层流泡状流的近似解析解

当前描述泡状流的双流体模型无法求得解析解,只能通过数值计算的方法进行模拟.本文则针对最基本的泡状流（垂直圆管内稳态层流泡状流）,通过对其双流体模型进行积分,得到比较直观的揭示层流泡状流流场成因的近似解析表达式.并用数值积分的方法迭代求解该表达式,所得到的数值结果与实验数据吻合很好.虽然该表达式是积分形式的,仅能算是近似的解析解,但它揭示了影响泡状流流场的因素,在理论上向前迈进了一步.     

垂直圆管内湍流泡状流的数值研究

在经典Euler/Euler型水动力模型基础上,引入考虑不同直径气泡的种群平衡方程来描述气液两相泡状流,对液相和气相分别建立了基本方程,通过对气泡的受力分析并考虑气泡之间聚合和破碎效应后给出了本构方程,建立了封闭的双流体模型并用于垂直管道湍流泡状流的三维数值模拟.模型预测值与实验数据的比较结果表明该模型能较好地模拟垂直管道湍流泡状流中的相含率分布、速度分布、湍动能分布、气泡直径分布以及气泡直径分布的演变过程.     

耦合EMMS曳力与简化双流体模型的气固流动模拟

提出了一种耦合EMMS曳力的简化双流体模型,该模型忽略固相黏度,用简单的经验关联式来计算固相压力,并且耦合考虑了介尺度结构的EMMS曳力模型来计算气固相间作用力。采用简化双流体模型成功模拟一个三维实验室尺度鼓泡流化床,数值模拟结果与完整双流体模型以及实验测量结果进行了比较,结果表明耦合EMMS曳力的简化双流体模型模拟结果与完整双流体模型耦合EMMS曳力的模拟结果基本相当,并且都与实验结果吻合良好,然而简化双流体模型的计算速度是完整双流体模型的两倍以上。这表明曳力模型在气固模拟中起着主导作用,而固相应力的作用是其次的,耦合EMMS曳力的简化双流体模型在实现工业规模气固反应器快速模拟中具有巨大潜力。     

耦合EMMS曳力与简化双流体模型的气固流动模拟

提出了一种耦合EMMS曳力的简化双流体模型,该模型忽略固相黏度,用简单的经验关联式来计算固相压力,并且耦合考虑了介尺度结构的EMMS曳力模型来计算气固相间作用力。采用简化双流体模型成功模拟一个三维实验室尺度鼓泡流化床,数值模拟结果与完整双流体模型以及实验测量结果进行了比较,结果表明耦合EMMS曳力的简化双流体模型模拟结果与完整双流体模型耦合EMMS曳力的模拟结果基本相当,并且都与实验结果吻合良好,然而简化双流体模型的计算速度是完整双流体模型的两倍以上。这表明曳力模型在气固模拟中起着主导作用,而固相应力的作用是其次的,耦合EMMS曳力的简化双流体模型在实现工业规模气固反应器快速模拟中具有巨大潜力。     

真空循环精炼过程中钢液流动的数学模拟:流动的数学模型

考虑到RH过程的物理特性,特别是上升管内气液两相流的行为和两相间的动量传输,建立了该精炼过程中整个装置内钢液流动的三维数学模型.在该模型中,将钢包,插入管和真空室视为一个整体,基于双流体模型处理和描述了气液两相流,并采用了特殊修正的k-ε双方程模型.给出了该模型的有关细节.     

喷动床内气固二相流动行为的计算模拟

采用双流体模型结合颗粒动理学理论对喷动床内气固二相流体流动行为进行了计算模拟研究。模型中运用颗粒动理学理论描述颗粒相应力封闭流体控制方程,使用Gidaspow曳力模型描述气固相间作用。喷动床内颗粒在浓相区的体积分数很大,采用Schaeffer′s模型描述颗粒间的摩擦应力。模拟计算结果表明,喷动床内分喷射区、喷泉区、环隙区3个区域,在射流入口处形成一个瓶颈。模拟计算得到的颗粒速度和空隙度分布与实验数据进行比较,计算结果与实验结果吻合较好。     

