Comparative study of two fluid model and dense discrete phase model for simulations of gas-solid hydrodynamics in circulating fluidized beds

Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and the dense discrete phase model(DDPM)under the Eulerian-Lagrangian framework,this work conducts the comparative study of the gas-solid hydrodynamics in a CFB riser by these two different models.Results show that DDPM could be used to predict gas-solid hydrodynamics in the circulating fluidized bed,and there are differences between TFM and DDPM,especially in the radial distribution profiles of solid phase.Sensitivity analysis results show that the gas-solid drag model exhibits significant effects on the results for both the two models.The specularity coefficient and the restitution coefficient in the TFM,as well as the reflection coefficient and the parcel number in the DDPM,exhibit less impact on the simulated results.

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.

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

The USM-θ model 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-θ model 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-θ model 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-θ model 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.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper.The Jeffrey fluid has two parameters,the relaxation time λ1 and retardation time λ2.The governing equations are simplified using the case of mild stenosis.Perturbation method is used to solve the resulting equations.The effects of non-Newtonian nature of blood on velocity profile,temperature profile,wall shear stress,shearing stress at the stenotsis throat and impedance of the artery are discussed.The results for Newtonian fluid are obtained as special case from this model.

REVIEW ON MATHEMATICAL ANALYSIS OF SOME TWO-PHASE FLOW MODELS

The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.

Fluid Flow Behavior of Liquid in Cylindrical Vessels Stirred by One or Two Air Jets

Based on the two-phase model (Eulerian-Eulerian model), the three dimensional fluid flow in water and that liquid steel systems stirred by one or two multiple gas jets are simulated. In the Eulerian-Eulerian two-phase model, the gas and the liquid phase are considered to be two different continuous fluids interacting with each other through the finite inter-phase areas. The exchange between the phases is represented by source terms in conversation equations. Turbulence is assumed to be a property of the liquid phase. A new turbulence modification - model is introduced to consider the bubbles movement contribution to and . The dispersion of phases due to turbulence is represented by introducing a diffusion term in mass conservation equation. The mathematical simulation agrees well with the experiment results. The study results indicate that the distance of two nozzles has big effect on fluid flow behavior in the vessel. Using two gas injection nozzles at the half radii of one diameter of the bottom generates a much better mixing than with one nozzle under the condition of the same total gas flow rate.

A THREE-FLUID MODEL OF THE SAND-DRIVEN FLOW

The sand-driven flow is studied from the continuum viewpoint in this paper. The crux of this work is how to model the stresses of the particle phase properly. By analysing the two-fluid model which usually, works in solving gas-particle two-phase .flow,. we find that this model has many. deficiencies for studying the sand-driven flow,even for the simplest case- the steady, two-dimensional fully-developed flow.Considering this, we have proposed the three-fluid model in which the upward particles and the downward-particles ore regarded as two kinds of fluids respectively.It is shown that the three-fluid model is better than the two-fluid model in reflecting the internal structure of the flow, region and the influence of the boundary situations on the flow. and it is advantageous to find an approximate solution in that the main components of the particle-phase stresses can be explicitly expressed by those variables in the three-fluid model.In the end, the governing equations as well as the boundary. conditions for the three-fluid model are provided with a discussion.

CFD studies of scraper built in SPA clarifying tank based on mixture solid-liquid two-phase flow model

In the industrial process of producing the strong phosphoric acid(SPA),clarification of the solution is essential to the ultimate product.However,the large viscosity of sediment and the induced interface interaction result in difficulties when the SPA is clarified.CFD numerical methodology was applied to simulate internal flow field and performance of the low speed scraper based on Mixture solidliquid two-phase flow model.Sediment deposition was generated by loading solid particles at the bottom of clarifying vessel.The moving mesh and RNG k-εmodel were used to simulate the rotational turbulent flow in clarifying tank.Variables studied,amongst others,were the scraper rotation speed and the mounting height,which could affect the solid suspension height.Features of flow field and solid volume fraction distribution in computational domain were presented and analyzed.The numerical reports of the scraper torque and velocities of inlet and outlet filed were obtained.It seems the torque value of rotatio-nal axis and particle suspending height augment with an increasing rotating speed.Meanwhile,a high revolving speed is good for the deposition discharge.The particle fraction distribution in meridional surface and horizontal surface at fixed rotation speed were analyzed to determine the corresponding optimal installation height.The simulating results reflect the flow field is marginally stirred by the scraper and proper working parameters are obtained,in which case the comprehensive properties of the scraper and the clarifying tank are superior.

