賽氏黏度測量之電腦模型

Abstract

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.