本研究藉由改變有限長圓柱其自由端嵌入的圓蓋尺寸，探討圓蓋尺寸的改變對流場結構之影響。實驗於閉迴路循環直立式水洞中進行，將嵌入圓蓋的有限長圓柱垂直設置於水洞透明測試段之壁面上，測試段大小為30 cm（長）× 30 cm（寬）× 130.5 cm（高），圓蓋尺寸分別為1D（6.4 mm）、2D（12.8 mm）、3D（19.2 mm）以及4D（25.6 mm），共四個尺寸，其厚度皆為0.5D（3.2 mm），圓柱直徑為6.4 mm，圓柱長度為160 mm，展弦比（AR）為25；實驗之雷諾數（ReD）分別為195、250、360、560、880以及1080，共六個雷諾數；觀測平面分別為圓柱縱切之平面（XY平面）與圓柱橫切之平面（YZ平面），以流場可視化與質點影像測速儀（PIV）觀察在不同雷諾數下自由端嵌入不同尺寸圓蓋之有限長圓柱的流場結構。實驗結果分別為瞬時流場結果與平均流場結果，瞬時流場結果包括流場可視化與瞬時流線場（依據瞬時速度向量結果），透過頻譜分析定點速度時序資料，以求得其速度變化之頻率（頻譜分析之結果）；平均流場結果包括平均流線場（依據平均速度向量結果）、平均速度場、下洗角以及紊流強度場。於實驗結果及其分析發現，靠近自由端的位置有明顯的下洗效應，其隨著位置逐漸遠離自由端而逐漸減弱；隨著圓蓋尺寸的增大，可使流體流經圓柱自由端後緣時產生的下洗效應減弱，而隨著下洗效應的減弱，靠近自由端的流場逐漸由三維流場轉變為近似二維流場的流場。

The study investigated the effect of changing the size of the cap at the free end of the finite-length cylinder on the flow field. The experiments were conducted in the closed-loop vertical water tunnel with the test section of 30 cm (length) × 30 cm (width) × 130.5 cm (height). Four different sizes of the caps are 1D (6.4 mm), 2D (12.8 mm), 3D (19.2 mm) and 4D (25.6 mm), and the thickness of all the caps is 0.5D (3.2 mm). The diameter of the cylinder is 6.4 mm and its length is 160 mm give the Aspect Ratio (AR) 25. The experiments were conducted at different Reynolds numbers (ReD), which were 195, 250, 360, 560, 880 and 1080. The observation planes include the longitudinal section of the cylinder (XY-plane) and the transverse section of the cylinder (YZ-plane). The study observed the flow structure of the finite-length cylinder with a cap of different sizes at the free end at different Reynolds numbers through long-exposure flow visualization and Particle Image Velocimetry (PIV). The experimental results include the instantaneous flow fields and the mean flow fields. The results of the instantaneous flow field include the flow visualization images and the instantaneous streamline fields based on the instantaneous velocity vector. The time sequence data of the velocity of the fixed-point were analyzed through spectrum analysis to obtain the frequency of the velocity variation (results of spectrum analysis). The results of the mean flow field include the mean streamline fields based on the mean velocity vector, the mean velocity fields, the downwash angle and the turbulence intensity fields. The longitudinal section experimental results show that there is an obvious downwash effect close to the free end, and the downwash effect gradually decreases away from the free end. Increasing the size of the cap decreases the downwash effect generated by the fluid flowing through the rear edge of the free end of the cylinder. As the downwash effect decreases, the flow field near the free end gradually changes from a three-dimensional flow field to a flow field that approximates two-dimensional.

[1] M. M. Zdravkovich, “Flow Around Circular Cylinders Volume 1: Fundamentals,” 1997.
[2] A. Roshko, “On the Development of Turbulent Wakes from Vortex Streets,” NASA Technical Reports Server, 1954.
[3] D. Sumner, “Flow above the free end of a surface-mounted finite-height circular cylinder: A review,” Journal of Fluids Structures, pp. 41–63, 2013.
[4] M. Einian, D. Bergstrom, and D. Sumner, “Numerical Simulation of the Flow Around a Surface-Mounted Finite Square Cylinder,” ASME 2010 3rd Joint US-European Fluids Engineering, 2010.
[5] R. J. Pattenden, S. R. Turnock, and X. Zhang, “Measurements of the flow over a low-aspect-ratio cylinder mounted on a ground plane,” Experiments in Fluids, pp. 10–21, 2005.
[6] 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, pp. 141–158, 2004.
[7] J. C. Jhang, “Preliminary study on a round tube jet in vertical water tunnel,” National Taiwan University of Science and Technology, 2009.
[8] H. L. Dryden, “The role of transition from laminar to turbulent flow in fluid mechanics,” University of Pennsylvania, Bicentennial Conference, 1941.
[9] A. Roshko, “On the persistence of transition in the near-wake,” Problems of Hydrodynamics and Continuum Mechanics, 1969.
[10] W. Linke, “New measurements on aerodynamics of cylinders particularly their friction resistance,” Physikalische Zeitschrift, p. 900, 1931.
[11] M. S. Bloor, “The transition to turbulence in the wake of a circular cylinder,” Journal of Fluid Mechanics, pp. 290–304, 1964.
[12] J. H. Gerrard, “A disturbance-sensitive Reynolds number range of the flow past a circular cylinder,” Journal of Fluid Mechanics, pp. 187–196, 1965.
[13] M. Morkovin, “Flow around circular cylinders - a kaleidoscope of challenging fluid phenomena,” Proc. ASME Symp. on Fully Separated Flow, Philadelphia, pp. 102–118, 1964.
[14] T. Okamoto and M. Yagita, “The Experimental Investigation on the Flow Past a Circular Cylinder of Finite Length Placed Normal to the Plane Surface in a Uniform Stream,” Bulletin of JSME, pp. 805–814, 1973.
[15] H. Sakamoto and M. Arie, “Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer,” Journal of Fluid Mechanics, pp. 147–165, 1983.
[16] M. S. Adaramola, O. G. Akinlade, D. Sumner, D. J. Bergstrom, and A. J. Schenstead, “Turbulent wake of a finite circular cylinder of small aspect ratio,” Journal of Fluids and Structures, pp. 919–928, 2006.
[17] R. C. Flagan and J. H. Seinfeld, “Fundamentals of Air Pollution Engineering,” 1988.