PEMFC船形堵块阴极流场的性能

建立流体体积(VOF)两相流模型,研究船形堵块流道的排水性能。建立不同开孔率的船形堵块流道三维模型,研究船形堵块及开孔率对质子交换膜燃料电池(PEMFC)性能的影响。船形堵块流道峰值净功率密度相较于传统直流道可提升9.4%,相较于同堵塞率下的梯形堵块流道可提高2.9%,具有较好的强化传质作用。通过提高船形堵块流道的开孔率,PEMFC可以获得更好的性能。在相同开孔率下,船形堵块流道的氧气摩尔浓度较直流道和梯形堵块流道分别提高28.6%和14.0%。结果表明,相较于传统直流道,船形堵块流道可降低排水周期和流道内平均水含量,具有更好的排水性能。

基于多孔介质方法的钠冷快堆冷却剂沸腾现象模拟

基于两流体六方程模型针对钠的气液两相分别构建守恒方程,采用蒸发冷凝模型表征两相质量交换,分别使用显式和隐式处理方法对蒸发冷凝模型进行计算,同时考虑了Sobolev阻力模型、两相对流换热模型以及相间动量交换等本构关系,开发了适用于模拟钠冷快堆冷却剂沸腾的多孔介质分析方法,利用KNS-37失流实验L22工况数据进行了对比验证,并利用L29工况流量数据验证模型的适用性。结果表明,所建立的钠沸腾多孔介质分析方法可以较好地模拟钠冷快堆沸腾现象,预测沸腾发生时间在6.3 s左右,与实验相差0.2 s,温度和流量的总体变化趋势与实验数据吻合较好。

带N策略的双阶段休假M/M/1排队系统驱动的流体模型性能分析

基于工厂订单装配系统的运行机制,本文构建并分析了具有N策略和两种混合休假策略的M/M/1排队系统驱动的流体模型。首先对驱动系统进行描述,将马尔可夫过程的无穷小生成元写成块状雅克比矩阵形式。引入库存量建立三维马尔可夫过程,得到稳态下流体排队满足的微分方程组,运用矩阵分析方法和Laplace变换(LT)方法得出系统平稳库存量的数学表达式。进而运用Laplace-Stieltjes变换(LST)导出稳态条件下缓冲器的平均库存量。最后,利用数值分析,给出参数变化对系统性能指标的影响。

基于双流体模型的气力卸船机水平管道气固两相流研究

应用欧拉双流体模型,对水平管道内气力输送过程进行仿真研究。在进行研究前,对欧拉双流体模型进行验证,与其他学者提出的压降预测公式以及试验结果进行对比,具有较好的一致性。对100 t/h气力卸船机的水平气力输送管道进行气-固双流体模拟,研究不同固-气比对压降以及速度的影响,得出管道在不堵料的情况下固-气比存在极大值的结论。

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

基于可压缩两相流模型的注射成型填充模拟

基于现有的超算平台及有限体积法计算程序,开发了一种用于注射成型的三维数值模拟计算模型。该模型数值方法基于可压缩两相流,考虑了熔体和气体的密度变化,即将熔体和空气这两种不同性质的流体,采用同一套控制方程进行计算。采用有限体积法进行离散,通过压力隐式算子分割算法(PISO)求解压力-速度耦合方程组,结合流体体积(VOF)法进行界面追踪。首先模拟了带圆柱嵌件的平板型腔填充过程,采用六面体为主导的方法划分了三种不同网格系统,定量比较三种网格下的速度基本一致,从而验证了网格的收敛性。考虑到计算效率,选取M2(网格数为106876个)网格系统,模拟了温度、剪切速率和压力在不同截面上的分布。结果表明,在填充时间(t)为0.6,0.8,1.4 s时刻下熔体流体前沿的界面追踪模拟与实验吻合;在更复杂的不均匀厚度凹槽平板熔体填充模拟过程中,塑料熔体注入型腔时,会先在薄壁凹槽内流动,随后流进厚壁区域。在t为0.125,0.25,0.375 s时刻下的流动前沿会产生形状像喷泉的流锋,这种流动现象可以通过三维模型预测,与商业软件仿真结果呈现基本一致。随着填充速率的增大,注射压力数值与Moldflow结果更接近。

