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研究生:朱國棟
研究生(外文):Ju, Gwo-Dong
論文名稱:密閉圓筒中三維流場之數值模擬
論文名稱(外文):Numerical Simulation of Three-dimensional Flow in a Closed Cylindrical Container by a Rotating Disc
指導教授:楊德良楊德良引用關係---
指導教授(外文):Der-Liang Young
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學系研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:6
中文關鍵詞:對稱性破壞軸對稱非軸對稱邊界擾動週期混沌
外文關鍵詞:symmetric breakingaxisymmetricnon-axisymmetricperturbed boundary conditionperiodicchaotic
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流體在旋轉圓筒之渦流運動,為一古典而有趣的流力問題之一,隨著探討工具的進步,
由理論、數模及實驗等各方位之研究,目前已有很好的進展。然而絕大部份的研究,
均假設流場為軸對稱,且僅適於低雷諾茲數的流場,至於較高之雷諾茲數,從實驗中發
現,當Re超過某一臨界值後,流場會轉變為一非軸對稱的現象。在時間上也可能出現週
期性或非週期性的結果,此種所謂的對稱性破壞(symmetry breaking),為流場不穩定的
現象,也是流體動力學最為困難之題目。
為了探討真實的三維流場,乃採用廖清標博士所發展的三維非定常Navier-Stokes方
程式之數值模式,並加以改進,來探討密閉圓筒的流場。在此,我們固定細長比As=2.5,
並以兩種路徑來尋求非軸對稱的臨界雷諾茲數 ,1)純底盤旋轉:底盤由靜止開始啟動,
Re保持不變。當Re=4664時,起初流場屬於軸對稱的現象,但計算至t>1200時,流場開始
呈現非軸對稱的現象。當Re=4800時,流場自始至終皆呈現非軸對稱;2)加入邊界擾動:
用意是讓非軸對稱的現象提早發生,且類似於實驗上無法抑制邊界上的擾動,然後將擾動
過的流場當作初始條件。當Re=3445時,呈現間歇性的非軸對稱流場,而當Re=4664則是一
直處於非軸對稱的狀態。
在時間上,我們亦以兩種路徑來描述流場的運動行為,1)純底盤旋轉:Re=4664時,流
場屬於週期運動(periodic)。2)加入邊界擾動後的流場:Re=3445時,流場最後屬於次和諧
(subharmonic)運動,而Re=4664在不同的點卻有著不同的特性,有的是週
期性運動,有的則
屬於混沌運動。
吾人認為渦漩迸裂之發生與環向渦度值有密切關係,而做一初步之探討。發現當環向渦度
達到最大值時,會發生渦漩迸裂,並得到滿意之推論。
It is a classical and interesting problem of fluid mechanics for the
vortex motion of fluids within a cylindrical container with rotating bottom
disc. Theories, numerical simulations, and experiments have been well
undertaken in the exploring processes. However, almost researches assume
flow field is axisymmetric in space breaking and merely valid for the low
Reynolds numbers. When Re exceeds some critical value, flow field may become
non-axisymmetric state, as observing in the experiment. In time breaking,
flow field may show periodic or aperiodic results or even chaotic behavior.
And this is the so called symmetry breaking in nonlinear dynamics and is a
phenomenon of hydrodynamics instability and is a difficult subject of flow
dynamics.

To explore really three-dimensional flow field, we use and improve Dr. C. B.
Liao''s numerical model of the Navier-Stokes equations. Here, we select a fixed
aspect ratio As=2.5 and search the critical Reynolds number Re
of the non-axisymmetry
in two routes. 1)unperturbed boundary condition: The bottom disk rotates from
rest for a constant fixed Re. When Re equals to 4664, the flow
field is symmetric
initially, whereas it becomes non-axisymmetric until t>1200.
When Re equals to 4800,
the flow field always reveals non-axisymmetric phenomena. 2)perturbed boundary
condition :The purpose is to let flow field become non-
axisymmetric more earlier.
That is also similar to the experimental installation which can''t restrain the
perturbation from the boundary, and then we take the perturbed
field as an initial
condition and recapture the original unperturbed boundary
condition. When Re equals
to 3445, the flow field shows non-axisymmetric intermittently.
When Re equals to 4664,
it is non-axisymmetric all the time.



As far as time breaking is concerned, we also describe the motion of the
flow field in two routes. 1)unperturbed boundary conditions: When Re equals
to 4664, the flow field is periodic. 2) perturbed boundary
condition: When Re equals to
3445, the flow field is subharmonic in the long run. However,
when Re equals to
4664, there is different character at different domain points.
Some domain points are
periodic and some show chaotic behavior.

It is convinced that vortex breakdown and azimuthal vorticity play a close
relationship. So the topic is deeply discussed and is concluded
that when azimuthal
vorticity reaches the maximum value, the vortex breakdown generates.
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