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.

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.

Global Well-Posedness and Large-Time Behavior to the 3D Two-Fluid Model with Degenerate Viscosities

In the paper, we study a compressible two-fluid model in ℝ3, where γ±>1. The pressure of the two fluids is equal. Different from previous research, we consider that viscosity coefficient both μand λare functions of density. The global well-posedness of the three-dimensional compressible two-phase flow model is an open problem due to its dissipative, nonlinear structure. In the paper, setting m±=M±and Z=P−P¯, by exploiting the dissipation structure, we obtain energy estimates for (Z,w,n)and its derivatives, then we obtain the time decay rates for (Z,w,n). So we derive global well-posedness and large time behavior to the three dimensional compressible two-fluid model.

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.

压裂复杂裂缝中支撑剂输送数值模拟研究

在非常规储层水力压裂施工过程中,水力裂缝容易与天然裂缝交汇形成复杂裂缝,支撑剂的运移和铺置形态直接决定了储层的增产效果。为了研究支撑剂在复杂裂缝中的铺置规律,基于欧拉-欧拉方法建立了支撑剂-压裂液两相流数学模型,并利用复杂裂缝室内实验装置与数值模拟的砂堤铺置形态对比的方式进行了模型验证,结果表明,选取的模型可用于研究滑溜水在复杂裂缝内的携带支撑剂的运移铺置规律。以相似准则为基础,建立了简化的复杂裂缝平板模型,并将砂堤形态参数、砂堤面积进行归一化处理,获得了压裂液排量、黏度、支撑剂粒径、裂缝宽度以及裂缝形态对支撑剂在复杂裂缝中铺置的影响规律。结果表明:增大排量、黏度和减小粒径均有利于支撑剂向裂缝深处运移,并且排量对支缝中的砂堤形态影响最明显,但增大排量不利于支撑剂填充近井地带。缝宽的影响体现在壁面效应,在注入时间相同的情况下,当压裂液黏度从1 mPa·s增加到5 mPa·s时,主缝砂堤的归一化长度平均增加了37.9%,归一化高度平均降低了61.4%。裂缝结构越复杂,所有支缝中的支撑剂铺置面积占比越高,分流作用越大。随着复杂裂缝的支缝数量、级数以及支缝延伸长度的增大,支缝中的砂堤高度与长度均有所降低;相对于T1型裂缝,T3和T5型裂缝中的砂堤长度、高度减小最多。

基于启动时间和完全故障的双阶段休假排队系统的流体模型性能分析

基于风力发电路灯的能量转化机制,该文构建并分析了具有启动时间和完全故障策略的M/M/1排队系统驱动的流体模型.首先,对驱动系统进行模型描述,运用矩阵几何解方法得到驱动系统的稳态概率分布.其次,引入流体模型的净输入率结构,并利用概率分析方法得到流体库存水平在稳态条件下的微分差分方程组,进而运用Laplace-Stieltjes transform(LST)方法得到稳态条件下库存量的均值及空库概率.根据性能指标构建系统的费用函数,在数值分析中给出系统参数对性能指标和费用的影响.

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。

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

过滤双流体模型的水平管道内稠油输送数值模拟

针对介观尺度下蜡晶颗粒聚团在管壁形成宏观尺度下石蜡层的现象,采用过滤双流体模型研究水平管道输送伴有固态沥青质的稠油的液固两相流流动和传热特性.对比均匀结构曳力模型和亚格子曳力模型的模拟结果,获得了颗粒相时均体积分数、颗粒相压力和过滤传热系数的修正系数等参数分布规律.同时分析了壁面温度对稠油温度分布和传热的影响.结果表明:与均匀模型Gidaspow model相比,过滤模型能够揭示蜡晶颗粒非均匀流动结构对液固两相流的变化规律.Filtered modelⅡ的结果更加接近于试验结果,Filtered modelⅡ的结果随着蜡晶颗粒体积分数的增加而减小.当蜡晶颗粒相体积分数增加到12%时,加入壁面修正的亚格子模型的误差仅为4.1%.而ZAMBRANO等人模拟结果与试验压降的误差为12.9%.亚格子尺度模型能够详细地再现沥青质颗粒聚团的介观尺度流动行为,为稠油输送过程中的蜡晶聚集以及流动过程的预测提供了新的方法.

