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研究生:吳東州
研究生(外文):Don-Joe Wu
論文名稱:三維矩形管層流場之非等格距數值分析
論文名稱(外文):Numerical Solutions to Laminar Flow in a 3-D Rectangular Duct Using Non-Uniform Grid
指導教授:雷顯宇
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:機械與機電工程學系
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:2006
畢業學年度:94
語文別:中文
論文頁數:77
中文關鍵詞:SIMPLER分佈變化率阻尼因子雷諾數
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由於奈米科技在近年來被廣泛的應用在各個領域,因此不論傳統或高科技產業都朝縮小尺寸增加產量前進,也由於奈米科技的發展,造成電腦記憶容量及處理速度大幅的躍近,使得運用數值方法模擬流場的計算流體力學技術能有快速的發展且越來越多複雜的問題均有可能因為科技的進步而被解決。

本文主要是用自撰之FORTRAN程式(使用Patankar之SIMPLER Algorithm的數值方法),而為了能夠有效且快速的計算出正確的流場,採用非等格距(Non-Uniform Grid)的格點配置來分析內流場裡的物理現象,並與等格距(Uniform Grid)的格點配置做一比較與驗證,以證明使用非等距離格點配置能以相較於等距離格點少的格點數亦得到同等正確的解。

本文先以入口為完全發展流(Fully Developed Flow)解析解及均勻流(Uniform Flow)並固定入口截面為1:1來與數值方法及經驗公式相互比較,皆可得到極佳的結果。證明本文程式在解決三維矩形管層流內流場之正確性。在非等格距的測試中,入口為均勻流,以等格距較密的網格取出一組夠準的數據當做標準,爾後再以非等格距較少的格點數驗證非等格距同樣能有不錯的結果。再來以非等格距的優勢,做層流場內不同雷諾數的測試。找到分佈變化率α與阻尼因子β的最佳值(α=0.1,β=3.5,經由入口截面1:1情況下測試出相較於等格距可節省92 %的格點)後,試著改變矩形管入口截面比例,針對Y-Z方向探討是否可再透過非等距格點安排能有節省格點數的空間。結論為當入口截面比例為1:2時,Y-Z方向的格點數只要取20×30,而1:4時則為20×50即可得到正確數值解。最後再以會造成迴流區的入口障礙物問題,驗證非等格距格點配置同樣可以在障礙物問題中突顯它的優勢。上述的分析皆能得到不錯的結果,證實了非等格距格點確實能有效地減少格點的數量以節省運算時間,同時得到正確數值解。

本文程式對三維矩形管的內流場非等格距系統提供了基本架構,可擴大於求解熱場、增加障礙物,並可進一步應用於圓管及紊流場等等,更能符合實際工程上的應用。

關鍵字:SIMPLER、分佈變化率、阻尼因子、雷諾數
The application of naro technology in both conventional and high tech. industries has grown rapidly in recent years. The RAM & HD storage & CPU speed are also benefited from it. Flow simulations using Computational Fluid Dynamics (CFD) replaces many experiments in analyzing complicated flow & heat transfer problems.

The objective of this thesis is to analyze the 3-D fluid flow in a rectangular duct using a self written FORTRAN program with Patankar’s SIMPLER Algorithm. The Non-Uniform grid & Uniform grid set-up are both studied and results are compared in an attempt to verify the advantages of Non-Uniform grid set-up in saving the total numbers of grids needed and hence the computation time.

Both the fully developed flow & developing flow in the entrance region of a 3-D square duct are analyzed. Results are compared with those of analytical solution (fully developed flow) & empirical relation (developing flow) with very high accuracy. The advantages of Non-Uniform grid set-up is confirmed through the comparison of results at Re D=30. Then, the program is used to study the effects of the values of α & β in the Non-Uniform grid set-up. It is found a total saving as mush as of 92% in the no. of grids & computation time could be reached with Non-Uniform grid set-up. The rectangular ducts with cross-section area aspect ratio of 1 : 2 & 1 : 4 are studied in order to examines the effect of aspect ratio to its total number. of grid. All the results show the much greater advantages of Non-Uniform grids set-up over uniform grids.

It is recommended the effects of obstructions & forced convection study in the 3-D rectangular flow could be further analyzed. The Non-Uniform grids set-up could also be applied to circular pipe flow or internal turbulent flow.

