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A diffusion-inertia model (DIM) for calculating of the monodispersed bubble flows in an isothermal flow in a turbulent liquid has been presented. The comparison of the results of the simulation with various experimental data shows that the DIM adequately describes the variety of physical phenomena occurring in bubble flows. The DIM has been incorporated in a three-dimensional computing code that allows one to use this model for engineering calculations.

A statistical model of clustering (accumulation) of monodispersed particles in homogeneous isotropic turbulence taking into account absolutely elastic collisions has been presented. The effect of collisions on clustering of particles has been analyzed in a wide range of variation of their concentration, inertia, and size.

A nonlinear model of turbulent viscosity (the explicit algebraic Reynolds stress model) for gas-dispersed flow with small heavy particles has been presented. The calculations have been checked by comparison with the experimental data on the effect of the fine-dispersed admixture on turbulent flow of air in a pipe.

A theoretical model is given for describing the inverse effect of small heavy particles on the intensity of turbulence in various flows. Analysis is performed of the effect of particles on isotropic homogeneous shear and wall turbulence.

Comparison with the data of direct numerical calculations in isotropic turbulence with constant temperature gradient is used for verifying the statistical model of heat transfer in gas-dispersed turbulent flows. Analysis is made of the effect of thermal inertia of particles on the correlations between turbulent heat fluxes and intensities of temperature fluctuations in the dispersed and continuous phases.

The effect of clustering of particles under conditions of homogeneous isotropic turbulence on Rayleigh scattering of radiation is analyzed. It is demonstrated that, similarly to the diagnostics of molecular structure of liquid using X-ray scattering, the radial distribution function of macroscopic particles, which characterizes the clustering phenomenon, may be determined by way of measuring the intensity of scattering of infrared or microwave radiation. An approximate relation for clustering coefficient is obtained, which may be employed for estimating the increase in reflected radiation of microwave radar from cumulus clouds owing to turbulent clustering of water drops in the cloud.

The effect of temperature fluctuations on thermal radiation transfer under conditions of isotropic turbulence is analyzed. Simple analytical dependences are given for estimating the fluctuations of radiation intensity and of radiation flux in a plane layer of nonscattering medium. The solution of model problem is given for microwave radiation of cloud layer in the Earth atmosphere.

A statistical model is given for determining the kernel of coagulation in the presence of turbulent, Brownian, gradient, and gravitational mechanisms of collisions in view of accumulation effect.

A statistical model is given for determining the kernel of collisions of small aerosol particles in homogeneous isotropic turbulence in view of Brownian motion. The suggested model is based on the kinetic equation for the probability density function of distribution of relative velocity of two particles. Analysis is performed of the effect of Brownian motion on the relative velocity of two particles (transport effect) and on the radial distribution function (accumulation effect).

A transonic turbulent flow of spontaneously condensing steam in Laval nozzles is treated. Analysis is made of the effect of flow turbulence at the nozzle inlet on steady and unsteady spontaneous condensation.

A statistical model is given for describing the clustering of small heavy particles in homogeneous isotropic turbulence. The suggested model is based on the kinetic equation for the probability density function of distribution of relative velocity of two particles. Analysis is performed of the phenomenon of clustering of low-inertia particles at high values of the Reynolds number.

A statistical model is given for determining the kernel of collisions of inertial particles (droplets, bubbles) in the entire range of variation of the density ratio between the dispersed and continuous phases. The model is based on the assumption that the joint probability density function of velocities of continuous medium and particles is a Gaussian distribution. The ranges of variation of bubble sizes are determined, in which the decisive part is played by the “inertial” and “spatial” collision mechanisms.

A two-point statistical model based on the kinetic equation for the probability density function (PDF) of relative velocity is used to perform analysis of relative dispersion of inertial particles in isotropic turbulence. It is demonstrated that, in the case of highly inertial particles, the Richardson law for dispersion may be valid only in the case of very high values of the Reynolds number.

Two statistical models are given for determining the collision rate of bidisperse particles exhibiting different inertia in a homogeneous isotropic turbulence. One of these models is based on the assumption that the joint probability density function of gas and particle velocities is a Gaussian distribution. The second model follows from the kinetic equation for the probability density of the velocities of two particles. These two models are compared with each other and with data of direct numerical simulation.

A statistical model is given of the formation of ordered structures (clusters) in a homogeneous isotropic turbulent field. The suggested model is based on the kinetic equation for the probability density function of relative velocity of a pair of particles. The solution of the problem is treated for a steady-state rarefied system of dispersed particles in view of pair interaction.

Statistical models are given of the dispersion of inertial particles in inhomogeneous wall turbulence and homogeneous isotropic turbulence. The models are based on the kinetic equations for the one-point and two-point probability density functions of particle velocities. Comparison is made with the data of direct numerical calculations for channel and isotropic flows, known from the literature.

