臺灣博碩士論文加值系統

本文利用晶格波茲曼法來模擬低雷諾數、穩態、不可壓縮的二維Y型渠道熱混合流。在進出口給定適當壓差使得流體能夠流動，並藉由在後段長直渠道的壁面上置入不同形狀的突起物，使得流體在衝擊到突起物後，流場與溫度場產生局部的變化，加速流場的熱混合效率。
通常在兩平板間的渠道流動置入障礙物時，會增加流體的擾動進而影響到流體的熱傳。也由於此種型態的流動在結構設計上對於熱傳效應有極大的關連，因此在實際應用設計上具有其重要性。如果進一步考慮流體具有不同溫度在渠道內混合時，渠道的幾何形狀對流體傳熱有顯著的影響，因此值得我們加以探討。
在後段長直渠道部份，置入不同數量的波浪突起物以及接地圓，當流體流經這些突起物時，因為壓力阻力的關係，使得流體產生迴流，大大的影響了渠道內的溫度分佈，更加速了流體的熱混合效率。
以另一種角度來解讀場協同理論，說明對於熱混合問題，協同角的增加，會加速高溫及低溫流體的熱交換，以達到較好的熱混合效率。

This study applies the Lattice Method to simulate low Reynolds number, steady-state and 2-D incompressible thermal mixing flow in a multi-branch channel. The pressure difference of inlet and outlet is set appropriately so that the fluid particles can be driven. To accelerate the efficiency of the thermal mixing, the distinct shapes of obstacles are inserted into the straight wall being in back of the multi-branch channel. After the fluid particles bomb into the obstacles, the variation of the flow and temperature field then generated.
When the fluid particles flow past the inserted obstacles in two parallel plates, the perturbation caused by the impact will affect the heat transfer of the flow. This type of flow is associated with the fabrication design along with the effect of heat transfer so that the application is very important. If we consider the flow with temperature difference mix inside the channel, the geometry of the channel will have great effect on thermal characteristics.
We place numbers of obstacles being in the form of wavy-like and touch down circle in the back straight part of multi-branch channel. When fluid particles flow past these obstacles, the recirculation regions are raised due to the pressure drag. The recirculation region impact on the temperature distribution magnificently and hasten the efficiency of the thermal mixing.
Taking another view of field synergy principle specify the thermal mixing problem. The increase of intersection angle will accelerate the heat exchange rate between high-temperature and low-temperature fluid particles.

目錄
摘要 Ⅰ
ABSTRACT Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
圖目錄 Ⅵ
符號說明 XIII
第一章、緒論 1
1-1 研究背景 1
1-2 晶格波茲曼法簡介 2
1-3 晶格波茲曼法文獻回顧 4
1-4 場協同理論之文獻回顧 8
1-5 研究動機 10
1-6 研究動機 11
第二章、晶格波茲曼法理論 13
2-1 流體力學方程式 13
2-2 波茲曼方程式 13
2-3 晶格波茲曼法理論 14
2-3-1 晶格氣體細胞自動機與晶格波茲曼法 14
2-3-2 連續波茲曼方程式與晶格波茲曼法 20
2-4 晶格波茲曼BGK方程式之無因次化 27
第三章、D2Q9模型與邊界處理方法 32
3-1 LBGK模型與巨觀方程式 32
3-2 晶格波茲曼法之熱模型 43
3-2-1 He之熱模型 44
3-2-2 簡化後之熱模型 48
3-3 邊界處理方法 2-3 燃燒器系統 51
3-3-1 完全反彈邊界 51
3-3-2 速度與壓力邊界 52
3-3-3 曲面邊界 55
3-3-4 熱模型之邊界 57
第四章、場協同理論 2-4 安全及控制系統 61
4-1 對流熱傳的物理機制 61
4-2 對流熱傳的場協同原理 63
4-3 迴流(橢圓形)流動的場協同理論 65
第五章、數值模擬結果與討論 68
5-1 程式流程與驗證 68
5-2 不具障礙物之Y型渠道熱混合流分析 69
5-3 下壁面具波浪突起物之Y型渠道熱混合流分析 71
5-4 上下壁均面具波浪突起物之Y型渠道熱混合流分析 74
5-5 上下壁均面具一接地圓之Y型渠道熱混合流分析 77
第六章、結論與未來展望 104
6-1 結論 104
6-2 建議與未來展望 105
參考文獻 107

