Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer(PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes(RANS) model and a large-eddy simulation(LES).The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups(30 μ m,50 μ m,and 95 μ m) and the gas-particle velocity correlation for 30 μ m and 50 μ m particles.From the measurements,theoretical analysis,and simulation,it is found that the two-phase velocity correlation of sudden-expansion flows,like that of jet flows,is less than the gas and particle Reynolds stresses.What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows.The measurements,theoretical analysis,and numerical simulation all lead to the above-stated conclusions.Quantitatively,the results of the LES are better than those of the RANS model.     

Studies on gas turbulence and particle fluctuation in dense gas-particle flows

Particle fluctuation and gas turbulence in dense gas-particle flows are less studied due to complexity of the phenomena. In the present study, simulations of gas turbulent flows passing over a single particle are carried out first by using RANS modeling with a Reynolds stress equation turbulence model and sufficiently fine grids, and then by using LES. The turbulence enhancement by the particle wake effect is studied under various particle sizes and relative gas velocities, and the turbulence enhancement is found proportional to the particle diameter and the square of velocity. Based on the above results, a turbulence enhancement model for the particle-wake effect is proposed and is incorporated as a sub-model into a comprehensive two-phase flow model, which is then used to simulate dilute gas-particle flows in a horizontal channel. The simulation results show that the predicted gas turbulence by using the present model accounting for the particle wake effect is obviously in better agreement with the experimental results than the prediction given by the model not accounting for the wake effect. Finally, the proposed model is incorporated into another two-phase flow model to simulate dense gasparticle flows in a downer. The results show that the particle wake effect not only enhances the gas turbulence, but also amplifies the particle fluctuation.     

分级进风燃烧室内含颗粒的湍流反应流的实验研究

应用三维激光粒子动态分析仪(PDA)，对分级进风燃烧室内含颗粒的湍流反应流的气 固两相瞬时速度场进行了实验测量，同时对单相湍流反应流的瞬时速度场也进行了实验测 量. 得到了两种情况下燃烧室内气固两相和单相气体的平均轴向与切向速度、轴向与切向脉 动速度均方根值和轴向-切向脉动速度二阶关联量的分布.     

气固两相流动的湍流脉动扩散数学模型及其应用

本文提出了气固两相流动的湍流扩展数学模型，本模型用k-ε双方程模型求解气相湍流场，并根据气流脉动的频谱、能谱曲线提出了随机富工级数来模拟气相脉动速度，用拉氏方法描述颗粒的运动，故称为脉动频谱随机颗粒轨道模型。本文还给出了本模型在气固多相射流和流化床内应用的实例。     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

On basic equations of turbulent swirling gas-solid flows and their application in cyclones

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model. These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.     

强旋湍流气粒两相流动的PDPA研究

采用相多普勒颗粒分析仪（ＰＤＰＡ）对切向进气，轴向缩口出口的旋风筒内强旋单相和气粒两相流动进行了实验研究，给出了强旋流场中，两相湍流的运动及相互作用规律     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

基于五阶WENO格式的燃气在药床中流动过程二维两相流研究

为研究内弹道初始阶段中心点火管燃气在膛内药床中的流动特性和传播规律,设计了可视化点传火实验平台,并进行了膛内假药床的点传火实验。基于加权本质无震荡(weighted essentially non-oscillatory, WENO)格式,构造了膛内轴对称二维内弹道两相流模型,对膛内燃气在假药床中的流动过程进行数值模拟。计算结果与可视化实验结果符合较好,全局压力平均误差为5.35%。表明数值计算准确地描述了燃气流动特性,完整地呈现了点火管燃气在假药床中的发展过程。在点火初始阶段,膛内压力径向效应明显,气相沿径向传播较快,药床药粒基本不会发生运动;随着燃气逐渐在膛内传播,膛内压力呈现径向一致、轴向梯度分布的特征,在压力梯度作用下,气相轴向速度开始占据主导,径向速度在膛底和中部区域减小为零,而固相速度随气相速度变化而变化;气相在到达弹底前,由于固相颗粒的壅塞,会提前出现速度反向波动现象。     

Turbulent flow structure and bubble distribution in an axisymmetric nonisothermal impinging gas-liquid jet

The flow structure of a bubbly impinging jet in the presence of heat transfer between the two-phase flow and the surface is numerically investigated on the basis of the Eulerian approach. The model uses the system of Reynolds-averaged Navier–Stokes equations in the axisymmetric approximation written with account for the inverse effect of the bubbles on the average and fluctuating flow parameters. The influence of the gas volumetric flow rate ratio and the dimensions of the bubbles on the flow structure in a gas-liquid impinging jet is studied, In the presence of gas bubbles the liquid velocity is higher than the corresponding value in the single-phase flow. A considerable, more than twofold, anisotropy between the axial and radial turbulent fluctuations in the gas-liquid impinging jet is shown to exist. An addition of air bubbles leads to a considerable growth in the liquid velocity fluctuations in the two-phase flow (up to 50% compared with the single-fluid liquid impinging jet). An increase in the disperse phase dimensions leads to intensification of turbulence of the liquid.     

