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研究生:吳博濬
研究生(外文):Wu, Po-Chun
論文名稱:於正方形密閉容器內轉動平板之濃度混合現象研究
論文名稱(外文):Mixing phenomenon by rotating a flat plate inside a square enclosure
指導教授:李雄略李雄略引用關係
指導教授(外文):Lee, Shong-Leih
學位類別:碩士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
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:2015
畢業學年度:103
語文別:中文
論文頁數:45
中文關鍵詞:質傳擴散平板混合
外文關鍵詞:mass transferdiffusionflat platemixing
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本研究題目於正方形密閉容器內置入一厚度趨近於零的均勻剛性平板,使平板置於容器正中間並以其中心為旋轉軸轉動,研究其對濃度混合之影響。使用低濃度甲醇水溶液為流體。容器下半部初始濃度為1,流體為甲醇水溶液;容器上半部初始濃度為0,流體為純水,四壁靜止且為不可穿透邊界。設定50≤Re≤500以及無因次平板長度0.3≤d≤0.9此兩項變數來探討不同設定下對濃度場之影響並分析流場中剪應力之分布。本文使用有限差分法處理統御方程式。
本研究能有效模擬平板轉動對濃度混合之現象,並由結果發現Re數以及平板長度增加會使濃度混合更有效率。當平板長度縮短時會使得離平板較遠的區域難以透過平板轉動增加濃度混合效果,也因此增加濃度場達平衡之時間。結果亦可發現Re數增加會使平板上剪應力變化更為明顯。


A numerical study of the mixing phenomenon by a rotating rigid flat plate inside a square enclosure is presented. The walls of the enclosure and the flat plate are impermeable. The flat plate is placed centrally with in the enclosure, it can rotate about its centroid axis and the thickness is negligible. The fluid is initially considered to be at rest at the initial concentration of the lower half of the enclosure as high concentration, while the upper half as low concentration. The influence of the non-dimensional length of the flat plate and frequency of the flat plate which is the function of the Reynolds number are numerically investigated. The governing equations are solved with finite difference method.
It is observed that the numerical method can efficiently simulate the mixing phenomenon. From the results, it was found that the mixing of the concentration is more efficient by increasing the Reynolds number and the length of the flat plate and the shear force is increased with the Reynolds number increases.

圖目錄 I
符號目錄 II
第一章 緒論 1
1.1介紹 1
1.2文獻回顧 2
1.3研究動機 5
第二章 理論分析 6
2.1問題描述 6
2.2統御方程式 7
2.3邊界條件 8
第三章 數值方法 9
3.1 網格系統 9
3.2 隱式法 9
3.3 NAPPLA法則 10
3.3.1動量方程式之差分 10
3.3.2壓力連結方程式之差分 11
3.4濃度方程式之差分 12
3.5隱式虛擬邊界法 13
3.5.1強制點計算 14
3.6鬼點 16
3.7零厚度沉浸邊界 16
3.8剪應力計算 17
3.9濃度場均勻度 18
3.10計算流程 19
第四章 結果與討論 20
4.1數值結果 20
第五章 結論 24
參考文獻 25

[1] A. Bejan, Convection Heat Transfer, fourth ed., Wiley, New York, 2013.
[2] Yunus A. Çengel, Heat Transfer: A Practical Approach, second ed., McGraw-Hill, New York, 2003.
[3] R. Roslan, H. Saleh, I. Hashim, Natural Convection in a Differentially Heated Square Enclosure With A Solid Polygon, The Scientific World Journal 2014 (2014) Article ID 617492.
[4] J.C. Mandal C.R. Sonawane, Simulation of flow inside differentially heated rotating cavity, International Journal of Numerical Methods for Heat and Fluid Flow 23 (2013) 23-54.
[5] M. Y. Gokhale, Fathia Moh. Al Samman, Effects of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate with constant heat flux, International Journal of Heat and Mass Transfer 46 (2003) 999-1011.
[6] Dong-Hyeog Yoon, Kyung-Soo Yang, Klaus Bremhorst, Effects of Schmidt Number on Turbulent Mass Transfer Around a Rotating Circular Cylinder, Journal of Fluids Engineering 113 (2011) Issue 8.
[7] J. Serrano-Arellano, M. Gijón-Rivera, Conjugate heat and mass transfer by natural convection in a square cavity filled with a mixture of Air–CO2, International Journal of Heat and Mass Transfer 70 (2014) 103–113.
[8] M. Sheikholeslami, D. D. Ganji, Three dimensional heat and mass transfer in a rotating system using nanofluid, Powder Technology 253 (2014) 789–796.
[9] J. Serrano-Arellano, M. Gijón-Rivera, J. M. Riesco-Ávila, J. Xamán, G. Álvarez, Numerical investigation of transient heat and mass transfer by natural convection in a ventilated cavity: Outlet air gap located close to heat source, International Journal of Heat and Mass Transfer 76 (2014) 268-278.
[10] Dipankar Chatterjee, Satish Kumar Gupta, Bittagopal Mondal, Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center, International Communications in Heat and Mass Transfer 56 (2014) 71-78.
[11] J. B. Chiu, Mixed convection inside a square enclosure with a rotating flat plat, Master’s thesis, National Tsing Hua University (2014).
[12] K. W. Chen, Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Grid System, Master’s thesis, National Tsing Hua University (2013).
[13] G. S. Cyue, Implicit Virtual Boundary Method for Moving Flat Plates of Zero Thickness, Master’s thesis, National Tsing Hua University (2014).
[14] S. L. Lee and R. Y. Tzong, Artificial pressure for pressure-linked equation, International Journal of Heat and Mass Transfer 35 (1992) 2705-2716.
[15] S. L. Lee, Weighting function scheme its application on multidimensional conservation equations, International Journal of Heat and Mass Transfer 32 (1989) 2065-2073.
[16] S. L. Lee, A strongly implicit solver for two-dimensional elliptic differential equations, Numerical Heat Transfer 16 (1989) 161-178.
[17] B. Gebhart and L. Pera, The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, International Journal of Heat and Mass Transfer 14 (1971) 2025-2050.

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