本研究旨在研究臨界雷諾數下之有限高圓柱表面流場特性。透過風洞試驗探討量測有限高圓柱於不同高層之±90°與180°的壓力訊號，以判斷有限高圓柱流場隸屬於次臨界區、穩定單分離泡區、穩定雙分離泡區之分界，也透過Cpb與"Cp±90°差值"之變化相態圖，探討流場於過渡區間之特性。
另外，透過二維力平衡儀量測有限高圓柱與二維圓柱在不同表面粗糙度下於臨界雷諾數中的阻力係數與升力係數，並探討Drag crisis現象。由實驗結果發現有限高圓柱在不同粗糙度下，三維圓柱臨界雷諾數依舊有提早發生，並依舊存在著臨界區轉換現象。並透過阻力對升力變化圖，探討流場於過渡區間之特性。
最後，透過快速傅立葉轉換(FFT)與加總經驗模態分析法(EEMD)進行有限高圓柱各高層之±90°的壓力訊號的時頻分析，也透過相關性分析，對於尾流流場之三維性，有更多證據可以判斷與說明。

This study aims on the characteristics of flow field of a finite circular cylinder surface at critical Reynolds number. Experiments were made in a low-speed wind tunnel to measure the pressure signals of ±90° and 180° on a finite circular cylinder surface. The critical regime can be divided into four regions, which are the transition of subcritical regime to one-bubble regime, stable one-bubble regime, the transition of one-bubble regime to two-bubble regime and stable two-bubble regime. The instantaneous flow characteristics in the critical transition range can be discussed with the distributions of the real-time “Cpb & the difference of Cp±90°” data.
In addition, the drag coefficient and the lift coefficient in the critical Reynolds number of a finite cylinder and a two-dimensional cylinder are measured by a two-dimensional force balance, and drag crisis phenomenon is also discussed. From the experimental results, the critical transition phenomenon is delayed to higher Reynolds number for the finite smooth circular cylinder model, compared to that of the 2D smooth circular cylinder model. However, the situation was opposite for rough surface of 2D circular cylinder model and finite circular cylinder model. The instantaneous flow characteristics in the critical transition range can be discussed with the distributions of the real-time “CD & CL” data.
Finally, we analyzed the pressure signals and force signals by using the method of fast Fourier transform and ensemble empirical mode decomposition. We also used correlation analysis to get more evidences for the three-dimensional wake flow field.

[1]H. Chowdhury, F. Alam, and A. Subic, "Aerodynamic performance evaluation of sports textile," Procedia Engineering, vol. 2, no. 2, pp. 2517-2522, 2010.
[2]J. Miau et al., "Design aspects of the ABRI wind tunnel," in The international wind engineering symposium, IWES, 2003.
[3]T. Von Kármán, "Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt," Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, vol. 1911, pp. 509-517, 1911.
[4]A. Roshko, "Experiments on the flow past a circular cylinder at very high Reynolds number," Journal of Fluid Mechanics, vol. 10, no. 3, pp. 345-356, 1961.
[5]E. Achenbach, "Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re= 5× 10 6," Journal of Fluid Mechanics, vol. 34, no. 4, pp. 625-639, 1968.
[6]P. Bearman, "On vortex shedding from a circular cylinder in the critical Reynolds number regime," Journal of Fluid Mechanics, vol. 37, no. 3, pp. 577-585, 1969.
[7]C. Farell and J. Blessmann, "On critical flow around smooth circular cylinders," Journal of Fluid Mechanics, vol. 136, pp. 375-391, 1983.
[8]M. Zdravkovich, "Conceptual overview of laminar and turbulent flows past smooth and rough circular cylinders," Journal of wind engineering and industrial aerodynamics, vol. 33, no. 1-2, pp. 53-62, 1990.
[9]M. Zdravkovich, "Flow around circular cylinders volume 1: fundamentals," Oxford University Press, Oxford, vol. 19, p. 185, 1997.
[10]A. Capone, C. Klein, F. Di Felice, and M. Miozzi, "Phenomenology of a flow around a circular cylinder at sub-critical and critical Reynolds numbers," Physics of Fluids, vol. 28, no. 7, p. 074101, 2016.
[11]K. S. Hyun and P. K. Chang, "The criterion of separation of incompressible laminar boundary layer flow over an axially symmetric body," Journal of the Franklin Institute, vol. 325, no. 4, pp. 419-433, 1988.
[12]J. Miau, H. Tsai, Y. Lin, J. Tu, C. Fang, and M. Chen, "Experiment on smooth, circular cylinders in cross-flow in the critical Reynolds number regime," Experiments in fluids, vol. 51, no. 4, pp. 949-967, 2011.
[13]J. McClean and D. Sumner, "An experimental investigation of aspect ratio and incidence angle effects for the flow around surface-mounted finite-height square prisms," Journal of Fluids Engineering, vol. 136, no. 8, p. 081206, 2014.
[14]A. Ayoub and K. Karamcheti, "An experiment on the flow past a finite circular cylinder at high subcritical and supercritical Reynolds numbers," Journal of Fluid Mechanics, vol. 118, pp. 1-26, 1982.
[15]T. Fox and G. West, "Fluid-induced loading of cantilevered circular cylinders in a low-turbulence uniform flow. Part 1: mean loading with aspect ratios in the range 4 to 30," Journal of Fluids and Structures, vol. 7, no. 1, pp. 1-14, 1993.
[16]D. Sumner, J. Heseltine, and O. Dansereau, "Wake structure of a finite circular cylinder of small aspect ratio," Experiments in Fluids, vol. 37, no. 5, pp. 720-730, 2004.
[17]M. Adaramola, O. Akinlade, D. Sumner, D. Bergstrom, and A. Schenstead, "Turbulent wake of a finite circular cylinder of small aspect ratio," Journal of Fluids and Structures, vol. 22, no. 6-7, pp. 919-928, 2006.