Physically based modeling and animation of tornado

Realistic modeling and rendering of dynamic tornado scene is recognized as a challenging task for researchers of computer graphics. In this paper a new physically based method for simulating and animating tornado scene is presented. We first propose a Two-Fluid model based on the physical theory of tornado, then we simulate the flow of tornado and its interaction with surrounding objects such as debris, etc. Taking the scattering and absorption of light by the participating media into account, the illumination effects of the tornado scene can be generated realistically. With the support of graphics hardware, various kinds of dynamic tornado scenes can be rendered at interactive rates.

Experimental Determination and Modeling of Bubble Size Distributions in Bubble Columns

Using a five point conductivity technique local values of bubble size,bubble velocity and gas fractionhave been experimentally determined in a 288 mmID and 4.3 m high bubble column as a function of axial andradial position for the air/water and CO2/N2/aqueous MDEA systems.The experimental results are comparedwith predictions from a fundamental two-fluid model.The implementation of a non-steady lateral drag term inthe two-fluid model has been shown.In addition to improving the physical realism of the model,it is found togive slight improvements in the predictions of the distributions of local bubble size.Predictions of bubble size arefound in reasonable agreement with experimental values in the heterogeous flow regime,whereas they are stil1found to be unreliable at low gas velocities.Local void predictions are found in reasonable agreement with experi-mental values,but deviations occur in the homogeneous flow regime towards the wall.This is attributed to defi-ciencies in the simplified bubble size

Numerical simulation of stratified turbulent two-phase flow in aquatic environment

The two fluid model of stratified turbulent two phase flow in aquatic environment is developed in this paper. The motion of each phase is described by a unified multi fluid model in an Eulerian coordinate system. The laws of turbulent transportation for each phase, and the restriction of each other between the two phases are completely simulated. The complex two phase turbulence with strong buoyancy effects is selected to examine numerically. The extensive experimental data obtained in stratified flow are used here. Comparison of the results of numerical simulation with the experimental data is conducted. It has shown that the results of numerical simulation are satisfactory.

基于气−水两相流的注热CO_(2)增产CH_(4)数值模拟研究

注CO_(2)增产煤层气技术(CO_(2)−ECBM)可以降低温室气体排放,具有清洁能源生产和环境保护的功能。为研究气−水两相流条件下,在含水煤层中注CO_(2)增产CH_(4)的排采规律以及不同初始含水饱和度、不同CO_(2)注入条件对CH_(4)产量、CO_(2)储存和储层渗透率的影响,构建了竞争吸附、温度变化、煤体变形以及水运移的流−固−热耦合模型,通过与现场数据、已有试验以及现有模型的数值解结果,对比证明了模型有较高的准确性并对模型的优势做出具体阐述,随后利用COMSOL开展了CO_(2)−ECBM数值模拟。结果表明:注CO_(2)可以提升CH_(4)产气速率和产气量,这表明了注CO_(2)增产的可行性。随着CO_(2)持续注入,储层CH_(4)浓度降低,CO_(2)浓度升高,注气井附近温度升高,生产井附近温度降低且从注气井到生产井的温度缓慢下降;注气抽采期间,水相相对渗透率逐渐减小,气相相对渗透率逐渐增大。由于有效应力、基质收缩/膨胀共同作用,储层渗透率呈现“降低—升高—降低”的趋势;煤层初始含水饱和度越大,CH_(4)产量越低,渗透率下降幅度越小。累计CH_(4)产量最大下降15.19%,忽略煤层中水的影响会高估CH_(4)产量,在进行数值模拟时要考虑煤层水的影响;CO_(2)注入温度与注入压力越大,CH_(4)产量越大,渗透率下降幅度越大。累计CH_(4)产量分别增加13.27%、39.77%,渗透率分别下降20.4%、46.14%,提高CO_(2)注入温度和注入压力有利于提高CH_(4)产量。