A dual-scale turbulence model for gas-liquid bubbly flows☆

A dual-scale turbulence model is applied to simulate cocurrent upward gas–liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubble-induced turbulence. Single-phase standard k-εmodel is used to compute shear-induced turbulence and another transport equation is added to model bubble-induced turbulence. In the latter transport equation, energy loss due to interface drag is the production term, and the characteristic length of bubble-induced turbulence, simply the bubble diameter in this work, is introduced to model the dissipation term. The simulated results agree well with experimental data of the test cases and it is demonstrated that the proposed dual-scale turbulence model outperforms other models. Analysis of the predicted turbulence shows that the main part of turbulent kinetic en-ergy is the bubble-induced one while the shear-induced turbulent viscosity predominates within turbulent vis-cosity, especially at the pipe center. The underlying reason is the apparently different scales for the two kinds of turbulence production mechanisms:the shear-induced turbulence is on the scale of the whole pipe while the bubble-induced turbulence is on the scale of bubble diameter. Therefore, the model reflects the multi-scale phe-nomenon involved in gas–liquid bubbly flows.     

颗粒尾涡增强湍流的大涡模拟以及气固两相流中湍流变动的数值模拟

The turbulence enhancement by particle wake effect is studied by large eddy simulation （LES） of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present-authors based on the LES resuits. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results.     

基于离散颗粒法模拟搅拌釜气含率分布

The discrete particle method was used to simulate the distribution of gas holdup in a gas-liquid standard Rushton stirred tank. The gas phase was treated as a large number of bubbles and their trajectories were tracked with the results of motion equations. The two-way approach was performed to couple the interphase momentum exchange. The turbulent dispersion of bubbles with a size distribution was modeled using a stochastic tracking model, and the added mass force was involved to account for the effect of bubble acceleration on the surrounding fluid. The predicted gas holdup distribution showed that this method could give reasonable prediction comparable to the reported experimental data when the effect of turbulence was took into account in modification for drag coefficient.     

用相指示器函数方法(分散元概率密度函数)推导及验证湍流稀两相流动的欧拉-欧拉模型

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent flows.Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows.It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced.An extension of the standard k-c turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.     

液固两相流中磨蚀-腐蚀的数值模拟

Erosion-corrosion of liquid-solid two-phase flow occurring in a pipe with sudden expansion in cross-section is numerically simulated in this paper. The global model for erosion-corrosion process includes three main components: the liquid-solid two-phase flow model, erosion model and corrosion model. The Eulerian-Lagrangian approach is used to simulate liquid-solid two-phase flow, while the stochastic trajectory model was adopted to obtain properties of particle phase. Two-way coupling effect between the fluid and the particle phase is considered in the model. The accuracy of the models is tested by the data in the reference. The comparison shows that the model is basically correct and feasible.     

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors (I) Turbulent Gas-Solid Flow-Reaction Model

Gas-solid two-phase turbulent flows, mass transfer, heat transfer and catalytic cracking reactions are known to exert interrelated influences in commercial fluid catalytic cracking(FCC) riser reactors.In the present paper, a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was developed. The model took into account the gas- solid two-phase turbulent flows, inter-phase heat transfer, mass transfer, catalytic cracking reactions and their nterrelated influence. The k-V-kp two-phase turbulence model was employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration. Boundary conditions for the flow-reaction model were given. Related numerical algorithm was formed and a numerical code was drawn up. Numerical modeling for commercial FCC riser reactors could be carried out with the presented model.     

鼓泡床内气液两相流动的二阶矩模型与代数应力模型的模拟比较

A full second-order moment(FSM) model and an algebraic stress (ASM) two-phase turbulence model are proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column.Predication gives the bubble and liquid velocities,bubble volume fraction,bubble and liquid Reynolds stresses and bubble-liquid velocity correlation.For predicted two-phase velocities and bubble volume fraction the is only silight difference between these two models,and the simulation results using both two models are in good agreement with the particle image velocimetry(PIV) measurements.Although the predicted two-phase Reynolds stresses using the FSM are in somewhat better agreement with the PIV measurements than those predicted using the ASM,the Reynolds stresses predicted using both two models are in general agreement with the experiments.Therefore,it is suggested to use the ASM two-phase turbulence model in engineering application for saving the computation time.     

用扩散流动模型分析悬浮床内的气固两相向上流动

A mathematical model of two-dimensional turbulent gas-particle two-phase flow based on the modified diffusion flux model (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux model, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by κ-ε-κp two-fluid model, which shows a reasonable agreement. It is confirmed that the modified diffusion flux model is suitable for simulating the multi-dimensional gas-particle two-phase flow.     

运用粒子图像测速仪研究双层Rushton桨搅拌槽内湍流特性

Particle Image Velocimetry （PIV） has been used to investigate turbulence characteristics in a 0.48 m diameter stirred vessel filled to a liquid height （ H = 1.4T ） of 0.67 m. The agitator had dual Rushton impellers of 0.19 m diameter （ D = 0.4T ）. The developed flow patterns depend on the clearance of the lower impeller above the base of the vessel, the spacing between the two impellers, and the submergence of the upper impeller below the liq- uid surface. Their combinations can generate three basic flow patterns, named, parallel, merging and diverging flows. The results of velocity measurement show that the flow characteristics in the impeller jet flow region changes very little for different positions. Average velocity, trailing vortices and shear strain rate distributions for three flow patterns were measured by using PIV technique. The characteristics of trailing vortex and its trajectory were described in detail for those three flow patterns.
Since the space-resolution of PIV can only reach the sub-grid rather than the Kolmogorov scale, a large-eddy PIV analysis has been used to estimate the distribution of the turbulent kinetic energy dissipation. Comparison of the distributions of turbulent kinetic energy and dissipation rate in merging flow shows that the highest turbulent kinetic energy and dissipation are both located in the vortex regions, but the maxima are at somewhat different lo- cations behind the blade. About 37% of the total energy is dissipated in dual impeller jet flow regions. The obtained distribution of shear strain rate for merging flow is similar to that of turbulence dissipation, with the shear strain rate around the trailing vortices much higher than in other areas.     

