本研究以實驗方法探討圓柱流場於雷諾數1.7ⅹ105 ~ 4ⅹ105之間圓柱流場的各種物理特性。實驗利用圓柱兩側θ=±80°、±90°之壓力孔訊號作為判斷的依據，作為圓柱流場隸屬於次臨界區、預臨界區之B State流場、預臨界區之A State流場乃至於進入單分離泡區之依據。
實驗利用不同表面粗糙度之圓柱進行各種試驗，以熱線探針(Hot-wire)觀察並量測流場速度。為了對量測到的數據進行分析，吾人利用快速傅立葉轉換(Fast Fourier Transform)求得熱線探針之渦流溢放訊號，並使用小波轉換(Wavelet Transform)彌補快速傅立葉無法獲得之訊號的瞬時頻率。在實驗的過程中，利用四種不同表面粗糙度之圓柱，並搭配數種的分析方式，發現在不同表面粗糙度下，圓柱流場仍存在預臨界區流場轉換的現象，並針對對預臨界區之B State流場、預臨界區之A State流場以及單分離泡區流場等三種流場分別進行圓柱表面的壓力係數量測。
同時利用熱膜感測器(Thermal tuft)量測圓柱表面分離點之角度與分離泡之角度；實驗亦利用熱線探針在圓柱後方量取圓柱尾流速度，計算圓柱尾流在不同流場時之尾流寬度，吾人亦使用經驗模探分離法(EMD)將訊號中的高頻訊號與低頻訊號進行拆解，並使用相關性分析，目的是對通過圓柱的臨界流場有更多的了解。

This study aims to investigate the phenomenon of flow around a circular cylinder at Reynolds numbers between 1.7×105 and 4×105. The pressure taps signals on the circular cylinder were used to determine the pre-critical regime B state regime, the pre-critical regime A state regime and the one bubble regime. The experiment used different circular cylinders characterized by different relative roughness. Velocity measurements were carried out with a single hot-wire situated in the wake region. Both of the pressure and velocity signals obtained were analyzed with fast Fourier and Wavelet transformations. This study shows that in the case of different surface relative roughness cases, different flow states are observable, and pressure coefficients in the pre-critical regime B state regime, in the pre-critical regime A state regime and in the one bubble regime were obtained. In order to understand more features about flow over the circular cylinder, we used Thermal tuft to measure the separation angle and the separation bubble, meanwhile the wake flow was measured by hot-wire. Finally, by the method of Empirical Mode Decomposition, these two components were extracted separately from the raw signals. Subsequent data analysis on each component provided more insights into the characteristic behaviors of State A.

[1] Taylor, G. I., “Pressure Distribution Round the Cylinder,” Advisory Committee of Aeronautics., Rep. & Memo 191, 1916.
[2] Zdravkovich, M. M., “Conceptual Overview of Laminar and Turbulent Flow past Smooth and Rough Circular Cylinders,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 33, pp. 53-62, 1990.
[3] Fage, A. and Johansen, F. C., “The Structure if Vortex Sheets,” Philosophical Magazine., 7th Series, Vol. 5, pp. 417-441, 1928.
[4] Morkovin, M. V., “Flow around Circular Cylinders,” Proceedings ASME Symposium on Fully Separated Flow, Philadelphia., pp. 102-118, 1964.
[5] Roshko, A, “Perspectives on Bluff Body Aerodynamics,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp. 70-100, 1990.
[6] Williamson, C. H. K., “Vortex Dynamics in the Cylinder Wake,” J Fluid Mech., Vol. 28, pp. 477-539, 1996.
[7] Humphreys, J. S., “On a Circular Cylinder in a Steady Wind at Transition Reynolds Numbers,” J. Fluid Mech., Vol. 9, pp. 603-612, 1960.
[8] Szepessy, S., “On the Spanwise Correlation of Vortex Shedding from a Circular Cylinder at High Subcritical Reynolds Number,” Phys. Fluids, Vol. 6, pp. 2406-2416, 1994.
[9] Schewe, G., “Reynolds Number Effects in Flow around more-or-less Bluff Bodies,” Journal of Wind Engineering and Industrial Aerodynamics., Vol. 89, pp. 1267-1289, 2001.
