竖直上升气液泡状流数学模型封闭的研究

竖直上升管气液两相流广泛应用于相变传热、核反应堆等工业过程。本文以竖直上升气液两相流为研究对象,运用欧拉双流体模型,针对表观液速为0.45m/s、表观气速分别为0.015m/s和0.1m/s的泡状流数值模拟过程中的升力、壁面润滑力、湍流扩散力、气泡诱导湍流（BIT）等封闭模型,开展数值模拟比较研究。模拟发现：①低气速泡状流中,升力和壁面润滑力的同时加入能够改善壁面附近的气含率,气泡在这两个力作用下在径向上达到一个相对平衡,得到与实验气含率类似的壁面峰,模拟的液相速度较合理;低气速时,BIT的影响可以忽略。②高气速泡状流中,BIT对气-液两相流的模拟结果影响比较明显,湍动耗散源项的加入能使液速分布的模拟结果得到改善,Troshko模型相对Sato模型更能反映气泡诱导湍流对液相湍流的作用。③高气速时升力的引入使气含率产生壁面峰,加入湍流扩散力能使峰值略微降低,但仍没有解决高气速时引入升力出现的气含率壁面峰问题,说明在径向上湍流扩散力还不足以抵抗升力。     

适用欧拉-拉格朗日方法模拟气液泡状流的气泡破碎模型

欧拉-拉格朗日方法已被广泛应用于模拟鼓泡塔等气-液反应器内的流型、气泡尺寸（或气含率）及其分布。文献中该方法主要基于临界Weber数观点来描述气泡破碎行为,且破碎后的子气泡尺寸由随机数确定。但现有实验和理论研究表明,临界Weber数约束不能体现气体密度等物性参数和泡内气体重分布对气泡破碎行为的影响。针对这些不足,提出了适用欧拉-拉格朗日框架且考虑泡内气体重分布贡献的气泡破碎机理模型,并利用开源软件OpenFOAM开发了基于新破碎模型的求解器。新模型预测结果能较好地吻合实验测量的时均轴向液速、气泡尺寸及其分布等实验数据。特别地,考虑泡内气体重分布现象的破碎机理模型成功预测了实验观测的气泡尺寸双峰分布特征。     

鼓泡塔气液两相流不同曳力模型的数值模拟

采用欧拉-欧拉双流体模型对圆柱形鼓泡塔内气液两相流动进行了三维数值模拟. 通过UDF自定义程序对气相出口边界进行了速度修正,解决了模拟中自由区域内有漩涡的问题;分别使用单一气泡尺寸模型和群体平衡模型(PBM)计算气泡尺寸,并比较其对气含率分布的预测结果,分别采用Schiller-Naumann, Grace和Tomiyama曳力系数模型进行模拟. 结果表明,在全塔径均匀进气的简化条件下,单一气泡尺寸模型不适用,在合适的Hamaker数下,PBM模型中原用于颗粒计算的Abrahamson模型可计算气泡聚并速率;Tomiyama曳力模型耦合PBM模型可更好地描述塔内流动情况,并与文献值吻合良好. Schiller-Naumann模型所得平均气含率与实验值相差约40%,而Grace模型所得湍动耗散比Tomiyama的结果高14.5%,气含率分布与文献值相差16.3%.     

蛇形管内汽液泡状流与传热的数值模拟

建立了含有相变过程的汽液泡状流VOF数值模型,通过同实验进行流型对比,验证了模型的有效性。模拟研究了蛇形管内汽液泡状流传热过程,结果表明：二次流导致冷热流体混合;在单汽泡流动时,弯管壁面上温度场在汽泡经过后具有良好的恢复能力;在汽泡串流动时,二次流将弯管下半部温度较高的流体带入上半部,有效提升上半部壁温,从而造成上壁面温度在汽泡经过前后出现较大的变化。     

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。     

加压鼓泡塔反应器中气液两相流CFD数值模拟

对加压气液鼓泡塔反应器内的气液两相流进行了二维数值模拟,模拟的压力为0.5～2.0 MPa,表观气速为0.120～0.312 m/s;模拟采用了Euler-Euler模型,并耦合了气泡群平衡模型（PBM）预测气泡尺寸,该模型考虑了气泡聚并与破碎对气泡的影响。液相湍流采用标准k-ε模型,两相间的作用力只考虑曳力。模拟获得了局部气含率、局部气/液相时均轴向速度及其径向分布等数据,并与实验结果进行比较。结果表明,局部气含率、局部气相速度模拟结果与实验结果吻合较好,局部液相速度径向分布特征模拟结果与文献结果相符。     

基于介尺度稳定性条件的多相流曳力与群体平衡模型

介尺度结构和介尺度机制是化工、冶金、能源等过程工程中的重要科学问题。尽管多相流数理模型在过去的几十年中已取得长足进展,但仍存在准确性依赖可调参数、模型适用性有限、计算量大等问题,难以适应当前快速发展的新工艺和新过程开发的需求。实际上,基于平均化方法的多流体方程组需要若干子模型封闭,如相间作用力、聚并/破碎核函数以及湍流模型等;这些子模型决定了多流体模型的模拟准确性。从介科学角度发展介尺度物理模型为解决这些问题提供了新的思路。模型可以解析多相流非均匀结构演化的控制机制,进而改进或重构子模型。总结了基于介尺度稳定条件的两类介尺度封闭模型：一类用于封闭相间动量传递,如介尺度曳力;另一类用于封闭离散相特征参数的演化,如介尺度群体平衡模型,计算气泡或液滴尺寸。进而综述了这些模型在流化床、鼓泡塔、气升式环流反应器、搅拌槽、转定子乳化器等多相流设备中的应用,并展望了未来发展方向和关键科学问题。     

