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The purpose of the study is to present an explicit self-consistent algebraic Reynolds stress model (ARSM) for two-phase turbulent flows combined with diffusion-inertia model (DIM). The modulation of turbulence by small heavy particles whose diameter is not greater than the Kolmogorov length scale is considered. The volume concentration of dispersed phase is assumed to be sufficiently small so that inter-particle collisions can be neglected; however, the mass concentration is fairly large ( ρ p ≫ ρ f ). Calculations were performed for turbulent flow in a vertical tube and turbulent flow past a backward-facing step. It was shown that the suggested turbulence model correctly predicts anisotropy of velocity fluctuations and the turbulence modulation by particles. In the presence of small particles turbulence of the flow in a vertical tube is attenuated. The level of turbulence attenuation is increased with increasing particles mass loading and decreased with increasing particle response time. In turbulent flow past the backward-facing step regions with attenuating and enhancing turbulence are observed.

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 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.

The objective of the paper is twofold: (i) to present a model (the so-called diffusion-inertia model) for predicting dispersion and deposition of aerosol particles in two-phase turbulent flows and (ii) to examine the performance of this model as applied to the flows in straight ducts and circular bends. The model predictions compare reasonable well with both experimental data and Lagrangian tracking simulations coupled with fluid DNS or LES.

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 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.

The objective of the paper is to analyse the effects of flow turbulence and inlet moisture on the process of spontaneous condensation of supercooled steam. Calculations of steady and unsteady spontaneously condensing transonic turbulent flows in Laval nozzles are presented. Comparisons of model predictions with experimental data are discussed.

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The objective of the paper is to present a statistical model for predicting collision rates of inertial particles immersed in turbulent flow. This model is valid over the entire range of particle inertia (from the zero-inertia to the high-inertia limit) and accounts for two mechanisms influencing the collision rate, namely, the particle relative motion induced by turbulence and the accumulation effect that leads to an additional enhancement to the collision rate. The model is applicable to near-homogeneous two-phase turbulent flows with colliding or coalescing particles.

The effects of particle inertia and particle-to-fluid density on the time scales that measure the dispersion of particles by isotropic turbulence are investigated. Numerical calculations are performed by means of a kinematic simulation method coupled with Lagrangian tracking of discrete particles. Moreover, a simple semi-empirical model for predicting the time scales of the fluid velocity seen by a particle as well as of the fluid–particle velocity covariance and the particle velocity variance is proposed. Comparisons between simulations and model predictions are presented.

The objective of the paper is to present a statistical approach to modelling dispersion and preferential concentration of inertial particles suspended in the turbulent fluid. This approach departs from kinetic equations for the one-point and two-point probability density functions of particle velocity distributions in turbulent Gaussian fluid flow fields. Preferential concentration of particles in sheared as well as in isotropic turbulent flows is analysed from a unified viewpoint, and an analogy between both phenomena is discussed.

A three-fluid model of the dispersed-annular regime of two-phase flow is suggested. The model is based on the conservation equations of mass, momentum, and energy for the gas phase, the dispersed phase (droplets), and the film. Additionally, this model includes the equation for the number density of particles of the dispersed phase, which is used to determine the mean particle size. Calculations are compared with experimental data on the entrainment coefficient, film and droplet flow rates, film thickness, pressure drop, and droplet size.

As intermediate quantities available from various existing numerical computations, the fluid Lagrangian time scales are of primary importance in the development of probability density function models for turbulent flows. Similarly, the time scales of the fluid seen by discrete particles in two-phase flows are essential for the development of dispersion models based on stochastic differential equations. Such time scales are obviously depending not only on the particle properties but also on the fluid Lagrangian and Eulerian time scales. A model is proposed here to estimate the directional dependence of the fluid Lagrangian time scales and drift coefficients in one-directional equilibrium turbulent shear flows, based on a local homogeneity assumption in the frame of the generalized Langevin model. Through comparison with available direct and large eddy simulation predictions in channel flows and in a homogeneous shear flow, the model is shown to lead to significant improvements in the streamwise and spanwis...

The purposes of the paper are twofold: (i) to present a rational approach to the modeling of inertial particle transport in anisotropic turbulent flows and (ii) to show how the anisotropy of fluid turbulence timescales affects the particle fluctuating velocities in homogeneous shear flow. For these purposes, the directional dependence of the Lagrangian autocorrelations of fluid velocities is incorporated into the statistical probability density function (PDF) model proposed previously. The anisotropic timescale (ATS) model is evaluated against numerical simulations for homogeneous shear turbulent flows and is compared to results predicted by the isotropic timescale (ITS) model. The new ATS model for the PDF of the particle velocity distribution in turbulent flow appears to yield slightly improved results over the ITS model.

The objective of the paper is to present a statistical model for predicting transport and deposition of high-inertia colliding particles in two-phase turbulent flows. This model is based on a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a turbulent flow field. The model developed is applied to the simulation of fluctuating particle motion and deposition in vertical pipe flow.

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.

This paper presents two statistical models for predicting collision rates of bidisperse heavy particles suspended in homogeneous isotropic turbulence. One of the models is based on the assumption that the joint fluid-particle velocity distribution function is Gaussian. The other model stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles. The validity of these models is tested against DNS data by Zhou, Wexler, and Wang [J. Fluid Mech. 433, 77 (2001)]. Comparisons between the model predictions and DNS results demonstrate encouraging agreement.

The objective of the paper is to present a statistical model for predicting pair dispersion and preferential concentration of particles suspended in an isotropic homogeneous turbulent flow field. This model is based on a kinetic equation for the probability density function of the relative velocities of two particles. The model developed is applied to predict the pair relative velocity statistics and the accumulation effect of heavy particles in a steady-state suspension. The effect of particle inertia on the predicted Eulerian two-point particle velocity correlations is demonstrated and compared with known results of numerical simulation.

The objective of the paper is to present and compare two models for the collision rate of inertial particles immersed in homogeneous isotropic turbulence. The merits and demerits of several known collision models are discussed. One of the models proposed in the paper is based on the assumption that the velocities of the fluid and a particle obey a correlated Gaussian distribution. The other model stems from a kinetic equation for the probability density function of the relative velocity distribution of two particles. The predictions obtained by means of these two models are compared with numerical simulations published in the literature.