[10] Nikias, N., Macdonald, J. H. G., Andersen, T. L., Jakobsen, J. B., Savage, M. G. and McAuliffe, B. R., “Wind Tunnel Testing of an Inclined Aeroelastic Cable Model-Pressure and Motion Characteristics, Part I,” EACWE 5 Florence., Italy 19th – 23th, 2009.
[11] Jakobsen, J. B., Andersen, T. L., Macdonald, J. H. G., Nikias, N., Savage, M. G. and McAuliffe, B. R., “Wind Tunnel Testing of an Inclined Aeroelastic Cable Model-Pressure and Motion Characteristics, Part II,” EACWE 5 Florence., Italy 19th – 23th, 2009.
[12] Miau, J. J., Chou, J. H., Cheng, C. M., Chu, C. R., Woo, K. C., Ren, S. K., Chen, Z. L., Hu, C. C. & Chen, J. L., "Design Aspects of the ABRI Wind Tunnel," The International Wind Engineering Symposium, Taipei County, Taiwan, 2003.
[13] 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，成大航太所碩士論文，2005。
[14] 方忠浩,”圓柱表面流場在預臨界區之特性探討,”成功大學航太所碩士論文,2011.
[15] Sumer, B. M. and , J., “Hydrodynamics around Cylindrical Structures,” World Scientific, 1997.
[16] Zdravkovich, M. M., “Flow around Circular Cylinders,” Oxford University Press., Vol. 1, pp. 1-18, 1997.
[17] Williamson, C. H. K., “Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Number,” J. Fluid Mech., Vol. 206, pp. 579-627, 1989.
[18] Wieselsberger, C., “New Data on the Law of Hydro and Aerodynamics Resistance,” Physikalsche Zeitschrift, Vol. 22, pp. 321-328, 1922.
[19] Zdravkovich, M. M., “Conceptual Overview of Laminar and Turbulent Flow past Smooth and Rough Circular Cylinders,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 33, pp. 53-62, 1990.
[20] Bearman, P. W., “On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number,” J. Fluid Mech., Vol. 37, pp. 577-585, 1969.
[21] Schewe, G., “On the Force Fluctuations Acting on a Circular in Crossflow from Subcritical up to Transcritical Reynolds Numbers.” J. Fluid Mech., Vol. 133, pp. 265-285, 1983.
[22] Roshko, A., “Experiments on the Flow past a Circular Cylinder at Very High Reynolds Number,” J. Fluid Mech., Vol. 10, pp. 345-356, 1961.
[23] Schewe, G., “Reynolds Number Effects in Flow around more-or-less Bluff Bodies,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 89, pp. 1267-1289, 2001.
[24] Prandtl, L., “Motion of Fluid with Very Little Viscosity,” NACA TM No. 452, 1928.
[25] Schlichting, H., “Boundary-Layer Theory,” McGRAW-HILL, New-York, 1975.
[26] Higuchi, H., Kim, H. J., and Farell, C., “On Flow Separation and Reattachment around a Circular Cylinder at Critical Reynolds Numbers,” Journal of Fluid Mechanics, Vol. 200, pp. 149-171, 1989.
[27] Von Papen, T., Steffes, H., Ngo, H. D., and Obermeier, E., “A Micro Surface Fence Probe for the Application in Flow Reversal Areas,” Sensors and Actuators A: Physical, Vol. 97-98, pp. 264-270, 2002.
[28] Tu, J. K., Miau, J. J., “Design and Manufacturing of MEMS Thermal Film Sensor and Its Application for Experimental Fluid Dynamics”Journal of Aeronautics, Astronautics and Aviation, Series A, Vol.41, No.4, pp.229 - 236 ,2009.
[29] Miau, J. J., Tu, J. K., Chou, J. H., and Lee, G. B., “Sensing Flow Separation on a Circular Cylinderby Micro-Electrical-Mechanical-System Thermal-Film Sensors,” AIAA Journal, Vol. 44, No. 10, pp. 2224-2230, 2006.
[30] Tani, I., “Low-Speed Flows Involving Bubble Separation,” Prog. Aeronautical Science, Vol. 5, pp. 70-90, 1964.
