本研究是探討流場流經一個平滑的圓柱表面時的分離現象，雷諾數範圍介於4.1x105~5.67x105，利用可饒式熱膜感測器平貼於圓柱表面進行流場量測，在運用快速傅立葉轉換以及希伯特黃轉換來進行分析。由於本實驗在穿音速風洞中進行，所以同時考慮可壓縮流場所造成的壓縮效應。利用熱膜感測器的特性，量測在流線方向上，圓柱表面上的流場分離現象。研究結果可以清楚地發現，在分離點發生前以及分離流場中，會有倍頻產生，此時渦流溢放訊號也會較強。流場分離的不定常現象亦可在本研究中發現。

An experimental investigation of flow around a smooth circular cylinder was carried out in a transonic wind tunnel,at Reynolds numbers 4.1x105~5.67x105,corresponding the Mach numbers in a range of 0.4 to 0.7. Unsteady characteristics of flow separation were studied with an
array of self-made micro-electrical-mechanical-system (MEMS) film sensors, which were flushed with the cylinder surface, aligned in the circumferential direction. By correlation analysis of the signals obtained by two neighboring sensors, it is found that the location of flow
separation can be identified by comparing the correlation coefficients obtained, which falls in the region where the correlation coefficients drops pronouncedly along the circumferential direction. By FFT analysis of the signals of each MEMS sensor, an interesting feature noted
is that in the neighborhood of the flow separation pioint, the signal fluctuations contain a harmonic component of the vortex shedding frequency. Further, the results obtained by Hilbert-Huang Transformation of the signals measured indicate that downstream of the flow separation point, the fluctuating energy contained in the vortex
shedding frequency component was reduced greatly. Since the
experiments were made in a transonic wind tunnel, the effect of flow compressibility was discussed. As noted, through the present Reynolds numbers studied, the Strouhal numbers corresponding to the vortex shedding frequencies reduced remained about 0.2, distinguished different
from those reported by the studies made in the low-speed wind tunnels, in the regime of the critical Reynolds numbers.

[1] 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.
[2] Chung, K. M., Miau, J. J., and Yeh, J. S., “Development and Calibration
of ASTRC/NCKU Transonic Wind Tunnel,” NSC 83-0424-E006-141T Report, Taiwan, 1994.
[3] 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 for Nonlinear and Nonstationary Time Series Analysis,”Proceedings of Royal Society of London, Series A,
Vol. 454, pp.903-995, 1998.
[4] Zdravkovich, M. M., Flow Around Circular Cylinders, Vol. 1, Oxford University Press, 1997.
[5] Morkovin, M. V., “On the Question of the Instability Upstream of Cylindrical Body,” NASA CR No. 3231, Dec. 1979.
[6] Wieselsberger, C. M., “The Drag of Cylinders in Fluids at Low Speeds,”Proceedings Royal Society, Series A, Vol. 186, pp.472-9, 1946.
[7] Bearman, P. W., ” On Vortex Shedding From a Circular Cylinder in the Critical Reynolds Number Regime,” J . Fluid Mech., Vol. 37, part 3, pp. 577-585, 1969.
[8] Einsner, F., “ Pressure Measurements on Cylinder Surrounded by Flow Fluid,” Journal of Mathematic and Mechanics, vol. 5, pp. 486-9, 1925.
[9] Kamiya, N., Suzuki, S., and Nishi, T., “ On the Aerodynamic Force Acting on a Circular Cylinder in the Critical Range of the Reynolds Number,” AIAA Meeting, Paper, No. 1975, 1979.
[10] Higuchi, H., J. Kim, H., and Farell, C., “On Flow Separation and Reattachment around a Circular Cylinder at Critical Reynolds Numbers,”J . Fluid Mech., vol. 200, pp. 149-171, 1989.
[11] Schewe, G. “Sensitivity of Transition Phenomena to Small Perturbations in Flow around a Circular Cylinder,” Journal Fluid Mechanics, Vol. 172, pp. 33-46.1985.
[12] Almosnino, D., and McAlister, K.W., “Water Tunnel Study of Transition Flow around Circular Cylinders,” NASA, No. 85879, 1984.
[13] 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.
[14] Stanton T. E., “On the Effect of Air Compression on Drag and Pressure Distribution on Cylinders of Infinite Aspect Ratio,” British Aeronautical Research Council, Rep ＆ Memo No. 1210, 1929.
[15] Murthy, V. S., and Rose, W.C.,” From Drag, Skin Friction, and Vortex Shedding Frequencies for Subsonic and Transonic cross Flow on Circular Cylinder, ” Proceedings AIAA 10th Fluid and Plasma Dynamics Conference, Albuquerque, No. 687, 1977.
[16] Lindsey, W. F., “Drag of Cylinders of Sample Shapes,” NACA Technical Report 619, 1938.
[17] Stack, J. “Compressibility Effects in Aeronautical Engineering,”NACA, ACR. No. 207, 1941.
[18] Fage, A. and Falkner, V. M., “Further Experiments on The Flow around a Circular Cylinder.” Aeronautical Research Committee, Rep. and Memo No. 1369, 1930.
[19] Breuer, K. S., “MEMS Sensors for Aerodynamic Application the Good,the Bad,” AIAA paper No. 251, 2000
[20] Anthony, R. J., Jones, T. V., and LaGraff, J. E., “Visualization of Transition Boundary Layer Heat Flux Using High Density Thin Film Array,” AIAA paper No. 553, 2001
[21] White, F. M., Viscous Fluid Flow, 2nd edition, McGraw-Hill, 1991.
