The objective of this paper is twofold: (1) to present a statistical model of particle transport and heat transfer in turbulent flows and (2) to examine the performance of this model in various turbulent flows going from a simple flow to a more complicated one. This model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations performed in various turbulent flows.

The objective of the paper is twofold: (i) to present a new statistical model for predicting the transport and dispersion of the particulate phase (particles and bubbles) in turbulent flows and (ii) to examine the performance of this model in channel flow emphasizing the effect of particle accumulation. The model presented is based on a kinetic equation for the probability density function (PDF) of velocity distribution and covers the entire range of the particle-to-fluid density ratio (from heavy particles in a gas to bubbles in a liquid).

The paper deals with collisions resulting from the interaction between particles (droplets, bubbles) and turbulent eddies of the continuous fluid medium (gas or liquid). A statistical model is developed for predicting the collision rate. This model is valid for arbitrary values of the particle-to-fluid density, the particle inertia parameter, and the ratio between the particle size and the fluid turbulent lengthscale.

A coherent scattering of electromagnetic waves by clusters of inertial Rayleigh particles in atmospheric turbulence is considered. A preliminary estimate based on the Maxwell-Garnett theory and the Rayleigh approximation for single clusters demonstrates an importance of the coherent scattering contribution. It is confirmed by a general solution in a combination with theoretical estimates for the two-point probability density function for low-inertia spherical particles in isotropic turbulence. An approximate analytical expression for the coefficient characterizing effect of coherent scattering by the particle clusters is derived. The calculations for small Stokes numbers typical of water droplets in cumulus clouds yield an estimate of the coherent scattering effect on the microwave radar reflection. The model suggested allows solving the inverse problem to determine the pair correlation function for cloud particles. It is expected to be important for the investigations on particle–turbulence interaction in the atmosphere. The theoretical model developed is true not only in the limit of low-inertia particles and can be potentially used at arbitrary Stokes numbers in other applications.

The paper concerns the effects of particle inertia, density, and size on acceleration statistics. A simple analytical model for estimating the acceleration variance of particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of qualitative describing the particle acceleration variance over the entire range of the particle-to-fluid density ratio. Comparisons of model predictions with numerical simulations and experimental data are presented.

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.

The objective of the paper is to advance a code for calculating the behaviour of aerosol-shaped fission products (FP) in the primary circuit of a nuclear reactor. This FP may come into the circuit from the fuel during a severe accident. The paper is focused on development of models for predicting the deposition and coagulation rates of aerosols. Comparisons of model predictions with experimental data and direct numerical simulations are discussed.

The purpose of this paper is twofold: (i) to advance and extend the statistical two-point models of pair dispersion and particle clustering in isotropic turbulence that were previously proposed by Zaichik and Alipchenkov (2003 Phys. Fluids15 1776–87; 2007 Phys. Fluids 19, 113308) and (ii) to present some applications of these models. The models developed are based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. These models predict the pair relative velocity statistics and the preferential accumulation of heavy particles in stationary and decaying homogeneous isotropic turbulent flows. Moreover, the models are applied to predict the effect of particle clustering on turbulent collisions, sedimentation and intensity of microwave radiation as well as to calculate the mean filtered subgrid stress of the particulate phase. Model predictions are compared with direct numerical simulations and experimental measurements.

Two simulation methods, namely Reynolds-Averaged Navier–Stokes (RANS) equations, and Probability Distribution Function (PDF) are currently widely used for the modeling of multiphase flows. These two approaches are supplemented with appropriate closure equations that take into account all the pertinent forces and interaction effects on the solid particles, such as: particle–turbulence interactions; turbulence modulation; particle–particle interactions; particle–wall interactions; gravitation, drag and lift forces. The two methods have been used in order to simulate the turbulent particulate flow in upward pipes. The flow domain in all cases was a cylindrical pipe and the computations were carried for upward pipe flow. Monodisperse as well as polydisperse mixtures of particles have been considered. In general, the average velocity results obtained from the two methods are in close agreement, because the methods predict well the average velocity distribution of the carrier fluid as well as the solids. Thus, the differences in the average axial velocities predicted by the methods are not substantial. Differences in the turbulence intensity are more significant. A comparison of the numerical results obtained shows the relative importance of retaining the diffusion terms in both the axial and radial directions in the RANS method. Also the comparisons of the results show the relative effect of the lift forces in the distribution of solid particles.

The paper is aimed at the application of a model for simulating the dispersed turbulent flows. The model presented proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

The purpose of this paper is twofold: (i) to present statistical models that describe particle–turbulence interactions as well as particle–particle collisions and (ii) to gain a better understanding of the effect of inter-particle collisions on transport, deposition, and preferential concentration of heavy particles in turbulent channel flows. The models presented are based on a kinetic equation for the probability density function of the particle velocity distribution in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations.

The paper concerns the effect of particle inertia on acceleration statistics. A simple analytical model for predicting the acceleration of heavy particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of describing the influence of both Stokes and Reynolds numbers on the particle acceleration variance. Comparisons of model predictions with numerical simulations are presented.

This chapter contains sections titled: The Eulerian and Lagrangian Approaches to the Description of Fluid Flow and Particle Motion Lagrangian Statistical Characteristics of Turbulence Turbulent Diffusion A Semiempirical Model of Turbulent Diffusion Models of Two-phase Disperse Turbulent Flows Deposition of Particles from a Turbulent Flow Interaction of Particles in a Turbulent Flow Chemical Reactions in a Turbulent Flow Concepts of Chemical Kinetics Method of Moments Approximations for Chemical Reaction Rates The PDF Method

This chapter contains sections titled: Kinetic Equations of Coagulation Fundamental Features of the Coagulation of Particles A Model of Turbulent Diffusion Hydrodynamic, Molecular, and Electrostatic Forces Conducting Particles in an Electric Field Coagulation of Particles in a Turbulent Flow Breakup of Particles

A new concept of an in-vessel corium melt catcher is proposed. The lower part of an elongated reactor vessel, which is filled with a sacrificial material of a proper composition, porosity, and arrangement, is used as such a catcher. The concept accounts of the scientific and design experience with the development of the ex-vessel corium catcher for the Tyan’van NPP with VVER-1000 reactors.

The purposes of the paper are threefold: (i) to refine the statistical model of preferential particle concentration in isotropic turbulence that was previously proposed by Zaichik and Alipchenkov [Phys. Fluids 15, 1776 (2003)], (ii) to investigate the effect of clustering of low-inertia particles using the refined model, and (iii) to advance a simple model for predicting the collision rate of aerosol particles. The model developed is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of particle pairs. Improvements in predicting the preferential concentration of low-inertia particles are attained due to refining the description of the turbulent velocity field of the carrier fluid by including a difference between the time scales of the of strain and rotation rate correlations. The refined model results in a better agreement with direct numerical simulations for aerosol particles.