格子玻尔兹曼浸没边界法在动边界容器颗粒沉降中的应用

摘要

颗粒沉降的计算流体动力学(CFD)模拟在工程过程中的成本效益性能预测方面以及预测自然现象来降低潜在的损害风险方面中起到至关重要的作用。大多数CFD研究者由于建模的困难或者认为无关紧要而没有考虑边界的运动。格子玻尔兹曼方法(LBM)以其在复杂几何形状模型中的计算效率而闻名。它在移动边界问题中的应用需要与适当的方法耦合来提高其计算性能和精确度。因此，本文发展构建了一种混合方法，将流体求解与固体结构求解器解耦，以使其适合在多核处理器上实现并行计算。
　　该方法结合了LBM、浸没边界法(IBM)以及硬球分子动力学(HSMD)模型。斯托克斯的阻力计算采用基于IBM的动量交换来实现水动力的相互作用，避免了迭代计算。HSMD模型对离散粒子的运动学和轨迹进行了评估。单颗粒的三维(3D)沉降模拟算例被认为是一个基准，模拟结果与解析解和前人的终端粒子速度的实验结果吻合较好。
　　新提出的方法用于模拟由谐波振荡的弹性矩形容器引起的封闭流动。根据薄板线弹性变形理论计算边界位移所用的解析变形方程。混合的LB-IBM方法能捕捉刚性边界壁面与封闭的含有颗粒流体的动力学响应之间的耦合关系。结果表明，沉降和颗粒位置对边界振幅和流场随后的变化敏感。颗粒分布分析表明存在粒子结构。尽管存在壁面运动和由此产生的强烈的颗粒碰撞，但流场里的湍流水平与固定壁面内的流场相比还低。

目录

声明

摘要

Abstract

Table of Contents

1 Introduction

1．1 Background

1．2 Objectives

2 NumericaI Methods

2．1 Lattice Boltzmann Method

2．1．1 Evolution of Lattice Boltzmann Method

2．1．2 Distribution Functions

2．1．3 Velocity Space

2．1．4 Boltzmann Equation

2．1．5 BGK Collision Operator

2．2 Discrete Boltzmann equation from the Boltzmann equation

2．2．1 The equilibrium distribution function for D3Q19 lattice modeI

2．3 Lattice—Boltzmann equation from the Boltzmann equation

2．3．1 Approximate Maxwell—Boltzmann Distribution Function

2．3．2 Equilibrium distribution for D2Q9 Lattice Model

2．4 Details on the Lattice Boltzmann method

2．4．1 Chapman—Enskog expansion

2．4．2 Computational Sequence

2．4．3 Inclusion of external forces to the LBM

2．5 Incompressible assumption

2．6 Conversion of units between physical and Lattice quantities

2．7 Parametrization of force

2．8 The Bounce—Back Boundary condition

2．9 Interaction between Solid—Fluid Boundary

2．10 Immersed Boundary Method

2．10．1 Coupling of Fluid and Immersed Object

2．10．2 Hydrodynamics Interaction Force

2．11 Particle Equation of Motion

2．11．1 Hard Sphere Molecular Dynamics(HSMD)Modeling

2．11．2 Lubrication Forces

2．11．3 Hard sphere kinematics

3 Particle Sedimentation Using Hybrid LBM—IBM Scheme

3．1 Introduction

3．2 Summary of the Lattice—Boltzmann Method

3．3 Immersed Boundary Method and the Hydrodynamics Interaction Force

3．3．1 Particle Hydrodynamic Force

3．3．2 Force Density from the Cuboid Walls

3．3．3 SoIid—Fluid Interaction Force Modification

3．3．4 Slip Velocity

3．3．5 Porosity

3．4 Numerical results and discussions

3．4．1 Numerical Set Up of a Single Particle Sedimentation in a Cavity

3．4．2 Sedimentation of 7200 Spherical Particles in a Newtonian Fluid

3．5 Chapter Summary

4 Transverse Harmonic Oscillation of Container Walls and the Influenceon Particle-Laden Newtonian Fluid:an LBM--IBM Approach

4．1 Introduction

4．2 Problem Formulation and NumericaI Model

4．2．1 Forced Vibration of a Clamped Lamina

4．2．2 Fluid—Lamina Interaction Model

4．3 Simulation Method

4．3．1 Boundary Condition and Force Density on a Stationary Wall

4．3．2 Boundary Condition and Force Density on an Oscillating Wall

4．3．3 Point—Particle Immersed Boundary Model

4．3．4 The Finite Wall Model

4．3．5 Particle Model and Kinematics

4．3．6 Model Error Comparison

4．4 Configuration and Parameter Setup

4．4．1 Flow Th rough a Channel

4．4．2 Stationary Fluid in an Oscillating Cube

4．4．3 Single and Multiparticle Settling in a Rectangular Box

4．5 Numerical Results and Discussions

4．5．1 Flow Through Stationary Channel Walls

4．5．2 Grid Convergence Study

4．5．3 An ExternaI Force Governed FSI

4．5．4 Single Particle Sedimentation in a Cubic Box

4．5．5 Multiparticle Sedimentation

4．5．6 Particles Flow Parameters

4．6 Chapter Summary

5 Influence of Wall Motion on Particle Sedimentation Using Hybrid LB—IBM Scheme

5．1 Introduction

5．2 Motivation

5．3 Immersed Boundary Model

5．4 Model and Parameter Setup of an Oscillating Rectangular Container

5．5 NUmerical results and discussions

5．5．1 Effect of Side Walls HorizontaI Motion

5．5．2 Effect of Horizontal Walls Vertical Oscillatory Motion

5．5．3 SinusoidaI oscillations of a rectangular box filled with spherical particles

5．5．4 Effects of wall Motion on Many Particle Sedimentation

5．5．5 Distribution of Particles Concentration

5．6 Chapter Summary

6 Conclusions and Future Outlook

6．1 Conclusion

6．1．1 Conclusion for Chapter 3

6．1．2 Conclusion for Chapter 4

6．1．3 Conclusion for Chapter 5

6．2 Innovation

6．3 Outlook

References

Appendix

Publications

Acknowledgment