前人對於縱向渦流實驗縱然很多,但對於實驗結果,卻沒有完整分析縱向渦流之
特性,因此本研究中主要利用粒子影像測速技術(Particle Image Velocimetry)於低、中
雷諾數(ReD = 3820、9440)之條件下探討二維圓柱近域尾流區之縱向渦旋的產生與脫
離過程以及流場中的組織性結構,同時使用擁有高時間解析及足夠達到統計穩定的樣
本數之熱線測速儀(Hot-Wire Anemometry)加以佐證其速度量測之精確性,並利用正交
特徵分解(Proper Orthogonal Decomposition, POD)PIV 數據,為所得到的龐大矩陣結果
進行分析,進而研究 secondary vortex 於圓柱後尾流的特性。
圓柱尾流存在具有組織性的大尺度相干性結構,本實驗使用 POD 進行降維分析,
分析尾流能量變化,並使用頻譜分析辨認出大尺度相干性結構。 在低、中速實驗中,
由流場的上游(0.5 - 6 d)和中游(6 - 11.5 d)兩區段中 organized motion 的能量貢獻來觀
察其卡門渦街和縱向渦流的能量占比,且發現其能量占比隨著與圓柱的距離增加而衰
退,衰退速率亦與雷諾數呈正相關性關係,並利用熱線測速儀和 PIV 結果之 FFT 圖,
分析縱向渦流的頻率,其中於低速流場可同時觀測到比卡門渦街主頻(115 Hz)小或大
的頻率峰值,如 45 Hz 和 160 Hz,於中速流場也可同時觀測到比卡門渦街主頻(300
Hz)小或大的頻率峰值,如 37 Hz 和 1307 Hz,意旨縱向渦流之頻率並非以固定規律出
現於頻譜之中。
本研究也針對 POD 的三項參數進行分析。第一項為拍攝視場,拍攝視場(Field of
View, FOV)大小的選擇主要為完整拍攝週期性尾流並分析其能量,根據斯特勞斯哈爾
數(Strouhal number)可求得,於本研究沿 x 方向約需使用 5.5 d (d :圓柱直徑),沿 z 方
向則需 12.5 d 來進行分析。第二項為樣本(sample)數量之影響,透過遞增樣本數並與總樣本數以直方圖相交法找出足以描述上游與中游的樣張數。第三項為流場重建時所
使用模態的數量,透過本實驗誤差所得之能量計算標準藉以精確決定所需之模態後重
建紊態流場。

Although there are many experiments on the study of longitudinal vortices, the characteristics of longitudinal vortices have not been thoroughly analyzed for the experimental results. Therefore, in this study, the particle image velocimetry (PIV) is used to investigate at low and medium Reynolds numbers (3820 and 9440) and to identify the generation of the longitudinal vortex and the process of the vortex shedding in the near-wake region of the two-dimensional cylinder. PIV and the proper orthogonal decomposition (POD) analysis method is applied to study the characteristics of the secondary vortex in the wake behind the cylinder. The information of each instantaneous flow field was projected to different modes. Also, organized structures in the flow field were measured by Hot-Wire Anemometry (HWA) to prove the accuracy of the velocity measurement made by PIV.
There are organized large-scale coherent structures in the near wake behind the cylinder. In this experiment, POD was used for dimensionality reduction analysis to analyze the change of wake energy, and spectrum analysis was used to identify the large-scale coherent structure in each mode. In the low and medium velocity experiments, the energy contribution of the organized motion in the upstream (0.5 - 6 d) and midstream (6 - 11.5 d) sections of the flow field was used to observe the energy proportion of the Karman vortex street and the longitudinal vortex. By observation, its energy ratio declines with the increase of the distance from the cylinder, and the decline rate is also positively correlated with the Reynolds number, which means a higher Reynolds number declines faster. The results of hot-wire and PIV are analyzed by the fast Fourier transform so the dominant frequencies of the longitudinal vortex can be acquired. The domain of frequency peaks is smaller or larger than the main frequency of the Karman vortex street (115 Hz) in low-speed flow fields that can be observed simultaneously, such as 45 Hz and 160 Hz. In addition, the domain of frequency peaks is smaller or larger than the primary frequency of the Karman vortex street (305Hz) can also be observed at the same time, such as 37 Hz and 1307 Hz in the case at Re = 9440, meaning that the frequencies of the longitudinal vortices do not appear in the frequency spectrum with a regular pattern.
Three POD parameters are analyzed in the study. Selection of the field of view (FOV) is made so that it can completely capture the periodic wake and analyze its energy, which is obtained according to the Strouhal number and the researches of Wu et al. (1996), and Williamson (1996), and Scarano et al. (2009). For this study, the analysis used approximately 5.5 d (d: cylinder diameter) along the streamwise direction and 12.5 d along the span-wise direction. The second term is the effect of the number of samples by increasing the number of samples and intersecting the total number of samples with the Histogram Intersection Similarity Method (HISM) to find the number of samples that are sufficient to describe the upstream and midstream flow field. The third item is the number of modes used to reconstruct the flow field, and the energy standard obtained through the measurement error of PIV can determine the required modes to reconstruct the turbulent flow field.

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