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研究生:黃昭清
研究生(外文):Chao-Ching Huang
論文名稱:分離熱源在背向階梯流道內之混合對流研究
論文名稱(外文):Mixed Convection in a Backward-Facing Step with Discrete Heat Sources
指導教授:許燦輝
指導教授(外文):Tsan-Hui Hsu
學位類別:碩士
校院名稱:國立高雄應用科技大學
系所名稱:機械與精密工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:71
中文關鍵詞:背向階梯分離熱源個人電腦定置法方程式階梯熱塊混合對流
外文關鍵詞:backward-facing stepdiscrete heat sourcecomputerbeforedatamixed convection
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本文以數值計算方法來模擬求解牛頓系流體在裝置分離熱源之背向階梯流道內的混合對流熱傳問題,等溫流體從流道進口端進入,通過背向階梯,流經足夠長之流道後,出口時已成為完全發展流,流道平行板面與背向階梯均為絕熱壁面,在背向階梯下游放置數個凸起加熱塊。系統控制方程式有流線、動量及能量函數,經無因次化後配合適當之邊界條件以數值模擬方法求解,數值計算是用三次樣線交換方向定置法(SADI;Spline Alternating-Direction Implicit Method)並以個人電腦上求解,影響流道混合對流內流場與熱場的數值參數主要有Reynolds 數,Prandtl數,Grashof數,以及相關凸起熱塊之物質參數。本文以流道內流場與數據圖等幫助探討不同參數對整個流道流場與熱傳之影響,結果顯示Re數影響熱塊散熱大於Gr數,熱塊增高與拉長彼此間距能增強熱塊之散熱。
Mixed convection in a backward-facing step channel with discrete heat sources is numerically investigated in this study. The ambient fluid flows into the channel, through the backward-facing step, and becomes fully-developed flow before leaving the exit opening. Both the horizontal flat walls and the backward-facing step are kept adiabatic. Several discrete protruding heat blocks are situated on the bottom wall behind the backward-facing step. The governing equations include stream function, momentum function, and energy function. The controlled equations in dimensionless form coupled with corresponding boundary conditions are solved by using cubic spline collocation method in a personal computer. The governing parameters appearing in present study are Reynolds number, Re, Prandtl number, Pr, Grashof number, Gr, and several material parameters of the protruding heat sources. The numerical results of the flow fields are discussed with plots of isotherm, streamline and the data configuration. The results indicate that the Re number affects the heat transfer for the heat sources more significantly than the Gr number. In addition, enlarging the height of the heated blocks or increasing the distance between the heat sources will enhance the heat transfer from the heat sources.
目錄
中文摘要…………………...…………………………………………………. i
英文摘要………...……………………………………………………………. ii
致謝…………………………………………………………………………… iii
目錄…………………………………………………………………………… iv
表目錄………………………………………………………………………… vi
圖目錄…………………………………………………………….................... vii
符號說明………………………………………………………….................... x
第一章 緒論………………………………………………………………….. 1
1-1 研究目的與動機及其背景……………………………………... 1
1-2 相關文獻回顧…………………………………………………... 2
1-3 研究方法……………………………………………………….. 5
1-4 本文架構……………………………………………………….. 5
第二章 理論分析……………………………………………….. 6
2-1 物理模型……………………………………………………….. 6
2-2 基本假設……………………………………………………….. 6
2-3 統馭方程式…………………………………………………….. 7
2-4 系統的邊界狀況……………………………………………….. 8
2-5 無因次化分析………………………………………………….. 8
2-6 邊界條件……………………………………………………….. 10
第三章 數值方法…………...……………………………………...………… 12
3-1 數值解析…………….…….......................................................... 12
3-2 數值方法……………………………………………................. 13
3-2.1 線函數表示法及其性質…………………….................. 14
3-2.2 利用三次樣線函數求解…………...……………..……. 18
3-3.3 邊界條件之處理…………………………...…..………. 22
3-3 解題方法與程序……………………………….……………….. 23
第四章 結果與討論………………………………………………………….. 25
