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研究生：	賴意婷 Lai, Yi-Ting
論文名稱：	運用晶格玻茲曼法於垂直通道內奈米流體經方柱渦流釋出之混合對流熱傳研究 Mixed Heat Convection of Nanofluid Flow with Shedding Vortex Behind a Square Cylinder in Vertical Channel Using Lattice Boltzmann Method
指導教授：	吳鴻文 Wu, Horng-Wen
學位類別：	碩士 Master
系所名稱：	工學院 - 系統及船舶機電工程學系 Department of Systems and Naval Mechatronic Engineering
論文出版年：	2018
畢業學年度：	106
語文別：	英文
論文頁數：	88
中文關鍵詞：	晶格玻茲曼法、垂直通道、方柱繞流、奈米流體、混合對流、渦流釋出、熱傳分析
外文關鍵詞：	Lattice Boltzmann Method, Vertical Channel, Square Cylinder, Nanofluid, Mixed-Convection, Vortex Shedding, Heat Transfer
相關次數：	點閱：75 下載：0
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本文使用晶格玻茲曼法模擬垂直通道內的混合熱對流問題，屬於二維不可壓縮暫態流場。在基液(H_2 O)內添加少量的〖Al〗_2 O_3金屬奈米粒子，並流經放置方型障礙物之垂直通道，以晶格玻茲曼法模擬渦流釋出現象。考慮方柱繞流在不同的理查森數(Ri=1,5與10)及奈米流體濃度(ψ=0,0.02及0.04)之條件，計算紐賽數(Nu)及阻力系數(Cd)的變化，探討渦流釋出對混合對流的影響，且設定適當的入口均勻流速度，以確保流場的適用性及避免太大的壓縮效應。
研究結果顯示，隨著理查森數的減小，強制對流效應加劇，提升流場的熱傳率，紐賽數也隨之上升。若固定Gr數，雷諾數隨著理查森數減小而上升，進而導致流場之阻力係數減小。
接著分析奈米粒子濃度對熱傳效果及阻力係數的影響，研究發現提高奈米粒子濃度亦能提升熱傳率，隨著奈米粒子濃度從0增加到0.04，紐賽數也隨著奈米粒子濃度的增加而上升。由結果可以看出，當添加金屬奈米粒子佔基液的比例極低時，改變奈米粒子濃度對阻力係數的影響並不大，研究結果顯示在奈米粒子濃度為0, 0.02及 0.04時，阻力係數幾乎沒有改變，由以上結果可知在實際工程問題中，添加少量金屬奈米粒子可以增加熱傳效率，且對提升散熱效果有很大的幫助。

In this thesis, the Lattice Boltzmann Method is used to simulate the mixed convection in vertical channels, which belongs to a two-dimensional incompressible transient flow field. A small amount of 〖Al〗_2 O_3 metal nanoparticles were added in the base liquid. The nanofluid flows through a vertical channel in which the square obstacle was placed. The vortex shedding phenomenon was simulated by the Lattice Boltzmann Method in this study. In addition, the variation of the Nusselt number (Nu) and drag coefficient (Cd) of the flow around a square cylinder were calculated with different Richardson numbers (Ri=1, 5 and 10) and nanofluid concentrations (ψ=0, 0.02 and 0.04). Then, the results were used to explore the influence of vortex shedding on heat dissipation. Moreover, the author also set an appropriate inlet uniform flow rate to ensure the applicability of the flow field to avoid too large compression effect.
The results display that a decrease in Richardson number could not only increase the impact of forced convection and the heat transfer on the flow field, but also get an increase in Nusselt number. In addition, if Gr had fixed, the Reynolds number would rise with a decrease in the Richardson number according to the equation. In other words, this phenomenon made the drag coefficient get a decrease.
Then, the author observed the effect of nanoparticle concentration on the heat transfer effect and drag coefficient. Increasing the nanoparticle concentration also enhances the heat transfer efficiency. As the nanoparticle concentration increases from 0 to 0.04, the Nusselt number (Nu) increases. The results present that when the extremely low proportion of metal nanoparticles were added, the effect of changing the nanoparticles concentration on the drag coefficient (Cd) is not significant. Whether the concentration of the nanoparticle is at 0, 0.02 or 0.04, the drag coefficient is hardly changed. In practical engineering problems, adding a small amount of metal nanoparticles can increase the heat transfer efficiency, which is of great help in improving the heat dissipation effect.

