以直接數值模擬具轉盤密閉圓筒中之流場週期性運動

Direct Numerical Simulation for the Periodic Motion in a Closed Cylinder with a Rotating Disk

楊德良(Der-Liang Young) ； 胡文勇(Wen-Yaung Hu) ； 廖清標(Chin-Biau Liao)

《中國航空太空學會學刊》 27卷3期 (1995/09) Pp. 355-365

https://doi.org/10.6124/TAASRC.199509_27(3).09

摘要

本文利用數值模式來直接摸擬具轉盤密閉圓筒流場的運動，流場的控制方程式爲Navier-Stokes方程式，將它無因次化後，控制方程式出現兩個參數：細長比As與雷諾數Re。我們固定As=2.0而改變雷諾數以製造不同的流場，結果發現當流場雷諾數爲2,000時，流場最後到達穩定狀態；當雷諾數爲3,000時，流場以頻率織0,4063做週期運動；當雷諾數改爲5,000時，流場以頻率0.052做週期運動；當雷諾數增爲5,500時，流場的運動頻率變爲0.026，此頻率恰爲雷諾數5,000運動頻率之一半，週期則增爲兩倍，這可能是所謂的週期倍增(period doubling)現象。利用頻譜與相位圖的分析，我們更能清楚了解流場的特性。希望此類之計算結果能提供一些訊息，使在密閉圓筒流場特性的研究能更進一步，諸如更合理的解釋渦漩迸裂，分岐與混沌等有趣的物理現象。

關鍵字

週期性運動 ； 分岐 ； 週期倍增 ； 非週期性運動 ； 混沌

並列摘要

This study makes use of the numerical method, a semi-projection method, to directly simulate the flow field in a cylinder with a rotating disk at the end-wall. The governing equations are Naiver-Stokes equations. After nondimensionalizing, the governing equations are associated with two parameters the aspect ratio, As and Reynolds number, Re. We fix the As=2.0 and vary the Re to study the different flow fields. We discover that when Re=2,000 the flow is steady. Increasing Reynolds number to 3,000, 5,000 and 5,500, the flow fields are periodic motions with frequencies 0.04063, 0.052 and 0.026, respectively. The frequency of Re=5,500 is half that of Re=5,000. Then the period is double. This may be the phenomenon of the period doubling. We use the Fourier spectrum and phase plane to analyze the computational data. They make us understand the flow field more clearly. We hope this analysis can provide some information to extend the research of other related field problems, such as the details of vortex breakdown, bifurcation and chaos, and so forth.

並列關鍵字

Periodic motion ； Bifurcation ； Period doubling ； Nonperiodic motion ； Chaos