气液固三相湍流流动的E/E/L模型与模拟

采用基于双流体模型与粒子分散模型相结合的方法 ,建立了一个用于描述气液固三相湍流流动的Eulerian/Eulerian/Lagrangian模型 (简称E/E/L模型 ) .在Euler坐标系中考虑了气液两相 ,利用双流体模型来表述气液两相的相互关系 ;同时在Lagrange坐标系中考察了颗粒的运动 ,并把颗粒对气液两相的影响耦合于双流体模型中 .以流化床内气液固三相湍流流动为例进行的数值模拟结果与实验结果吻合良好 .所提出的模型及其模拟具有很好的准确性和可靠性 ,为研究气液固三相湍流流动提供了一种新的途径     

运用单元系综平均方法研究"层流"泡状流压力场

在考虑真实流体粘度、忽略气泡尾迹区影响的前提下,通过对真实流体绕球形气泡的流场进行研究,运用单元系综平均方法推导出液相界面平均压力与液相平均压力差pli-pl的表达式,反映了液体粘度对该压力差的影响. 由于湍流泡状流相对雷诺数较大,无法忽略尾迹区对其气泡周围压力场的影响,因此该表达式只适用于"层流"泡状流.     

垂直圆管内液氮流动沸腾的理论模型及数值模拟

分析了液氮流动沸腾过程中气液两相间动量、能量以及质量的传输规律,建立了相应的理论模型,新模型重点修正了界面面积浓度和气泡挣脱直径的计算式;采用新建立的理论模型作为封闭方程对CFX-4.3中内建的双流体模型进行了修正,并采用修正后的双流体模型模拟了液氮在垂直圆管内的流动沸腾过程.数值模拟的结果与文献中的实验数据吻合较好,证明了本文所建模型的合理性.通过数值模拟发现,两相流参数分布的不均匀性对液氮流动沸腾过程中的热质传输特性有重要影响.     

亚格子湍动能模型及循环流化床气固湍流特性分析

以气相大涡-颗粒相二阶矩双流体模型为框架,基于单相流亚格子湍动能推导方法,考虑固相影响推导气相亚格子湍动能方程,建立了适用于气固两相流动的气相亚格子湍动能模型;同时考虑气相亚格子湍动能与颗粒相速度脉动二阶矩之间的脉动能量传递,补充了气固相间脉动能量作用模型。模拟了循环流化床内气固两相湍流流动过程,模拟结果与实验数据吻合较好,并较未考虑湍流模型的模拟结果更接近实验值。比较了不同亚格子湍流模型对颗粒运动的影响,与Smagorinsky亚格子涡黏模型相比,亚格子湍动能模型能够更好地模拟两相流的湍流特性。分析了气体表观速度对湍流作用的影响。研究表明,随着气体表观速度的增加,气相亚格子湍动能和亚格子能量耗散逐渐增加,径向分布的非均匀性增强。     

Interfacial area concentration in boiling bubbly flow systems

The interfacial area, which describes available area for the interfacial transfer of mass, momentum and energy, is a crucial parameter in a two-fluid model formulation. From this point of view, this study performed (i) extensive survey on existing models and correlations developed for boiling bubbly flows, (ii) extensive survey on existing interfacial area database for boiling bubbly flows, (iii) formulation of the physical model based on bubble number density transport equation, (iv) simplification of the model to identify the dominant parameters governing the interfacial area, and (v) finalization of the model based on the collected extensive data and development of the interfacial area correlation. The developed correlation of the interfacial area concentration agreed with 569 adiabatic flow data and 343 boiling flow data within averaged relative deviations of ±21.1% and ±31.0%, respectively.     