Content
摘要	I
致謝	III
ABSTRACT	IV
CONTENT	VI
LIST OF TABLES	VIII
LIST OF FIGURES	IX
NOMENCLATURE	XII
CHAPTER 1. INTRODUCTION	1
1.1	Background	1
1.2	Literature review	4
1.3	Objectives and motivation of present study	7
CHAPTER 2. NUMERICAL THEORY	9
2.1	Lattice Boltzmann Method	9
2.1.1	Lattice Gas Cellular Automata	9
2.1.2	BGK approximation and Lattice Boltzmann Equation	12
2.1.3	Chapman-Enskog Analysis and D2Q9 model	15
2.2	Thermal Lattice Boltzmann Method	25
2.3	Boussinesq approximation and buoyancy force	26
2.4	Nanofluid theorem	27
2.5	Boundary treatment	29
CHAPTER 3. PROGRAM ROUTE AND VERIFICATION	36
3.1	Program route	36
3.2	Verification and mesh independence test	38
CHAPTER 4. RESULTS AND DISCUSSION	42
4.1	Geometric model and flow parameters	42
4.2	Richardson numbers effect	44
4.3	Nanoparticle concentrations effect	47
CHAPTER 5. CONCLUSIONS AND FUTURE WORK	49
5.1	Conclusions	49
5.2	Future Work	50
REFERENCES	51

List of Table
Table 1 Summary of the literature review in LBM model	59
Table 2 Summary of the literature review in thermal LBM model	60
Table 3 Summary of the literature review in nanofluid	61
Table 4 Verification of drag coefficient	61
Table 5 Mesh independence test	62
Table 6 Physical property	62

List of Figures 
Figure 1 D2Q9 model	63
Figure 2 D2Q4 model	63
Figure 3 Complete Bounce-Back (CBB)	64
Figure 4 The areas adjacent to the boundary	64
Figure 5 The unknown distribution function	65
Figure 6 Overview of one cycle of the LB algorithm	65
Figure 7 Model of  drag coefficient verification	66
Figure 8 Drag verification (Re=100)	66
Figure 9 Drag verification (Re=200)	67
Figure 10 Model of  Nusselt number verification	67
Figure 11 Temperature distribution	68
Figure 12 Streamline plot	68
Figure 13 Nusselt number verification	68
Figure 14 Mesh independent for drag coefficient (Cd)	69
Figure 15 Mesh independent for average Nusselt number (Nu)	69
Figure 16 Model and boundary condition	70
Figure 17 Temperature contour at Ri=1 and ψ=0	70
Figure 18 Streamline contour at Ri=1 and ψ=0	71
Figure 19 Temperature contour at Ri=5 and ψ=0	71
Figure 20 Streamline contour at Ri=5 and ψ=0	72
Figure 21 Temperature contour at Ri=10 andψ=0	72
Figure 22 Streamline contour at Ri=10 and ψ=0	73
Figure 23 Temperature contour at Ri=1 andψ=0.02	73
Figure 24 Streamline contour at Ri=1 and ψ=0.02	74
Figure 25 Temperature contour at Ri=5and ψ=0.02	74
Figure 26 Streamline contour at Ri=5and ψ=0.02	75
Figure 27 Temperature contour at Ri=10 andψ=0.02	75
Figure 28 Streamline contour at Ri=10 and ψ=0.02	76
Figure 29 Temperature contour at Ri=1 and ψ=0.04	76
Figure 30 Streamline contour at Ri=1 and ψ=0.04	77
Figure 31 Temperature contour at Ri=5 and ψ=0.04	77
Figure 32 Streamline contour at Ri=5 and ψ=0.04	78
Figure 33 Temperature contour at Ri=10 andψ=0.04	78
Figure 34 Streamline contour at Ri=10 and ψ=0.04	79
Figure 35 The variation of average Nusselt number (Nu) at ψ=0	79
Figure 36 The variation of average Nusselt number (Nu) at    ψ=0.02	80
Figure 37 The variation of average Nusselt number (Nu) at  ψ=0.04	80
Figure 38 The variation of average Nusselt number (Nu) at ψ= 0, Re=100	81
Figure 39 The Nusselt numbers (Nu) on different sides at       ψ= 0 and Ri=1	81
Figure 40 The Nusselt numbers (Nu) on different sides at       ψ= 0 and Ri=5	82
Figure 41 The Nusselt numbers (Nu) on different sides at       ψ= 0 and Ri=10	82
Figure 42 Drag coefficients with different Richardson numbers (Ri) at ψ=0	83
Figure 43 Drag coefficients with different Richardson numbers (Ri) at ψ=0.02	83
Figure 44 Drag coefficients with different Richardson numbers (Ri) at ψ=0.04	84
Figure 45 The Nusselt numbers (Nu) on different sides at ψ= 0, Ri=5	84
Figure 46 The Nusselt numbers (Nu) on different sides at ψ= 0.02, Ri=5	85
Figure 47 The Nusselt numbers (Nu) on different sides at ψ= 0.04, Ri=5	85
Figure 48 The variation of average Nusselt number (Nu) at Ri=1	86
Figure 49 The variation of average Nusselt number (Nu) at Ri=5	86
Figure 50 The variation of average Nusselt number (Nu) at Ri=10	87
Figure 51 Drag coefficients with different nanoparticle concentrations (ψ) at Ri=1	87
Figure 52 Drag coefficients with different nanoparticle concentrations (ψ) at Ri=5	88
Figure 53 Drag coefficients with different nanoparticle concentrations (ψ) at Ri=10	88
                                    

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