Mechanics, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 102–112, March–April, 2000.     

Radial expansion of a granular medium in spherical and cylindrical layers

An exact solution that describes the fields of displacements and stresses in an expanding spherical layer is constructed within the framework of the theory of small strains of a granular medium with rigid particles. For finite strains, the problem reduces to a nonlinear system of ordinary differential equations, which is solved by numerical methods. Similar solutions are found in the problem for a cylindrical layer. Based on these solutions, the effect of the dilatancy of the granular medium on the stress-strain state near expanding cavities is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 190–196, May–June, 2009.     

Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles

The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls.     

Flow of electrically charged aerosols past bodies

An experimental investigation was made of the flow of electrically charged aerosols with solid or liquid disperse phase past bodies. Air flows with solid particles (sand, iron) and water drops were produced by special apparatus. The regimes in which the disperse particles and the bodies were charged or neutral were studied. A system of dimensionless numbers and their values are indicated for the different gas-dynamic and electric flow regimes. The main features of the flows are explained and the integrated electric characteristics of the bodies determined. The possibility of controlling the flow of a disperse medium by means of electric fields is demonstrated. It is shown that the inductive charging of liquid films near sharp edges of a body has a strong influence on the electric characteristics of the body (when air with water drops flows past it).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–79, July–August, 1982.     

Investigation of Two-Fluid Methods for Large Eddy Simulation of Spray Combustion in Gas Turbines

An extension of the large eddy simulation (LES) technique to two-phase reacting flows, required to capture and predict the behavior of industrial burners, is presented. While most efforts reported in the literature to construct LES solvers for two-phase flow focus on Euler–Lagrange formulation, the present work explores a different solution (‘two-fluid’ approach) where an Eulerian formulation is used for the liquid phase and coupled with the LES solver of the gas phase. The equations used for each phase and the coupling terms are presented before describing validation in two simple cases which gather some of the specificities of real combustion chamber: (1) a one-dimensional laminar JP10/air flame and (2) a non-reacting swirled flow where solid particles disperse (Sommerfeld and Qiu, Int. J. Multiphase Flow 19(6):1093–1127, 1993). After these validations, the LES tool is applied to a realistic aircraft combustion chamber to study both a steady flame regime and an ignition sequence by a spark. Results bring new insights into the physics of these complex flames and demonstrate the capabilities of two-fluid LES.     

Vortices,Complex Flows and Inertial Particles

The properties of vortical structures at high Reynolds number in uniform flows and near rigid boundaries are reviewed. New properties are derived by analysing the dynamics of the main flow features and the related integral constraints, including the relations between mean swirl and bulk speed, the relative level of internal fluctuations to bulk properties, and connections between the steadiness and topology of the structures. A crucial property that determines energy dissipation and the transport of inertial particles (with finite fall speed) is the variation across the structure of the ratio of the mean strain rate (Σ) to the mean vorticity (Ω). It is shown how, once such particles are entrained into the vortical regions of a coherent structure, they can be transported over significant distances even as the vortices grow and their internal structure is distorted by internal turbulence, swirling motions and the presence of rigid boundaries. However if the vortex is strongly distorted by a straining motion so that Σ is greater than Ω, the entrained particles are ejected quite rapidly. These mechanisms are consistent with previous studies of entrained and sedimenting particles in disperse two phase flows over flat surfaces, and over bluff obstacles and dunes. They are also tested in more detail here through laboratory observations and measurements of 50–200-μm particles entrained into circular and non-circular vortices moving first into still air and then onto rigid surfaces placed parallel and perpendicular to the direction of motion of the vortices.     

Equations of convective instability of a two-phase medium with modulation of the gravity force

Thermal convection in a heterogeneous medium consisting of a fluid and solid particles is studied under conditions of finite-frequency vibrations. Equations of convection are derived within the framework of the generalized Boussinesq approximation, and the problem of stability of a horizontal layer to infinitesimal perturbations under the condition of vertical vibrations is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 21–28, March–April, 2008.     

Changes of a porous structure in flow of a monodisperse medium

The motion of fluids with suspended particles in porous media is considered. A mathematical model for the interaction of a monodisperse suspension with a porous structure is proposed. Changes in the parameters of the medium and the flow are studied for equilibrium regimes. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 113–121, March–April, 2000.     

Thermo–elasto–plastic stresses in functionally graded materials under consideration of the fabrication process

Summary  The present study analyzes elasto–plastic thermal stresses in some particle-reinforced functionally graded material plates (FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface contains distributed metal particles in a ceramic matrix. We use the thermo–elasto–plastic constitutive equation of a particle-reinforced composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto–plastic thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are considered: the first kind (FGP1) represents distributed ceramic particles in the metal matrix, and the second one (FGP2) represents distributed metal particles in the ceramic matrix. We modify the thermo–elasto–plastic constitutive equation of a particle-reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied. The first one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from the room temperature, and the last one is the heating after cooling from the fabrication temperature. The particle volume fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the finite element method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication temperature on the maximum tensile matrix stress are discussed. Received 22 November 2000; accepted for publication 24 April 2001     

Unsteady radiative-convective heat transfer in a high-temperature gas-particle flow past a semi-transparent plate

Numerical simulations of unsteady radiative-convective heat transfer in a turbulent flow of a mixture of gases and solid particles past a semi-transparent plate are performed. An ablation process is demonstrated to occur on the plate surface in the case of intense radiative heating of the plate by an external source with emission in a limited spectral range. Temperature fields and distributions of heat fluxes in the boundary layer and in the plate are calculated. Calculation results are presented, which allow determining the effect of ablation and reflecting properties of the plate surface on the thermal state of the medium in the system containing the boundary layer and the plate under conditions of plate heating by a high-temperature source of radiation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 140–146, May–June, 2009.     

Functional central limit theorem for flows generated by stochastic equations with interaction

For flows that describe the motion of interacting particles in a random medium, we show the existence of a stationary solution. For this solution, we prove a functional central limit theorem. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 85–97, January–March, 2006.     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

Asymptotic behavior of the conducting properties of high-contrast media

The asymptotic-shielding effect and the asymptotic behavior of the conductivity of a medium containing closely spaced, perfectly conducting inclusions. It is proved that in the presence of asymptotic shielding for pairs of adjacent particles, the original continuous problem can be approximated by a finite-dimensional problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 128–140, May–June, 2005.     

A Stochastic Model for Particulate Suspension Flow in Porous Media

A population balance model for a particulate suspension transport with size exclusion capture of particles by porous rock is derived. The model accounts for particle flux reduction and pore space accessibility due to restriction for large particles to move through smaller pores – a particle is captured by a smaller pore and passes through a larger pore. Analytical solutions are obtained for a uniform pore size medium, and also for a medium with small pore size variation. For both cases, the equations for averaged concentrations significantly differ from the classical deep bed filtration model.