本研究是發展一套四維質點影像測速技術，以定量量測紊流場中三維空間隨時間變化之速度場資訊，進而探討微尺度紊流(fine scale turbulence)之基本結構。四維質點影像測速技術乃由高速連續來回掃瞄之雷射光頁產生器、兩台同步高速攝影機、影像處理系統和自製之同步控制器所組構而成，可獲取隨時間變化的三維空間質點影像(每張二維量測影像大小約1.4 cm 1.2 cm，含480 420 pixels，空間解析度約29μm，可解析紊流場中Kolmogorov尺度)，透過空間與影像間的數學轉換函數，得到四維全場速度場資訊。
本實驗針對由垂直振動網柵於一水箱中，所產生之零平均剪應力(zero-mean-shear)紊流場，作四維速度場量測並分析紊流場之微尺度結構。含兩例：單網柵和雙網柵紊流場，前者紊流強度會隨離網柵距離增加而遞減，後者可於兩網柵中心區產生一近似靜態等向性紊流(nearly stationary isotropic turbulence)。我們定量量測兩紊流場之四維速度資訊，並計算紊流場之渦度(vorticity)、主應變率方向(principle strain rate direction)以及動能消散率場(kinetic energy dissipation rate field)，再藉由統計分析方法分析紊流之微小尺度結構。
單/雙網柵紊流場之實驗結果均顯示紊流微小尺度結構與紊流場中速度梯度具相關性，即流場中具有明顯速度梯度處，其動能消散率值較高，而紊流微小尺度結構即由那些在流場中具最高消散率值的部分所組成，其分佈具有高度的間歇性並且高消散率部分僅在整體量測空間中佔很少的比例，約2%而已。我們發現單/雙網柵(零平均剪應力)紊流場之微小尺度結構並存有“似線”(line-like)、“似面”(sheet-like)和“似塊”(blob-like)三種基本結構，此發現與Burger (1948) 和 Townsend (1951)對紊流渦度場之描述類似，也與Shy et al. (1999)應用三維雷射誘導螢光量測技術，針對同樣的網柵紊流場作純量消散率場(scalar dissipation rate field)量測結果相似，但與Buch & Dahm (1991)於自由剪力(free shear)紊流噴流流場之純量消散率場之量測結果，即似面結構為所有紊流微尺度之唯一結構，有很大的不同，顯示自由剪力紊流與零平均剪力紊流存有不同特性。
單/雙網柵紊流場似線結構之平均直徑約為1~2 Kolmogorov尺度，我們估算所有微尺度結構，當其長度大於其直徑3倍以上則歸類為似線結構，約佔20%/25%；當微尺度結構之長度近似於其寬度但遠大於其厚度時，則歸類為似面結構，約佔12%/8%。介於似線與似面結構中難以定義之結構約為38%；而似塊結構(長寬高大致約相等)則佔約30%。本研究有助評估現有紊流模式和直接數值模擬之可靠度，並可用之發展新一代的紊流模式。

