Numerical simulation of dilute turbulent gas‐particle flow with turbulence modulation

A numerical study of a dilute turbulent gas‐particle flow with inelastic collisions and turbulence modulation in an Eulerian framework is described. A new interpretation is provided for the interaction/coupling terms, based on a fluctuating energy transfer mechanism. This interpretation provides for a new robust closure model for the interaction terms with the ability to predict the turbulence dampening as well as the turbulence enhancement phenomenon. Further, the model developed herein is investigated along with a variety of other published closure models used for the interaction/coupling terms, particle drag, and solid stress. The models are evaluated against several sets of benchmark experiments for fully‐developed, turbulent gas‐solid flow in a vertical pipe. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.     

The dependence of particle deposition velocity on particle inertia in turbulent pipe flow

Recent measurements of particle deposition velocities on the walls of a pipe in turbulent flow (Liu and Agarwal, 1974) show a decline with increasing particle size beyond a critical particle size. A stochastic model of particle deposition is presented which explains this result. As in other models, the deposition process is composed of turbulent diffusion, together with inertial projection through the boundary layer; in this model, both processes are particle inertia dependent, in opposing ways. The observed decline is due to the increased fractional penetration of the boundary layer with increasing particle size being insufficient to compensate for the reduced rate of transport to that region.

A simple expression is given for the particle deposition velocity in terms of the r.m.s. velocity at that point and the fractional penetration of the boundary layer. The inertial dependence of the particle velocity is expressed in terms of the particle's response to the turbulent velocity fluctuations of its neighbouring fluid by relating the velocity spectral densities of the particle and fluid using a linear dimensionless form of the equation of motion of the particle. The fractional penetration of the boundary layer is based on Stokes' drag with a quiescent fluid.

The deposition profile shows good agreement with the experiments of Liu and Agarwal.     

DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure

The gas and particle motions in a bubbling fluidized bed both with and without chemical reactions are numerically simulated. The solid phase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D Navier-Stokes equations for 2-phase flow with fluid turbulence calculated by large Eddy simulation (LES), in which the effect of particles on subgrid scale gas flow is taken into account. The gas/particle flow structure, the mean velocities and turbulent intensities can be predicted as a function of several operating parameters (particle size, bed temperature, and inlet gas velocity). The lower the inlet gas velocity, the higher the ratio of particle collision. The distributions of the particle anisotropic velocity show that the particles have no local equilibrium, and the distribution of gas kinetic energy corresponds to the distribution of gas-particle coupling moment in the fluidized bed. An intensive particle turbulent region exists near the wall, and the gas Reynolds stress is always much higher than the particle stress. The presence of the large reactive particles in the fluidized bed may affect significantly the gas and particle velocities and turbulent intensities. The effects of the bed temperature and inlet gas velocity on the gas particle flow structure, velocity, and turbulent intensity are also studied.     

A second‐order moment method applied to gas–solid risers

Second‐order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third‐order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third‐order velocity moments and the fluid‐particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A second-order moment three-phase turbulence model for simulating gas-liquid-solid flows

To simulate the bubble, liquid and particle turbulence properties and their interactions in three-phase flows, a second-order moment three-phase turbulence model for gas-liquid-solid flows is proposed. The bubble, liquid and particle Reynolds stress equations, bubble-liquid and liquid-solid two-phase correlation equations are derived using the mass-weighed and time averaging and the closure models of diffusion, dissipation and pressure-strain terms similar to those used in single-phase flows. The two-phase correlation equations are closed with a two-time-scale dissipation term. The proposed model is applied to simulate gas-liquid flows and gas-liquid-solid flows in a channel. The prediction results for two-phase flows are in good agreement with the PIV measurement results. The prediction results for three-phase flows give the gas, liquid and solid velocities, volume fractions and Reynolds stresses, showing that in the case studied the turbulent fluctuation of 5 mm bubbles is stronger than that of liquid, while the turbulent fluctuation of 0.5 mm particles is weaker than that of liquid. Bubbles enhance liquid turbulence, while particles reduce liquid turbulence.     

RANS modeling of a particulate turbulent round jet

A complete and accurate model for the symmetric gas–solid turbulent round jet is accomplished using the Reynolds Averaged Navier–Stokes (RANS) equations. The two-fluid model was used to describe the averaged characteristics of the two phases, including the particle mass concentration, the turbulent kinetic energy and its dissipation in the mixture. Particle–turbulence interaction (turbulence modulation) is described by a two-way coupling model. The drag, lift and gravitation forces are incorporated into the system of equations using appropriate closure equations. A finite difference numerical scheme was used for the solution of the set of the governing equations and the results of the model were validated by comparison with data from several experiments. The influence of two types of particles, namely glass and electrocorundum, of different sizes and different loadings on the velocity and turbulence structure of the jet is examined. The computational results show the influence of the particulate phase on the velocity and turbulence structure of the jet.The significance of this study is that for the first time it presents explicitly the full RANS equations for a fluid jet with particles in an unabridged way and specifies the entire set of closure relations that are used for fluid–particle interactions including the equations for the extended k–ε model, the two-way particle–turbulence interactions and turbulence modulation as well as the inclusion of a lateral Saffman force.     

