Dilute Two-phase Flow Research Articles

Agent for treating raw coal

Modeling particle dispersion in turbulent flows is very complex. Several publications in this field have dealt with both the experimental and modeling aspects of turbulent particle dispersion. This paper gives a broad overview of different modeling techniques discussed in the literature in order to describe the problem of particle dispersion in dilute flows. Unlike other reviews of this subject, this paper maintains a simple approach in explaining mathematically and conceptually the complex issues involved in modeling. Some fundamental concepts, such as key characteristics of turbulent flow and the nature of interaction between turbulence and an individual particle under simplified conditions, are discussed. The authors have attempted to present several definitions (such as homogeneous flow, stationary condition, and integral time scale) that are commonly used to imply certain assumptions or as conceptual tools to derive a model. As indicated, a review of models that are capable of predicting the dispersion of dilute concentration of particles in turbulent flows is presented. The models are described in a simplistic way through use of previously explained ideas and concepts. One of the important practical applications of such dilute two-phase flow models deals with the problem of pulverized-coal combustion. The final part of the paper discusses some of the key issues involved in comprehensive pulverized-coal combustion models. The primary objective of this work is to provide a basic understanding of the subject and hence to serve as an introduction to the theoretical world of turbulent particle dispersion.

PIV Technique for the Simultaneous Measurement of Dilute Two-Phase Flows

A Particle Image Velocimetry (PIV) image processing technique has been developed which can be applied to solid-liquid two-phase turbulent flows. The main principle of the technique is to utilize a two-dimensional median filter to generate separate images of the two phases, thus eliminating the errors induced by the distinct motion of the dispersed component. The accuracy and validity of the technique have been studied in the present research for different filter widths, f, and for 4 groups of different sized dispersed particles ranging from an effective image diameter of dp=2.9 pixels to 13 pixels in combination with tracer particles with an effective image size of dt∼2.4 pixels. The results have shown that the errors introduced by the filter are negligible, and mainly arise in regions of large velocity gradients that are sensitive to the slight loss of information incurred by the processing. The filter width f also affects the algorithm’s ability to correctly separate and identify the dispersed phase particles from the two-phase images, with the main result that above a critical particle image size ratio, dp/dt≈3.0, the particle size had no significant influence on the number of particles identified, or the accuracy of the displacement calculation. Sample results of particle-fluid interaction and cross-correlation terms which can be obtained from the method are also presented. [S0098-2202(00)01104-4]

Temperature decay in two-phase turbulent flows

Direct numerical simulations of dilute two-phase flows are conducted to study the decay of the fluid and particle temperatures in isotropic turbulence. Both one-way and two-way coupling between phases are considered. The effects of the particle response time ( τ p), the Prandtl number ( Pr), the ratio of specific heats ( α), and the mass loading ratio ( φ m ) on the carrier fluid and particle temperature statistics are studied. The results indicate that the variance of the fluid and particle temperatures, the dissipation rate of the fluid temperature and the high wavenumber values of the fluid temperature spectrum are increased as the magnitudes of φ m and/or αPr increase. The decay rate of the fluid and particle temperature variances are similar when the values of αPr are small. For large αPr values, the variance of the particle temperature is higher than that of the fluid and is strongly dependent on the initial conditions. The Lagrangian auto-correlation coefficient of the particle temperature ( R p T ) also behaves differently for different magnitudes of α and Pr. For small values of α, R p T decreases as the magnitude of particle response time increases. For large values of α, R p T increases with increasing τ p.

A k-.EPSILON. Model for Dispersed Dilute Two-Phase Flows Using a Statistical Theory.

A statistical theory is applied to the modelling of turbulent correlations for dispersed dilute two-phase flows. And a k-e model for the two-phase flows is derived. The experimental data of two-phase turbulent flows of air and solid particles in a round jet is used to validate the proposed model. The predictions of the profiles of mean velocities of both phases and the turbulent shear stress of the gas-phase show good agreement with the experimental data.

