以DEM模擬振動床及剪力流之顆粒混合研究

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呂立鑫(Li-Shin Lu) 查詢紙本館藏

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機械工程學系

論文名稱

以DEM模擬振動床及剪力流之顆粒混合研究
(Study of granular mixing in vibrated beds and sheared flows by DEM simulations)

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摘要(中)

本論文主要運用軟球模式的三維離散元素法（DEM）來模擬顆粒體在振動床和剪力設備中的運動，探討主題包含速度場分佈、迴流運動、擴散運動及各種與顆粒混合有關的流動性質。
本文首先系統性地提出六項簡單碰撞系統的測試，以動量守恆定律和動能守恆定律來驗證DEM程式的準確性。同時，再模擬振動床中的顆粒運動，其中明顯的對稱迴流現象與相關文獻的實驗結果極為吻合。其實，因為邊壁摩擦作用所產生的顆粒迴流運動，是振動顆粒床中非常重要的運動機制，所以本文詳細探討振動條件（包含振動加速度及振動頻率）對於對稱迴流形成的影響。文中為了有效描述顆粒對流運動和擴散運動的特性，分別定義無因次化對流率Jconv和垂直方向自我擴散係數Dyy，並且以培利數Pe來作為這兩種效應的比值。培利數在對稱迴流的形成過程中，扮演非常重要而有趣的角色，因此文中有詳盡的討論。另外，為了探討顆粒的混合行為，兩群等量而顏色不同的的玻璃珠以上下分置的初始擺放方式，放入振動床中。同時，為了衡量不同顆粒的混合狀態，本文使用Lacey index來作為混合度M以量化混合狀態，而且還可以利用最小平方法的線性擬合，從M隨時間的變化歷程中獲知混合速率。模擬的結果顯示，混合速率隨Dyy的加大而變快，且呈現指數關係的增快趨勢。另外一方面，為了衡量靜電力對顆粒流動的效應，本文定義靜電力和顆粒重量的比值為靜電數Es。模擬的結果發現，粒子溫度隨靜電數的加大而線性上升，而且混合速率常數是以冪次法則隨靜電數的加大而增快。在顆粒剪力流的模擬中，顏色不同的玻璃珠隨機堆積且上下分置，下邊壁等速移動後就會造成顆粒的混合。對於混合層厚度隨時間的變化歷程，DEM的模擬結果與利用擴散方程式的計算結果頗為吻合，這亦表示擴散運動是剪力流內顆粒混合的重要機制。

摘要(英)

This thesis examines the mixing behaviors of granular materials subjected to external vertical vibration and sheared force. Three-dimensional discrete element computer simulation is used to study the velocity distribution, convective flow, diffusive motion and granular mixing in both vibrated granular bed and sheared granular flow.
A series of systematic validation tests for the DEM program, including six tests of simple collision system and a test of macroscopic phenomenon. The conservation laws of momentum and kinetic energy are used to verify tests of collisions between particles or between particles and boundaries. Also, the simulation result of symmetric convection rolls are compared with the experimental result. With frictional sidewalls, the convection flow is a very important phenomenon in the vibrated granular bed. The influence of vibrating conditions, including vibration acceleration and frequency, on the formation of symmetric convection flow is investigated in this work. In order to characterize the convective flow and the diffusive motion of granular materials, the dimensionless convection flow rate, Jconv, and the vertical self-diffusion coefficient, Dyy, are defined, respectively. The Péclet number, Pe, is employed to characterize the ratio of the convective flow to the diffusive motion in vertical direction. The role of Pe in the formation of symmetric convection flow is discussed in detail. Moreover, the top-bottom initial loading pattern of two groups of glass beads with different colors is employed to investigate mixing behavior of granular materials. The well-known Lacey index is employed as the mixing degree, M, to quantify the mixing quality. The mixing rate is calculated from a least-square fit using the time evolution of M. The simulation results demonstrate that the mixing rate increases with increasing Dyy in exponential relation. In order to characterize the effect of electrostatic force on the granular flow, the Electrostatic Number Es is defined as the ratio of the electrostatic force to the particle weight. The simulation results demonstrate that the granular temperatures increase linearly with the increasing Es number. Meanwhile, the mixing rate constants increase with the increasing Es number in power law relations. In the simulation of sheared granular flow, the initial loading of identical glass beads with different colors is also arranged in a top-bottom loading pattern. The transverse mixing of particles is caused by the moving bottom wall with a constant velocity along the x direction. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.