Keywords:SIMPLER、Slope of the Distribution、Damping factor、Reynolds Number
中文摘要………………………………………………………………… i
英文摘要….……………………………………………………………..iii
目錄…………………………………………………...…………………iv
表目錄…...………………………………………………………...….…vi
圖目錄…………………………...……………………………………...vii
符號說明………………………………………………………………....x
第一章 緒論……………………………………………………………..1
1-1 前言……………………………………………………………...1
1-2 研究動機………………………………………………………...1
1-3 文獻回顧………………………………………………………...2
第二章 理論分析與數值方法…………………………………………..3
2-1 基本假設………………………………………………………...3
2-2 統御方程式……………………………………………………...3
2-3 格點配置………………………………………………………...5
2-3-1 交錯式格點………………………………………………..5
2-3-2 交錯式格點於邊界上的配置……………………………..6
2-3-3 非等格距參數……………………………………………..6
2-4 SIMPLER之理論模式………..……..…………..…………….…7
2-5 SIMPLER之數值方法…….….....….…………….……………...8
2-5-1動量離散方程式…………………………………………...8
2-5-2壓力修正方程式…………………………………………...9
2-5-3壓力離散方程式…………………………………………..11
2-5-4 SIMPLER法求解步驟..…………………………………..11
2-6代數方程式求解法…………………………………………...…12
2-7邊界條件………………………………………………………...13
2-8誤差標準的設定………………………………………………...13
2-9加速收斂的方法………………………………………………...14
第三章 結果與討論…….………………………………………………16
3-1 Bench mark之測試………………………...……………………16
3-1-1完全發展流測試……………..……...……………………16
3-1-2入口均勻流測試……………..……...……………………17
3-2 流場測試……………...…………………...……………………18
3-2-1等格距最佳化測試…………..……...……………………18
3-2-2非等格距比較………………..……...……………………19
3-2-3效率比較……………………..……...……………………19
3-2-4層流場內不同雷諾數格點配置的測試.…………………19
3-2-5不同入口截面比例Y-Z方向格點配置的測試.…………20
3-3 迴流區測試…………...…………………...……………………21
3-3-1入口障礙物高度與迴流區長度之關係…….……………21
3-3-2模擬二維平板流情況………..……...……………………21
3-3-3三維矩形管流情況…………..……...……………………21
3-3-4等格距之最佳化……………..……...……………………22
3-3-5非等格距之比較……………..……...……………………22
第四章 結論與展望…….………………………………………………23
4-1 結論…………….………………………………………………23
4-2 未來展望……….………………………………………………24
參考文獻…………..…….………………………………………………25
附表………………..…….………………………………………………27
附圖………………..…….………………………………………………31
附錄A 動量離散方程式推導……..……………………………………69
附錄B 壓力修正值離散方程式推導..….…………...…………………72
附錄C 壓力虛擬值離散方程式推導..….…………...…………………74
附錄D TDMA代數方程式推導..….………………...…………………76
[1]廖欽彬,“不同障礙物分佈對平行板層流場影響之數值分析”,國立臺灣海洋大學,1998
[2]周癸翰,“不同障礙物分佈對圓管層流場影響之數值分析”, 國立臺灣海洋大學,2000
[3]錢志宏,“不同障礙物分佈對三維矩形管層流場影響之數值分析”,國立臺灣海洋大學,2001
[4]謝耀昌,“非等格距平行板層流場之數值分析”, 國立臺灣海洋大學,2005
[5]Patankar S . V . , “Numerical Heat Transfer and Fluid Flow”,
McGraw-Hill, New York. , 1981
[6]Fletcher C . A . J, “ Computational Techniques for Fluid Dynamics 2 – Specifi c Techiques for Different Flow Categories ”,
Springer-Verlag ,1987
[7]V. M. Filippov “Experimental Investigation of the Development of Laminar Flow in Rectangular Ducts”, Fluis Mechanics-Soviet Research, Vol.9,No.3, 1980
[8]MOTOYOSHI TACHIBANA , NOBUYOSHI KAWABATA , and HIROKAZU GENNO “Steady Laminar Flow of Power-law Fluids in the Inlet Region of Rectangular Ducts” Vol.30, No.3, 1986
[9]A. R. Berker,“Integration Des Equations Du Movement Dun Fluid Visqueux Incompressible”, Encyclopedia of Physics Vol.8, 1963
[10]Md. Moazzem Hossain and Gregory B . Raupp,“Three-Dimensional Developing Flow Model for Photocatalytic Monolith Reactors”,AICHE Journal, Vol.45, No.6, 1999
[11]L . S . Han ,“Hydrodynamic Entrance Lengths for Incompressible Laminar Flow in Rectangular Ducts”, J. Appl. Mech , Vol.27 , 1960
[12]G . S . Beavers , E . M . Sparrow and R . A . Magnuson,“Experiment on Hydrodynamically Developing Flow in Rectangular Ducts of Arbitrary Aspect Ratio”, Int . J . Heat Mass Transfer, Vol.13, 1969
[13]R . Quadir and M . Zamir ,“ Entry Length and Flow Development in Tubes of Rectangular and Elliptic Cross Section
,Laminar and Boundary Layers”,Vol. 14 , 1997
[14]C . L . Wiginton and C . Dalton, “ Incompressible Laminar Flow in the Entrance Region of a Rectangular Duct ” Journal of Applied Mechanics ,Vol.37, 1970
[15]Pozrikidis C. “Introduction to Theoretical and Computation Fluid Dynamics”,New York Oxford, 1997
[16]G . de Vahl Davis and C.Fletcher “Computational Fluid Dynamics”Amsterdam;New York;North-Holland , 1988
[17]C . Pozrikidis “Introduction to Theoretical and Computational Fluid Dynamics”New York;Oxford University Press , 1997
[18]David F . Rogers “ Laminar Flow Analysis ”Cambridge;New York;Cambridge University Press , 1992
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