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研究生:黃銘陸
研究生(外文):Ming-lu Hwang
論文名稱:多孔性材質裝置熱傳增強的數值研究
論文名稱(外文):Numerical Study of Heat Transfer Enhancement in Porous Medium Devices
指導教授:楊玉姿楊玉姿引用關係
指導教授(外文):Yue-Tzu Yang
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
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:2009
畢業學年度:97
語文別:中文
論文頁數:158
中文關鍵詞:燒結多孔性渠道三維紊流週期間隙加熱塊對流熱傳噴流衝擊數值計算熱傳增強
外文關鍵詞:jet impingementsintered porous channelheat transfer enhancementconvective heat transferperiodically spaced heated blocks3-D turbulent flownumerical calculation.
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本文係利用數值模擬來探討多孔性材質裝置的熱傳增強。紊流統御方程式乃是以控制體積法(Control Volume Approach)為基礎,配合有限差分法(Finite Difference Method)及冪次法則(Power Law Scheme)來離散為差分方程式再求解。對於紊流的行為與結構則是以k – ε紊流模式配合牆函數(Wall function)來描述。採用適當的平均擴散係數求解固體與流體、與多孔性區域間耦合的問題。動量方程式中的速度及壓力則以SIMPLE (Semi-Implicit Method for Pressure-Linked Equation)法來耦合。至於格點則採用不等間距交錯式格點系統來設計。
本文將呈現已經和實驗文獻完成驗證的三個實例。包括實例一:具有週期性間斷加熱塊之矩形多孔性材質渠道其紊流流場與傳熱特性之數值模擬。相關的參數包括相對區塊高度h/H = 0.12~0.549、 相對區塊寬度wb/H = 0.24~0.47、相對區塊間隙s/H = 0.235~0.704、不同顆粒平均直徑(d = 0.7~1.16) 及雷諾數Re = 5269~15000。模擬的結果顯示:置入多孔性材質於渠道中,確實能改善熱傳性能。加熱塊之間雖只有少量的流體流過,但藉由多孔性介質具有高熱傳導率之特性,因此仍能將電子零件產生的熱有效的逸散出去。文中定義參數幾何因子(GF = hs / Hwb),顯示它與有效紐賽數Nu*有密切的關係,可以提供設計者一些參考。實例二:填充多孔性材質之熱交換器內部紊流流場與傳熱特性之數值模擬。相關的參數變化為雷諾數(Re = 5000 15000),達西數(Da =10-1 -10-6)和多孔材質半徑比 (e = 0.0 ~1.0)。模擬的結果顯示:考量熱傳與壓降兩個效應,部分填滿的效果較完全填滿來得好。根據模擬與分析最佳的部份填滿半徑比值大約是0.8。在此條件下熱傳性能可以大大的提升,壓力梯度也可以被控制在合理的範圍內。實例三:受限狹縫噴流,對於多孔性金屬區塊時的紊流場與傳熱特性之數值模擬。相關參數的變化是雷諾數(Re=5000~30,000)、噴嘴寬度對多孔性介質區塊高度比(Wj/H=0.22, 0.35, 1.24)和噴嘴到多孔性介質區塊上表面的距離對區塊高度的比(C/H=0~3)。模擬的結果顯示當Re數變大時,壓降也隨之增加。此外,當Re和C/H兩者為固定值時,Wj/H減少則壓降參數增加。對目前的系統而言:在不同的Wj/H和 C/H下,紐賽數Nu 隨泵浦馬力增加而增加。對於已知泵浦馬力的情形下,通常不具有旁道(亦即 C/H =0)的平均紐賽數(Nu)大於具有旁道(亦即C/H =1-3) 的平均紐賽數(Nu)。從本實例的研究範圍發現在相同的泵浦馬力下,最佳的冷卻性能是在Wj/H=0.35和 C/H=0的情況。
本數值預測研究對多孔性介質的共軛熱傳效應提供了一個詳細的觀察而且也進一步確認所用之數值熱傳模型的可用性。
Abstract
Numerical simulations have been carried out to investigate the heat transfer enhancement in porous medium devices in the present paper. The turbulent governing equations are solved by a control-volume-based finite difference method with power-law scheme and the well known k –ε turbulence model and its associate wall function to describe the turbulent structure. The appropriate averaging for diffusion coefficients is used to solve the coupling between solid, fluid and porous regions. The semi-implicit method for pressure-linked equation (SIMPLE) algorithm was used to couple the pressure and velocities. In this grid design, non-uniform staggered grids are used.
