本研究建立了一個篩板洗滌器的計算流體動力學（CFD）模型,用以預測其顆粒去除效率。該模型亦能模擬出擴散及慣性機制交互作用而產生的粒子清除效率U型曲線。然而,於流場中跟蹤粒子的計算相當複雜,且硬體設備效能需求高,若使用三維(3D)流場結構來進行建模的試誤將花費大量時間,這將不利於找到適當的模型設置及洗滌塔設計。
為降低軟體計算的複雜性及時長,本研究提出了降維法來簡化三維流場至二維(2D)流場,用以分析連續流場施予粒子的力在不同的組合下,對粒子清除效率的影響。降維法及用戶自定義模型的合理性是通過2D及3D流場的泡沫密度的一致性來進行驗證。其中,流體施予粒子的力組合在2D流場中被分析,模擬結果顯示除了拖曳力之外,還應包含其他力(例如:升力,壓力梯度力,虛擬質量力等),才能正確地模擬篩板上的粒子流動情形。該力組合亦使得模擬在各種操作條件下,得到與文獻中實驗數據相符的結果。出乎意料地,該模型預測出粒徑由0.1至3.0μm的顆粒去除效率呈現U形曲線,且該現象無法由關係式預測而得。本文的最後, 使用具有與2D模型相同設置的3D模型來驗證兩者清除效率的一致性。結果表明, 2D模型與3D模型的粒子清除效率預測結果相當接近。

In this thesis, a computational fluid dynamics (CFD) model of a sieve plate scrubber was built to predict its particle-removal efficiency and predict the U-shaped curve of the particle-removal efficiency as particles became smaller. Due to the complexity of particle tracking, it takes considerable time to simulate the model by using a three-dimensional (3D) structure, which is not conducive to finding the appropriate setting of particle forces. Instead, this work presented a dimension-reduction method to estimate the particle force setting by using a two-dimensional (2D) structure. The rationality of the dimension-reduction method and user-defined function was validated by the consistency in froth density for both 2D and 3D models at various air-inlet velocities. Furthermore, the result of the particle forces setting showed that besides the drag force, other forces, such as the lift force, pressure-gradient force, gravity force, and virtual mass force, should be employed in the CFD model to predict the particle-removal efficiency of the sieve plate scrubber. The prediction results of the 2D model remarkably match the particle-removal efficiency results of experimental data from the literature for various gas velocities and particle sizes. In addition, the model predicts the U-shaped curve of the particle-removal efficiency for the particle-diameter range from 0.1 to 3.0μm. Furthermore, a 3D model with the setting of the particle forces as in the 2D model was used to validate the consistency between the 2D and 3D models. The result showed that the particle-removal efficiency of the 3D model was considerably close to the prediction results of the 2D model.

Table of Content
謝誌 i
摘要 ii
Abstract iii
Table of Content iv
List of Figure vi
List of Tables viii
Chapter 1. Introduction 1
1.1 Background 1
1.2 Literature Review 2
1.2.1 Particle Control Equipment 2
1.2.2 CFD Simulation of Particle Control Equipment 4
1.2.3 Research of Particle Scavenging Efficiency Estimation 5
1.2.4 Research of Sieve Plate CFD Simulation 6
1.2.5 Research of Deformed-Sieve Plate CFD Simulation 8
1.2.6 Research of 3D to 2D Model Simulation 11
1.2.7 The U-shaped Curve of Particle-Removal Efficiency 13
1.3 Motivation and Contribution 15
Chapter 2. Mathematical Modeling 17
2.1 Introduction of Commercial CFD Software 17
2.2 CFD Modeling approach 18
2.2.1 Governing Equations 18
2.2.2 Viscous Model 19
2.2.3 Interphase Momentum Exchange Term 20
2.2.4 Surface Tension 21
2.3 Particle Motion 22
2.3.1 Drag Force 22
2.3.2 Lift Force 23
2.3.3 Virtual Mass Force and Pressure Gradient Force 23
2.3.4 Particle Collision, Breakup, and Coalescence 24
2.3.5 Discrete Random Walk Model 26
2.4 Solution Algorithm 27
Chapter 3. Validation of the user-defined drag coefficient in 2D sieve tray 29
3.1 Introduction 29
3.2 Introduction for Previous Experiment for Sieve Plate Hydraulics 29
3.3 Simulation for Sieve Plate Hydraulics 31
3.4 Results and Discussion 35
3.4.1 Hydraulic Results of Sieve Tray 35
3.4.2 Particles Affect by the Primary Phase 39
3.5 Conclusion 41
Chapter 4. Modeling on particle scavenging in a sieve plate scrubber 42
4.1 Introduction 42
4.2 Introduction for Previous Experiment of Sieve Particle Scavenging 42
4.3 Simulation for particle scavenging of the sieve plate 45
4.4 Results and Discussion 50
4.4.1 Grid Size Sensitivity 50
4.4.2 Validation of the Dimension-Reduction Method 51
4.4.3 Forces Acting on Particles 55
4.4.4 Effect of Particle Concentration on Particle-Removal Efficiency 58
4.4.5 Validation of Particle-Removal Efficiency 59
4.4.6 Comparison of 2D and 3D Models 62
Chapter 5. Conclusion 64
Nomenclature 65
Appendix 68
Reference 70

