本研究觀察不同平面下，自由流流經有限長圓柱後之尾流區流場結構。實驗於閉迴路循環直立式水洞中進行，將1D圓蓋之有限長圓柱設置於水洞透明測試段。有限長圓柱直徑為6.4~mm，圓柱長度為160~mm，圓柱展弦比為25，1D圓蓋之直徑為6.4~mm，厚度為0.5D（3.2~mm）。實驗觀察的流場共有六個雷諾數，分別為195、250、360、560、880及1080。本研究使用流場可視化及質點影像測速儀（PIV）的方法觀察兩個切平面方向：圓柱橫向切平面（YZ平面）及圓柱縱向切平面（XY平面），觀測橫向切平面（YZ平面）距離自由端不同位置的流場表現，比較自由端對於尾流區域的影響。YZ平面共有四個位置，分別為X/D~=~-2、X/D~=~-7、X/D~=~-10及X/D~=~-12；Z/D~=~0。PIV比較3種設定分析參數的組合：分析範圍、節點數量及視窗大小，並比較不同分析參數組合的分析結果，分析參數的選擇主要會影響判別視窗的重疊率，當重疊率越高時，流場的PIV速度結果越不易受到空間中局部極端速度的影響。頻譜分析時，比較PIV分析結果中不同觀察點的時序資料，獲得最顯著尾流區渦旋逸放頻率。PIV瞬時結果包含流線場（依據瞬時速度向量）及渦度場；PIV平均結果包含流線場（依據平均速度向量結果）、速度場、渦度場、紊流強度場及雷諾應力場，並根據PIV瞬時結果繪製平均相位圖。實驗分析結果發現，當觀察平面越遠離自由端時，流場結構受到來自自由端的下洗效應越弱，且流動形態呈現較規律的渦旋逸放，尾流區的渦旋增強混合作用。平均相位圖顯示流場大規模且重複的渦漩結構，更易於觀察流場結構週期擺動的特性。

This study is designed to observe the near wake flow field structure of the finite-length cylinder in various planes. The experiments were conducted in the closed-loop vertical water tunnel with the test section of 30~cm~(length)~$\times$ 30~cm~(width)~$\times$ 30~cm~(height). The diameter of the 1D cap is 6.4~mm, and its thickness is 3.2~mm. The diameter of the cylinder is 6.4~mm and its length is 160~mm in the test section giving the aspect ratio equal to 25. The experiments were conducted at different Reynolds numbers, which were 195, 250, 360, 560, 880 and 1080. Two orthogonal planes, the transverse plane~(YZ-plane), and the longitudinal plane~(XY-plane), of the cylinder are observed by using the flow visualization and PIV techniques. The near wake flow fields, which are near to and away from the free end, are compared and analyzed. There are four observation YZ-planes, X/D~=~-2, X/D~=~-7, X/D~=~-10, and X/D~=~-12, and there is one observation XY-plane, Z/D = 0. Three sets of PIV analysis parameters, which are related to ROI~(region of interest), number of nodes, and interrogation window size, are used and the output velocity vectors are compared with one another. These analysis parameters have their own effects on the interrogation window overlap ratio. The higher overlap ratio shows the more stable PIV output results, and the PIV output results are less disturbed by the local extreme velocity component. For the spectrum analysis, the same time-sequence data at the different observation points in the near wake were used to analyze their individual most significant vortex shedding frequencies. The experiment results include flow visualization results and PIV results. The PIV instantaneous results show the instantaneous streamline fields~(based on the instantaneous velocity vector)~and instantaneous vorticity fields. The PIV average results show the mean streamline fields, mean velocity fields~(base on the time-averaged velocity vector), time-averaged velocity vector fields, mean vorticity fields, turbulence intensity fields and Reynolds stress fields. The phase-averaged PIV results~(velocity and vorticity) are plotted to compare with the selected instantaneous PIV results. As the observation flow fields are away from the free end of the finite-length cylinder, the downwash flow effect reduces, and the flow pattern displays relatively rhythmic shedding of vortices. The phase-averaged results show clear vortice in one period, and give average results in different phases.

[1] A. E. Perry, M. S. Chong, and T. T. Lim, “The vortex-shedding process behind two-dimensional bluff bodies,” J. Fluid Mech., vol. 116, pp. 77–90, Mar. 1982.

[2] O. Reynolds, “An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels,” Proceedings of the Royal Society of London, vol. 35, pp. 84-99, 1883.
[3] M. M. Zdravkovich, Flow around circular cylinders Volume 1:Fundamentals. Oxford ; New York: McGraw-Hill New York, 1997.
[4] M. Ozgoren, “Flow structure in the downstream of square and circular cylinders,” Flow Measurement and Instrumentation, vol. 17, no. 4, pp. 225–235, 2006.
[5] J. H. Lienhard, Washington State University, Technical Extension Service, Washington State Univerisity, College of Engineering, and Research Division, “Synopsis of lift, drag, and vortex frequency data for rigid circular cylinders.” Pullman, Wash.: Technical Extension Service, Washington State University, 1966.
[6] D. Sumner, “Flow above the free end of a surface-mounted finite-height circular cylinder: A review,” Journal of Fluids and Structures, vol. 43, pp. 41–63, 2013.
[7] M. Adaramola, O. Akinlade, D. Sumner, D. Berstrom, and A. Schenstead, “Turbulent Wake of a Finite Circular Cylinder of Small Aspect Ratio,” Journal of Fluids and Structures, vol. 22, pp. 919-928, Aug. 2006.
[8] M. Einian, D. J. Bergstrom , and D. Sumner, “Numerical Simulation of the Flow Around a Surface-Mounted Finite Square Cylinder,” in ASME 2010 7th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, and Flow-Induced Vibration and Noise: Volume 3, Parts A and B, (Montreal, Quebec, Canada), pp. 103-110, ASMEDC, Jan. 2010.
[9] C. W. Park and S. J. Lee, “Effects of free-end corner shape on flow structure around a finite cylinder,” Journal of Fluids and Structures, vol. 19, no. 2, pp. 141–158, Feb. 2004
[10] R. C. Flagen and J. H. Seinfeld, Fundamentals of Air Pollution Engineering. Englewood Cliffs, N.J: Pretice Hall, 1988.
[11] Q. R. Su, “Experimental Study on the Flow Field Due to a Finite-length Cylinder with Embedded Cap of Different Sizes at Its Free end,” Master’s thesis, National Taiwan University of Science and Technology, 2020.
[12] S. C. Chapra and R. P. Canale, Numerical methods for engineers, Seventh edition. New York, NY: McGraw-Hill Education, 2015.
[13] F. M. White, Viscous Fluid Flow. McGraw-Hill New York, 1974.
[14] J. C. Jhang, “Preliminary Study on a Round Tube Jet in Vertical Water Tunnel,” Master’s thesis, National Taiwan University of Science and Technology, 2009.