CFB中环核结构的模拟

In this paper, the stochastic particle-trajectory model is proposed for simulating the dynamic behavior of circulating fluidized bed (CFB). In our model, the motion of solid phase is obtained by calculating the individual particle trajectory while gas flow is obtained by solving the Navier-Stokes Equation including two-phase interaction. For the calculation of solid phase, the motion of each particle is decomposed into a collision process and a suspension process. In suspension process, the less important and/or unclear forces are described as a random force considering gravity, drag force and pressure gradient. As a result, the proposed model gives some numerical simulations of CFB. It indicates that the stochastic particle-trajectory model can be used to simulate qualitatively the annulus-core structure of CFB and the influences of stochastic factors cannot be ignored. In a CFB, the coupling of stochastic factors between two phases makes the radial voidage decreased. Moreover, the upward motion of particles is mitigated by both stochastic factors and turbulence between two phases.     

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.     

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.     

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 .     

鼓泡床内气泡-液体两相湍流代数应力模型的数值模拟

现有的气泡 -液体两相流动的数值模拟中 ,或者不考虑湍流 ,或者仅仅考虑液体湍流 ,但是直接模拟和PIV测量结果都表明气泡由于尾迹的作用有强烈的湍流脉动 .本文首次推导和封闭了同时模拟气泡湍流脉动和液体湍流脉动的二阶矩输运方程两相湍流模型 ,并在此基础上建立了代数应力气泡 -液体两相湍流模型 .用代数应力模型模拟了二维矩形断面鼓泡床内气泡 -液体两相流动 .预报结果给出了气泡和液体两相速度场、两相Reynolds应力及湍动能分布和气泡体积分数分布 .模拟结果与PIV测量结果符合很好 ,表明了模型的合理性 .研究结果表明 ,原先静止的液体在气泡因浮力而产生的上升运动的作用下产生回流流动 ,而气泡则只有上升运动 .气泡速度始终大于液体速度 .在床内气泡湍流脉动确实始终很强烈 .液体则由于气泡的作用以及自身速度梯度产生的双重作用而发生湍流脉动 .气泡的脉动显著地大于液体的脉动 .两相湍流脉动都是各向异性的 ,而且气泡湍流脉动的各向异性比液体的更强烈     

On the second-order moment turbulence model for simulating a bubble column

Two versions of the second-order moment two-phase turbulence model are proposed in this study for simulating bubble-liquid two-phase turbulent velocity fluctuations and their interactions in bubble-liquid flows under the dispersed bubble regime. One of them is a full transport equation model; the other is an algebraic stresses model. The proposed model is used to simulate liquid and gas mean velocities, gas volume fraction, liquid and gas Reynolds stresses and turbulent kinetic energy in a 2-D bubble column. Furthermore, the bubble and liquid velocities, Reynolds stresses and gas volume fraction are measured using the PIV. The simulation results are in good agreement with the PIV results and experimental data in the literature. The studies reveal the liquid recirculation and bubble up-rising flow patterns, and anisotropic liquid and bubble normal Reynolds stresses. Bubble fluctuation is observed to be stronger than liquid fluctuation. Moreover, both the liquid velocity gradient and bubble-liquid interaction are important for the generation of liquid turbulence.     

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.     

双尺度二阶矩两相湍流模型和水平槽道内两相流动的数值模拟

对有颗粒碰撞的两相流动,常常采用将颗粒湍流模型和反映颗粒碰撞作用的动力学模型叠加的方法来构造稠密两相流动的二阶矩湍流模型,在理论上不协调.基于将颗粒脉动分成湍流引起的大尺度脉动和颗粒间碰撞产生的小尺度脉动的概念,建立了两相流动的双尺度二阶矩湍流模型.用该模型对水平槽道内两相流动进行了数值模拟.预报结果和实验结果符合,和单尺度二阶矩湍流模型的结果接近,表明了本模型的可行性.模拟结果还给出了大尺度和小尺度雷诺正应力分布,发现在同一方向上前者比后者大.     

Numerical studies of pulverized coal combustion in a tubular coal combustor with slanted oxygen jet

A pure two-fluid model for turbulent reacting gas-particle flow of coal particles is developed using a unified Eulerian treatment of both the gas and particle phases. The particles' history caused by mass transfer due to moisture evaporation, devolatilization and char reaction is described. Both velocity and temperature of the coal particles and the gas phase are predicted by solving the momentum and energy equations of the gas and particle phases, respectively. A k-ε-k_k two-phase turbulence model, EBU-Arrhenius turbulent combustion model and four-flux radiation heat transfer model are incorporated into a comprehensive model. The above comprehensive mathematical model is used to simulate two-dimensional gas-particle flows and pulverized coal combustion in a newly designed tubular oxygen-coal combustor of blast furnace. Predicted results of isothermal gas-particle flows are in good agreement with those obtained by measurements. The results also show that the proposed tubular oxygen-coal combustor prolongs the coal particle residence time and enhances the mixing of coal and oxygen. Results indicate that smaller coal particles of 10 μm diameter are heated and devolatilized rapidly and have volatile combustion in the combustor, while larger coal particles of 40 and 70 μm in diameter are heated but not devolatilized, and combustion of such particles does not occur in the tubular combustor.