題目：藉由粒子影像測速及正交特徵分解辨認近域尾流之大尺度相干性結構
研究生：黃柏翔
指導教授：張克勤、葉思沂
利用熱線測速(Hot-Wire Anemometry, HWA)之高時間解析與高樣本數驗證粒子影像測速(Particle Image Velocimetry, PIV)於高、低雷諾數(ReD = 3900、9500)條件下之可信度，藉著PIV空間性與時間序列之優勢，使用正交特徵分解(Proper Orthogonal Decomposition, POD)進行降維分析，將各個瞬時流場訊息投射於不同模態，模態越高相對能量貢獻越低，低模態且低頻率大尺度為主導流場的卡門渦街，隨著模態越高，其能量占比越低，為卡門渦街分解之小尺度渦流，並加以驗證是否為泰勒微尺度，並隨著位置由上游極靠近圓柱位置逐漸至下游，流場能量逐漸衰減。
將個別模態對應之時間係數進行快速傅立葉(Fast Fourier Transform, FFT)及連續小波轉換(Continuous Wavelet Transform, CWT)，可以得知主導流場之頻率與頻率分布，辦別其流場除了含有卡門渦街之頻率外，亦含有表示小尺度渦流之二倍與三倍諧波頻率，並繪製其大尺度相干性結構流場。
紊流常以雷諾分解(Reynolds Decomposition)進行表示，每一瞬間為一平均值與擾動值組成，然而愈靠近鈍體之尾流，其大規模(擬)週期性(quasi-periodic)運動愈劇烈，擾動值應含有些許規律部分，利用POD能量貢獻最大且在FFT與CWT分析結果中，擁有規律行為之模態進行提取，此時雷諾分解之擾動值並不能完整表達該流場行為，而將擾動值進一步分解為週期速度與剩餘隨機擾動，使得擾動值成為更接近純粹的紊流，在遠離鈍體區域，週期運動能量衰減，則適用雷諾分解，換言之雷諾分解並不全然適用於鈍體尾流區域。
關鍵字：粒子影像測速、正交特徵分解、大尺度相干性結構、擬週期結構能量、小波轉換

The coherent structures in the very upstream wake subregion behind a long circular cylinder at two Reynolds numbers of 3900 and 9500 and a Strouhal number of 0.21 are identified and extracted using particle image velocimetry (PIV) along with the proper orthogonal decomposition (POD) analysis method. The quasi-periodic frequencies are identified with the resolved vorticity field, a fast Fourier transform (FFT), and a continuous wavelet transform (CWT). The results clearly show the periodic nature of the Kármán vortex street, which is primarily constituted by the 1st, 2nd and 3rd harmonic frequencies. The POD analysis identifies not only the large-scale structure (Kármán vortex) in the low-order modes, but also recognizes the small-scale eddies, which appear in the high-order modes but have low a kinetic energy contribution. The 2nd and 3rd harmonic frequencies dominate the high-order modes with small-scale eddies. Taking advantage of the improved high spatial resolution and high sampling rate of particle image velocimetry (PIV), the measured information of the spatially phase-correlated vorticity can be employed to examine the coherent structure dynamics. Among all of the available techniques for phase-resolved flow field reconstruction that have been employed to determine the spatial-temporal features of multi-scale coherent structures, proper orthogonal decomposition (POD) has been widely employed. The aim of this study is to identify and extract the vortex structure from the velocity data measured using PIV in the wake flow closer to the long circular cylinder (2-D), within the first five diameter, which has been less studied in the literature on this topic than other aspects of this topic.
Key-words: PIV, POD, Coherent structure, Energy of organized motion, CWT

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