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研究生:王贊維
研究生(外文):Tzan-Wei Wang
論文名稱:二階黏彈性流體通過水平流道內凹槽之分析
論文名稱(外文):An Analysis of a Second Grade Viscoelastic Fluid Past a Cavity in a Horizontal Channel
指導教授:許政行許政行引用關係
指導教授(外文):Cheng-Hsing Hsu
學位類別:碩士
校院名稱:中原大學
系所名稱:機械工程研究所
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:2009
畢業學年度:97
語文別:中文
論文頁數:153
中文關鍵詞:彈性係數凹槽黏彈性流體迴流區雷諾數
外文關鍵詞:Viscoelastic FluidRecirculationCavityReynolds NumberElastic Coefficient
相關次數:
  • 被引用被引用:1
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本研究以數值模擬方法來探討水平流道內二階黏彈性流體流經一凹槽之流動行為分析。藉由改變彈性係數、雷諾數與凹槽長度來解析流體流動之穩態現象,並探討黏彈性流體在各種條件下產生的各種流場。
本研究在數值方法上主要採用有限差分法。並先將連續方程式與動量方程式轉換為渦度與流線方程式,之後在將其以有限差分法進行離散。求解方式則採用高斯-賽德法(Gauss-Seidel Method)、鬆弛法(Relaxation Method)來計算其結果。
結果顯示,隨著彈性係數與雷諾數增加,凹槽內的迴流區發展高度相對降低。且受到彈性係數與雷諾數的影響,於凹槽内所產生之迴流區,其最高點並不如以往所解析之於凹槽中心顯現,而會在後向階梯(上游)與前向階梯 (下游)間飄移而產生兩種流場現象。當特定雷諾數與彈性係數時,前後向階梯的迴流區高度會相等,此為第三種流場。分析結果發現,當彈性係數與雷諾數小於一定曲線函數時,會產生後向階梯之迴流區發展高度會大於靠近前向階梯。
This text studies second grade viscoelastic fluid past a cavity in a horizontal channel. By changing Reynolds number, elastic coefficient and cavity length, various flow patterns were studied. The results of the steady state viscoelastic fluid flow characteristics were obtained.
A finite difference method was used to discretize the vorticity and stream function equations. The Gauss-Seidel method with successive over relaxation (SOR) was implemented in the difference equation to obtain the solutions.
The analysis the reveals that by changing the elasticity coefficient and Reynolds number, the recirculation height reduces in the cavity. The flow patterns were shown and drifted in the cavity due to the influence of the Reynolds number and the elastic coefficient. When the height of the recirculation at the backward-facing step is higher than that at the forward-facing step of the cavity, we categorized this flow pattern as the first kind of the cavity flow. On the contrary, when the height of the recirculation at the forward-facing step is higher than that at the backward-facing step of the cavity, the flow pattern was termed the second-kind flow pattern. Third kind of the flow was present when both heights are equal. The results showed that the first kind flow pattern was occurred when the Reynolds number and the elastic coefficient were smaller than some critical numbers.
中文摘要 I
ABSTRACT II
誌謝 III
目錄 V
圖目錄 VII
符號說明 XI
第一章 緒 論 1
1-1 研究背景與動機 1
1-2 文獻回顧 3
1-3 本文結構 5
第二章 理論分析 7
2-1 基本描述與條件定義 7
2-2 統御方程式 8
2-3 無因次化參數 10
