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系統識別號 U0002-2307201014132100
中文論文名稱 非對稱固定壁濃度二行程平板型質量交換器效率改善之研究
英文論文名稱 Performance Improvement on Double-pass Parallel-Plate Laminar Counterflow Mass Exchangers under Asymmetric Uniform Wall Concentrations
校院名稱 淡江大學
系所名稱(中) 化學工程與材料工程學系碩士班
系所名稱(英) Department of Chemical and Materials Engineering
學年度 98
學期 2
出版年 99
研究生中文姓名 郭奇縉
研究生英文姓名 Chi-Jin Kuo
學號 697400975
學位類別 碩士
語文別 中文
口試日期 2010-07-06
論文頁數 146頁
口試委員 指導教授-何啟東
委員-蔡少偉
委員-葉和明
委員-何啟東
中文關鍵字 共軛格拉茲問題  質量交換器  分離變數法  非對稱壁濃度 
英文關鍵字 conjugated Graetz problem  external recycle  mass exchanger  separation of variables  asymmetric wall concentrations 
學科別分類
中文摘要 本研究的目的為探討在非固定管壁濃度的狀態下,改變上下板壁濃度之比例對二行程平板型質量交換器的質傳之影響。本研究的二行程數學模型所推導的偏微分方程組屬於共軛格拉茲系統,利用分離變數法(separation of variables)、層疊法(superposition method)和正交展開方法(orthogonal expansion technique),可求得通道內之濃度分佈及平均謝塢數(sherwood number),並探討上下板壁濃度的不同比例對質傳效率提昇百分比之影響。
結果顯示,上下壁濃度的比例不同,其質傳效率也隨之改變,且隨著質傳格拉茲數的增加,平均謝塢數也會提升而導致質傳效率增加,此外,中間薄膜位置的不同及薄膜的孔隙度也會對質傳效率造成一定的影響。同時因為迴流裝置的不同所造成的預混效應、流體滯留時間及能源消耗也會有所改變。將以上條件所得結果與單行程質量交換系統相互比較,以獲得最佳操作條件與設計參數。
英文摘要 A new device of double-pass mass exchanger under asymmetric wall concentrations is to divide a parallel-plate channel by inserting a permeable barrier into two subchannels. The adjustment of the ratio of wall concentrations and the recycle effect was introduced to analyze the improvement of mass transfer efficiency in double-pass devices under asymmetric wall concentrations. The theoretical formulation of such conjugated Graetz problems were developed and the analytical solutions were obtained by using the separation of variables and superposition method. The theoretical predictions of the double-pass mass exchanger with external recycle were compared with those in single-pass devices under the same working dimensions. The average outlet concentration distribution and mass-transfer efficiency improvement were represented graphically with mass-transfer Graetz number and permeable membrane location as parameters. The effects of the membrane parameter and recycle ratio are also discussed in this study.
論文目次 中文摘要 I
英文摘要 II
目錄 III
圖目錄 VI
表目錄 XIII
符號說明 XV

第一章 緒論………………………………………………………1
1.1 前言………………………………………………………1
1.2 迴流效應對系統的影響…………………………………3
1.3 研究動機與目的…………………………………………5
第二章 文獻回顧…………………………………………………6
2.1 文獻回顧…………………………………………………6
2.2 格拉茲問題………………………………………………8
第三章 基本理論…………………………………………………11
3.1 齊性解……………………………………………………19
3.1.1 二行程無迴流模型………………………………………19
3.1.2 管末端出口迴流模型……………………………………22
3.1.3 出口迴流至管末端模型…………………………………25
3.1.4 管末端迴流至入口模型…………………………………28
3.1.5 出口迴流至入口模型……………………………………31
3.2 完全解……………………………………………………34
3.2.1 二行程無迴流模型………………………………………36
3.2.2 管末端出口迴流模型……………………………………37
3.2.3 出口迴流至管末端模型…………………………………39
3.2.4 管末端迴流至入口模型…………………………………40