CFD SIMULATION OF FLUID CATALYTIC CRACKING IN DOWNER REACTORS

A mathematical model has been developed for the simulation of gas-particle flow and fluid catalytic cracking in downer reactors. The model takes into account both cracking reaction and flow behavior through a four-lump reaction kinetics coupled with two-phase turbulent flow. The prediction results show that the relatively large change of gas velocity affects directly the axial distribution of solids velocity and void fraction, which significantly interact with the chemical reaction. Furthermore, model simulations are carried out to determine the effects of such parameters on product yields, as bed diameter, reaction temperature and the ratio of catalyst to oil, which are helpful for optimizing the yields of desired products. The model equations are coded and solved on CFX4.4.     

CFD SIMULATION OF FLUID CATALYTIC CRACKING IN DOWNER REACTORS

A mathematical model has been developed for the simulation of gas-particle flow and fluid catalytic cracking in downer reactors. The model takes into account both cracking reaction and flow behavior through a four-lump reaction kinetics coupled with two-phase turbulent flow. The prediction results show that the relatively large change of gas velocity affects directly the axial distribution of solids velocity and void fraction, which significantly interact with the chemical reaction. Furthermore, model simulations are carried out to determine the effects of such parameters on product yields, as bed diameter, reaction temperature and the ratio of catalyst to oil, which are helpful for optimizing the yields of desired products. The model equations are coded and solved on CFX4.4.     

基于颗粒湍流和颗粒碰撞相互作用规律的湍流模型的研究

颗粒湍流和颗粒碰撞的相互作用规律是两相流动中的核心问题。用颗粒湍流模型和颗粒碰撞的动力论模型叠加的方法在研究两相湍流流动方面取得了一定的成效,但是还有待改进。本文基于颗粒湍流形成大尺度脉动和颗粒间碰撞引起小尺度脉动的概念,从双流体模型出发,建立了两相流动的双尺度kp-pε两相湍流模型。利用该模型对下行床和突扩室内的气固...     

Analysis of erosion behaviour in a turbocharger radial turbine

An analysis of the erosion behaviour of a turbocharger radial turbine is presented. The solution domain includes both sides of the radial turbine scroll with double intake and the rotor channel. In the analysis a dilute gas-particle flow assumption is employed. The gas turbulence is defined by the k-ε model. In solving the gas phase equation, the computer code Harwell-FLOW3D is employed, which is based on a finite volume formulation using non-orthogonal body-fitted structured gridding and a pressure correction method. The particle phase is described by a Lagrangian approach, while particle paths are computed deterministically, neglecting the turbulent dispersion. For the computation of particle trajectories the code PTRACK is employed, which has been developed at ABB. Computations are carried out for several particle size classes. The results show that particles are thrown back into the scroll by the rotor at high rates. This seems to be the main source of erosion effects in the scroll. It has been observed that particles are unequally distributed between the scroll sides on their re-entry, resulting in greater erosion on one of the scroll sides. The maximum erosion along the scroll is found to be likely to occur near the scroll end.     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented.The Saffman lift force acting on a particle in a shear flow istaken into account.It is shown that particle migration across the boundary layer leads tointersections of particle trajectories.The corresponding modification of dusty gas model isproposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at aconstant speed are obtained by using the method of matched asymptotic expansions.Themethod of the calculation of particle phase parameters in Lagrangian coordinates isdescribed in detail.Some numerical results for the case of small particle concentration aregiven.     

强旋湍流气－固两相流动的颗粒随机轨道法模拟

应用颗粒随机轨道模型，并与一种新的代数Ｒｅｙｎｏｌｄｓ应力模型相结合，对新型煤粉涡旋燃烧炉内强旋湍流气。固两相流动进行了数值模拟。得到了与实验相符合的颗粒相密度分布和质量流分布。计算结果表明，在涡旋燃烧炉内的强旋湍流流场中，外壁附近颗粒浓度最高，颗粒停留时间加长，气－固两相间滑移速度增大。