2-4 流線與渦度方程式 11
2-5 邊界條件 13
第三章 數值方法 15
3-1 格點選擇 15
3-2 高斯-賽得法、SOR鬆弛技巧、交互掃描法 16
3-3 差分方程式 21
3-4 數值收斂標準 23
3-5 邊界條件 23
3-6 計算流程 28
第四章 結果與討論 29
4-1 參數選擇 29
4-2 凹槽為W=0.5之流場變化 29
4-3 凹槽為W=1.0之流場變化 32
4-4 凹槽為W=1.5之流場變化 35
4-5 不同凹槽長度之趨勢比較 38
第五章 結論 40
第六章 未來展望 40
參考文獻 42
附 錄 105

圖一 流場模型示意圖 46
圖二 程式模擬計算之流程圖 47
圖三 驗證牛頓流體在凹槽內流場的趨勢比較圖 48
圖四 W=0.5,E=0.0005,Re=20~80 流線之發展趨勢 49
圖五 W=0.5,E=0.0005,Re=100~300 流線之發展趨勢 50
圖六 W=0.5,E=0.0005,Y1&Y2高度變化圖 51
圖七 W=0.5,E=0.0006,Re=20~80 流線之發展趨勢 52
圖八 W=0.5,E=0.0006,Re=100~300 流線之發展趨勢 53
圖九 W=0.5,E=0.0006,Y1&Y2高度變化圖 54
圖十 W=0.5,E=0.0007,Re=20~80 流線之發展趨勢 55
圖十一 W=0.5,E=0.0007,Re=100~300 流線之發展趨勢 56
圖十二 W=0.5,E=0.0007,Y1&Y2高度變化圖 57
圖十三 W=0.5,E=0.0008,Re=20~80 流線之發展趨勢 58
圖十四 W=0.5,E=0.0008,Re=100~250 流線之發展趨勢 59
圖十五 W=0.5,E=0.0008,Y1&Y2高度變化圖 60
圖十六 W=0.5,E=0.0009,Re=20~80 流線之發展趨勢 61
圖十七 W=0.5,E=0.0009,Re=100~210 流線之發展趨勢 62
圖十八 W=0.5,E=0.0009,Y1&Y2高度變化圖 63
圖十九 W=0.5,E=0.001, Re=20~80 流線之發展趨勢 64
圖二十 W=0.5,E=0.001, Re=100~175 流線之發展趨勢 65
圖二十一 W=0.5,E=0.001,Y1&Y2高度變化圖 66
圖二十二 W=0.5,E=0.0~0.001 ,Y1&Y2高度差比較圖 67
圖二十三 W=1.0,E=0.0005,Re=20~80 流線之發展趨勢 68
圖二十四 W=1.0,E=0.0005,Re=100~300 流線之發展趨勢 69
圖二十五 W=1.0,E=0.0005,Y1&Y2高度變化圖 70
圖二十六 W=1.0,E=0.0006,Re=20~80 流線之發展趨勢 71
圖二十七 W=1.0,E=0.0006,Re=100~300 流線之發展趨勢 72
圖二十八 W=1.0,E=0.0006,Y1&Y2高度變化圖 73
圖二十九 W=1.0,E=0.0007,Re=20~80 流線之發展趨勢 74
圖三十 W=1.0,E=0.0007,Re=100~300 流線之發展趨勢 75
圖三十一 W=1.0,E=0.0007,Y1&Y2高度變化圖 76
圖三十二 W=1.0,E=0.0008,Re=20~80 流線之發展趨勢 77
圖三十三 W=1.0,E=0.0008,Re=100~240 流線之發展趨勢 78
圖三十四 W=1.0,E=0.0008,Y1&Y2高度變化圖 79
圖三十五 W=1.0,E=0.0009,Re=20~80 流線之發展趨勢 80
圖三十六 W=1.0,E=0.0009,Re=100~190 流線之發展趨勢 81
圖三十七 W=1.0,E=0.0009,Y1&Y2高度變化圖 82
圖三十八 W=1.0,E=0.001, Re=20~80 流線之發展趨勢 83
圖三十九 W=1.0,E=0.001, Re=100~160 流線之發展趨勢 84
圖四十 W=1.0,E=0.001,Y1&Y2高度變化圖 85
圖四十一 W=1.0,E=0.0~0.001 ,Y1&Y2高度差比較圖 86
圖四十二 W=1.5,E=0.0005,Re=30~80 流線之發展趨勢 87
圖四十三 W=1.5,E=0.0005,Re=100~300 流線之發展趨勢 88
圖四十四 W=1.5,E=0.0005,Y1&Y2高度變化圖 89
圖四十五 W=1.5,E=0.0006,Re=30~80 流線之發展趨勢 90
圖四十六 W=1.5,E=0.0006,Re=100~240 流線之發展趨勢 91
圖四十七 W=1.5,E=0.0006,Y1&Y2高度變化圖 92
圖四十八 W=1.5,E=0.0007,Re=30~80 流線之發展趨勢 93
圖四十九 W=1.5,E=0.0007,Re=100~180 流線之發展趨勢 94
圖五十 W=1.5,E=0.0007,Y1&Y2高度變化圖 95
圖五十一 W=1.5,E=0.0008,Re=30~140 流線之發展趨勢 96
圖五十二 W=1.5,E=0.0008,Y1&Y2高度變化圖 97
圖五十三 W=1.5,E=0.0009,Re=30~115 流線之發展趨勢 98
圖五十四 W=1.5,E=0.0009,Y1&Y2高度變化圖 99
圖五十五 W=1.5,E=0.001, Re=30~80 流線之發展趨勢 100
圖五十六 W=1.5,E=0.001,Y1&Y2高度變化圖 101
圖五十七 W=1.5,E=0.0~0.001 ,Y1&Y2高度差比較圖 102
圖五十八 不同凹槽長度E & Re關係比較之圖 103
圖五十九 不同凹槽長度E & H關係之比較圖 104
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