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研究生:蔡政臻
研究生(外文):Jheng-Jhen Tsai
論文名稱:使用JointPDF重新檢驗平面混合流場之自我保持狀態
論文名稱(外文):Reexamination of the self-preservation state in the planar mixing layer with Joint PDF
指導教授:張克勤張克勤引用關係
指導教授(外文):Keh-Chin Chang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:124
中文關鍵詞:傾斜角平面混合層自我保持
外文關鍵詞:planar mixing layerself-preservinginclined angleJPDF
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傳統上,對於二維平面紊態混合層(planar mixing layer)流場,其流場狀況確切發展達自我保持狀態位置的判斷方式,通常是藉由觀察紊流特性量分佈輪廓不再隨下游位置改變來判斷,但此方式並未能充分精確地界定出流場是否已進入自我保持狀態,因此本研究利用交叉式探管之熱線測速儀(hot-wire anemometry),所量得的主流向(streamwise)瞬時速度u以及側向(transverse)瞬時速度v,建構成的JPDF(joint probability density function)影像圖形,在 處會呈現一傾斜的橢圓形分佈,因此,藉由圖形辨識方法與理論計算出橢圓形的傾斜角(inclined angle),觀察此涵蓋三種二階紊流特性量的單一參數傾斜角值,是否隨著主流向位置演進至一漸近不變值(asymptotic constant),以作為判斷流場是否到達自我保持(self-preservation)狀態的依據;此外,透過對JPDF影像圖形的真圓度(roundness)演化分佈以曲線擬合所形成的曲線,與其在高低速兩側自由流區的漸近值之間的交點處,作為新的混合長度定義,可發現與過去對於剪力流層混合長度(δ=y0.95-y0.05)的定義範圍有明顯差距.並將此新一定義範圍與skewness factor和flatness factor的峰值位置之間距作比較,亦可發現彼此十分接近,因此未來或許可使用偏態與峰態係數之峰值位置間距長度,作為流場中新的混合長度定義。
Traditionally, achievement of the self-preserving state in a planar turbulent mixing layer is justified by the invariant sectional profiles of some turbulent flow quantities. However, this is not a precise approach to justify the achievement of self-preserving state in turbulent mixing layer. It is observed the joint probability function (JPDF) of the fluctuating velocities of streamwise and transverse components exhibits an inclined elliptic shape at the position of η=0 which denotes the transverse position of the half of the values of high-speed and low-speed stream velocities (i.e.y0.5 ). The inclined angle (β) at η=0 (i.e. β︱η=0 ) is mathematically a function of Reynolds stress and two root-mean-squared fluctuating velocities of streamwise and transverse components. The value of β︱η=0 will approach an asymptotic level as the flow state moves into the self-preserving. Thus, the evolution of β︱η=0 , which is a single parameter in the turbulent mixing layer, is suggested to monitor the achievement of self-preserving state. As β︱η=0 reaches its asymptotic value, it indicates the achievement of self-preserving state. In addition, the transition from the shear layer to the two other free stream regions can be monitored through the transverse variation of the roundness of JPDF, which is better than the conventional approach distinguished by y0.95 and y0.05.
摘要 I
Abstract II
誌謝 IV
目錄 V
表目錄 VI
圖目錄 VII
符號說明 X
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 實驗設備與條件 4
1.4 研究目標 6

第二章 Joint PDF影像圖形之傾斜角的圖形辨識法與理論解 7
2.1紊流與統計基礎特性驗證 7
2.1.1 Statistical Stationary Analysis 7
2.1.2 Nyquist Theorem 8
2.1.3 檢驗平面混合紊流之自我保持狀態的傳統判別方式 9
2.2 JPDF影像圖形的識別方法 10
2.3 JPDF影像圖形傾斜角特性之辨識應用 14

第三章 結果與討論 16
3.1 相同速度比不同雷諾數對紊流特性量演化之影響 16
3.2 相同雷諾數不同速度比對紊流特性量演化之影響 18
3.3 以FFT方法確認流場之自我保持狀態的截面位置 20
3.4 JPDF影像圖形的延伸應用 22

第四章 結論與建議 25
4.1 結論 25
4.2 未來工作及建議 25
參考文獻 27
附錄 77
自述 124
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Azim, A. M., Islam, S. A., and Ali, T. M., “Mixing layer flow with initial non-parallel streams,” Proceedings of Int. Con. on Mechanical Engineering, ICME2005 28-30 December 2005, Dhaka, Bangladesh.

Bell, J. and Mehta, R., “Development of a two-stream mixing layer from tripped and untripped boundary layers,” AIAA Journal, Vol.28, No.12, 1990, pp.2034-2042.

Bradshaw, P., “The effect of initial conditions on the development of a free shear layer,” Journal of Fluid Mechanics, Vol.26, No.02, 1966, pp225-236.

Dimotakis, P. E., “The mixing transition in turbulent flows,” Journal of Fluid Mechanics, Vol.409, 2000, pp.69-98.

Druault, P., Delville, J., and Bonnet, J., “Experimental 3D analysis of the large scale behavior of a plane turbulent mixing layer,” Flow,Turbulence and Combustion, Vol.74, No.2, 2005, pp.207-233.

Dziomba, B. and Fiedler, H. E., “Effect of initial conditions on two-dimensional free shear layers,” Journal of Fluid Mechanics, Vol.152, 1985, pp.419-442.

Guo, F., Chen, B., Guo, L., and Zhang, X.,“Effects of Velocity Ratio on turbulent Mixing Layer at high Reynolds number,”The 6th International Symposium on Measurement Techniques for Multiphase Flows, Journal of Physics : Conference Series 147(2009).

Kolmogorov, A. N., “The local structure of Turbulence in Incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR, Vol. 30, No. 4., 1941., pp301-305

Li, C. T., Chang, K. C., and Wang, M. R., “Evolution of Joint PDF of Turbulent velocities in planar mixing layer,” Int. Conf. on Jets, Wakes and Separated Flows, ICJWSF-2008 September 16-19, 2008, Techanical University of Berlin, Berlin, Germany.

Rogers, M. M. and Moser R. D., “Direct simulation of a self-similar turbulent mixing layer, ”Physics of Fluids, Vol.6, No.2, 1994, pp.903

Townsend, A. A., The Structure of Turbulent Shear Flow: Cambridge, London, 1976, Chaps.6, 195.

Uozumi, J. and Asakura, T., “First-order probability density function of the laser speckle phase,” Optical and Quantum Electronics, Vol.12, No.6, 1980, pp.477-494.

李權庭,平板混合紊流結構之實驗分析,國立成功大學航空太空工程學系碩士論文,2004。

吳韋志,背向階梯下游流場發展之實驗分析,國立成功大學航空太空工程學系碩士論文,2009。
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