基于颗粒流运动论的喷动流化床气固流动行为三维模拟

1 INTRODUCTION Spout-fluid beds have been of increasing interest in the petrochemical, chemical and metallurgic indus-tries since spout-fluid beds can reduce some of the limitations of both spouting and fluidization by su-perimposing the two type of systems[1―4]. In recent years, spout-fluid beds have become an alternative for gas/solid contactors in coal gasification. Spout-fluid bed coal gasifiers have been adopted for APFBC-CC (advanced pressurized fluidized bed combus-tion-combined…     

PDF modelling of turbulent non-premixed combustion with detailed chemistry

Although the significant advantage for the probability density function (PDF) methods of the exact treatment of chemical reactions in turbulent combustion problems, a detailed chemistry mechanism (e.g., the GRI mechanism) has not been implemented in the practical calculations by now due to the prohibitive computation of PDF methods. In this work, a detailed mechanism (GRI-Mech 3.0, consisting of 53 species and 325 elemental reactions) is firstly incorporated into the PDF calculation of a turbulent non-premixed jet flame (Sandia Flame D). The flow is formulated in the boundary layer form. The joint composition PDF closure level is applied and a multiple-time-scale (MTS) k-ε turbulence model is combined for the closure of turbulent transport terms. The molecular mixing process is modelled by the Euclidean minimum spanning tree (EMST) mixing model. The solutions are obtained by using the space marching algorithm for turbulence equations and node-based Monte Carlo particle method for PDF evolution equation. The chemical reaction source terms are integrated directly. Extensive comparisons between the predictions and the measurements are made, which involve radial profiles of mean and rms (root mean square), conditional mean, scatter plots of scalars and conditional PDF distribution etc. The flame structures are well represented by the present calculation, including intermediate species (e.g. CO and H₂) mass fractions, pollutant NO emission and local extinction.     

A collision model for fine particles in a turbulent system

A model is proposed to describe the collision rate of small particles suspended in a turbulent system. The model combines the possible collision mechanisms: 1) collisions due to the relative velocity between fluid and particles, and 2) collisions due to the turbulent diffusion of particles. This model also accounts for the effect of particle concentration on the collision rate. It was found that the turbulent diffusion of particles plays an important role in the collision of equally sized particles as well as of unequally sized particles. The model predictions also show that the collision rate of particles is strongly affected by the concentration of solid particles and by the turbulence intensity. Much more reliable predictions than previously possible have been obtained with the present model.     

Computation of wall to suspension heat transfer in vertical pipes

In this article, turbulent gas-solid flow in a vertical pipe is investigated for predicting the heat transfer from the heated wall to the suspension. The Eulerian-Eulerian model is used, incorporating a four-way coupling; i.e., considering inter-particle collisions as well as particle-wall collisions. Both the phases are simulated based on Reynolds averaged Navier-Stokes equations (RANS) with a two-equation k ? ? turbulence model for the gas phase and a granular temperature equation for the solid phase. The closure of the granular temperature (kinetic energy associated with the random motion of the particles) equation is done by the use of kinetic theory of granular flows. The main objective of the study is to investigate the variations of two-phase heat-transfer coefficient and Nusselt number with flow parameters like flow Reynolds number, particulate loading, and particle size. In comparison to single-phase flow, heat transfer is found to be significantly increased with the increase in Reynolds number and particulate loading. This happens because of the presence of the solid particles in a gas flow, which bring changes to the heat-transfer characteristics of the gas phase. Heat transfer increased by adding solid particles for particulate loading in the range of 1 to 20 and particle size in the range of 30 to 50 µm.     

Numerical simulation and validation of dilute turbulent gas-particle flow with inelastic collisions and turbulence modulation

This work describes a theoretical and numerical study of turbulent gas-particle flows in the Eulerian framework. The equations describing the flow are derived employing Favre averaging. The closures required for the equations describing the particulate phase are derived from the kinetic theory of granular flow. The kinetic theory proposed originally is extended to incorporate the effects of the continuous fluid on the particulate phase behavior. Models describing the coupling between the continuous phase kinetic energy and particulate phase granular temperature are derived, discussed, and their effect on the flow predictions is shown.The derived models are validated with benchmark experimental results of a fully developed turbulent gas-solid flow in a vertical pipe. The effect of the models describing the influence of turbulence on the particle motion as well as the turbulence modulation due to the presence of particles is analyzed and discussed.     

