蛋形顆粒群之流固耦合分析

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姓名

周超(Zhou Chao) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

蛋形顆粒群之流固耦合分析
(Interaction Analysis of Egg-Shaped Particles with Fluid)

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摘要(中)

本文採一種雙向流動態耦合數值分析法來模擬蛋形顆粒在流體中的運動。該模擬在一個固定歐拉網格下實現。採用流體體積法(Volume of Fluid method)來描述多相液体介面和固液介面。通過大渦模擬(Large Eddy Simulation)求解流場壓力，再將顆粒表面受力積分求得流體對固體作用力。流體固體相互作用通過由固體邊界速度指定網格面速度來實現。顆粒的運動軌跡和顆粒間的碰撞則通過離散元素法(Discrete Element Method)跟踪，顆粒間的相互作用力基于彈性力學接觸理論。本論文首先使用該耦合模型模擬了單顆粒的運動，並與實驗結果進行比對。然後用此數值方法模擬了不同形狀卵形顆粒和多顆粒的沉降與碰撞行為。

摘要(英)

In this thesis, we adopted a two-way dynamic coupled numerical method to simulate the motion of egg-shaped particles in fluid. The simulation is actualized in a fixed Eulerian grid. The Volume of Fluid (VOF) method is used to track the fluid-fluid and solid-fluid interfaces. Apply the Large Eddy simulation (LES) to solve the flow field stress, and then integral the traction on the particle surface to obtain the hydrodynamic force on the structure. The fluid-solid interaction is realized by specifying the cell-face velocity which is designated by the velocity of the structure boundary. The particle trajectories and collisions between the particles are calculated by the discrete element method (DEM), and the interaction forces between the particles are based on the elastic contact theory. The accuracy of this analysis method is verified by simulating the motion of a single egg-shaped particle and compared with the experimental results. Examples of settlement of a single particle and collision of particles are simulated by the numerical method.

關鍵字(中)

★ 流體體積法
★ 離散元素法
★ 流固耦合
★ 大渦模擬
★ 蛋形顆粒

關鍵字(英)

★ Volume of Fluid method
★ Discrete Element Method
★ Fluid-Solid interaction
★ Large Eddy simulation
★ Egg-shaped particle

論文目次

Contents
摘要 I
ABSTRACT II
Acknowledgement III
Contents IV
Figure Captions VII
Table Captions XII
Chapter 1 Introduction 1
1.1 Research background 1
1.2 Research motivation and purpose 3
1.3 Research method 3
1.4 Thesis contents 4
Chapter 2 Literature Review 5
2.1 Discrete element method 5
2.1.1 Generation of discrete element method 5
2.1.2 Elliptical particle system 6
2.1.3 Development process of particle contact judgment 7
2.2 Fluid-solid interaction 8
2.2.1 Classification of fluid-solid interaction 9
2.2.2 Solving method of fluid-solid interaction 9
2.2.3 Fluid and ellipsoidal particles interaction 12
Chapter 3 Computational Analysis of Fluid-Solid Interaction 13
3.1 Flow chart of fluid-solid interaction analysis 14
3.2 The VOF method for calculating the fluid-solid interface 15
3.3 Turbulence model 19
3.4 Resultant forces on solid surface 21
Chapter 4 Motion Analysis of Egg-Shaped Particles 23
4.1 Shape description of a egg-shaped particles 23
4.1.1 Generation of a 2D egg-shaped particle 24
4.1.2 Generation of a 3D egg-shaped particle 26
4.1.3 Calculation of the physical parameters of a 3D egg-shaped particle 28
4.1.4 Discretization of surface for egg-shaped particle 31
4.2 Contact judgement of the egg-shaped particle 34
4.2.1 Contact analysis of the egg-shaped particle and the plane 38
4.2.2 Contact analysis between the egg-shaped particles 39
4.3 Analysis and calculation of contact force between the egg-shaped particles 46
4.3.1 Normal contact spring of the egg-shaped particle 48
4.3.2 Tangential contact spring of the egg-shaped particle 53
4.4 Motion analysis of the egg-shaped particles 54
4.4.1 Translation and rotation of the egg-shaped particle 54
4.4.2 Time integration method for the solid part 56
4.4.3 Rotation of the principle axis direction vector of the egg-shaped particle 57
Chapter 5 Numerical and Experimental Validation 60
5.1 Validation of volume and moment of inertia formulas 60
5.2 Validation of calculation for surface forces 61
5.3 Validation of drag coefficient of a sphere 64
5.4 Sedimentation experiment of a single egg-shaped particle 69
Chapter 6 Numerical Results and Analysis 79
6.1 Sedimentation simulation of six egg-shaped particle 79
6.2 An egg-shaped particle slide along the slope 83
6.3 Simulation of large egg-shaped particle impacting on multiple small particles 86
6.4 Simulation of the different incident angles 89
6.5 Multiphase flow simulation 95
6.6 Collision of two egg-shaped particles in fluid 97
Chapter 7 Conclusions 105
References 106
Appendix A: Formula of a Space Vector Rotation 111
A-1 Derivation of rotation formula 111
Appendix B: Derivation of the Navier-Stokes Equations 115
B.1 Initial form of the N-S Equations 115
B.1.1 Force acting on the element 115
B.1.2 Velocity and acceleration acting on the fluid 116
B.2 Simplification of stress form 117
B.3 N-S Equations for incompressible fluid 118
B.4 Rewrite the acceleration item d"u"/dt 120

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2016-7-12

推文