3.2.5 出口迴流至入口模型……………………………………42
3.3 平均謝塢數………………………………………………44
3.4 能源消耗之增加率問題…………………………………46
3.4.1 二行程無迴流模型………………………………………47
3.4.2 管末端出口迴流模型……………………………………47
3.4.3 出口迴流至管末端模型…………………………………48
3.4.4 管末端迴流至入口模型…………………………………48
3.4.5 出口迴流至入口模型……………………………………48
第四章 結果與討論………………………………………………49
4.1 二行程無迴流模型之結果與討論………………………49
4.2 管末端出口模型之結果與討論…………………………57
4.3 出口迴流至管末端模型之結果與討論…………………69
4.4 管末端迴流至入口模型之結果與討論…………………80
4.5 出口迴流至入口模型之結果與討論……………………94
4.6 增加的能源消耗問題……………………………………104
4.7 數值例……………………………………………………107
第五章 結論與建議………………………………………………116
5.1 二行程無迴流模型………………………………………116
5.2 管末端出口迴流模型……………………………………117
5.3 出口迴流至管末端模型…………………………………118
5.4 管末端迴流至入口模型…………………………………119
5.5 出口迴流至入口模型……………………………………120
5.6 五種模型之比較…………………………………………121
5.7 未來研究方向……………………………………………123
參考文獻 124
附錄(一)速度分佈 133
附錄(二)正交性質 135
附錄(三)積分公式 139
附錄(四)單行程無迴流模型 142
圖目錄
圖3.1 二行程無迴流之平板式質量交換系統………………...20
圖3.2 管末端出口迴流迴流之平板式質量交換系統………...23
圖3.3 出口迴流至管末端之平板式質量交換系統…………26
圖3.4 管末端迴流至入口之平板式質量交換系統…………29
圖3.5 出口迴流至入口之平板式質量交換系統……………...32
圖4.1.1 二行程無迴流裝置,在 , 時,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係………51
圖4.1.2 二行程無迴流裝置,在 0.5時,以不同 來對比,改變薄膜參數來看無因次出口濃度對質傳格拉茲數 的關係……………………………………………………...52
圖4.1.3 二行程無迴流裝置, 時,不同 間作對比,改變薄膜位置之平均謝塢數 對質傳格拉茲數 的關係
…………………………………………………………...53
圖4.1.4 二行程無迴流裝置,在 0.5時,以不同 來對比,改變薄膜參數來看平均謝塢數 對質傳格拉茲數 的關係……………………………………………………...54
圖4.1.5 二行程無迴流裝置, 時,不同 間作對比,改變薄膜位置之質量傳送效率 對質傳格拉茲數 的關係
…………………………………………………………...55
圖4.1.6 二行程無迴流裝置, 時,不同 間作對比,改變薄膜位置之 對質傳格拉茲數 的關係………..56

圖4.2.1 管末端出口迴流裝置, , , ,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係…59
圖4.2.2 管末端出口迴流裝置, , ,以不同 對比,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………...60
圖4.2.3 管末端出口迴流裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………..61
圖4.2.4 管末端出口迴流裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次平均入口濃度對質傳格拉茲數 的關係………………………………………………62
圖4.2.5 管末端出口迴流裝置, , ,以不同 對比,改變薄膜位置之無因次平均入口濃度對質傳格拉茲數 的關係………………………………………………63
圖4.2.6 管末端出口迴流裝置, , , ,改變薄膜位置之平均謝塢數對質傳格拉茲數 的關係………64
圖4.2.7 管末端出口迴流裝置, , ,以不同 對比,改變薄膜位置之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………..65
圖4.2.8 管末端出口迴流裝置, 0.5, ,以不同 對比,改變薄膜參數之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………...66
圖4.2.9 管末端出口迴流裝置, , ,以不同 對比,改變薄膜位置之質傳效率 對質傳格拉茲數 的關係
…………………………………………………………...67
圖4.2.10 管末端出口迴流裝置, , ,以不同 對比,改變薄膜位置之 對質傳格拉茲數 的關係…..68
圖4.3.1 出口迴流至管末端裝置, , ,改變薄膜位置及迴流數之無因次出口濃度對質傳格拉茲數 的關係
…………………………………………………………...71
圖4.3.2 出口迴流至管末端裝置, , ,以不同 對比,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………...72
圖4.3.3 出口迴流至管末端裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………..73
圖4.3.4 出口迴流至管末端裝置, , ,改變薄膜位置及迴流數之平均謝塢數對質傳格拉茲數 的關係…74
圖4.3.5 出口迴流至管末端裝置, , ,以不同 對比,改變薄膜位置之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………..75
圖4.3.6 出口迴流至管末端裝置, 0.5, ,以不同 對比,改變薄膜參數之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………...76
