论文总字数：43849字

摘 要

气体-颗粒两相流动在工业生产中十分常见，而近年来随着微纳技术的发展，微尺度下的气粒两相流动因其与宏观尺度下不同的流动传热特性受到了广泛的关注。因此，微尺度气粒两相流动的研究，对微通道流动、微燃烧、芯片散热等领域的发展有着重要的意义。而格子Boltzmann方法在其诞生几十年来，以它计算量小、稳定性高、边界易处理等特点得到了迅速的发展，十分适用于应对气固两相流动的复杂工况。

本文使用格子Boltzmann方法，利用C 和Matlab，首次对微尺度滑移区封闭方腔气体-静止颗粒自然对流进行模拟研究。选取基于Boussinesq假设的CLBGK模型和一种结合非平衡外推和空间插值的曲线边界处理格式，对多种不同工况下的常规尺度方腔自然对流进行了数值模拟，并与前人实验结果进行了比对，结果显示模拟结果与前人数据吻合度高，流动和换热随瑞利数的增大而增强，壁面努塞尔数Nu与瑞利数Ra呈幂函数关系。同时，针对边界处理，对比了阶梯近似法和复杂边界处理格式，结果表明，后者在计算速度、数值稳定性、计算精度上均胜过前者。

为应对微尺度下的滑移效应，本文提出在气固交界面使用基于实际物理量的速度滑移温度跳跃边界处理格式。结果表明，虽然颗粒的存在会增大气体流速，但将抑制导热的进行；滑移效应随克努森数Kn的增大而增强，主要体现在边界附近，而对整体流场和温度场影响不大；最终给出传热关联式。

关键词： 微尺度，格子-Boltzmann方法，速度滑移，温度跳跃，瑞利数，克努森数

Abstract

With the development of micro-nano technology, gas-particle flow at micro-scale has received great attention due to its different characteristics from macroscopic scale. The study of micro-scale gas-particle flow plays an important role in the development of microchannel flow, micro-combustion technology, chip heat dissipation and many other fields.

The lattice Boltzmann method has been developed rapidly in recent decades due to its edges such as small calculation cost, high numerical stability and simple treatment at boundaries. It’s very suitable for dealing with the complicated working conditions of gas-particle flow. In this paper, the flow and heat transfer of gas-particle natural convection in the micro-scale slip zone is carried out using the lattice Boltzmann method. The main work is as follows:

Using the selected CLBGK model which is based on Boussinesq hypothesis, and a curve boundary processing format combined with non-equilibrium extrapolation and spatial interpolation, the natural convection of conventional closed-cavity cavities and the natural cavity containing static particle under various different working conditions are numerically simulated and compared with the previous results. The results show that the simulation results are consistent with previous ones, the flow and heat transfer increase with the increase of Ray-leigh number. The Nusselt number and Rayleigh number are Power function relationship. At the same time, for the boundary treatments, the extrapolation format and the format mentioned above are compared. The results show that the format mentioned above are better in all fields.

Furthermore, the numerical simulation of the micro-scale gas-particle flow in the slip zone was carried out. In order to cope with the slip effect at the micro scale, a velocity slip and temperature jump boundary treatment based on the actual physical quantity is used for the boundary. The results show that although the presence of particles will increase the velocity of the flow, it will inhibit the conductance of heat conduction. The slip effect will increase with the increase of Knudsen number, mainly in the vicinity of the boundary, but not on the overall field. The Nusselt number of the wall is a Power function relationship with the Rayleigh number, and has a linear relationship with the Knudsen number.

KEY WORDS: slip zone, Lattice-Boltzmann method, speed slip, temperature jump, Knudsen number, Rayleigh number

目 录

摘 要 1

Abstract 2

第一章 绪论 1

1.1研究背景及意义 1

1.2格子Boltzmann方法的发展 2

1.3气固两相流研究现状 3

1.4本文研究内容 4

第二章 格子Boltzmann方法的基本原理及模型选用 5

2.1引言 5

2.2格子Boltzmann方法的基础理论 5

2.2.1 Boltzmann方程 5

2.2.2 格子Boltzmann方程 6

2.2.3 LBM的基本模型及宏观方程的恢复 7

2.3不可压LB模型 9

2.3.1 等温模型 9

2.3.2不可压缩热格子Boltzmann模型 11

2.3.3 CLBGK模型 12

2.4不可压LB模型的边界处理格式 15

2.4.1 启发式格式 15

2.4.2 动力学格式 16

2.4.3 外推格式 17

2.4.4 复杂边界处理格式 18

2.5本章小结 20

第三章 宏观尺度自然对流的模拟和验证 21

3.1引言 21

3.2算法的实现 21

3.3封闭空腔自然对流 24

3.4封闭方腔气体-颗粒两相流动 30

3.4.1 冷壁面-高温颗粒 30

3.4.2 边界处理格式对比 32

3.4.3 定温壁面-变温颗粒 33

3.5本章小结 35

第四章 微尺度滑移区气固流动数值模拟 36

4.1引言 36

4.2速度滑移边界条件 36

4.3温度跳跃边界条件 38

4.4滑移区封闭方腔-静止颗粒自然对流 39

4.5本章小结 46

第五章 总结与展望 47

5.1全文总结 47

5.2 对未来工作的展望 48

参考文献 49

附录 52

致 谢 58

第一章 绪论

1.1研究背景及意义

气固两相流动传热作为日常生产生活中最常见的现象之一，密切影响着生产生活中多个领域的各种问题，如煤的流化床燃烧发电、各类化工原料的生产加工以及纳米材料的制造等等。基于此，进行气固两相流中流动传热规律的研究，对于提高生产效率，改善生活的各个方面都具有非常重要的意义。而颗粒与流体之间的流动，是一个相互作用双向耦合的复杂过程，在颗粒改变周围流场和温度场的同时，流场和温度场也在对颗粒产生着影响，必须针对每一个颗粒，从微观的角度进行分析，以探究气固两相流动中各种复杂的现象。

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