關鍵字(中)

★ 對流
★ 擴散
★ 剪力流
★ 振動床
★ 顆粒混合
★ 離散元素法

關鍵字(英)

★ convection
★ diffusion
★ sheared flow
★ vibrated bed
★ granular mixing
★ DEM

論文目次

Contents
Abstract I
Acknowledgements IV
List of Figures VIII
List of Tables XIII
Nomenclature XIV
Chapter 1 Introduction 1
1.1 Motivation……………………………………………………………………..1
1.2 Mechanisms of granular mixing……………………………………………….4
1.3 Granular materials in vibrated beds and shear cells……………………7
1.4 Computer simulations of granular materials……………………………9
1.5 Topics of the present research………………………………………………..11
Chapter 2 Simulation Method 14
2.1 Particle forces………………………………………………………………..14
2.1.1 Contact forces………………………………………………………..15
2.1.2 Gravitational force……………………………………………………18
2.1.3 Electrostatic charge force…………………………………………….18
2.2 Equations of motion………………………………………………………….19
2.3 Determination of simulation parameters……………………………………..20
2.4 Implementation……………………………………………………………….22
Chapter 3 Validation tests of DEM Simulation for Particle Collisions 28
3.1 Introduction…………………………………………………………………..28
3.2 Validation tests of simple collision systems…………………….29
3.2.1 Test 1: tests of normal collisions between two particles……………..30
3.2.2 Test 2: tests of the oblique collision between two particles….31
3.2.3 Test 3: test of three-particle collision………………………………...31
3.2.4 Test 4: test of oblique collision between particle and boundary..32
3.2.5 Test 5: pseudo-static test between particle and boundary……………32
3.2.6 Errors in the conservation of kinetic energy with various Vrmax…..33
3.3 Validation test of velocity field in a vibrated bed……………………33
3.4 Summary………………………………………………………………...…...36
Chapter 4 Mixing in a vibrated granular bed: convective and diffusive effects47
4.1 Introduction…………………………………………………………………..47
4.2 Simulated system……………………………………………………………..49
4.3 Mixing index…………………………………………………………………50
4.4 Results and discussion……………………………………………………….52
4.4.1 Sidewall convection………………………………………………….52
4.4.2 Convection flow rate…………………………………………………52
4.4.3 Self-diffusion coefficient……………………………………………..54
4.4.4 Péclet number………………………………………………………...56
4.4.5 Solid-like state………………………………………………………..57
4.4.6 Phase diagram of convection forming………………………………..58
4.4.7 The time evolution of mixing degree……………………………...…59
4.4.8 Mixing rate…………………………………………………………...60
4.5 Summary……………………………………………………………………..62
Chapter 5 Mixing in a vibrated granular bed with the effect of electrostatic force 85
5.1 Introduction…………………………………………………………………..85
5.2 Simulated system……………………………………………………………..87
5.3 Electrostatic number………………………………………………………….88
5.4 Results and discussion………………………………………………………..89
5.4.1 Granular temperature…………………………………………………89
5.4.2 The time evolution of mixing degree……………………………...…91
5.4.3 Mixing rate constant………………………………………………….93
5.5 Summary…………………………………………..…………………………95
Chapter 6 Mixing in a Sheared granular Flow 103
6.1 Introduction…………………………………………………………...…….103
6.2 Simulated system……………………………………………………………105
6.3 Mixing layer thickness……………………………………………………...106
6.4 Results and discussion………………………………………………………107
6.4.1 Velocity distributions and solid fraction profiles………………..….108
6.4.2 Development of mixing thickness…………………………………..109
6.4.3 Diffusion equation and apparent self-diffusion coefficient……….111
6.5 Summary…………………………………………………………………….114
Chapter 7 Conclusion 129
7.1 Summary of results………………………………………………………….129
7.2 Broader issues…………………………………..…………………………..132
Bibliography 134
Appendix 144

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指導教授

蕭述三(Shu-San Hsiau)

審核日期

2006-1-17

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