[31] Farell, C., and Blessmann, J., “On Critical Flow around Smooth Circular Cylinders,” J. Fluid Mech., Vol. 136, pp. 375-391, 1983.
[32] Achenbach, E., “Influence of Surface Roughness on the Cross-Flow around a Circular Cylinder,” J. Fluid Mech., Vol. 46, pp. 321-335, 1971.
[33] Uematsu, Y., and Yamada, M., “Effects of Aspect Ratio and Surface Roughness on the Time-Average Aerodynamic Force on Cantilevered Circular Cylinders at High Reynolds Numbers,” Journal of Wind Engineering and Industrial Aerodynamics, 54/55, pp. 301-312, 1995.
[34] West, G. S., and Aplet., C. J., “Measurement of Fluctuating Pressures and Force on a Circular Cylinder in the Reynolds Number Range 104 to 2.5 105,”Journal of Fluids and Structures, Vol. 7, pp. 227-244, 1993.
[35] Masaru, K., Suzuki, K. A. and Hagino, M., “Contribution to the Free-Stream Turbulence Effect on the Flow past a Circular Cylinder,” Journal of Fluid Mechanics., Vol. 115, pp. 151-164, 1982.
[36] Fage, A. and Warsap, J. H., “The Effect of Turbulence and Surface Roughness on the Drag of a Circular Cylinder,” Aeronautical Research Council, Rep. & Memo. 1283, 1930.
[37] Nakamura, Y., and Tomonari, Y., “Effects of Surface Roughness on the Two Dimensional Flow past Circular Cylinders,” Journal of Fluid Mechanics., Vol. 123, pp. 363-378, 1982.
[38] Shih, W. C. L., Wang, C., Coles, D. and Roshko, A., “Experiments on Flow past Rough Circular Cylinders at Large Reynolds Numbers,” Journal of Wind Engineering and Industrial Aerodynamics., Vol. 49, pp. 351-368, 1993.
[39] Miau, J. J., Tsai, H. W., Lin, Y. J., Tu, J. K., Fang, C. H., Chen, M. C., ”Experiment on Smooth, Circular Cylinders in Cross-Flow in the Critical Reynolds Number Regime,” Exp Fluids, Vol. 51, pp. 949-967, 2011.
[40] Jørgensen, F. E., How to Measure Turbulence with Hot-Wire Anemometry-A Practical Guide, Dantec Dynamics, 2002.
[41] 杜榮國, “MEMS熱膜感測器設計製造及應用於探討非定常流分離現象,” 成功大學航太所碩士論文, 2003.
[42] Schewe, G., “On the Force Fluctuations Acting on a Circular in Cross-Flow from Subcritical up to Transcritical Reynolds Numbers,” J. Fluid Mech., Vol. 133, pp. 265-285, 1983.
[43] Barlow, J. B., Rae, D. W. Jr., Pope, A., “Low Speed Wind Tunnel Testing,” John Wiley & Sons, New York, 1984.
[44] Uematsu, Y. and Yamada, M., “Effects of Aspect Ratio and Surface Roughness on the Time-Averaged Aerodynamic Forces on Cantilevered Circular Cylinders at High Reynolds Numbers”, Journal of Wind Engineering and Industrical Aerodynamics, 54/55, pp. 301-312, 1995.
[45] Bearman, P. W., “On Vortex Shedding from a Circular cylinder in Critical Reynolds Number.”, J. Fluid Mech., Vol. 37, pp. 577-585, 1969.
[46] 蔡星汶, “圓柱表面流場在臨界區之空氣動力實驗研究,”成功大學航太所碩士, 2006.
[47] Huang, N.E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen. N. C., Tung, C. C., and Liu, H. H., “The Empirical Mode Decomposition and the Hilbert Spectrum of Nonlinear and Non-Stationary Time Series Analysis,” Proc. R. Soc. Lond. Vol. A454, pp. 903-995, 1998.
[48] Raghuveer, M. R., and Ajit, S. B., “Wavelet transform – Introduction to Theory and Applications,” Addison-Wesley, 1998.
[49] Grossmann, A. and Morlet, J. “Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape.”, SIAM J. MATH. ANAL., Vol. 15, NO. 4, pp. 723-736, 1984.