[22] Tu J. K., Miau J. J., Chou J. H., and Lee G. B., “Sensing Flow Separation on a Circular Cylinder by MEMS Thermal-Film Sensors”, 43rd AIAA Aerospace Science Meeting and Exhibit, No. 299, 2005.
[23] 蔡星汶，圓柱表面流場在臨界區之空氣動力實驗研究，成大航太碩士論文，2006。
[24] Roshko, A., “Perspectives on Bluff Body
Aerodynamics,” J. Wind Eng. Ind. Aerodynamics., Vol. 49, pp.17-100, 1993.
[25] Lee, T., “Investigation of Unsteady Boundary Layer Developed on a Rotationally Oscillating Circular Cylinder,” AIAA Journal, Vol. 37, No. 3, March 1999.
[26] Nakagawa, T., “Mach Number Effects on Vortex Shedding of a Square Cylinder and Thick Symmetrical Airfoil Arranged in Tandem,” Proc R. Soc. Lond. Series A, Vol. 407, pp.283-297, 1986.
[27] Ju, J., and Wu, W., “Numerical Simulation of Unsteady 2-D Compressible Flow around a Circular Cylinder,” J. of Thermal Science, Vol.9, No.2, 2000.
[28] Blevins, R. D., “The Effect of Sound on Vortex Shedding from Cylinders,” J. Fluid Mech., Vol. 161, pp. 211-231, 1985.
[29] Dwyer, H. A., and Mccroskey, W. J., “Oscillating Flow over a Cylinder at Large Reynolds number,” J. Fluid Mech., vol. 61, part 4, pp. 753-767, 1973.
[30] Liu, W. P., and Brodie, G. H., “A Demonstration of MEMS-based Active Turbulence Transitioning,” International Journal of Heat and Fluid Flow, Vol. 21 pp. 297-303, 2000.
[31] Achenbach, E., “Distribution of Local Pressure and Skin Friction around a Circular Cylinder in Cross-flow up to Re = 5x106,” J. Fluid Mech., Vol. 34, part 4, pp. 625-639, 1968.
[32] Burbeau, A., and Sagaut, P., “Simulation of a Viscous Compressible Flow past a Circular Cylinder with High-Order Discontinuous Galerkin Methods,” Computers & Fluids ,Vol. 31, pp. 867–889, 2002.
[33] Ishigaki, H. “Skin Friction and Surface Temperature of an Insulated Flat Plate in a Fluctuating Stream,” J. Fluid Mech., Vol. 46, part 1, pp. 165-175, 1971.
[34] Zebib, A., “Stability of Viscous Flow past a Circular Cylinder,” Journal of Engineering Mathematics, Vol. 21, pp. 155-165, 1987.
[35] Menendez, A. N. and Ramapriant, B. R., “The Use of Flush-Mounted Hot-Film Gauges to Measure Skin Friction in Unsteady Boundary layers,” J. Fluid Mech., Vol. 161, pp. 139-159, 1985.
[36] Saito, T., Menezes, V., Kuribayashi, T., Sun, M., Jagadeesh, G., and Takayama, K., “Unsteady Convective Surface Heat Flux Measurements on Cylinder for CFD Code Validation,” Shock Waves , Vol. 13, No. 5, pp.327–337, 2004.
[37] 杜榮國,苗君易,曾雅祺 “應用MEMS熱膜感測器探討鈍形體於 諾數104下渦流位錯現象,” 2006 AASRC/CCAS Joint Conference, 2006.
[38] 蔡星汶,苗君易,林映如 “圓柱表面流場在臨界區之空氣動力實驗研究,” The 30thNational Conference on Theoretical and Applied Mechanics, December 15-16, 2006.
[39] Itiro Tani, “Bondary-Layer Transition,” Annual Rev. Fluid Mech., Vol. 1,pp. 169-196, 1969.
[40] 杜榮國，MEMS 熱膜感測器設計製造及應用於探討非定常流動分離現象，成功大學航太所碩士論文，2003。
[41] 林映如，臨界圓柱流場之非定常三維特性探討，成功大學航太所碩士論文，2007。
[42] Batham, J. P., “Pressure Distributions on Circular Cylinders at Critical Reynolds Numbers.”, J. Fluid Mech., Vol.57, part 2, pp. 209-228, 1973.
[43] Bellhouse B. J. and Schultz, D. L., “Determination of Mean and Dynamic Skin Friction, Separation and Transition in Low-Speed Flow with a Thin-Film Heated Element,” J. Fluid Mech., Vol. 74, part 2, pp. 379-400, 1966.
[44] Farell, C. and Blessmann, J.,“On Critical Flow around Smooth Circular Cylinders,” J. Fluid Mech., Vol.136, pp.375-391, 1983.
[45] Davies, T. and Walker, G., “On Solutions of the Compressible Laminar Boundary-Layer Equations and Their Behavior near Separation,” J. Fluid Mech., Vol. 80, part 2, pp. 279-292, 1977.
[46] Liakopoulos, A. and Hsu, C.C., “On a Class of Compressible Laminar Boundary-Layer Flows and the Solution Behavior near Separation,” J. Fluid Mech., Vol. 149, pp. 339-363, 1984.
[47] Poots, G., “Compressible Laminar Boundary-Layer Flow at a Point of Attachment,” J. Fluid Mech., Vol. 22, part 1, pp. 197-208, 1966.
[48] Roshko, A., “Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number.”, J. Fluid Mech., Vol.10, pp. 345-356, 1961.
[49] Despard. R. A. and Miller, J. A., “Separation in Oscillating Laminar Boundary-Layer Flows,” J. Fluid Mech., Vol. 47, part 1, pp. 21-31, 1971.