A diffusion-inertia model is suggested for the description of the transport of low-inertia particles of arbitrary density in turbulent flows. Comparison with experimental data is used to demonstrate the validity of the suggested model for the calculation of the motion of bubble in a vertical pipe under different conditions of the effect of the gravity force.

This paper is a continuation of the papers [1, 2] dealing with the development of a three-fluid model of a two-phase medium for the dispersed-annular mode of flow. Calculations and experiments are performed to determine the liquid film thickness and the pressure drop.

Two models are given for determining the collision rate of inertial particles in a homogeneous isotropic turbulence. The advantages and disadvantages of the known models of particle collisions are discussed. One of the models suggested by us is based on the assumption that the joint probability density function of gas and particle velocities is a Gaussian distribution. The second model follows from the kinetic equation for the probability density of the relative velocity of two particles. These two models are compared with each other and with the available data of direct numerical simulation.

A transonic turbulent flow of supercooled steam under conditions of spontaneous condensation is treated. Analysis is made of the effect of flow turbulence at the nozzle inlet on the process of spontaneous condensation.

This paper is a continuation of the paper [1] dealing with the development of a three-fluid model of a two-phase medium for a dispersed-annular mode of flow. The processes of deposition of droplets from the flow core and of entrainment of droplets from liquid film are treated.

A three-fluid one-dimensional model of two-phase medium is suggested which is based on the equations of conservation of mass, momentum, and energy for the gas phase, dispersed phase (droplets), and film. The model includes the equation for the number density of particles of the dispersed phase, which is used to determine the average particle size. The calculation results are compared with the experimental data on the size of droplets in dispersed flow.

A method is suggested for the simulation of the evolution of the size distribution of droplets as a result of simultaneous processes of nucleation (spontaneous condensation), heterogeneous condensation/evaporation, and coagulation. The results of analysis of the effect of initial moisture on spontaneous condensation of steam in transonic nozzles are given.

The problem on the thermal interaction between a hot thermal particle and ambient water is treated. The stability of a growing vapor film to small perturbations of its spherical shape is investigated.

Collisions of aerosol particles caused by their involvement in Brownian and turbulent motion are treated. Analysis is performed of the ratio between the collision and coagulation nuclei depending on the particle size.

The paper deals with the problem on thermal explosion in a two-phase polydisperse combustible mixture. Analysis is performed of the effect of the size distribution of fuel droplets and of radiation heat transfer on the conditions of ignition. The inclusion of the polydispersity of droplets and semitransparency of diesel fuel made possible a serious revision of the known estimates of the importance of thermal radiation.

The paper deals with the boundary conditions for continuous equations of conservation of mass, momentum, and turbulent stresses of the disperse phase in a two-phase flow. The boundary conditions and some assumptions made in deriving them are verified by comparison with the results of numerical solution of the kinetic equation for the probability density function (PDF) of the particle velocity.

An analysis is performed of equilibrium solutions of equations for the second moments of fluctuations of the velocity and temperature of particles in a homogeneous shear flow, in a homogeneous flow subjected to tensile or compressive strain, and in a wall layer. The stability of equilibrium solutions to small perturbations is investigated. Algebraic models are given for turbulent stresses in the dispersed phase.

The limiting laws of turbulent transfer of momentum and heat at high values of the Reynolds number are used to derive wall functions (“wall laws”) under conditions of a flow of gas with variable physical properties along a permeable surface.

High-Rayleigh-number natural-convection heat transfer on inclined surfaces is treated. The analysis of the effect of thermogravitational forces on turbulent transfer of momentum and heat in the wall region is based on the balance equations for the second moments of pulsations of velocity and temperature. Analytical dependences are derived for the coefficient of turbulent thermal conductivity and for the Nusselt number in a wide range of values of the Prandtl number.

The problem on the thermal interaction of a hot spherical particle with ambient water heated to the boiling point is solved. The level of physical parameters is treated that corresponds to the interaction between molten core droplets and cooling water in the case of severe accident in a nuclear reactor. In calculating the heat transfer via the vapor shell, the thermal radiation of the particle is included. An analytical solution in isobaric approximation is derived for the initial stage of interaction. As demonstrated by the results of comparison with a complete numerical solution, the oscillations of vapor pressure and vapor shell thickness do not affect the mean parameters of heat transfer from particle to water. Results are obtained that illustrate the damping effect of thermal radiation of the particle on the oscillation of the particle vapor shell. The possible destruction of a melt droplet under the effect of oscillation of pressure in the vapor shell is estimated, and the value of the droplet size is obtained at which its further destruction is unlikely.

A mathematical model is given for the calculation of binary condensation of H2O/H2SO4 in plumes of jet engines in the presence of chemical transformations, which includes the coagulation of particles along with the processes of nucleation and condensation growth of droplets. The model enables one to derive information about the evolution of the size and composition distribution function of aerosols