臺灣博碩士論文加值系統

本論文之主要目的以二維非穩態數值計算平台，模擬傾斜式方形空穴內臨界Ra值10^7到10^9的流場行為，採用步進演算法計算N-S方程式，由二維的數值模擬，了解傾斜式方形空穴內不穩定發生的行為。本研究數值方法採用步進(Fractional Step Method)演算法，將N-S方程式中的速度與壓力分別處理，求解壓力Poisson方程式，並配合理想氣體方程式獲得密度值，再由質量流率中求得速度值，在二維非穩態的數值計算中把密度變化考慮到方程式，可以獲得更正確的結果。在時間項與非線性對流項分別以二階準確Adams-Bashforth方法與二階方法處理之。判斷混沌方面則是使用相軌跡方法(phase trajectory method) 與頻譜分析(frequency spectrum)，可以看出週期或是為混沌行為。
研究之流場範圍自10^7到10^9、傾斜角度Φ=45°，依研究數值顯示，傾斜空穴內的流場在Ra = 10^7仍為層流場，提高Ra值達到 6×10^8將變成紊亂之流場。

The objective of the present study is to explore when and how the instability of 2-D natural convection in a tilted cavity. The time-dependent governing equations are solved by using the fractional step method. The time-advancement sequence is treated using the second-order Adams-Bashforth scheme, while the spatial discretization is made by the second-order QUICK scheme. The problem to be investigated is the natural convection in 2-D dimensions under the formulation without any approximations.
The problem is the natural convection in a two-dimensional tilted cavity for a range of Ra from 107 to 109 with inclined angle Φ=45°air. The cavity flows at Ra = 10^7 is steady, laminar. As Ra is further increasing to 6×10^8 or more.

目錄
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……xiii
第一章 前言……1
1.1 研究動機……1
1.2研究背景與目的……1
第二章 文獻回顧……3
第三章 統御方程式……5
第四章 數值方法……8
4.1 步進演算法……8
4.2 程式演算的步驟……10
4.3 混沌判斷準則……11
4.4 邊界條件……12
第五章 結果與討論……14
5.1 程式驗證……14
5.2 二維傾斜式方形空穴問題探討……14
5.3 流況一(傾斜角度0度時Ra=10^9……15
5.4 流況二(傾斜角度45度時Ra=10^7)……16
5.5 流況三(傾斜角度45度時Ra=10^8……16
5.6 流況四(傾斜角度45度時Ra=6×10^8)……17
5.7 流況五(傾斜角度45度時Ra=10^9……18
5.8 比較傾斜角度45度時Ra=10^7和Ra=10^8……19
5.9 比較傾斜角度45度時Ra=10^8和Ra=6×10^8……19
5.10 比較傾斜角度45度時Ra=10^8和Ra=10^9……20
第六章 結論……21
參考文獻……64
Extend Abstract
作者自述

參考文獻
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