This research is to develop a four-dimensional particle image velocimetry (PIV) technique, to measure quantitatively full spatio and temporal velocity fields in turbulence, and thus to investigate the canonical structures of fine scale turbulence. The four-dimensional PIV technique is consisted of a high-speed successive scanning laser sheet, a pair of synchronized high-speed stereo CCD cameras, a fast image processing system, and a home-built synchronizer for these components. Thus, four-dimensional velocity fields in a turbulent flow can be extracted from these full spatial images with temporal variations, each image field of view 1.4 cm×1.2 cm (480×420 pixels) in which the spatial resolution is about 29μm that may be sufficient to resolve the Kolmogorov scale of turbulence.
Applying this full spatiotemporal PIV technique to a zero-mean-shear turbulence that was generated by vertically-oscillated grids in a water tank, the corresponding velocity fields and thus fine scale structures of the turbulent flow can be obtained. Two cases are studied, one grid turbulence and two grids turbulence, the former having a decaying near-homogeneous turbulence while the latter creating a stationary near-isotropic turbulence within the core region between the two grids, as verified by previous LDV measurements (Shy et al. 1997). From these four-dimensional velocity field measurements, the associated vorticity fields, principle strain rate directions, and kinetic energy dissipation rate fields can be obtained. Following that fine scale structures of turbulence may be identified from these kinetic energy dissipation rate fields.
Both results of one-grid/two-grids turbulence reveal that fine scale structures are correlated with flow velocity gradients; the larger the velocity gradient, the higher kinetic energy dissipation rate that marks the fine scale structure of turbulence. It is found that the distribution of fine scale structures where highest values of the dissipation rate are concentrated has a very high degree of intermittency and only occurs about 2% in the whole measuring data volume at any given times. For one-grid/two-grids turbulent flows, three canonical fine structures coexist, including “line-like”, “sheet-like”, and “blob-like” structures. This finding is similar to the descriptions of turbulent vorticity distributions proposed by Burger (1948) and Townsend (1951) and is also consistent with measurements of scalar dissipation rates by Shy et al. (1999) using the same apparatus and three-dimensional laser-induced fluorescence technique, but it differs drastically that found by Buch & Dahm (1991) in a free-shear turbulent jet flow in which they concluded that the only universal canonical structure is the “sheet-like” structure. This discrepancy indicates that zero-mean-shear and free-shear turbulent flows are different.
For the present one-grid/two-grids turbulent flows, the average diameter of the “line-like” structure is about 1~2 Kolmogorov scale. We estimate all fine scale structures existing in both one-grid/two-grids turbulent flows, and it is found that the “line-like” structure (its length is at least three times greater than its average diameter) has 20%/25%, the “sheet-like” structure (its length and width are about the same but its thickness is very small) has 12%/8%, and the “blob-like” structure (its length, width and thickness are about the same) has 30%/30%, respectively. The remaining fine scale structures that are difficult to define and in between the “line-like” and “sheet-like” structures have about 38% for both one-grid/two-grids turbulent flows. These results are useful to validate existing turbulent models and the results of direct numerical simulations as well as for developing a new turbulent model.

目 錄
摘要.....................................................................I
英文摘要................................................................II
誌謝....................................................................IV
目錄.....................................................................V
圖表目錄...............................................................VII
符號說明.................................................................X
第一章 前言..............................................................1
1.1 動機........................................................1
1.2 問題所在....................................................2
1.2.1 實驗量測技術方面......................................2
1.2.2 微尺度紊流結構方面....................................3
1.3 解決提案....................................................4
1.4 論文概要....................................................6
第二章 文獻回顧..........................................................8
2.1 振動網柵紊流場之特性........................................8
2.2 三維質點影像測速技術........................................9
2.3 能量平衡理論...............................................10
2.4 能量平衡方程式.............................................12
2.5 微尺度紊流結構.............................................14
第三章 四維質點影像量測技術.............................................20
3.1 影像擷取系統與同步控制方法.................................20
3.2 速度場資料結構.............................................22
3.3 三維影像校正方法以及資料處理流程...........................23
3.4 實驗誤差評估...............................................27
第四章 流場實驗設備與參數計算...........................................36
4.1 振動網柵實驗設備...........................................36
4.2 實驗參數之計算.............................................37
4.2.1 振動網柵紊流場參數估算...............................37
4.2.2 紊流動能消散率之計算.................................38
4.2.3 渦度場之計算.........................................39
4.2.4 主應變方向之計算.....................................40
第五章 結果與討論.......................................................44
5.1 振動網柵紊流場.............................................44
5.1.1 單網柵紊流場.........................................44
5.1.2 雙網柵紊流場.........................................47
5.2 統計分析...................................................48
5.2.1 累加分佈函數.........................................48
5.2.2 微尺度結構分析.......................................51
第六章 結論與未來工作...................................................68
參考文獻................................................................70

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