本研究是應用四維質點影像測速技術，定量量測一液態紊流噴流場之空間三維速度場與其時間序列資訊，並計算紊流動能消散率與應變率場，配合小波函數轉換(wavelet transform)，來獲得紊流噴流場的平坦度因子(flatness factor)與延伸自相似率(extended self-similarity, ESS)的特性，以分析紊流噴流場的微尺度結構與間歇性 (small-scale structures and intermittency)的分佈特性。從所得速度場資訊，可進一步地計算紊流場的渦度(vorticity)、主應變率方向(principle strain rate direction)以及動能消散率場，並分析紊流噴流場的微尺度結構。結合小波轉換可獲得平坦度因子，可用以判斷紊流場之間歇性程度。經由所計算之平坦度因子，得知紊流噴流微尺度渦結構之特性時間尺度約 ，特性空間尺度約 ， 和 為Kolmogorov時間與空間尺度。本實驗室所發展之四維質點影像測速技術，確實可以在紊流噴流場中，解析到噴流場中空間與時間的Kolmogorov尺度，由實驗證實微尺度結構乃由高動能消散率的特定結構所形成，且其分佈具有高度的間歇性，另外高動能消散率值的部分，只佔所量測空間中約3~5 %的比例。 將紊流噴流三維的速度場，經由ESS的特性分析後，比對其時間與空間的速度資料後，可發現無論在何種情形下，在噴流方向標度指數(scaling exponent)的斜率值，比其他兩個水平方向的斜率值還低，尤其是在時間序列的速度資料中特別明顯，這結果與Romano & Antonia (2001)在紊流噴流場中，計算低階(2階到8階)速度結構函數(velocity structure function)之結果相似，但是在高階處(10階到20階)，將速度結構函數之斜率值與Kolmogorov (1941)之理論(簡稱K41)、Kolmogorov於1962年修正後之log-normal紊流模式、Frisch et al. (1978)的 紊流模式以及She & Leveque (1994)的SL紊流模式等四大模式做一比對，發現所得斜率均介於紊流 模式與SL模式的值之間。由實驗分析結果，可知沿著噴流方向，紊流噴流場其間歇性的程度，會隨著越遠離噴嘴其間歇程度會增加，而以 模式與SL模式兩間歇性模式，較為接近紊流噴流場的微尺度間歇性的結構分佈。經過空間微尺度拓撲結構的對照之後，可以發現在噴流場的微尺度結構大部分為“斑點(spotty)”結構，而“似線(line-like)”以及“似面(sheet-like)”結構在噴流場中則較為少數，這一點與Tsurikov & Clemens (2002)於氣態的同軸噴流場(co-flow)所發現的結果有所不同。本研究將有助於新紊流間歇性模式的發展，並進一步瞭解紊流場中微尺度結構的分佈情形。 This thesis uses a four-dimensional particle image velocimetry (4D-PIV) technique to measure quantitatively full spatial and temporal velocity data fields of a turbulent jet in a water tank for investigating fine scale structure of turbulence based on the turbulent kinetic energy dissipation rate fields. Applying the wavelet transformation to calculate the flatness factor and the extend self-similarity (ESS) from these PIV data, we are able to evaluate small-scale structures and intermittency of turbulent jet. From these flatness factor calculations, it is found that the characteristic temporal and spatial scales of small intense vortical structures are on the order of and , where and are the Kolmogorov time and length scales, respectively. These 4D-PIV measurements can also provide the corresponding vorticity fields, the principle strain rate directions, and the kinetic energy dissipation rate fields. Thus, the fine scale structures of the turbulent jet can be identified from these kinetic energy dissipation rate fields. The present 4D-PIV technique which has been developed in our laboratory can resolve the Kolmogorov scales of the turbulent jet. It is found that the distribution of fine scale structures of the turbulent jet in which highest values of the dissipation rate are concentrated has a very high degree of intermittency and only occupies about 3~5% in the whole measuring data volume at any given times. We also analyze these PIV data using the ESS method to investigate the scaling exponent based on high-order velocity structure functions. For both temporal and spatial velocity data, we found what the scaling exponent of high-order velocity structure function in the axial direction is lower than that in the other two transverse directions. We compare our scaling exponent results with four different models, respectively the Kolmogorov model in 1941 (K41), the log-normal model (Kolmogorov 1962), the model (Frisch et al. 1978), and the SL model (She & Leveque 1994). It is found that our experiment results are in between the model and the SL model. The level of intermittency on the turbulent jet in the far field is increasing with the distance away the jet nozzle. From fine scale topological structures of kinetic energy dissipation rate fields, it is found that the spotty-like structure is the main structure of the present turbulent jet in the far field. However, both line-like and sheet-like structure are also observed. These results may be useful to understand fine scale structures of turbulence.