Modeling of Axisymmetric Two-phase Dilute Flows

This paper deals with the numerical treatment of Eulerian approach for dilute two-phase compressible flows (gas-particles mixtures) in axisymmetric configurations. For dilute flows, two classes of models depending on the dispersed phase volumetric fraction can be found. The volume occupied by the particles may be considered, that yields a model in which the gas phase and the dispersed phase equations are coupled through the void fraction and the source terms (Delhaye model). The void fraction effects can be neglected, that means the gas phase is a carrier phase for the particles (Ishii model). The mathematical nature of the two models is demonstrated from analysis of characteristic directions. For the Delhaye's model, a centered scheme is used to solve the system of partial differential equations, while an upwind TVD scheme is used for the Ishii's one. Then, it is shown that the problem of symmetry boundary conditions does not depend on the physical approach, as long as the flow remains dilute. However, a classical treatment for symmetry boundary conditions at the geometrical axis leads to large errors. A particular treatment for this boundary is presented: a new class of particles, described by a supplementary system of equations, is required.

Lagrangian predictions of the dispersion of heavy particles in a dilute two-phase flow: on the inertia effect

Lagrangian predictions of the dispersion of heavy particles in a dilute two-phase flow: on the inertia effect

Fundamental aspects of modeling turbulent particle dispersion in dilute flows

Modeling particle dispersion in turbulent flows is very complex. Several publications in this field have dealt with both the experimental and modeling aspects of turbulent particle dispersion. This paper gives a broad overview of different modeling techniques discussed in the literature in order to describe the problem of particle dispersion in dilute flows. Unlike other reviews of this subject, this paper maintains a simple approach in explaining mathematically and conceptually the complex issues involved in modeling. Some fundamental concepts, such as key characteristics of turbulent flow and the nature of interaction between turbulence and an individual particle under simplified conditions, are discussed. The authors have attempted to present several definitions (such as homogeneous flow, stationary condition, and integral time scale) that are commonly used to imply certain assumptions or as conceptual tools to derive a model. As indicated, a review of models that are capable of predicting the dispersion of dilute concentration of particles in turbulent flows is presented. The models are described in a simplistic way through use of previously explained ideas and concepts. One of the important practical applications of such dilute two-phase flow models deals with the problem of pulverized-coal combustion. The final part of the paper discusses some of the key issues involved in comprehensive pulverized-coal combustion models. The primary objective of this work is to provide a basic understanding of the subject and hence to serve as an introduction to the theoretical world of turbulent particle dispersion.

A thermodynamically consistent rate-dependent model for turbulent two-phase flows

The averaged equations of motion including the Clausius-Duhem inequality for multiphase mixtures are considered and the thermodynamics of the mean motion is studied. Based on the averaged entropy inequality, constitutive equations are formulated, and the thermodynamical constraints on material parameters are obtained. The resulting expressions for phasic stresses are anisotropic, rate-dependent and exhibit normal stress effects. It is shown that the present theory contains the recently developed turbulence models for dilute two-phase flows and kinetic models for dense granular flows as special cases. Using these limiting conditions, the material coefficients of the model for a two-phase mixture are evaluated. The special case of simple shear flows of dense two-phase mixtures are studied in details. It is shown that the model predictions are in good agreement with the experimental data for glass beads in water and air.

Effect of Selective Modification of Turbulence on Two-Equation Models for Particle-Laden Turbulent Flows

The effect of selective modification of turbulence by particles on K–ε models for dilute two-phase flows has been evaluated using data from direct numerical simulation of particle-laden isotropic turbulence. Simulation results were obtained using as many as 643 grid points and up to 106 particles. The ratio of the particle time constant to large-eddy turbulence time scale varied from 0.14 to 1.50 and particle mass loadings of 0.0, 0.1, 0.5, and 1.0 were used in the simulations. Simulation results demonstrate that the balance between enstrophy production by turbulent vortex stretching and viscous destruction is disrupted by momentum exchange with the particle cloud. Selective modification of the turbulence by lighter particles results in a significant attenuation of enstrophy production by turbulent vortex stretching. The decrease in enstrophy production causes the model constant Cε2 to increase for large mass loading. Heavy particles are found to act as a sink of enstrophy for all mass loadings used in the simulations. Preferential concentration of lighter particles by turbulence, however, can generate vorticity fluctuations, especially at higher mass loadings. For these cases conventional modeling of the destruction of dissipation by particles term in the ε equation requires that Cε3 be negative.