圖目錄
圖1-1 晶格波茲曼法與傳統數值方法的比較 44 12
圖2-1 HPP模型的矩形網格 29
圖2-2 FHP模型的碰撞規則 29
圖2-3 晶格氣體細胞自動機的碰撞與傳遞（HPP模型）：
（a）碰撞前；（b）碰撞後；（c）傳遞後 30
圖2-4 HPP模型的碰撞規則 31
圖2-5 FHP模型的碰撞規則 31
圖3-1 DnQb模型的網格結構 58
圖3-2 正方形晶格示意圖 59
圖3-3 D2Q9模型晶格速度向量示意圖 59
圖3-4 完全反彈邊界 60
圖3-5 完全反彈邊界於下壁面 60
圖3-6 位於渠道內的晶格向量示意圖 60
圖3-7 曲面邊界格點示意圖 61
圖4-1 平板邊界層流動示意圖 68
圖4-2 具有內熱源兩平板間熱傳示意圖 68
圖4-3 二維背向階梯流場示意圖 68
圖5-1 程式流程圖 80
圖5-2a 兩平行板間的流動 81
圖5-2b 數值解與解析解之比較圖 81
圖5-3 不具障礙物之渠道幾何形狀示意圖 82
圖5-4 不具障礙物渠道之速度向量圖(Re=105,Pr=0.7)
82

圖5-5 不具障礙物之渠道之速度向量局部放大圖(Re=105,Pr=0.7)