4-1 數值方法正確性之測試……………...………………………… 25
4-2 格點測試…………………………..………………………………….. 25
4-3 Renolds數對流場與熱傳的影響 26
4-4 浮力參數Ri對流場與熱傳的影響 27
4-5 熱塊高度對流場與熱傳的影響 27
4-6 熱塊間距對流場與熱傳的影響 27
4-7 熱塊位置對流場與熱傳的影響 28
第五章 結論與建議………………………………………………………….. 53
5-1 結論……………………………………...……………………… 53
5-2 對未來研究之建議…………………………………………… 54
參考文獻……………………………………………………………………… 55


表 目 錄
表 3-1 係數 , 和 之形式……………………………………………
12


圖 目 錄
圖2-1 物理模型圖……………………………………………………………… 6
圖3-1 三次樣線之基本型式-………………………………………………….. 15
圖3-2 三次樣線函數之二次微分區間圖……………………………………… 16
圖4-1 流線與速度向量圖 (Re=400.0, Re=800.0 in Ref. [30]) 29
圖4-2 再接觸點之位置比較圖 29
圖4-3 格點安排(431x63) 30
圖4-4 格點測試(熱塊1在不同格點時與Re數之關係) 30
圖4-5 Re=100.0時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=20,與h/b=0.2) 31
圖4-6 Re=200.0時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=20,與h/b=0.2) 31
圖4-7 Re=300.0時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=20,與h/b=0.2) 32
圖4-8 Re=400.0時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=20,與h/b=0.2). 32
圖4-9 不同Re數時流線放大視圖 (Ri=1, s/b=0.5, l/b=20,與h/b=0.2) 33
圖4-10 不同Re數時等溫線放大視圖 (Ri=1, s/b=0.5, l/b=20,與h/b=0.2) 34
圖4-11 熱塊上局部Nu數在l/b=20時之分佈圖(Ri=1.0, s/b=0.5與h/b=0.2) 35
圖4-12 熱塊上平均Nu數與Re數在l/b=20時之關係圖(Ri=1.0, s/b=0.5與h/b=0.2) 35
圖4-13 熱塊表面溫度受Re數影響圖(Ri=1.0, s/b=0.5, l/b=20, 與h/b=0.2) 36
圖4-14 Ri=0.1時流線(a)與等溫線(b)分佈圖(Re=300, s/b=0.5, l/b=20,與h/b=0.2) 36
圖4-15 Ri=0.5時流線(a)與等溫線(b)分佈圖(Re=300, s/b=0.5, l/b=20,與h/b=0.2) 37
圖4-16 Ri=5.時流線(a)與等溫線(b)分佈圖(Re=300, s/b=0.5, l/b=20,與h/b=0.2) 37
圖4-17 Ri=10.0時流線(a)與等溫線(b)分佈圖(Re=300, s/b=0.5, l/b=20, h/b=0.2) 38
圖4-18 不同Ri數時流線放大視圖 (Re=300.0, s/b=0.5, l/b=20,與h/b=0.2) 38
圖4-19 不同Ri數時等溫線放大視圖 (Re=300.0, s/b=0.5, l/b=20,與h/b=0.2) 39
圖4-20 熱塊上平均Nu數與Ri數在l/b=20時之關係圖(s/b=0.5與h/b=0.2) 40
圖4-21 h/b=0.4時流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, s/b=0.5, l/b=20) 41
圖4-22 h/b=0.6時流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, s/b=0.5, l/b=20) 41
圖4-23 不同熱塊高度時流線放大視圖 (Re=300.0, Ri=1.0, s/b=0.5, l/b=20) 42
圖4-24 不同熱塊高度時等溫線放大視圖 (Re=300.0, Ri=1.0, s/b=0.5, l/b=20) 43
圖4-25 不同熱塊高度下熱塊平均Nu數(Ri=1.0, l/b=20, 與s/b=0.5) 43
圖4-26 熱塊間距s/b=1.0時之流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, l/b=20,與h/b=0.2) 44
圖4-27 熱塊間距s/b=2.0時流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, l/b=20,與h/b=0.2) 44
圖4-28 熱塊間距s/b=3.0時流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, l/b=20,與h/b=0.2) 45
圖4-29 不同熱塊間距時流線放大視圖 (Re=300.0, Ri=1.0, l/b=20.0,與h/b=0.2) 45
圖4-30 不同熱塊間距時等溫線放大視圖 (Re=300.0, Ri=1.0, l/b=20.0,與h/b=0.2) 46
圖4-31 不同熱塊間距下熱塊平均Nu數(Re=300.0, Ri=1.0, l/b=20,與h/b=0.2) 47
圖4-32 Re=200.0時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=25,與h/b=0.2) 47
圖4-33 Re=300時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=25,與h/b=0.2) 48
圖4-34 Re=400時流線(a)與等溫線(b)分佈圖(Ri=1, s/b=0.5, l/b=25,與h/b=0.2) 48
圖4-35 不同Re數時流線放大視圖 (Ri=1, s/b=0.5, l/b=25,與h/b=0.2) 49
圖4-36 不同Re數時等溫線放大視圖 (Ri=1, s/b=0.5, l/b=25,與h/b=0.2) 50
圖4-37 熱塊距離背向階梯l/b=30時流線(a)與等溫線(b)分佈圖(Re=300, Ri=1.0, s/b=0.5與h/b=0.2) 50
圖4-38 熱塊距離背向階梯l/b=30時流線(a)與等溫線(b)分佈圖(Re=400, Ri=1.0, s/b=0.5與h/b=0.2) 51
圖4-39 熱塊上局部Nu數與Re數在l/b=30時之關係圖(Ri=1.0, s/b=0.5與h/b=0.2) 51
圖4-40 熱塊上平均Num數與Re數在l/b=30時之關係圖(Ri=1.0, s/b=0.5與h/b=0.2) 52
圖4-41 熱塊在背向階梯下游位置對平均Nu數影響(Re=300, Ri=1.0, s/b=0.5, 與h/b=0.2) 52
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