 
List of Figure
Figure 1. Evolution of the CFD model of sieve tray 8
Figure 2. Structures of the deformed sieve tray (a) full open valve tray [24]; (b) ConCap tray [25]; (c) sieve-fixed valve tray [22]; (d) bubble cap tray [23] 10
Figure 3. Experiment system and simulation geometries of pseudo-2D turbulent fluidized bed [27] 12
Figure 4. 2D and 3D model of the Tray dryer system [28] 13
Figure 5. U-shaped curve of particle-removal efficiency in the sieve plate scrubber [3] 14
Figure 6. Modeling procedure 28
Figure 7. Probe layout on the third tray [20] 30
Figure 8. The structure of commercial-scale sieve tray 31
Figure 9. Aerial view of the sieve tray 32
Figure 10. Mesh display of 2D and 3D sieve tray 32
Figure 11. The flow direction of the air and liquid phase 34
Figure 12. The monitored region in Fluent 35
Figure 13. froth density vs. flow time 36
Figure 14. Liquid velocity profile of x-direction 37
Figure 15. The interaction between particles and the primary phase, the primary was set as (a)liquid phase; (b)air phase. 40
Figure 16. Snapshot of particle flows in the sieve tray 41
Figure 17. The experimental system presented by Taheri and Calvert [3] 43
Figure 18. Removal efficiency vs generalized parameter 44
Figure 19. 3D geometry and mesh of the half sieve plate model 46
Figure 20. Dimension transformed from 3D to 2D geometries 48
Figure 21: 2D flow direction and discrete-phase boundaries 48
Figure 22: Structural mesh of the sieve plate scrubber 49
Figure 23. Sensitivity of the froth-density prediction to the number of meshes for (a) 2D geometry and (b) 3D geometry (vG= 0.387 m/s) 51
Figure 24. Snapshots of the liquid volume fractions at various flow times (vG= 0.387 m/s) in the (a) 2D model (0–20 s) and (b) 3D model (0–50 s) 52
Figure 25. Comparing the results of the 2D model, 3D model, and experiment for various air-inlet velocities. (a) holes average air velocities; (b) froth densities 54
Figure 26. Particle-removal efficiency versus dp (vG= 0.387 m/s) 56
Figure 27. Transient particle-removal efficiency as a function of flow time at various particle concentrations (dp=2.28μm; vG= 0.387 m/s) 58
Figure 28. Comparison of the results of the experiment, correlation, and 2D simulation of the particle-removal efficiency for various particle diameters. Notably, vG= (a) 0.232 m/s, (b) 0.387 m/s, (c) 0.775 m/s. 59
Figure 29. Comparison of the results of the experiment, correlation, and 2D simulation of the particle-removal efficiency for particle diameters in small sizes. vG= (a) 0.232 m/s, (b) 0.387 m/s, (c) 0.775 m/s in the U-shaped curve simulation. 61
Figure 30. Transient particle-removal efficiency as a function of flow time from the moment of particle injection a dp=1.5μm; b dp=2.28μm (vG=0.387ms) 63

 
List of Tables
Table 1. Correlations of liquid holdup for deformed sieve plate 11
Table 2. Specification of commercial-scale sieve plate tower 30
Table 3. The liquid velocity of the x-direction 37
Table 4. Comparing the results of the clear liquid height 38
Table 5. Comparing the results of the froth height 38
Table 6. Comparing the results of the froth density 38
Table 7: Particle injected condition 50
Table 8. Comparison table of the case number and the selection of particle force models (the symbol “o” represents the particle force model been selected) 55

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