- 學位論文
長方形Rayleigh-Bénard熱對流在臨界Ra下混沌行為之數值研究
Numerical Study of Chaotic Behavior under Conditions near the Critical Rayleigh-Bénard Convection in Rectangular Cavity
摘要
本研究目的在於探討長方型閉合式空穴內Rayleigh Bénard 熱對流混沌行為，Ra值範圍從〖10〗^5至5×〖10〗^8，藉由數值模擬瞭解二維矩型閉合式空穴在不同的Ra值內部流場的行為。本文採用直接數值模擬求解，以步進演算法(Fractional Step Method)計算Navier-Stoks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(phase trajectory method)與頻譜分析法(frequency spectrum)來觀察流場行為與混沌判斷。 研究結果發現將熱壁面至於下方，冷壁面至於上方，在長寬比為1時，流場在Ra=5×〖10〗^5時，整體流場處於層流狀態，當提升至Ra=6×〖10〗^6時轉變為週期流，直到Ra=5×〖10〗^7時，開始產生混沌現象。在長寬比為4時，在Ra值為5×〖10〗^5，流場為層流狀態，當Ra提高至6×〖10〗^6時，從層流轉變至週期流狀態中，當Ra提高為〖10〗^7時，流場保持在週期流狀態，直到超過Ra=5×〖10〗^7，流場內各點開始從週期流發生混沌狀態，兩個條件下皆在Ra=5×〖10〗^8時進入到紊流，AR=4的頻譜強度及速度皆高於AR=1。
並列摘要
The objective of the present study is to explore flow field circum stances in a two-dimensional cavity for a range of Rayleigh number from 〖10〗^5 to 〖10〗^8, The study used the solution through Direct Numerical Simulation, and Navier-Stokes equations are sloved by using the fractional step method. The results exhibited with phase trajectory method and frequency spectrum. The results found that the hot wall as for the bottom, cold wall as above, in the aspect ratio of 1, the flow field at Ra=5×〖10〗^5, the overall flow field in a laminar flow state, when Ra increase to 6×〖10〗^6 change to periodic state until Ra=5×〖10〗^7 begin to Chaos. In an aspect ratio of 4, Ra=5×〖10〗^5, the flow field for the laminar flow state, the transition from laminar flow to a periodic state when Ra increased to 6×〖10〗^6, when Ra=〖10〗^7, he flow field in the period to maintain flow state until more than Ra=5×〖10〗^7, starting from various points in the flow field-flow generating chaotic period, all in under two conditions Ra=5×〖10〗^8 into turbulence. AR=4 spectral intensity and speed are higher than AR=1.