83
圖5-6a 不具障礙物之渠道之無因次溫度分佈圖(Re=55,Pr=0.7)
83
圖5-6b 不具障礙物之渠道之無因次溫度分佈圖(Re=85,Pr=0.7)
84
圖5-6c 不具障礙物之渠道之無因次溫度分佈圖(Re=105,Pr=0.7)
84
圖5-7 具5個波浪突起物渠道幾何示意圖 85
圖5-8 具5個波浪突起物渠道速度向量圖(Re=105,Pr=0.7,
=0.6, =5/3)
85
圖5-9 具5個波浪突起物渠道速度向量局部放大圖(Re=105,Pr=0.7, =0.6, =5/3)
86
圖5-10 具5個波浪突起物渠道無因次溫度分佈圖
(Re=105,Pr=0.7, =0.6, =5/3)
86
圖5-11 5-11 具5個波浪突起物渠道速度向量圖
(Re=105,Pr=0.7, =0.9, =10/3)
87
圖5-12 圖5-12 具5個波浪突起物渠道速度向量局部放大圖
(Re=105,Pr=0.7, =0.9, =10/3)
87
圖5-13 具5個波浪突起物渠道無因次溫度分佈圖
(Re=105,Pr=0.7, =0.9, =10/3)
88
圖5-14 具5個波浪突起物渠道速度向量圖
(Re=105,Pr=0.7, =1.2, =10/3)
88
圖5-15 具5個波浪突起物渠道速度向量局部放大圖
(Re=105,Pr=0.7, =1.2, =10/3)
89
圖5-16 具5個波浪突起物渠道無因次溫度分佈圖
(Re=105,Pr=0.7, =1.2, =10/3)
89
圖5-17 Re數對平均協同角之影響(不同高度之波浪狀障礙物)
90
圖5-18 上下壁面均具波浪突起物渠道幾何示意圖 90
圖5-19 上下壁面均具波浪突起物渠道速度向量圖(case1)
(Re=105,Pr=0.7, =0.6, =10/3)
91
圖5-20 上下壁面均具波浪突起物渠道速度向量局部放大圖(case1,Re=105,Pr=0.7, =0.6, =10/3)
91
圖5-21 上下壁面均具波浪突起物渠道溫度分佈圖
(case1,Re=105,Pr=0.7, =0.6, =10/3)
92
圖5-22 上下壁面均具波浪突起物渠道速度向量圖
(case1,Re=105,Pr=0.7, =0.9, =10/3)
92
圖5-23 上下壁面均具波浪突起物渠道速度向量局部放大圖(case1, Re=105,Pr=0.7, =0.9, =10/3)
93
圖5-24 上下壁面均具波浪突起物渠道溫度分佈圖
(case1, Re=105,Pr=0.7, =0.9, =10/3)
93
圖5-25 上下壁面均具波浪突起物渠道速度向量圖
(case1, Re=105,Pr=0.7, =1.2, =10/3)
94
圖5-26 上下壁面均具波浪突起物渠道速度向量局部放大圖(case1, Re=105,Pr=0.7, =1.2, =10/3)
94
圖5-27 上下壁面均具波浪突起物渠道溫度分佈圖
(case1, Re=105,Pr=0.7, =1.2, =10/3)
95
圖5-28 Re數對平均協同角之影響(不同高度之波浪狀障礙物) 95
圖5-29 上下壁面均具波浪突起物渠道速度向量圖
(case2, Re=105,Pr=0.7, =0.6, =10/3)
96
圖5-30 上下壁面均具波浪突起物渠道速度向量局部放大圖(case2, Re=105,Pr=0.7, =0.6, =10/3)
96
圖5-31 上下壁面均具波浪突起物渠道溫度分佈圖
(case2, Re=105,Pr=0.7, =0.6, =10/3)
97
圖5-32 上下壁面均具波浪突起物渠道速度向量圖
(case2, Re=105,Pr=0.7, =0.9, =10/3)
97
圖5-33 下壁面均具波浪突起物渠道速度向量局部放大圖(case2, Re=105,Pr=0.7, =0.9, =10/3)
98
圖5-34 上下壁面均具波浪突起物渠道溫度分佈圖
(case2, Re=105,Pr=0.7, =0.9, =10/3)
98
圖5-35 上下壁面均具波浪突起物渠道速度向量圖
(case2, Re=105,Pr=0.7, =1.2, =10/3)
99
圖5-36 上下壁面均具波浪突起物渠道速度向量局部放大圖(case2, Re=105,Pr=0.7, =1.2, =10/3)
99
圖5-37 上下壁面均具波浪突起物渠道溫度分佈圖
(case2, Re=105,Pr=0.7, =1.2, =10/3)
100
圖5-38 Re數對平均協同角之影響(不同高度之波浪狀障礙物)
100
圖5-39 上下壁面均具一接地圓之渠道幾何示意圖 101
圖5-40 上下壁面均具一接地圓渠道速度向量圖
(case1, Re=105,Pr=0.7, =0.6, =5/3)
101
圖5-41 上下壁面均具一接地圓渠道速度向量局部放大圖
(case1, Re=105,Pr=0.7, =0.6, =5/3)
102
圖5-42 上下壁面均具一接地圓渠道溫度分佈圖
(case1, Re=105,Pr=0.7, =0.6, =5/3)
102
圖5-43 上下壁面均具一接地圓渠道速度向量圖
(case2, Re=105,Pr=0.7, =0.6, =5/3)
103
圖5-44 上下壁面均具一接地圓渠道速度向量局部放大圖(case2, Re=105,Pr=0.7, =0.6, =5/3)
103
圖5-45 上下壁面均具一接地圓渠道溫度分佈圖
(case2, Re=105,Pr=0.7, =0.6, =5/3)
104
圖5-46 Re數對平均協同角之影響(case1和case2)
104

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