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研究生:余信賢
研究生(外文):Hsin-Hsien Yu
論文名稱:賽氏黏度測量之電腦模型
論文名稱(外文):A Computer Model for Saybolt Viscosity Measurement
指導教授:陳大潘
指導教授(外文):Da-Pan Chen
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程系
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:2001
畢業學年度:90
語文別:中文
論文頁數:49
中文關鍵詞:有限單元賽氏黏度
外文關鍵詞:Finite ElementSaybolt Viscosity
相關次數:
  • 被引用被引用:0
  • 點閱點閱:151
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  • 下載下載:13
  • 收藏至我的研究室書目清單書目收藏:0
本文是有限單元分析之應用,主要在討論網格對流場分析的影響並建立賽氏黏度測量之電腦模型。首先介紹賽氏黏度計之測量方法及黏度間轉換與模型之設定,利用二維不可壓縮穩態之納維爾─史托克方程來作為系統模擬之方程式,之後討論解納維爾─史托克方程之方法(Babuska-Brezzi condition與近似趨近法),且對於有限單元的一些基本原理作介紹,並利用一些方法及技巧使問題簡化與解決,其後介紹將系統之變量求出的疊代方式(conjugate gradient method),並且對常見流場分析問題作研究。
This thesis is an application of finite element analysis, the goal is to discuss the influence of the mesh, and build a computer model for Saybolt viscosity measurement.
At first, we will introduce the method to measure the Saybolt viscosity and the transform between the Saybolt viscosity, kinematic viscosity, and absolute viscosity. And we will point out the model we build, and the difference between our model and real condition. In this paper, we use 2-D incompressible steady-state Navier-Stokes equations as the base function to solve our problem.
Secondly, will discuss the method we used — the penalty method. Besides, introduce some basic theory of finite element method, and use some tips to simplify the problem we met. And then, an introduction is given on conjugate gradient method we use to iterate the variation of system.
Finally, we will discuss some fluid problems and the advantage or disadvantage present in our computer model, and compare with the real condition.

中文摘要 ……………………………………………………………i
英文摘要 ……………………………………………………………ii
誌謝 …………………………………………………………………iii
目錄 …………………………………………………………………iv
表目錄 ………………………………………………………………vi
圖目錄 ………………………………………………………………vii
符號說明 ……………………………………………………………ix
一、緒論 ……………………………………………………………1
二、文獻回顧 ………………………………………………………3
三、賽氏通用黏度計 ………………………………………………9
3.1 測量裝置與方法 …………………………………………9
3.2 賽氏黏度與絕對黏度之轉換 ……………………………10
3.3 電腦模型與實際情況之關係 ……………………………11
四、有限單元數值計算與納維爾─史托克方程 …………………13
4.1 Babuska-Brezzi Condition ………………………………13
4.2 推導 ……………………………………………………13
4.3 線性三角單元 …………………………………………18
4.4 對流加速項的處理 ……………………………………19
4.5 有限單元的組合 ………………………………………20
4.6 Conjugate Gradient Method ……………………………23
五、程式之建構與計算 ……………………………………………27
5.1 產生網格及點資料 ……………………………………27
5.2 代入邊界條件 …………………………………………29
5.3 計算系統驅動力及勁度矩陣 …………………………29
5.4 代入Conjugate Gradient法計算速度變量 ……………30
5.5 將速度代回對流加速項作計算 ………………………30
六、實際範例與計算結果 …………………………………………31
6.1 Lid-Driven 2D Cavity Flow ……………………………31
6.2 Step Flow ………………………………………………35
6.3 Saybolt Viscosity Measurement …………………………40
七、結論 ……………………………………………………………44
參考文獻 ……………………………………………………………46
附錄 …………………………………………………………………48
[1] Dudley D. Fuller, “Theory and Practice of Lubrication for Engineers”, 2nd Edition, John Wiley and Sons, 1984.
[2] Robert D. Cook, David S. Malkus, Michael E. Plesha, “Concepts and Applications of Finite Element Analysis”, 3rd Edition, John Wiley and Sons, 1989.
[3] Richard H. Gallagher, “Finite Element Analysis, Fundamentals”, Prentice-Hall, Inc., 1975.
[4] O. C. Zienkiewicz, FRS, R. L. Taylor, “The Finite Element Method”, 4th Edition, Vol.1, McGraw-Hill, 1988.
[5] I. Babuska, “The Finite Element Method with Penalty”, Tech. Note BN-710, The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, August 1971.
[6] O. C. Zienkiewicz, “Constrained Variational Principles and Penalty Function Methods in Finite Element Analysis”, Lecture Notes in Mathematics : Conference on the Numerical Solution of Differential Equation, Edited by G. A. Watson, Springer-Verlag, Berlin, 207-214, 1974.
[7] J. N. Reddy, “Penalty Finite Element Analysis of 3-D Navier-Stokes Equations”, Computer Methods in Applied Mechanics and Engineering, 35, 87-106, 1982.
[8] Ralston Anthony, “A First Course in Numerical Analysis”, 1969.
[9] Alexander N. Brooks, J. R. Hughes, ”Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations”, Computer Methods in Applied Mechanics and Engineering, 32, 199-259, 1982.
[10] Alastair Cameron, “Basic Lubrication Theory”, 3rd Edition, Ellis Horwood, 1976.
[11] P. A. B. De Sampaio, “A Petrov-Galerkin Formulation for the Incompressible Navier-Stokes Equations Using Equal Order Interpolation for Velocity and Pressure”, International Journal for Numerical Methods in Engineering, vol

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