Turbulence intensity in dilute two-phase flows—3 The particles-turbulence interaction in dilute two-phase flow

We propose a simplified theory for the particles-turbulence interaction in a dilute two-phase flow with particles of arbitrary sizes. The theory takes into account two sources of turbulence in particle-laden flows: (i) the carrier fluid velocity gradients; and (ii) turbulent wakes behind the coarse particles. The theoretical description is based on the modified mixing-length theory and turbulent kinetic energy balance method. The solution of the problem for particle-laden flow does not require any additional quantitative empirical data; only the standard semi-empirical parameters for pure carrier fluid are used. The dimensional analysis of the system of equations is used to reduce to the minimum the number of nondimensional parameters in turbulent particle-laden flows. In the limits of fine and coarse particles the asymptotic expression for turbulence intensity is found. It is shown that in the former case the carrier fluid fluctuations intensity is found. It is shown that in the former case the carrier fluid fluctuations depend only on the value of the total mass content of the admixture; whereas in the latter one they are determined by the total mass content of the admixture, the density ratio of the phase and the aerodynamic properties of the particles. The proposed theory is applied to predict the fluctuations intensity in various types of turbulent particle-laden flows. The results of the calculations are in fairly good agreement with the experimental data.

Turbulence intensity in dilute two-phase flows—1 Effect of particle-size distribution on the turbulence of the carrier fluid

We deal with the effect of particle size and concentration on the intensity of turbulent fluctuations in two-phase flows. An interaction between polydisperse particles and the turbulence of the carrier fluid is considered. The theoretical analysis of that process is based on Prandtl's mixing-length theory, modified to account for the peculiarities of the viscous interaction of small particles and carrier fluid as well as an effect of the admixture inertia. For a particle-laden flow with a bidisperse particle-size distribution, the intensity of turbulent fluctuations of the particles and fluid is determined as a function of the particles sizes and their mass contents. It is shown that at a fixed total mass content of the admixture, the turbulence intensity in polydisperse flow is essentially different from that in monodisperse flow. Some results on the turbulence properties of a turbulent particle-laden jet with a polydisperse admixture are obtained.

Turbulence intensity in dilute two-phase flows—2 Temperature fluctuations in particle-laden dilute flows

We deal with the temperature fluctuations of the carrier fluid and particles in turbulent two-phase flows. The analysis of the temperature fluctuations is based on the modified mixing-length theory, which was used previously to evaluate the intensity of turbulent fluctuations in two-phase polydisperse flows. The dependences of the temperature fluctuations of the interacting phases on the particle sizes, the mass content of the admixture and its composition and physical properties have been predicted. The effect of heat transfer by radiation on the intensity of temperature fluctuations in two-phase flow is estimated.

The effects of particles on the stability of a two-phase wake flow

Analytical and numerical investigations of the effects of particles on the stability of two-phase wake flows are presented. The major simplifying assumptions are that the mean velocity profile of the two-phase flow is identical to that of the single-phase flow and that the fluctuations of the flow field have no effect on the particle initial velocity. The continuous-phase flow is assumed incompressible and inviscid. The resulting modified Rayleigh equation was solved numerically. The results presented are applicable to dilute two-phase flows consisting of solid particles or liquid drops in a gaseous environment. For the two-phase wake flow, it is found that the presence of the particles enhances the stability of the flow. For the absolutely unstable single-phase flow, the particles lower the imaginary part of the branch point and can transfer the flow to the convectively unstable region. For the convectively unstable flow, the particles can lower the most amplified rates in spatial instability.

A thermodynamical formulation for dispersed multiphase turbulent flows—1: Basic theory

Turbulent flows of dispersed multiphase solid-fluid mixtures are considered. From the global equations of balance for each phase and via a special ensemble-averaging technique, the local conservation laws for the mean motions are developed. Particular attentions are given to the averaged form of the Clausius-Duhem inequality and the fluctuation energies of the fluid phase and the particulate constituents. The thermodynamics of the mixture in the turbulent state is studied. The concept of coldness of turbulence for each phase is introduced, the free energy function is discussed and several thermodynamical relationships are established. Based on the averaged entropy inequality, constitutive equations for the stresses, energy and heat fluxes of various species are developed. It is shown that the model contains the recently developed turbulence models for dilute two-phase flows and dense granular flows as special limiting cases.

A unified theory on particle transport in a turbulent dilute two-phase suspension flow—II

A unified theory on particle transport in a turbulent dilute two-phase suspension flow—II