两相及多相体系的离散相行为与群体平衡模型

气体、固体和液体共存的两相及多相系统广泛存在于自然界和过程工业领域。两相及多相系统的研究方法有直接模拟法、离散颗粒模拟和双流体模型等.直接模拟法和离散颗粒模拟需要研究离散相的特征及物理过程,而提高双流体模型的精度,也必须注意离散相的分布特征以及微观行为,以确定相间相互作用.群体平衡模型作为一种联系离散相微观行为与宏观表征的方法,已经成为研究离散系统的有效工具。群体平衡模型可以描述不同操作过程离散相实体的微观行为.结合不同的多相系统的特点,对群体平衡模型的物理意义、方程形式和应用进行分析,从计算资源消耗、实现难易程度及其计算精度三方面对群体平街模型求解方法进行了比较,提出了群体平衡模型应用中存在的问题和发展方向.     

基于群体平衡原理的蒸汽发生器汽液两相流动与沸腾数值模拟

基于相似原理建立了耦合四叶梅花形支撑板的蒸汽发生器“单元管”三维物理模型。采用考虑汽泡聚合与破碎效应的MUSIG （multiple-size-group）模型描述二次侧汽泡尺度分布和水力特性,热相变模型计算二次侧汽液两相沸腾相变过程,对大亚湾蒸汽发生器汽液两相流动与沸腾过程进行数值研究。模拟结果表明,支撑板位置处汽、液相流速均急剧升高,产生射流,在离开支撑板孔口时迅速形成回流。两相邻支撑板间出现明显的汽泡由小到大的周期性变化过程,冷、热端沿程汽泡最大直径缓慢减小。二次侧平均传热系数与Rohsenow经验关联式的计算结果吻合较好。     

体积属性的群体平衡模型矩积分方法研究

研究以体积为内部属性的群体平衡模型的矩积分求解方法.以各向同性离散相系统的实体聚并、实体破碎和长大等为例,介绍了矩积分求解方法的求解过程.三个算例的模拟结果表明,与分析解相比,以体积为内部属性的群体平衡模型的矩积分求解方法相对误差在10-5以内,具有高精度、低计算量的特点,并具有数目和体积的自守恒性.     

On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group average bubble number density (ABND) model for handling the bubble size distribution of gas-liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. [1998. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41, 1103-1112], Hibiki and Ishii [2002. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45, 2351-2372] and Yao and Morel [2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47, 307-328] are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff [1993a. Structure of air-water bubbly flow in a vertical pipe—I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36, 1049-1060; 1993b. Structure of air-water bubbly flow in a vertical pipe—II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36, 1061-1072] and Hibiki et al. [2001. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44, 1869-1888]. In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas-liquid bubbly flows, the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models’ capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherical shape and allowed to move freely in bubbly flow regime.     

周期惯性力影响下矩形通道泡状流阻力特性

泡状流广泛存在于各种化工反应设备中,研究周期惯性力影响下矩形通道泡状流的阻力特性,可以为研究非稳态条件下的流动特性提供实验支持。本实验在常温常压条件下进行,摇摆工况选定为5°-8 s、10°-8 s、15°-8 s、15°-12 s和15°-16 s,实验结果表明摇摆条件下瞬态摩擦压降的变化具有明显的周期性,两相平均阻力系数是稳态摩阻系数的几倍到十几倍,随着两相Reynolds数的变大,瞬态摩阻系数的波动幅度和平均水平均变小;摇摆周期越小,摇摆振幅越大,即摇摆运动越剧烈,摩擦压降的波动幅度也越大;定义了周期惯性力的影响系数(摇摆条件与竖直条件下摩阻系数的比值),利用量纲分析和多元拟合方式得到关于影响系数的经验关系式,预测值与实验值符合程度较好。     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

泡状流中水合物生成预测模型及实验

针对可燃冰钻采井筒内易发生水合物生成和堵塞的工程问题,本文开展了泡状流条件下甲烷水合物生成实验,发现流速增加会提高水合物生成速率,黄原胶质量分数的增加会降低水合物生成速率。基于传质理论,构建了适用于可燃冰钻采井筒内泡状流条件下水合物生成预测模型,模型考虑了连续相流体流变性、气泡破裂、聚并和形变等因素对泡状流中气液界面分布和气液间传质规律的影响,并耦合实验数据,提出了气泡群间的综合传质系数经验公式,用于描述气泡间相互作用对气液间传质速率的影响。对比实验结果,所建立模型对水合物生成量和水合物生成速率的预测误差分别在±5%和±15%以内,满足工程计算需求。该模型的构建有助于精准预测油气和可燃冰钻采井筒内水合物风险,为建立经济、高效的井筒水合物防治方案奠定理论基础。     

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.     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

Eulerian–Lagrangian simulation of bubble coalescence in bubbly flow using the spring-dashpot model

The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.     

Interfacial area density in bubbly flow

The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.