Three practical cases have been validated using experiential data reported in the literature. It included Case 1: Numerical simulation of turbulent fluid flow and heat transfer characteristics in a rectangular porous channel with periodically spaced heated blocks. The relevant varied parameters were, the relative block height h / H = 0.12~0.549, the relative block width wb / H = 0.24~0.47, the relative block spacing s / H = 0.235~0.704, Reynolds number Re = 5269~15000, and the average bead diameter (d = 0.7~1.16). The results reveal that introducing porous medium into a fluid channel efficiently improves the heat transfer performance of fluid channels. Although only small volumes of fluid flowing through heated blocks, the higher heat conductivity of porous material helps to dissipate the heat generated from electric / electronic parts. The defined parameter GF (GF = hs /Hwb) shows strong correlation with the heat transfer coefficient (Nu*). The parameter GF can be used as a reference in the design of electronic parts. Case2: Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media. The relevant parameters were different values of the Reynolds number (Re = 5000~15000), the Darcy number (Da =10-1~10-6) and the porous radius ratio (e = 0.0~1.0). The results reveal that partially filling the conduit with porous medium is better than the fully filled one when both the heat transfer rate and pressure drop are considered. The optimum ratio of filled porous radius ratio is about 0.8 according to the simulations and analyses. Under such conditions, the heat transfer can be enhanced significantly while the pressure gradients can be controlled in an acceptable range. Case3: Numerical simulation of turbulent fluid flow and heat transfer characteristics in metallic porous block subjected to a confined slot jet. The relevant varied parameters were, the Reynolds number (Re=5000~30,000), the ratio of jet nozzle width to the porous block height (Wj/H = 0.22, 0.35, 1.24) and the ratio of the jet-to-foam tip distance to the porous block height (C/H = 0~3). The results reveal that the dimensionless pressure drop increased as Re increased. In addition, the value of dimensionless pressure drop increased as Wj/H decreased when the Re and C/H were specified. The Nu increased with dimensionless pumping power for current systems with various Wj/H and C/H. The Nu in the configuration without by-pass flow (i.e. C/H = 0) generally exceeded that with by-pass flow (i.e. C/H = 1~3) at a given pumping power. In this studied rage, the optimal cooling performance is Wj/H=0.35 and C/H=0 under the same dimensionless pumping power.
The numerical predications obtained from this study provide a detailed insight into the conjugate heat transfer effects and facilitate the validation of numerical heat transfer models for the porous medium.
中文摘要 I
英文摘要 III
誌謝 V
目錄 VII
表目錄 XI
圖目錄 XII
符號說明 XVI
第一章 緒論 1
1-1研究動機及背景 1
1-2文獻回顧 2
1-3探討之主題及方法 8
第二章 理論分析 11
2-1多孔性介質外流場之統御方程式 11
2-1-1統御方程式 11
2-1-2 k-ε雙方程式模式 15
2-1-3牆函數 18
2-2多孔性介質內部流場之統御方程式 21
2-2-1達西定理 21
2-2-2非達西效應 22
2-2-3統御方程式 29
2-3系統統御方程式 31
2-4 邊界條件與介面條件 37
第三章 數值方法 41
3-1 差分方程式之推導 41
3-1-1格點的配置 41
3-1-2差分方程式 43
3-1-3 u、v、w動量方程式之差分方程式 49
3-1-4 壓力修正方程式 50
3-1-5 收斂條件 53
3-2 差分方程式的解法 54
3-2-1代數方程式之解法 55
3-2-2數值程序 56
第四章 週期性加熱之多孔性介質矩形渠道熱傳特性之數值模擬 59
4-1問題探討 59
4-1-1前言 59
4-1-2文獻回顧 59
4-2數學公式 63
4-3計算與確認 66
4-4結果與討論 68
4-5結論 72
第五章 多孔性材質軸心圓管熱之交換器熱傳特性之數值模擬 83
5-1問題探討 83
5-1-1前言 83
5-1-2文獻回顧 84
5-2數學公式 88
5-3計算與確認 93
5-4結果與討論 95
5-5結論 101
第六章 狹縫噴流對多孔性材質散熱器衝擊時熱傳特性之數值模擬 113
6-1問題探討 113
6-1-1前言 113
6-1-2文獻回顧 113
6-2數學公式 116
6-3計算與確認 119
6-4結果與討論 120
6-5結論 126
第七章 結論與建議 143
7-1討論 143
7-2 未來研究方向與建議 143
參考文獻 145
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