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研究生:李建志
研究生(外文):CHIEN-CHIH LI
論文名稱:採用等向性有限元素微分法於正方形孔穴內混合對流現象之探討
論文名稱(外文):Investigation of mixed convection in a square cavity using the isoparametric differential method
指導教授:楊一龍
指導教授(外文):Yi-Lung Yang
學位類別:碩士
校院名稱:中華大學
系所名稱:機械工程學系碩士班
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:2011
畢業學年度:99
語文別:中文
中文關鍵詞:理查森數波形壁高階等向性元素微分法
外文關鍵詞:Richardson numberWavy wallhigh-order isoparametric element differential scheme
相關次數:
  • 被引用被引用:3
  • 點閱點閱:146
  • 評分評分:
  • 下載下載:11
  • 收藏至我的研究室書目清單書目收藏:0
本研究探討頂面驅動而底面具波形熱壁面之正方形孔穴內混合對流現象。採用高階等向性元素微分法求解可壓縮Navier-Stokes統御方程式,流通量之計算上分解成流速項、擴散項以及壓力項,各項之微分皆採用中央差分方式計算,而壓力項於近壁面以非中央之外插方式完成。加總之各點流通量利用預置矩陣以二階Runge-Kutta時間積分方式疊代。研究首先利用文獻結果驗證數值程式之開發,並針對不同網格數分析對熱傳結果之影響。文章透過流線、等溫線、局部紐塞數以及平均紐塞數方式探討不同馬赫數、理查森數、雷諾數以及波形壁之深淺對混合對流之影響,透過浮力、擴散與對流作用其波形壁有一最佳之深度其熱傳量最大,過深之波形壁雖然有更高之局部紐塞數但其波谷之迴流現象加劇造成局部近似絕熱之效果反而抑制整體熱量之傳遞。
A numerical study of mixed convection inside a lid-driven cavity with a hot wavy wall was carried out. This problem is solved by using a high order isoparametric element differential scheme for the steady compressible Navier-Stokes equations. The pointwise numerical fluxes are separated into convective/viscous fluxes and acoustic fluxes. All the fluxes are calculated by the central sceheme except the acoustic flux where non-central scheme is employed near the wall. The overall residual is integrated using the second-order Runge-Kutta scheme with a preconditioning matrix. The validation of the numerical code used is ascertained by comparing our results with previously published results. Effect of grid density on the heat transfer rate was investigated. Results are shown in the form of streamlines, isotherms, local and average Nusselt number distribution. The results are analyzed for a range of Mach numbers, Reynolds numbers and Richardson numbers for different undulations with different wave amplitude ratio. The results obtained show that there is an optimal amplitude ratio gives the highest heat transfer rate. With further increase of amplitude ratio, raises the local Nusselt number but decreases the average Nusselt number due to the recirculation region is magnified.
中文摘要 1
Abstract2
致謝.... 3
目錄.... 4
表目錄 6
圖目錄 7
符號定義 9

第一章 緒論 12
1.1 前言 12
1.2 文獻回顧 12
1.3 採用方法 17
1.4 章節安排 17

第二章 物理問題描述 18
2.1 混合對流問題與邊界條件 18
2.2 基本假設 18
2.3 無因次參數 18

第三章 數值方法 20
3-1 Navier-Stokes方程式 20
3-2 時間積分 21
3-3 流通量計算 21

第四章 結果與討論 23
4.1 剪切流場驗證 23
4.2 自然對流驗證 23
4.3 混合對流比較 24
4.4 波數影響 24
4.5 馬赫數之效應 25
4.6 葛拉斯赫夫數效應 25
4.7 雷諾數之影響 26
4.8 正弦波振幅之影響 27

第五章 結論及未來工作 29
5.1 結論 29
5.2 未來工作 30

參考文獻 31

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[6] Oztop, H. F. and Dagtekin, I., “Mixed convection in two-sided lid-driven differentially heated square cavity,” International Journal of Heat and Mass Transfer, Vol.47, 2004, pp. 1761-1769.
[7] Al-Amiri, A. and Khanafer, K. M., “Numerical simulation of double-diffusive mixed convection within a rotating horizontal annulus,” International Journal of Thermal Sciences, Vol.45, 2006, pp. 567-578.
[8] Shah, P., Rovagnati, B., Mashayek, F., and Jacobs, G. B., “Subsonic compressible flow in two-sided lid-driven cavity. Part II: Unequal walls temperatures,” International Journal of Heat and Mass Transfer, Vol.50, 2007, pp. 4219-4228.
[9] Al-Amir, A., Khanafer, K. M., Bull, J., and Pop, I., “Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity,” International Journal of Heat and Mass Transfer, Vol.50, 2007, pp. 1771-1780.
[10] Chiu, H. C. and Yan, W. M., “Mixed convection heat transfer in inclined rectangular ducts with radiation effects,” International Journal of Heat and Mass Transfer, Vol.51, 2008, pp. 1085-1094.
[11] Basak, T.,., Roy, S., Sharma, P. K. and Pop, I., “Analysis of mixed convection flows within a square cavity with linearly heated side wall(s),” International Journal of Heat and Mass Transfer, Vol.52, 2009, pp. 2224-2242.
[12] Ouertatani, N., Cheikh, N., B., Beya, B. B., Lili, T. and Campo, A., “Mixed convection in a double lid-driven cubic cavity,” International Journal of Thermal Sciences, Vol.48, 2009, pp. 1265-1272.
[13] Oztop, H. F., Zhao, Z., and Yu, B., “Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition,” International Communications in Heat and Mass Transfer, Vol.36, 2009, pp. 661-668.
[14] Castelloes, F. V., Quaresma, J. N. N. and Cotta, R. M., “Convective heat transfer enhancement in low Reynolds number flows with wavy walls,” International Journal of Heat and Mass Transfer, Vol.53, 2010, pp. 2022-2034.
[15] Sivasankaran, S., Sivakumar, V. and Prakash, P., “Numerical study on mixed convection in a lid-driven cavity with non-uniform heating on both sidewalls,” International Journal of Heat and Mass Transfer, Vol.53, 2010, pp. 4304-4315.
[16] Sivakumar, V., Sivasankaran, S., Prakash, P. and Lee, J., “Effect of heating location and size on mixed convection in lid-driven cavities,” Computers and Mathematics with Applications, Vol.59, 2010, pp. 3053-3065.
[17] Yang, Y. L., Lin, Y. C., “A Numerical Study of Natural Convective Heat Transfer in a Cavity Using a High-order Differential Scheme,” Journal of Aeronautics, Astronautics and Aviation, Series A, Vol.42, No.2, 2010, pp. 123-130.
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[24] de Vahl Davis, G., “Natural Convection of Air in a Square Cavity a Bench Mark Numerical Solution,” International Journal for Numerical Methods in Fluids, Vol. 3, 1983, pp. 249-164

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