圖4.3.7 出口迴流至管末端裝置, , ,以不同 對比,改變薄膜位置之質傳效率 對質傳格拉茲數 的關係
…………………………………………………………...77
圖4.3.8 出口迴流至管末端裝置, , , 0.5,改變迴流比之質傳效率 對質傳格拉茲數 的關係……78
圖4.3.9 出口迴流至管末端裝置, , ,以不同 對比,改變薄膜位置之 對質傳格拉茲數 的關係…..79
圖4.4.1 管末端迴流至入口裝置, , ,改變薄膜位置及迴流數之無因次出口濃度對質傳格拉茲數 的關係
…………………………………………………………...82
圖4.4.2 管末端迴流至入口裝置, , ,以不同 對比,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………...83
圖4.4.3 管末端迴流至入口裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………...84
圖4.4.4 管末端迴流至入口裝置, , ,改變薄膜位置及迴流數之平均謝塢數對質傳格拉茲數 的關係…85
圖4.4.5 管末端迴流至入口裝置, , ,以不同 對比,改變薄膜位置之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………...86
圖4.4.6 管末端迴流至入口裝置, 0.5, ,以不同 對比,改變薄膜參數之平均謝塢數對質傳格拉茲數 的關係
…………………………………………………………...87
圖4.4.7 管末端迴流至入口裝置, , ,以不同 對比,改變薄膜位置之質傳效率 對質傳格拉茲數 的關係
…………………………………………………………...88
圖4.4.8 管末端迴流至入口裝置, , , 0.5,改變迴流比之質傳效率 對質傳格拉茲數 的關係……89
圖4.4.9 管末端迴流至入口裝置, , ,以不同 對比,改變薄膜位置之 對質傳格拉茲數 的關係…..90
圖4.5.1 出口迴流至入口裝置, , ,改變迴流比及薄膜位置之無因次出口濃度對質傳格拉茲數 的關係
…………………………………………………………...93
圖4.5.2 出口迴流至入口裝置, , ,以不同 對比,改變薄膜位置之無因次出口濃度對質傳格拉茲數 的關係……………………………………………………..94
圖4.5.3 出口迴流至入口裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次出口濃度對質傳格拉茲數 的關係…………………………………………………….95
圖4.5.4 出口迴流至入口裝置, , ,以不同 對比,改變薄膜位置之無因次平均入口濃度對質傳格拉茲數 的關係……………………………………………..96
圖4.5.5 出口迴流至入口裝置, 0.5, ,以不同 對比,改變薄膜參數之無因次平均入口濃度對質傳格拉茲數 的關係……………………………………………..97
圖4.5.6 出口迴流至入口裝置, , ,改變迴流比及薄膜位置之平均謝塢數對質傳格拉茲數 的關係
………………………………………………………….98
圖4.5.7 出口迴流至入口裝置, , ,以不同 對比,改變薄膜位置之平均謝塢數對質傳格拉茲數 的關係
………………………………………………………….99
圖4.5.8 出口迴流至入口裝置, 0.5, ,以不同 對比,改變薄膜參數之平均謝塢數對質傳格拉茲數 的關係
………………………………………………………….100
圖4.5.9 出口迴流至入口裝置, , ,以不同 對比,改變薄膜位置之質傳效率 對質傳格拉茲數 的關係
………………………………………………………….101
圖4.5.10 出口迴流至入口裝置, , , 0.5,改變迴流比之質傳效率 對質傳格拉茲數 的關係…..102
圖4.5.11 出口迴流至入口裝置, , ,以不同 對比,改變薄膜位置之 對質傳格拉茲數 的關係…103





























表目錄
表4.6.1 二行程無迴流模型不同薄膜位置的能源消耗增加率
………………………………………………………….105
表4.6.2 管末端出口模型不同薄膜位置的能源消耗增加率…105
表4.6.3 出口迴流至管末端模型不同薄膜位置的能源消耗增加率……………………………………………………….105
表4.6.4 管末端迴流至入口模型不同薄膜位置的能源消耗增加率……………………………………………………….106
表4.6.5 出口迴流至入口模型不同薄膜位置的能源消耗增加率
………………………………………………………….106
表4.7.1 二行程無迴流模型Case 1的case study………………108
表4.7.2 二行程無迴流模型Case 2的case study………………108
表4.7.3 管末端出口迴流模型Case 1的case study……………109
表4.7.4 管末端出口迴流模型Case 2的case study……………109
表4.7.5 出口迴流至管末端模型Case 1的case study…………110
表4.7.6 出口迴流至管末端模型Case 2的case study…………110
表4.7.7 管末端迴流至入口模型Case 1的case study…………111
表4.7.8 管末端迴流至入口模型Case 2的case study…………111
表4.7.9 出口迴流至入口模型Case 1的case study……………112
表4.7.10 出口迴流至入口模型Case 2的case study……………112
表4.7.11 二行程無迴流模型,級數解收斂情形於 、 及 …………………………………………………..113
表4.7.12 管末端出口迴流模型,級數解收斂情形於 、 、 及 …………………………………113
表4.7.13 出口迴流至管末端模型,級數解收斂情形於 、 、 及 …………………………………114
表4.7.14 管末端迴流至入口模型,級數解收斂情形於 、 、 及 ………………………………….114
表4.7.15 出口迴流至入口模型,級數解收斂情形於 、 、 及 ………………………………115
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