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Numerical Simulations of Interactions of Solid Particles and Deformable Gas Bubbles in Viscous Liquids.

机译：粘性液体中固体颗粒与可变形气泡相互作用的数值模拟。

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摘要

Studying the interactions of solid particles and deformable gas bubbles in viscous liquids is very important in many applications, especially in mining and chemical industries. These interactions involve liquid-solid-air multiphase flows and an arbitrary-Lagrangian-Eulerican (ALE) approach is used for the direct numerical simulations. In the system of rigid particles and deformable gas bubbles suspended in viscous liquids, the Navier-Stokes equations coupled with the equations of motion of the particles and deformable bubbles are solved in a finite-element framework. A moving, unstructured, triangular mesh tracks the deformation of the bubble and free surface with adaptive refinement. In this dissertation, we study four problems. In the first three problems the flow is assumed to be axisymmetric and two dimensional (2D) in the fourth problem.;Firstly, we study the interaction between a rising deformable bubble and a solid wall in highly viscous liquids. The mechanism of the bubble deformation as it interacts with the wall is described in terms of two nondimensional groups, namely the Morton number (Mo) and Bond number ( Bo). The film drainage process is also considered. It is found that three modes of bubble-rigid wall interaction exist as Bo changes at a moderate Mo (> 10-5). The first mode prevails at small Bo where the bubble deformation is small. For this mode, the bubble is hard to break up and will bounce back and eventually attach to the rigid wall. In the second mode, the bubble may break up after it collides with the rigid wall, which is determined by the film drainage. In the third mode, which prevails at high Bo, the bubble breaks up due to the bottom surface catches up the top surface during the interaction.;Secondly, we simulate the interaction between a rigid particle and a free surface. In order to isolate the effects of viscous drag and particle inertia, the gravitational force is neglected and the particle gains its impact velocity by an external accelerating force. The process of a rigid particle impacting a free surface and then rebounding is simulated. Simplified theoretical models are provided to illustrate the relationship between the particle velocity and the time variation of film thickness between the particle and free surface. Two film thicknesses are defined. The first is the thickness achieved when the particle reaches its highest position. The second is the thickness when the particle falls to its lowest position. The smaller of these two thicknesses is termed the minimum film thickness and its variation with the impact velocity has been determined. We find that the interactions between the free surface and rigid particle can be divided into three regimes according to the trend of the first film thickness. The three regimes are viscous regime, inertial regime and jetting regime. In viscous regime, the first film thickness decreases as the impact velocity increases. Then it rises slightly in the inertial regime because the effect of liquid inertia becomes larger as the impact velocity increases. Finally, the film thickness decreases again due to Plateau--Rayleigh instability in the jetting regime. We also find that the minimum film thickness corresponds to an impact velocity on the demarcation point between the viscous and inertial regimes. This fact is caused by the balance of viscous drag, surface deformation and liquid inertia.;Thirdly, we consider the interaction between a rigid particle and a deformable bubble. Two typical cases are simulated: (1) Collision of a rigid particle with a gas bubble in water in the absence of gravity, and (2) Collision of a buoyancy-driven rising bubble with a falling particle in highly viscous liquids. We also compare our simulation results with available experimental data. Good agreement is obtained for the force on the particle and the shape of the bubble.;Finally, we investigated the collisions of groups of bubbles and particles in two dimensions. A preliminary example of the oblique collision between a single particle and a single bubble is conducted by giving the particle a constant acceleration. Then, to investigate the possibility of particles attaching to bubbles, the interactions between a group of 22 particles and rising bubbles are studied. Due to the fluid motion, the particles involved in central collisions with bubbles have higher possibilities to attach to the bubble.
机译：在许多应用中，特别是在采矿和化学工业中，研究固体颗粒与粘性液体中的可变形气泡之间的相互作用非常重要。这些相互作用涉及液-固-空气多相流，并且任意Lagrangian-Eulerican（ALE）方法用于直接数值模拟。在悬浮在粘性液体中的刚性颗粒和可变形气泡的系统中，将Navier-Stokes方程与颗粒和可变形气泡的运动方程式结合起来，并在有限元框架中求解。运动的，非结构化的三角形网格通过自适应细化来跟踪气泡和自由表面的变形。本文研究了四个问题。在前三个问题中，假定流动是轴对称的，而在第四个问题中，流动是二维的。（1）首先，我们研究了高粘性液体中上升的可变形气泡与固体壁之间的相互作用。当气泡与壁相互作用时，气泡变形的机理用两个无量纲来描述，即莫顿数（Mo）和键数（Bo）。还考虑了胶片排水过程。发现当Bo在中等Mo（> 10-5）处变化时，存在三种气泡-刚性壁相互作用模式。第一模式在气泡变形小的小Bo处占优势。对于这种模式，气泡很难破裂，会反弹并最终附着在刚性壁上。在第二种模式中，气泡在与刚性壁碰撞后可能破裂，这由薄膜排水决定。在第三种模式下（在高Bo处占优势），气泡在相互作用过程中由于底面赶上了顶面而破裂，其结果是；第二，我们模拟了刚性粒子与自由表面之间的相互作用。为了隔离粘性阻力和颗粒惯性的影响，忽略了重力，并且颗粒通过外部加速力获得了撞击速度。模拟了刚性粒子撞击自由表面然后反弹的过程。提供了简化的理论模型来说明颗粒速度与颗粒和自由表面之间的膜厚随时间变化之间的关系。定义了两个膜厚度。第一个是粒子到达其最高位置时获得的厚度。第二个是粒子落到最低位置时的厚度。这两个厚度中的较小者称为最小膜厚度，并且已经确定了其随冲击速度的变化。我们发现，根据第一膜厚度的趋势，自由表面和刚性颗粒之间的相互作用可分为三种状态。三种状态是粘性状态，惯性状态和喷射状态。在粘性状态下，第一膜厚度随着冲击速度的增加而减小。然后它在惯性状态下略有上升，因为液体惯性的影响随着冲击速度的增加而变大。最后，由于喷射过程中的高原-瑞利不稳定性，膜的厚度再次减小。我们还发现最小膜厚对应于粘性和惯性范围之间的分界点上的冲击速度。这个事实是由粘性阻力，表面变形和液体惯性的平衡引起的。第三，我们考虑了刚性颗粒和可变形气泡之间的相互作用。模拟了两种典型情况：（1）在没有重力的情况下，刚性粒子与水中的气泡碰撞；（2）在高粘性液体中，由浮力驱动的上升气泡与下降的粒子碰撞。我们还将模拟结果与可用的实验数据进行比较。最后，我们在二维上研究了气泡和颗粒群之间的碰撞。通过使粒子具有恒定的加速度来进行单个粒子与单个气泡之间的倾斜碰撞的初步示例。然后，为了研究颗粒附着在气泡上的可能性，研究了22个颗粒与上升的气泡之间的相互作用。由于流体运动，参与与气泡的中心碰撞的颗粒具有更高的附着在气泡上的可能性。

著录项

  • 作者

    Qin, Tong.;

  • 作者单位

    Virginia Polytechnic Institute and State University.;

  • 授予单位 Virginia Polytechnic Institute and State University.;
  • 学科 Mechanical engineering.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 154 p.
  • 总页数 154
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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