[18]J. L. Heseltine, "Flow around a circular cylinder with a free end," Masters Thesis, Department of Mechanical Engineering, University of Saskatchewan, Canada, 2003.
[19]G. West and C. Apelt, "The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 10 4 and 10 5," Journal of Fluid Mechanics, vol. 114, pp. 361-377, 1982.
[20]A. Fage, "The effects of turbulence and surface roughness on the drag of a circular cylinder," Rep, Memo., vol. 1283, p. 1, 1929.
[21]G. Buresti, "The effect of surface roughness on the flow regime around circular cylinders," Journal of wind engineering and industrial Aerodynamics, vol. 8, no. 1-2, pp. 105-114, 1981.
[22]E. Achenbach, "Influence of surface roughness on the cross-flow around a circular cylinder," Journal of fluid mechanics, vol. 46, no. 2, pp. 321-335, 1971.
[23]E. Achenbach and E. Heinecke, "On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6× 10 3 to 5× 10 6," Journal of fluid mechanics, vol. 109, pp. 239-251, 1981.
[24]R. Basu, "Aerodynamic forces on structures of circular cross-section. Part 1. Model-scale data obtained under two-dimensional conditions in low-turbulence streams," Journal of Wind Engineering and Industrial Aerodynamics, vol. 21, no. 3, pp. 273-294, 1985.
[25]J. Nikuradse, Laws of flow in rough pipes. National Advisory Committee for Aeronautics Washington, 1950.
[26]Z.-X. Tsai, "二維力平衡儀設計 & 布料粗糙度對圓柱空氣動力特性之影響," 成功大學航空太空工程學系學位論文, pp. 1-203, 2017.
[27]Y. Nakamura and Y. Tomonari, "The effects of surface roughness on the flow past circular cylinders at high Reynolds numbers," Journal of Fluid Mechanics, vol. 123, pp. 363-378, 1982.
[28]H. Chowdhury and F. Alam, "An experimental investigation on the aerodynamic drag coefficient and surface roughness properties of sport textiles," The Journal of The Textile Institute, vol. 105, no. 4, pp. 414-422, 2014.
[29]H. Chowdhury, Aerodynamic design of sports garments. INTECH Open Access Publisher, 2012.
[30]高義明, "內政部建研所環境風洞校驗及二維鈍形體空氣動力流場實驗研究," 成功大學航空太空工程學系學位論文, pp. 1-141, 2005.
[31]J.-J. Wang, "開放式低速風洞校驗及交叉軸式風力發電機空氣動力性能研究," 成功大學航空太空工程學系學位論文, pp. 1-54, 2017.
[32]蔡星汶, "圓柱表面流場在臨界區之空氣動力實驗研究," 成功大學航空太空工程學系學位論文, pp. 1-102, 2006.
[33]J. B. Barlow, W. H. Rae Jr, and A. Pope, "Low speed wind tunnel testing," INCAS Bulletin, vol. 7, no. 1, p. 133, 2015.
[34]H. J. Allen and W. G. Vincenti, "Wall interference in a two-dimensional-flow wind tunnel with consideration of the effect of compressibility," NATIONAL AERONAUTICS AND SPACE ADMINISTRATION MOFFETT FIELD CA AMES RESEARCH CENTER, 1944.
[35]I. Standard, "25178-2," Geometrical product specifications (GPS). Surface texture: Areal. Part, vol. 2, 2012.
[36]C. Williamson and A. Roshko, "Measurements of base pressure in the wake of a cylinder at low Reynolds numbers," Zeitschrift fur Flugwissenschaften und Weltraumforschung, vol. 14, pp. 38-46, 1990.
[37]方忠浩, "圓柱表面流場在預臨界區之特性探討," 成功大學航空太空工程學系學位論文, pp. 1-83, 2011.
[38]K. Pearson, "Notes on the history of correlation," Biometrika, vol. 13, no. 1, pp. 25-45, 1920.
[39]N. E. Huang et al., "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis," in Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, vol. 454, no. 1971, pp. 903-995: The Royal Society, 1998.
[40]Z. Wu and N. E. Huang, "Ensemble empirical mode decomposition: a noise-assisted data analysis method," Advances in adaptive data analysis, vol. 1, no. 01, pp. 1-41, 2009.
[41]T.-T. Chang, "有限高圓柱尾流在臨界雷諾數流場分析," 成功大學航空太空工程學系學位論文, pp. 1-67, 2016.
[42]H.-J. Niemann and N. Hölscher, "A review of recent experiments on the flow past circular cylinders," Journal of Wind Engineering and Industrial Aerodynamics, vol. 33, no. 1-2, pp. 197-209, 1990.
[43]陳孟巧, "探討圓柱在臨界區之流場轉換現象," 成功大學航空太空工程學系學位論文, pp. 1-86, 2011.
[44]C. Wieselsberger, "Further information on the laws of fluid resistance," naca-tn-121, 1922.
[45]G. Schewe, "On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers," Journal of fluid mechanics, vol. 133, pp. 265-285, 1983.
[46]G. Schewe, "Sensitivity of transition phenomena to small perturbations in flow round a circular cylinder," Journal of fluid mechanics, vol. 172, pp. 33-46, 1986.
[47]G. Schewe, "Reynolds-number effects in flow around more-or-less bluff bodies," Journal of Wind Engineering and Industrial Aerodynamics, vol. 89, no. 14-15, pp. 1267-1289, 2001.
[48]A. Jeang, F. Liang, W. Chiu, and L. J. Ping, "A Wind Tunnel Study on Coat Fabrics Drag," in Proceedings of the 14th IFToMM World Congress, 2015.