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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/48333

Title: 三維方腔拉穴流之分岔與穩定性分析
Anaylsis of Bifurcation and Stability in a
Authors: Tsao, Han
曹瀚
Contributors: 國立臺灣海洋大學:輪機工程學系
Keywords: 拉穴流場;非線性系統;渦漩結構;叉式分岔;霍普夫分岔;準週期分岔
lid-driven cavity flow;nonlinear system;cellular flow;pitchfork bifurcation;Hopf bifurcation;quasi-periodic bifurcation
Date: 2015
Issue Date: 2018-08-22T03:40:00Z
Abstract: 本文針對一三維矩型方腔槽中之拉穴流場,進行流場運動之數值 模擬,以探討其渦漩結構。矩形槽的四個邊牆與底部為不動之固體 邊界,唯其頂部(lid)為一流體邊界,在初始時整個矩形槽的流場為 靜止,而頂部之流體邊界突然存在一驅動速度,成為此流場之驅動 力,而開始造成流場運動。三維頂部驅動矩形槽中之流場,在60 年 代中期以後,即被廣泛的研究探討,所以截至目前為止研究的文獻 相當的豐富。隨著更多有關三維拉穴的研究出現,以及電腦計算硬 體的快速發展,人們始有能力模擬三維的拉穴流場,發現其流場特 性與二維的流場並不盡相同。依目前的研究文獻,所知的最大差別 乃是在相同值下,二維的流場有穩態存在,而三維流場為不斷變動 之不穩態流場。同時,在三維的流場中,有許多屬於三維流場才存 在的渦流特徵,這些是二維流場中所不存在的。因此近年來有關三 維拉穴流場的研究,著重於三維渦流場的特徵與其發生機制的探討。 本文的研究方向是求解不可壓縮流Navier-Stokes。論文架構在多 為正交曲線座標系統上,於非交錯網格之均勻網格上壓力與速度耦 合配置方式下,採用不可壓縮黏性流之統御方程式、控制方程無因 次化及空間離散格式之DRP方法以及時間離散方法之Runge-Kutta 高階顯性時間積分法。方法主要是依據質量的守恆性、動量守恆性、 邊界條件設定的正確性與避免物理性震盪的條件下率先採用控制方 程式之精確解作為離散模型,以非交錯的網格配置的有限差分方法, 建構三維曲線座標系統的統御方程式。延續與著重在數值模式開發, 從在三維頂蓋驅動方拉穴流場中渦漩結構的特徵與其發生機制的探 討。在目前的文獻中,我們主要集中在一系列複雜的三維非線性動 力現象,利用分岔理論與拓撲理論進行三維拉穴流場的分析與探討。 在研究非線性系統的動力學現象包括叉式分岔、霍普夫分岔、週期 性的超諧波和準週期分岔等三維非線性動力現象。本文主要探討在 近臨界Re值時對於拉穴場中三維渦漩結構的影響,其重點為不同值 下的三維流場演化以及其差異性。
In this paper, a three-dimensional rectangular square hole flow field pull chamber tank, the numerical simulation of the flow field of sports, in order to explore its swirling structure. Wall and the bottom four rectangular groove is solid boundaries do not move them, only the top (lid) is a fluid boundary, the entire flow field initially rectangular groove is stationary and the fluid boundary at the top of a sudden there is a driving speed,become the driving force of this flow field, and begun to cause the flow field sports. Three-dimensional rectangular tank top drive ilk field in the mid-60's, namely to explore a wide range of research, so far quite rich research literature. As more research about the three points appear Vera, and the rapid development of computer hardware computing, people before they have the ability to simulate three-dimensional flow field pull cave and found that the two-dimensional flow field characteristics of the flow field does not do the same. According to the present research literature, but the biggest difference is known at the same value, the two-dimensional steady-state flow field presence, but not three-dimensional steady flow field flow field is constantly changing it. Meanwhile, the three-dimensional flow field, there are many characteristics belong vortex only exists dimensional flow field, which is two-dimensional flow field that does not exist. So in recent years the study of flow field three Vera points, focusing on the characteristics of three-dimensional eddy current field to explore the mechanism of its occurrence. This paper is the continuation of our study of flow development from a motionless conductive state in a lid-driven cavity flow. In our previous paper [1-2] we focused mainly on a series of complex nonlinear bifurcations in a three-dimensional partially heated rectangular cavity. Prior to chaos, the dynamic phenomena in the investigated nonlinear system include pitchfork bifurcation, Hopf bifurcation, periodic ultra-harmonics, and quasi-periodic bifurcation. In this study the formation of different cellular flow structures and the scenario of pitchfork bifurcation are addressed. The solutions for the incompressible fluid flow investigated at different Reynolds numbers are computed from the divergence-free compensated solution algorithm and the wavenumber-optimized upwinding scheme for accurately approximating the convection terms. The three-dimensional cellular flow details and the physically meaningful vortical flow insight are extracted to improve our understanding of the change of three-dimensional vortical and cellular flow features with respect to the Reynolds number in the lid-driven cavity flow.
URI: http://ethesys.lib.ntou.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=G0010166010.id
http://ntour.ntou.edu.tw:8080/ir/handle/987654321/48333
Appears in Collections:[輪機工程學系] 博碩士論文

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