臺灣博碩士論文加值系統

本文探討平板混合紊流場中，主流向、側流向的速度自相關性(velocity autocorrelation)函式型式之研究。平板混合紊流場可分為自由流(free stream)區與剪力流(shear layer)區；剪力流區存在較大的速度梯度，剪力較大，其速度自相關性震盪漸減得比自由流區快。本文以七個前人用於不同領域的速度自相關性函式，探討各函式在自由流區與剪力流區的適用性，並以文獻上所述自相關性的四個必要條件：(1) 速度自相關性函式為偶函數；(2)原點處斜率為零；(3) 符合積分時間尺度的定義；(4) 慣性次區(inertial subrange)的能量頻譜(energy spectrum)在高頻呈一定斜率遞減；加上速度自相關性會負值的震盪共五個條件，用來檢視各函式之符合程度，並且比較能否有效近似實驗值。
在大氣研究中，二階自我迴歸模型(second-order autoregressive mode)常被使用於與實驗值相比較，由於二階自我迴歸模型不符合前述條件中的兩個必要條件：原點處斜率為零以及積分時間尺度定義，故本文將二階自我迴歸模型函式的參數加上參數間應具有的相關性，分別定義出符合上述兩個條件且僅具一個參數的AR1函式，以及為符合積分時間尺度定義且具兩個參數的AR2函式。
本文分別以不同的高低速比、軸向截面位置以及雷諾數的情況與主流向速度自相關性函式做比較，發現Csanady(1973)提出的函式與Altinsoy及Tugrul (2002)提出的函式較無法表現出主流向自相關性的趨勢。不管在主流向或側流向，Frekiel(1953)提出的含有一個調節參數的函式與本文所提具兩個參數的AR2函式，就圖形近似程度和標準差來看，較能代表實驗值變化。然而就函式所具參數值變化趨勢而言，Frekiel(1953)所提含有一個調節參數的函式，其調節參數m之值在側流向皆比主流向值較大一點，且參數變化趨勢能和流場的特徵(剪力流區或自由流區)ㄧ致。

The study seeks for the suitable form of the streamwise and transverse autocorrelation functions in planar mixing layer. The flow field of turbulent planar mixing layer can be divided into two parts: the free stream region and the shear layer region. The shear layer region is inherited with remarkable pressure gradient and possesses larger shear force than the free stream region. The velocity autocorrelation coefficients in shear layer region oscillate and decay faster than those in the free stream region. This study collects seven velocity autocorrelation functions from the literature, and investigates their applicability in both the free stream and shear layer regions. It is reported that there are four requirements for the velocity autocorrelation function including (1)an even function,(2)zero slope at origin(τ=0), (3)to meet the definition of integral time scale,and (4)the slope of the logarithm of the energy spectrum in the inertial subrange being -2 at high frequency. In this study, a fifth requirement that the velocity autocorrelation should have negative oscillation feature is included.
The second-order autoregressive (AR) mode, which is expressed with three parameters, is widely used in atmospheric science. However, the second-order autoregressive mode does not match two of the aforementioned requirements, that is, zero slope at τ=0 and to meet the definition of integral time scale. In this study, the modified two-parameter and one-parameter AR modes, named as AR2 and AR1 functions, respectively, are proposed to remedy the drawbacks of the original AR function.
It is found the functions proposed by Csanady(1973) and Altinsoy and Tugrul (2002) cannot fit the tendency of the streamwise autocorrelation coefficient, while the functions proposed by Frekiel(1953) with one parameter and AR2 with two parameters can fit the experiment data well.

目錄…………………………………………………… i
表目錄…………………………………………………iv
圖目錄.…………………………………………………v
符號說明 ……………………………………………ix
函式縮寫符號說明……………………………………xi
第一章 緒論………………………………………… 1
1.1前言…………………………………………………1
1.2文獻回顧……………………………………………2
1.3實驗設備……………………………………………6
1.4實驗條件與流程……………………………………7
1.5研究目標……………………………………………8
第二章 速度自相關性必要條件…………………… 9
2.1速度自相關性的必要條件…………………………9
2.2Lagrangian與Eulerian自相關性函式之關係……11
2.3數值方法……………………………………………14
2.3.1 標準差…………… ……………………………14
2.3.2 非線性最小平方法………………… …………14
第三章 結果與討論 ………………………………… 16
3.1以必要條件檢驗經驗式……………………………16
3.2積分時間尺度的選取範圍…………………………20
3.2.1 主流向(u方向)…………………………………20
3.2.2 側流向(v方向)…………………………………22
3.2.3 縱流向(w方向)…………………………………23
3.3自相關性經驗式的曲線近似………………………23
3.3.1 無調節參數函式……………………………… 23
3.3.2 一個調節參數函式…………………………… 23
3.3.3 兩個調節參數函式…………………………… 24
3.3.4 三個調節參數函式…………………………… 25
3.3.5 AR、AR2、AR1的比較………………………… 25
3.4 F1與AR2的比較……………………………………26
3.4.1 剪力流區所有函式的比較…………………… 26
3.4.2 自由流區所有函式的比較…………………… 27
3.5F1函式與AR2函式之比較………………………… 28
3.5.1 主流向(u方向………………………………… 28
3.5.2 側流向(v方向)…………………………………29
3.5.3 縱流向(w方向)…………………………………29
3.5.4 小結…………………………………………… 30
第四章 結論與建議………………………………… 31
參考文獻 ………………………………………………34

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