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.     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Numerical simulation of three‐dimensional gas‐solid particle flow in a horizontal pipe

A three‐dimensional model of particulate flows using the Reynolds Averaged Navier‐Stokes method is presented. The governing equations of the gas–solids flow are supplemented with appropriate closure equations to take into account all the relevant forces exerted on the solid particles, such as particle‐turbulence interactions, turbulence modulation, particle–particle interactions, particle–wall interactions, as well as gravitational, viscous drag, and lift forces. A finite volume numerical technique was implemented for the numerical solution of the problem. The method has been validated by comparing its results with the limited number of available experimental data for the velocity and turbulence intensity of the gas–particle flow. The results show that the presence of particles in the flow has a significant effect on all the flow variables. Most notably, the distribution of all the parameters becomes asymmetric, because of the gravitational effect on the particles and particle sedimentation. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

DEM simulation of the particle dynamics in two-dimensional spouted beds

A Discrete Element Method (DEM) is used together with the continuum model of turbulent fluids to simulate the periodic spouting of granular solids in a two-dimensional spouted bed. The bed is contained in a rectangular column of 152 mm width and 15 mm depth with a tapered base. Glass beads with a diameter of 2 mm are used as bed material. Simulations using the DEM together with a low Reynolds number k-ε turbulence model for the fluid phase yield predictions of the unstable spout regime, characterized as a periodic upward-moving particle jet. The simulation results compare well to experimental data obtained using a particle image velocimetry (PIV) technique, including fluid flow fields, time-averaged particle velocity profiles, and spout shape. Finally, DEM predictions for distribution of drag and net force on the particles, particle concentration fields, gas velocity and turbulence field are discussed.     

Predicting turbulence modulations at different Reynolds numbers in dilute-phase turbulent liquid–particle flow simulations

The present work examines the predictive capability of two-fluid CFD model based on the kinetic theory of granular flow in capturing the Reynolds number (Re) dependence of fluid-phase turbulence modulations in dilute-phase turbulent liquid–particle flows. The model predictions are examined using turbulent liquid–particle flow data in a vertical pipe at Re=17,000, 48,000, 65,000, and 76,000 in the particle concentration range of between 0.5% and 4.0% (v/v). The experimental data indicate that the fluid-phase turbulence intensities are enhanced with respect to the single-phase flow at Re≤48,000 but are attenuated at Re≥65,000. The simulation results indicate that the CFD model can successfully predict the turbulence modulations at Re=17,000, 65,000, and 76,000 both qualitatively and quantitatively, but not at the intermediate Re of 48,000. In this regard, (1) different drag correlations to describe the fluctuating drag force are needed to accurately predict the trends in the turbulence modulations as a function of Re, and (2) appropriate combinations of the drag correlations and turbulence closure models to describe the long-range fluid–particle interactions must be identified in each phase at different Re in order to accurately predict the turbulence modulation, granular temperature, and particle radial concentration profile.     

Prediction of the ignition characteristics of flammable jets using intermittency-based turbulence models and a prescribed pdf approach

A mathematical model capable of predicting the ignition hazards presented by turbulent releases of flammable materials is presented. The model is based on solutions of the fluid flow equations, with closure of this equation set achieved using either a k–?–γ turbulence model or an intermittency-based second moment closure. Solutions are coupled to a prescribed, three-part probability density function (pdf) to allow the prediction of the bimodal scalar distributions observed in intermittent free shear flows which can have a significant influence on ignition characteristics. Integration of this pdf over the flammable range of the release material then leads to the probability of ignition at any point in the flow. Predictions of the complete model are compared with data obtained in a number of jets, with comparisons for velocity and concentration fields, intermittency, concentration pdf's and ignition probabilities demonstrating that both turbulence modelling approaches are capable of reliably predicting ignition probabilities in the jet flows examined. Overall, results derived from the second-order modelling approach are superior to k–?–γ turbulence model predictions.     

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.     

DEM simulation of gas-solid flow behaviors in spout-fluid bed

Three-dimensional gas and particle turbulent motions in a rectangular spout-fluid bed were simulated. The particle motion was modeled by discrete element method and the gas motion was modeled by k-ε two-equation turbulent model. Shear induced Saffman lift force, rotation induced Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The gas-solid flow patterns, forces acting on particles, the particles mean velocities, jet penetration depths, gas turbulent intensities and particle turbulent intensities were discussed. Selected stimulation results were compared to some published experimental and simulation results.     

Fluid–particle correlated motion and turbulent energy transfer in a two-dimensional particle-laden shear flow

Discrete vortex simulations of a dilute two-dimensional particle-laden shear layer with one-way coupling were performed to study fluid–particle correlated motion and the transfer of turbulent kinetic energy between the phases. The resulting modification of carrier phase turbulence, estimated according to current computational models, was evaluated. Particle Stokes numbers were between 1.0 and 4.5, so that the particles showed considerable temporal concentration fluctuations due to centrifuging by the fluid flow structures, and the mass loading was 12% corresponding to a volume fraction of 6.0×10^?5.Fluid velocities and particle concentration and velocities and their covariances, which appear in a commonly used model equation for carrier phase turbulence modification, were evaluated. Additionally, the probability density functions of fluid velocity fluctuations viewed by the particles are presented and compared with their Eulerian counterparts. It was found that particles view reduced velocity fluctuations due to preferential clustering. The model for carrier-phase turbulence modification predicted turbulence reduction, depending on the particle Stokes number. The mechanism responsible for turbulence reduction was the correlated velocity fluctuations of fluid and particles and this reduction could reach values up to one third of the fluid flow dissipation. Preferential particle concentration together with a relative velocity between the phases could generate turbulent kinetic energy of the gas phase, however this production was nearly an order of magnitude smaller compared to reduction of turbulence due to the correlated motion. The findings were compared with experiments available in the literature and help to clarify the view when turbulence reduction or augmentation occurs.     