Population balance modelling for bubbly flows with heat and mass transfer

Population balance equations combined with a three-dimensional two-fluid model are employed to predict bubbly flows with the presence of heat and mass transfer processes. Subcooled boiling flow belongs to this specific category of bubbly flows is considered. The MUSIG (MUltiple-SIze-Group) model implemented in CFX4.4 is further developed to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements near the test channel exit is made for the radial distribution of the bubble Sauter diameter, void fraction, interfacial area concentration and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison was also performed against existing boiling model in CFX4.4 and the modified model developed in our previous work (Int. J. Heat Mass Transfer 45 (2002) 1197). Good agreement is better achieved with the local radial bubble Sauter diameter, void fraction, interfacial area concentration and liquid velocity profiles against measurements using the newly formulated MUSIG boiling model over the simpler boiling models. However, significant weakness of the model is still evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the model by the consideration of additional momentum equations or an algebraic slip model to account for bubble separation.     

群体平衡模型对复杂气液泡状流数值模拟

引言 气液泡状流广泛出现于航空航天、石油化工、核工程技术等领域,且多为复杂湍流泡状流.在工程领域中,准确预测这种复杂泡状流的含气率、气一液速度、气泡直径等参数对工业设备安全与优化分析十分重要.     

鼓泡塔反应器气液两相流CFD数值模拟

对圆柱形鼓泡塔反应器内的气液两相流动进行了三维瞬态数值模拟,模拟的表观气速范围为0.02～0.30 m•s^-1; 模拟采用了双流体模型,并耦合了气泡界面密度单方程模型预测气泡尺寸,该模型考虑了气泡聚并与破碎对气泡尺寸的影响。液相湍流采用考虑气相影响的修正k-ε模型,两相间的动量传输仅考虑曳力作用。模拟获得了轴向气/液相速度分布、气含率分布、湍流动能分布以及气泡表面面积密度等,对部分模拟结果与实验值进行了定量比较,结果表明模拟结果与实验结果吻合较好。     

Modelling of compressible gas-liquid flow in a convergent-divergent nozzle

A two-fluid model for compressible flow of gas bubbles dispersed in liquid moving through a convergent-divergent nozzle, which is used for a gas-assisted atomization, is presented. The model is developed for flows with high values of the gas volume fraction—up to the phase inversion values. Drag and virtual mass forces are considered. A new method is proposed to correct the virtual mass coefficient for the high bubble loadings. The mixture k-ε turbulence model is adapted for the nozzle flow. The particle number density equation is solved to calculate the distribution of the locally averaged bubble diameter. Curvilinear body fitted grids are utilized to represent the nozzle shape accurately. It is shown that for numerical stability it is necessary to discretize implicitly the virtual mass term and solve the momentum equations for two phases simultaneously in a coupled way. The comparison between the experimentally measured and the predicted pressure profiles along the nozzle wall demonstrated good overall agreement. Gravitational effects are analysed by modelling a three-dimensional case. The examination of the flow through the nozzle reveals the non-uniformities of the bubble size and volume fraction distributions. It is confirmed that the virtual mass force plays a major role in accelerating/decelerating flows with a relatively low interfacial drag.     

Numerical study of bubbly upflows in a vertical channel using the Euler–Lagrange two-way model

Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Stability analysis of a bubble column

The aim of the paper is to study the transition between homogeneous and heterogeneous flows in bubble columns, by taking into account the destabilizing effects of both added mass force and deformation of the bubbles. The transition is expressed in terms of instability of a uniform bubbly flow. Special attention is paid to closure relations involving pressure terms at the gas–liquid interface. The models presented in this paper give instructive information on the transition between homogeneous and heterogeneous flows in bubble columns, highlighting the respective weight of physical phenomena, modeled in terms of closure relations introduced in the two-fluid model.     

A two-fluid model for non-equilibrium two-phase critical discharge

A general two-fluid model is developed to predict critical (choked) flow of initially saturated or subcooled flow from pipes and nozzles. The model contains improvements in the basic formulation, constitutive relations and solution technique over previously published models. It consists of six conservation equations as well as a seventh equation representing bubble growth in bubbly flow. It allows for hydrodynamic as well as thermal non-equilibrium. The model considers the development of three flow regimes, namely, bubbly, churn and annular flow regimes. The model predictions were compared with the limited available experimental data for which the axial pressure distributions were recorded. Excellent agreement was obtained.