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研究生:鍾昀龍
研究生(外文):Yun-lung Chung
論文名稱:反算設計問題於一維全濕面型脊型與縱向熱交換器鰭片最佳幾何形狀之預測
論文名稱(外文):An Optimal Fin Design Problem in Estimating the Shape of Spine and Longitudinal Fully Wet Fins
指導教授:黃正弘黃正弘引用關係
指導教授(外文):Cheng-hung Huang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:系統及船舶機電工程學系碩博士班
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:157
中文關鍵詞:全濕面型熱交換器鰭片
外文關鍵詞:Fully wet fin
相關次數:
  • 被引用被引用:1
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  • 下載下載:37
  • 收藏至我的研究室書目清單書目收藏:0
在實際的工程問題中,經常存在著許多物理量無法經由量測或計算得知。為了得到這些物理量,往往須藉由其他可測量的資料來反算真正要求的物理量,關於這一類的問題我們稱之為反算問題(Inverse Problem)。
反算設計問題亦可稱為最佳化設計問題。在許多複雜的工程問題中,我們可以利用一些已知的設計資料來對問題作最佳化的處理,並藉由反算的技巧,在本論文中我們可以藉由它來預測全濕面型最佳幾何熱交換器鰭片外型。
在本論文我們只探討鰭片表面為全濕面型熱交換器鰭片,全濕狀態意味著鰭片表面溫度分布皆低於空氣中露點的溫度。而空氣的相對濕度和露點溫度有密不可分的關係,所以相對濕度的改變,鰭片本身的比濕也會改變,造成濕空氣中產生凝結潛熱的熱傳率有程度上的變化,便會影響全濕面型熱交換器鰭片的效率大小。對於全濕面型的熱交換器鰭片而言,其隨著不同的體積與形狀而產生不同的溫度分佈,故鰭片片的效率亦不同。本論文之目的在於當給定某一相同體積之熱交換器鰭片時來求得一個最高效率的幾何外型;或者在給定鰭片體積及希望效率下來預測其幾何外型。本論文是利用逆向傳導問題(Inverse Heat Conduction Problem)中的共軛梯度法(Conjugate Gradient Method)並結合有限差分法(Finite Different Method)來預測全濕面縱向及脊型熱交換器片之最佳幾何外型與效率分析。
在第二章中,我們利用共軛梯度法來預測當熱傳導係數與比爾特數為常數時,全濕面脊型及縱向熱交換器鰭片之最佳幾何外型,並從直接解問題算出鰭片溫度分布及鰭片效率值並跟參考文獻做比對,來驗證其正確性。另一方面我們將探討在一定空氣相對濕度、鰭片希望體積及比爾特數下之最佳幾何外型與效率。最後在給定希望效率及體積下來預測鰭片幾何外型。
在第三章中由於許多工程問題探討的熱傳特性都屬於溫度之函數,所以我們假設熱傳導係數與比爾特數皆為溫度之函數時,即屬於非線性的情況,利用共軛梯度法來預測當熱傳導係數與比爾特數改變時,脊型與縱向鰭片之最佳幾何外型。並探討比爾特數中溫度函數的斜率改變以及熱傳導係數的增減對於鰭片的影響。
There are many physical values that can not be obtained through direct measurement or calculation in real engineering problems. However they can be estimated by using inverse design method based on measuring data. These problems are called inverse problems.
Inverse problems are also called optimum design problems. In many complex engineering problems this technique can be used to handle optimum design problems. In this thesis it is applied to forecast the optimum shapes of the fully wet fins.
In this study, a fully wet fin design problem is examined which means fin temperature distribution is lower than dew point temperature on the fin surface. Under this condition relative humidity of surrounding air, specific humidity of fully wet fin and dew point temperature become important in calculating the fin temperature. When the above three physical values are changed, latent heats of condensation of moisture are also changed and so is fin efficiency. Different fin volume and shape will result in different fin temperature distribution and different fin efficiency. The purpose of this work is to estimate the optimum shape of fin based on the desired fin volume and desired efficiency. The optimum shapes for the spine and longitudinal fully wet fins are estimated in the present inverse design problem by using the conjugate gradient method and finite different method based on the desired fin efficiency and fin volume.
In chapter two, the optimum shapes of the spine and longitudinal fully wet fins are estimated by using the conjugate gradient method as the thermal conductivity and Biot number are both assumed constants. The fin temperature distribution and fin efficiency by numerical method are compared with analytical solution to proof the accuracy of the present numerical solution. The optimum shape and efficiency are estimated by varying relative humidity of surrounding air, the fin desired volume, and Biot number.
In many complex engineering problems the thermal conductivity and Biot number are function of temperature, for this reason it is assumed that they are function of temperature in chapter 3 and the inverse problem becomes nonlinear. In this chapter we examine the effects of the temperature dependent Biot number and thermal conductivity on the final optimum fin shape.
摘 要 ………………………………………………………………I
誌 謝………………………………………………………………VI
目 錄 ……………………………………………………………VII
表 目 錄 …………………………………………………………IX
圖 目 錄…………………………………………………………XII
符 號 說 明……………………………………………………XXIV

第 一 章 緒 論 …………………………………………………1
1 – 1 研 究 背 景 與 目 的 …………………………………1
1 – 2 文 獻 回 顧 ……………………………………………3

第 二 章 共軛梯度法於線性全濕面型脊型與縱向熱交換器鰭片
最佳幾何形狀之預測 …………………………………7
2 – 1 直 接 解 問 題 …………………………………………7
2 – 2 反 算 設 計 問 題 ……………………………………11
2 – 3 共 軛 梯 度 法 之 極 小 化 過 程…………………14
2 – 4 靈 敏 度 問 題 與 前 進 步 距 ……………………15
2 – 5 伴 隨 問 題 與 梯 度 方 程 式 ……………………17
2 – 6 數 值 計 算 流 程 ……………………………………20
2 – 7 結 果 與 討 論…………………………………………22

第 三 章 共軛梯度法於非線性全濕面型脊型與縱向熱交換器鰭片
最佳幾何形狀之預測…………………………………77
3 – 1 直 接 解 問 題…………………………………………77
3 – 2 反 算 設 計 問 題 ……………………………………79
3 – 3 共 軛 梯 度 法 之 極 小 化 過 程…………………83
3 – 4 靈 敏 度 問 題 與 前 進 步 距 ……………………84
3 – 5 伴 隨 問 題 與 梯 度 方 程 式 ……………………87
3 – 6 數 值 計 算 流 程 ……………………………………91
3 – 7 結 果 與 討 論…………………………………………93

第 四 章 結 語 ………………………………………………152
參 考 文 獻 ……………………………………………………153
自 述 …………………………………………………………157
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