Turbulence model predictions of the radial jet — A comparison of κ-ϵ models

The (κ-?) turbulence closure model has become a widely used means of predicting turbulent fluid flows. In this paper the turbulent radial jet, the round jet and the plane jet are calculated in their similarity regions using various versions of the (κ-?) model to determine which is the most satisfactory for both plane and axisymmetric flows. The most general predictions were obtained using a model which contained additional terms to account for the effect of irrotational strains on the production of turbulence energy. Additionally, detailed mean velocity profiles and turbulence kinetic energy profiles of the radial jet are compared to the available experimental data.     

TURBULENCE CLOSURE MODELING OF TWO-PHASE FLOWS

A second order turbulence closure model is developed for the numerical prediction of isothermal non-reacting, two-phase turbulent shear flows. This model is based on the two-equation (k - ?) model but treats the continuous (gas) phase and (solid) particulate phase as separate interacting continua. The presence of the particles will increase the dissipation rate in the gas phase and additional terms based on the particle size and loading are added to the traditional k and ? equations. The model is tested by making predictions of the spreading rate and velocity decay in the developing region of the two-phase axisymmetric jet. The predictions agree favorably with available experimental data in this region.     

流体-固体两相流的数值模拟

鉴于流体 -固体两相流及其数值模拟在化学工程中愈来愈广泛的应用 ,本文综述了Euler坐标系下流体相湍流模型、颗粒轨道模型以及流体 -颗粒双流体模型的基本原理和数值模拟方法 ;对相间耦合和颗粒间的相互作用也进行了介绍 ,特别是对能详细描述多颗粒间相互作用的颗粒离散单元法在流体 -固体两相流中的应用进行了详细描述 ;在评述各模型的优缺点和分析目前存在的问题的基础上 ,提出了今后的发展方向     

Assessment of large eddy and RANS stirred tank simulations by means of LDA

Large eddy simulations (LES) and Reynolds-averaged Navier-Stokes (RANS) calculations were performed on the flow in a baffled stirred tank, driven by a Rushton turbine at Re=7300. The LES methodology provides detailed flow information as velocity fluctuations are resolved down to the scale of the numerical grid. The Smagorinsky and Voke subgrid-scale models used in the LES were embedded in a numerical lattice-Boltzmann scheme for discretizing the Navier-Stokes equations, and an adaptive force-field technique was used for modeling the geometry. The uniform, cubic computational grid had a size of 240³ grid nodes. The RANS calculations were performed using the computational fluid dynamics code CFX 5.5.1. A transient sliding mesh procedure was applied in combination with the shear-stress-transport (SST) turbulence closure model. The mesh used for the RANS calculation consisted of 241464 nodes and 228096 elements (hexahedrons). Phase-averaged and phase-resolved flow field data, as well as turbulence characteristics, based on the LES and RANS results, are compared both mutually and with a single set of experimental data.     

EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971; Wells and Stock, 1983), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987).     

循环流化床提升管气固湍流的计算流体力学模拟——k-ε-kp-εp-Θ5参数双流体模型

提出了用k -ε-k_p-ε_p-Θ 5参数的双流体模型来模拟循环流化床提升管中的气固湍流 .模型用颗粒动力学理论描述颗粒与颗粒间的碰撞 ,用低Reynolds数湍流方程分别模拟气相和颗粒相的湍动 ,并且考虑了气固两相湍动的相互作用 .模拟所得颗粒速度和浓度的径向分布与实验结果吻合良好 .分析表明 :在时间和空间域上 ,采用颗粒相湍动与颗粒间碰撞分离处理和颗粒相湍能及耗散方程的引入是合理的 ;颗粒相湍动与两相湍动相互作用的封闭条件是影响模拟结果的重要因素 .     

Simulation of low pressure impactor collection efficiency curves

The collection efficiency of the low pressure impactors has been studied using numerical simulations. Flow field was modeled by solving the equations describing the time-average flow field (RANS) with a commercial CFD solver. Particle tracks were calculated separately using Lagrangian methods. Simulation results were verified against published experimental results. Effect of turbulent velocity fluctuations on the impactor resolution was investigated by comparing the ratio of the simulated to experimental impactor resolutions as a function of the turbulence level of the jet. It was found that the turbulence is the dominant mechanism reducing the resolution when the local Reynolds number is over 1800. Effect of jet-to-plate distance on the resolution of the low pressure impactor was studied in the case of low turbulence level. Highest resolution was achieved when the ratio of jet diameter to jet to plate distance (S/W) is 2. When the ratio is lower or higher, resolution is reduced because there is an increase in nonuniformity of the impaction conditions across the jet.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.