欧拉-欧拉双流体模型中颗粒黏性对液固散式流态化的影响

采用无黏性双流体模型、基于颗粒动理学的双流体模型以及Brandani和Zhang简化双流体模型探究了颗粒黏性对液固散式流化特性的影响规律。经与文献中实验数据和Gibilaro公式计算值对比后发现:3种双流体模型均能较好地预测整体固含率,与实验值相对偏差在3%以内,其中无黏性双流体模型和简化双流体模型对固含率预测更符合散式流态化特点;3种双流体模型对时均颗粒轴向速度预测均呈现整体环核结构的固有属性,其中简化双流体模型在较低和较高两组液速工况下预测的相对偏差平均值分别为0.277和1.028;当入口液速突然变化后,收缩过程中简化双流体模型对响应时间预测准确度略高,而膨胀过程中因低浓度区界面不稳定以及膨胀过程中床内颗粒形成的由浓到稀过渡段延长了稳定时间,3种模型预测均与理想过程存在一定偏差,其中液速较低时三者差异不明显,但液速较高时简化双流体模型准确性略高。基于颗粒动理学的双流体模型对动态过程模拟的计算耗时最长。

COSINE两流体八方程子通道程序湍流交混与空泡漂移模型有效性验证

COSINE是我国自主研发的核电厂堆芯与系统安全分析的一体化软件包,其中子通道程序cosSubc-2F采用两流体,三相场(连续液相、液滴相和气相)的建模方法,除了连续液相和液滴相共用一个能量守恒方程外,其余各相均包含质量、动量和能量三个守恒方程,共计八个独立的守恒方程。在子通道程序中,燃料组件被划分为一定数目的平行子通道,这些通道并不是封闭的,它们之间由于压力梯度等因素的影响发生着流体的质量、动量和能量交换。作为通道间相互作用的关键模型,湍流交混与空泡漂移模型对于子通道程序模拟结果的准确性十分重要。文章详细介绍了子通道程序cosSubc-2F中的湍流交混与空泡漂移模型机理,选取一系列实验进行测试,程序中湍流交混与空泡漂移模型有效性得到了充分验证,并通过结果的对比分析,为模型的开发优化提出建议。

变含水量泥流本构及泥流-桥墩冲刷的流固耦合分析

泥石流是山区主要的地质灾害之一,对山区桥梁破坏严重.在流动过程中,泥石流受到含水量的影响较大,其本构模型会发生变化.本文对泥石流的一种特殊形式——泥流的质量含水量进行分析,将含水量引入泥浆的Herschel-Bulkley模型中,提出质量含水量及剪切速率同时变化下的泥流材料本构模型,并与成都黏土泥浆流变实验对比,验证该模型的正确性.而后基于两相流体的Navier-Stokes方程,将该本构模型应用于三维泥流-桥墩立柱冲击的流固耦合分析中,通过与相关规范及文献冲击压力经验公式计算结果对比,证实了模型的实用性.

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。

Two-fluid modeling of Geldart A particles in gas-fluidized beds

We have investigated the effect of cohesion and drag models on the bed hydrodynamics of Geldart A particles based on the two-fluid （TF） model. For a high gas velocity U0 = 0.03 m/s, we found a transition from the homogeneous fluidization to bubbling fluidization with an increase of the coefficient C1, which is used to account for the contribution of cohesion to the excess compressibility. Thus cohesion can play a role in the bed expansion of Geldart A particles. Apart from cohesion, we have also investigated the influence of the drag models. When using the Wen and Yu drag correlation with an exponent n = 4.65, we find an under-prediction of the bed expansion at low gas velocities （U0 = 0.009 m/s）. When using a larger exponent （n = 9.6）, as reported in experimental studies of gas-fluidization, a much better agreement with the experimental bed expansion is obtained. These findings suggest that at low gas velocity, a scale-down of the commonly used drag model is required. On the other hand, a scale-up of the commonly used drag model is necessary at high gas velocity （U0 = 0.2 and 0.06 m/s）. We therefore conclude that scaling the drag force represent only an ad hoc way of repairing the deficiencies of the TF model, and that a far more detailed study is required into the origin of the failure of the TF model for simulating fluidized beds of fine powders.