In this paper, the numerical investigation of the bubble formation and rising in gas-liquid-solid flow systems has been done through a coupled numerical method of Volume of fluid (VOF) method and discrete element model (DEM). VOF is used to capture the interface of the bubble and DEM is employed to track the movement of particles. This coupled numerical method is validated through the good consistency of our calculated results to those experimental data (from other literatures) of the bubble rising in a gas-liquid-solid system. The calculation results in this paper disclose that the detachment time of the first formed bubble is longer for case I (when particles are laying at the bottom of the container) than for case II (when the particles are settling freely). The main reason is that a stronger circulation (induced by the sedimentation of particles) near the bottom of the container plays a stronger cutting role and speeds up the detachment of the bubble. Then, the effects of some factors including particle volume fractions, gas velocities, orifice sizes, surface tensions and liquid densities on the bubble formation and rising have also been investigated systematically. This work is useful for further researches on the gas-liquid-solid fluidized bed system. 1 Introduction The multiphase flow is a flow system of two or more coexisting phases with clear interfaces Currently, multiphase flows are generally divided into two categories: two phase flows and three phase flows${}^1$. Gas-liquid-solid three-phase flows have been widely used in chemical, petroleum, energy and environmental industries because of their large interphase heattransfer areas and good masstransfer efficiencies${}^{2-6}$ In a multiphase flow system, bubble rheological behaviors play important roles to the flow as the formation and rising of the bubbles could stir the liquid and enhance the disturbance of the flow. Hence, the study of the bubble formation and rising in multiphase flows has a remarkable increase in recent years. In order to understand the complexity of the multiphase flows, more and more attention has been paid to the numerical simulation of multiphase flows through different numerical methods of computational fluid dynamics (CFD)${}^7$ There are two major numerical methods for the study of multiphase flows: Eulerian–Eulerian (E-E)$^{5,\thinspace 8-12}$ and Eulerian-Lagrangian (E-L)${}^{13-17,19-20}$ method In the E-E method, different phases are treated as interpenetrating continuous media. In the E-L method, Navier-Stokes equations are solved in Eulerian frame for the continuous phase, and the particle orbital equation is solved in Lagrangian frame for the particles By using the E-E method, Chen et al.$^{\thinspace 9}$ calculated the axisymmetric gas-liquid transient flow, and Lu et al.$^{\mathrm{\thinspace 18\thinspace }}$calculated the diameter and rising speed of bubbles in a free bubbling fluidized bed. As for the E-L method, Wen et al.${}^{19}$ combined the two-fluid model with the discrete element method and established a closed E-E-L model to calculate gas-liquid-solid three-phase flows Volume of fluid (VOF) method${}^{21}$ could capture the motion of the gas-liquid interface and has been applied for the study of bubble rheological behaviors in gas-liquid-solid three-phase flows Li et …

中文翻译：

---

气固两相流系统中沉降颗粒对气泡形成的影响

本文通过流体体积（VOF）法和离散元模型（DEM）的耦合数值方法，对气液固流系统中气泡的形成和上升进行了数值研究。VOF用于捕获气泡的界面，DEM用于跟踪粒子的运动。通过我们的计算结果与那些在气液固系统中气泡上升的实验数据（来自其他文献）的良好一致性，验证了这种耦合的数值方法。本文的计算结果表明，情况I（当颗粒放在容器底部时）的第一个气泡的脱离时间要长于情况II（当颗粒自由沉降时）的分离时间。主要原因是靠近容器底部的更强的循环（由颗粒的沉淀引起）起着更强的切割作用，并加速了气泡的分离。然后，还系统地研究了一些因素，包括颗粒体积分数，气体速度，孔口尺寸，表面张力和液体密度对气泡形成和上升的影响。这项工作对于进一步研究气-液-固流化床系统很有用。1简介多相流是具有明确接口的两相或更多相共存的流系统。目前，多相流通常分为两类：两相流和三相流 还系统地研究了一些因素，包括颗粒体积分数，气体速度，孔口尺寸，表面张力和液体密度对气泡形成和上升的影响。这项工作对于进一步研究气-液-固流化床系统很有用。1简介多相流是具有明确接口的两相或更多相共存的流系统。目前，多相流通常分为两类：两相流和三相流 还系统地研究了一些因素，包括颗粒体积分数，气体速度，孔口尺寸，表面张力和液体密度对气泡形成和上升的影响。这项工作对于进一步研究气-液-固流化床系统很有用。1简介多相流是具有明确接口的两相或更多相共存的流系统。目前，多相流通常分为两类：两相流和三相流${}^{\mathrm{1个}}$。气液固三相流由于其较大的相间传热面积和良好的传质效率而被广泛用于化学，石油，能源和环境行业${}^{2-6}$在多相流动系统中，气泡的流变行为对流动起着重要作用，因为气泡的形成和上升会搅动液体并增强流动的干扰。因此，近年来对气泡形成和多相流上升的研究有了显着的增长。为了理解多相流的复杂性，通过不同的计算流体动力学（CFD）数值方法，对多相流的数值模拟越来越受到关注。${}^7$研究多相流的主要数值方法有两种：Eulerian – Eulerian（EE）$ ^ {5，\ thinspace 8-12} $和Eulerian -Lagrangian（EL）${}^{13-17，19-20}$方法在EE方法中，将不同阶段视为互穿的连续介质。在EL方法中，在连续相的欧拉框架中求解Navier-Stokes方程，在粒子的拉格朗日框架中求解颗粒轨道方程。$ ^ {\ thinspace 9} $计算了轴对称的气液瞬变流，Lu等人。$ ^ {\ mathrm {\ thinspace 18 \ thinspace}} $计算了自由鼓泡流化床中气泡的直径和上升速度。至于EL方法，Wen等。${}^{19}$ 将二流体模型与离散元方法相结合，建立了封闭的EEL模型，以计算气液固三相流流体体积（VOF）方法${}^{21}$ 可以捕获气液界面的运动，并已被用于研究气液固三相流中的气泡流变行为Li等…