Three-dimensional numerical simulation method for gas–solid injector

A three-dimensional turbulent gas–solid two-phase flow model for a gas–solid injector is developed in the present study. Time-averaged conservation equation for mass and momentum and a two-equation k– closure are used to model the carried fluid phase. The solid phase is simulated by using a Lagrangian approach. In this model, the drag and lift forces on particles, the multi-body collisions among particles and the mutual interaction between gas and particles were taken into account. Interparticle interactions and particle–wall collisions are emulated by using the three-dimensional distinct element method (DEM). A new correlation, which represents the transfer of kinetic energy of the particle motion to kinetic energy of the carrier fluid, is introduced in the additional source term S_d of the transport equation of turbulence kinetic energy, K. The calculated pressure distributions along the axis in the different parts of gas–solid injectors using pressured pneumatic conveying system under different driving jet velocities, pressures and values of angle of convergent section () are found to be in agreement with the experimental results. The axial mean velocity of particles and the behavior of gas and particles in the gas–solid injector are calculated, their results reasonably explaining actual phenomenon observed in experiment.     

Segregation and intermixing in polydisperse liquid–solid fluidized beds: A multifluid model validation study

Multifluid model (MFM) simulations have been carried out on liquid–solid fluidized beds (LSFB) consisting of binary and higher-order polydisperse particle mixtures. The role of particle–particle interactions was found to be as crucial as the drag force under laminar and homogenous LSFB flow regimes. The commonly used particle–particle closure models are designed for turbulent and heterogeneous gas–solid flow regimes and thus exhibit limited to no success when implemented for LSFB operating under laminar and homogenous conditions. A need is perceived to carry out direct numerical simulations of liquid–solid flows and extract data from them to develop rational closure terms to account for the physics of LSFB. Finally, a recommendation flow regime map signifying the performance of the MFM has been proposed. This map will act as a potential guideline to identify whether or not the bed expansion characteristics of a given polydisperse LSFB can be correctly simulated using MFM closures tested.     

Collision rate of small particles in a homogeneous and isotropic turbulence

A theoretical equation is derived for the collision rate of aerosol particles in a homogeneous and isotropic turbulent system. This equation takes into account the relative velocity between fluid and particles. The calculated results indicate that the relative velocity between fluid and particles is the main factor in the turbulent coagulation (agglomeration, coalescence) of unequally sized particles in an air flow. This hold true, even when the particle sizes are less than 1 micron. For particles of equal radii the coagulation coefficient reaches its minimum value, because the effect of motion relative to the fluid now becomes zero and only the spatial variation of turbulent motion remains to cause collisions between the particles. For particles following a fluid motion completely, as in a water stream, the equation for the collision rate reduces to the Saffman and Turner equation.     

Eulerian Model for Prediction of Particle Transport and Deposition in Turbulent Duct Flows with Thermophoresis

The Reynolds-averaged equations for turbulent particle population/transport in an Eulerian framework must be closed by specifying models for several terms: a turbophoretic force; a turbulent thermophoretic force; and a turbulent particle-diffusion term. In this article, new models are proposed for the turbophoretic term, as a particle-size dependent extrapolation of the corresponding turbulent fluid-velocity correlation, and for the turbulent thermophoretic term as an eddy-viscosity-scaled multiple of the corresponding mean thermophoretic term, appropriate for small low-inertia particles with τ⁺_p < 10. When the turbophoresis model is incorporated in a system of equations that describes particle motion within the surrounding fluid, it predicts particle deposition velocities that are in good agreement with experimental data over a range of particle sizes. When this equation system is included in a computational model to predict particle transport in turbulent pipe flows, the efficiency of particle deposition in pipes with upstream heating and downstream cooling is found to be in fair agreement with experimental measurements at two different Reynolds numbers, and over a range of particle sizes and temperature differences.

Copyright 2015 American Association for Aerosol Research     

Effects of the variation of mass loading and particle density in gas-solid particle flow in pipes

The method of two dimensional Reynolds Averaged Navier-Stokes (RANS) equations has been employed for the simulation of turbulent particulate flow. This approach was fitted with appropriate closure equations that take into account all the pertinent forces and effects on the solid particles, such as: particle-turbulence interactions; turbulence modulation; particle-particle interactions; particle-wall interactions; gravitation, viscous drag and lift forces. The flow domain in all cases was a cylindrical pipe and the computations were carried for upward pipe flow. The finite volume technique was used for the numerical solution of the governing and closure equations. The results show the effect of loading and particle density on the profiles of the velocity, the turbulence intensity and the solids concentration.