臺灣博碩士論文加值系統

本文旨在研究三維軸對稱理想流動。建立在三維流場對稱之性質下，由史托克流線函數推導三維流線、流線函數與速度位勢的關係。並利用所得之觀念設計線源與線沉及均勻流動的安排，期望以此推導迴轉成體四周流動的近似解。研究中，以Matlab求解所遇到之數學計算，分析在此方式分析流場時，在數學模式中所會遇到之奇異狀況以及無法求解之情形。

Abstract

This thesis aims to study the three-dimensional, axially symmetric, potential flow. By using the symmetric quality of the three-dimensional flow as our theoretical foundation, Stokes’ stream function can be used to infer the relationship among streamline, stream function and velocity potential. Then we use the result to design the arrangement of line sources and sinks in conjunction with a uniform flow. It is possible to develop approximate solution for flows about bodies of revolution. In this research, the mathematic calculation, resulting from using Matlab to resolve polyinomial , is used to analyze the flow. When the mathematic calculation is used, one would come across some strange situations, which one is unable to give an answer to. Thus, this thesis tried to find out an explanation to those situations.

目錄

誌……………………………………………………………...Ⅰ
中文摘要…………………………………………………………..……Ⅱ
英文摘要……………………………………………………………..…Ⅲ
目錄…………………………………………………………………...Ⅳ
第一章 緒論……………………………………………………………1
1-1 研究動機……………………………………………………...1
1-2 研究目的與本文組織………………………………………….1
第二章 理論介紹………………………………………………………3
2-1 史托克流線函數……………………………………………...3
2-2 三維速度場與流線、流線函數之間的關係推導…………….5
2-3 三維均勻流場……………………………………………….....7
2-4 三維的源流與沉流………………………………………….....9
2-5 三維軸對稱物體流場推導…………………………………...10
附圖………………………………………………………………..14
第三章 求解方式及實例演算…………………………………………18
3-1 基本假設與系統方程式、初始及設定條件...........................18
3-2 研究方法及步驟……………………………………………...19
3-3 以MATLAB解線性代數方程式...…………………………..21
3-3-1解的存在與唯一性判定……………..…..………….…22
3-3-2低確定性統…………………...………………….….…22
3-3-3過確定性系統…………………..…………….………..23
3-4 實例演算…………………………………………………...…24
附圖………………………………………………………………..31
第四章 研究分析與討論…………………………………………..…..45
附錄……………………………………………………………………..47
附表……………………………………………………………………..60
參考文獻………………………………………………………………..78

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