摘要本文使用扩散界面——浸入边界法数值研究了剪切流中与固体小球接触的液滴变形 问题。剪切流中的液滴变形问题前人已有较多研究。近年来对表面活性剂的影响、复合 液滴的运动等也成为研究的热门，本文则探讨了加入固体物质后对液滴变形的影响。通 过大量数值模拟结果，得到了三种不同的流动模态——分离模态，平衡模态和翻转模态； 并根据接触角和毛细数的变化做出相图。对于相图中模态的转化，通过理论分析做出解 释。对于平衡模态，本文对于流动机制进行了探究。首先，液滴的变形仍旧与毛细数成 线性关系，其斜率随接触角增大而增大；其次，小球的初始位置对平衡后液滴的变形并 无明显影响；最后，小球旋转角速度随毛细数的增大而增大。79556

毕业论文关键词 液滴变形 流固耦合 扩散界面法 运动模态

毕 业 设 计 说 明 书 外 文 摘 要

Title The numerical simulation of the deformation of droplets contacted with solid balls in shear flow

Abstract The deformation of a droplet contacted with two solid spheres in shear flow is investigated by the numerical simulations with a diffuse Interface-immersed boundary method in this thesis。 Lots of works about the deformation of a droplet in shear flow have been studied。 Recently, the effects of surfactants and compound droplet have been hot issues, while we focus on the effects for the deformation of a droplet by adding solid bodies。 Through lots of numerical results, three flow patterns are found: the separating pattern, the balance pattern and the tumbling pattern, and a phase diagram in terms of contact angle and capillary number is shown。 For the transition of patterns, a theoretical analysis is proposed to explain。 In the balance pattern, the mechanism is investigated in this thesis。 At first, the deformation is still a linear relationship for the capillary number and its slope rising with the increasing of contact angle。 Secondly, the initial position of spheres hardly has effect on the deformation。 Finally, the angular velocity of the spheres increases with the increase of the capillary number。

Keywords deformation of droplet; fluid-structure interaction; Diffsuse Interface model;  flow pattern

本科毕业设计说明书 第 I 页

目 次

1 绪论 1

1。1 引言 1

1。2 研究的发展及研究现状 1

1。3 本文工作 2

2 问题描述及数值方法 4

2。1 问题描述 5

2。2 数值方法介绍 8

3 数值模拟结果分析 8

3。1 程序计算结果验证 8

3。2 参数说明 8

3。3 模态划分 10

3。4 平衡模态的性质 12

3。5 三种模态的相图