傾斜方形空穴內自然對流混沌行為之數值模擬

Numerical Simulation of Natural Convection Chaotic Behavior in Tilted Square Cavity

黃建銘(Chien-Ming Huang)

指導教授 ： 吳文忠

國立虎尾科技大學/工程學院/航空與電子科技研究所/碩士(2011年)

https://doi.org/10.6827/NFU.2011.00137

摘要

本研究目的在於探討傾斜式方形閉合空穴內，Ra值範圍10^8至10^9，其方穴傾斜角度為30、45與60度。由二維數值模擬瞭解二維方形閉合式空穴在不同的傾斜角內部流場的行為。本文延續Chen[17]之研究，透過直接數值模擬法求解，以步進演算法(Fractional Step Method)計算Navier-Stokes方程式壓力項與速度項。第一步先其求解壓力Poisson方程式，再求解新的速度方程式，搭配相軌跡法與頻譜分析法來觀察流場行為與混沌判斷。
研究結果發現將熱壁面置於下方，Ra值在10^8時流場已經開始發生混沌現象。E點中央流場超過Ra=6×10^8也會開始讓流場進入混沌的狀況。傾斜30度與45度時，流場速度與流線未有明顯的差異性，當到達60度時，流場速度與流線將變得緩慢且不均勻。垂直速度對流場擾動所造成差異比較，相同溫差下流場速度大小30度為最大。

關鍵字

方形空穴 ； 步進演算法 ； 混沌行為

並列摘要

The objective of the present study is to explore flow field circumstances in a two -dimensional tilted cavity for a range of Rayleigh number from 10^8 to 10^9, with inclined angle 30, 45, and 60° in air. The study is extended Chen[17] that research the solution through Direct Numerical Simulation, and Navier-Stokes equations are solved by using the fractional step method. The results exhibited with phase trajectory method and frequency spectrum.
It was found that, the flows had exhibited chaotic motion, when Ra =10^8. As Ra=6×10^8, the flow field center of E point had transformed chaotic situation. There are no obvious difference for vertical velocity and streamline of 30°and 45° of tilted square cavity. When cavity tilted angle 60°, it become to irregular and slow compare with 30°and 45°. On the same Rayleigh number, the maximum of vertical velocity is 30 degrees.

並列關鍵字

Square Cavity ； Fractional Step Method ； Chaotic Behavior

參考文獻

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