由於風扇的發展歷史上已經非常悠久，隨著科技的發展，軸流式風扇的氣動力性能不斷提高，但也已經到達瓶頸，因此風扇的多目標性能最佳化成為研究重點，本文以常見的十四公分軸流風扇作為研究目標。建立一套具有可信度的最大風量、噪音分析模擬方法，接著列出有可能對於此兩項目標有影響的參數做田口法分析，並且利用此次田口法作為研究基礎。接著，縮小參數範圍並建立兩套最佳化方式，分別為田口灰關聯法與反應曲面法，以比較兩套最佳化方法的優劣；模擬研究結果顯示，以110 CFM、34 dBA當作最佳化目標，田口灰關聯法的最佳化結果為105.34 CFM、34.34dBA，誤差為4.23%、1%，而反應曲面法的最佳化結果為108.66 CFM、34.11dBA，誤差為1.1%、0.32%。綜合以上研究成果顯示，田口法能夠有效挑出貢獻度較大之控制因子，而不論是田口灰關聯分析及反應曲面法都能夠有效地為軸流式風扇進行性能優化，其中又以反應曲面法之效果更佳，但是需多耗時約60%時間，而本研究完成之系統化的多目標最佳化設計流程可應用於各式風扇之性能提升，如離心式、軸流式、斜流式風扇等。

This research establishes an optimizing scheme under the multi-objective constraint for a 14cm-in-diameter axial-flow fan, which is used extensively in the electronic thermal designs. Firstly, an 8-design-variable parametric study is executed comprehensively with the aids of CFD simulation results to realize their influences on the maximum flow rate and the acoustic noise. Next, these numerical data are analyzed via Taguchi method to find the corresponding performance contribution for each parameter by comparing their signal-to-noise (S/N) ratios. The outcomes indicate that the dominant variables in order are the twist angles on mid-section and tip-end of the blade, the forward-inclined angle, and the deviated distance of blade, which can be used to decrease the number and narrow the variation range of parameters considered in the 2nd optimum phase.
Thereafter, Taguchi-based gray correlation and response surface method are selected for conducting the in-depth optimization aiming at the design goal (110 CFM and 34 dBA). Subsequently, the response-surface method results in the aerodynamic and acoustic performances of 108.66 CFM and 34.11 dBA, which are deviated from the target by 1.1% and 0.32%, respectively. Also, Taguchi-based gray correlation analysis generates the slightly down-grade characteristics at 105.34 CFM (4.23%) and 34.34 dBA (1.1%) with a lesser analysis effort, which is roughly 60% of what needed in the response-surface method. In summary, this thesis demonstrates that Taguchi method can identify key parameters and their contributions. Also, both Taguchi based gray-correlation analysis and the response-surface method are capable to optimize the performance of an axial-flow fans near the design goal. Moreover, the multi-objective optimizing scheme established here can be utilized on the performance enhancement for other fan types under various design conditions.

[1] Eck, B., Fans: Design and Operation of Centrifugal, Axial-Flow, and Cross-Flow Fans. New York, Pergamon Press Oxford, 1973.
[2] Shepherd, D. G., Principles of Turbomachinery. New York, Macmillan Publishing Company, 1956.
[3] 蘇聖斌、陳世雄, “軸流泵葉輪與導葉之設計分析”，中國機械工程學會第十三屆學術研討會論文集，pp. 298-306，1996年。
[4] Lin, S. C., Huang, C. L., and Jan, H. B., "The Numerical and Experimental Analysis of Axial-Flow Fans," in The AASRC Aeronautics and Astronautics Conference, TaoYuan, Taiwan, pp. 107-117, 1999.
[5] 林鴻志，“Pentium4處理器冷卻風扇之製造與實驗研究”，國立台灣科技大學機械工程學系碩士論文，2001年。
[6] 嚴文祺，“軸流式風機的性能與噪音特性之整合研究”，國立台灣科技大學機械工程學系碩士論文，2017年。
[7] 陳文亮，“小型冷卻風扇之性能及噪音改善研究”，國立台灣科技大學機械工程學系碩士論文，1998年。
[8] Ye, X., Fan, F., Zhang, R., and Li, C., "Prediction of Performance of a Variable-Pitch Axial Fan with Forward-Skewed Blades," Energies, Vol. 12, No. 12. Article 2353, 2019.
[9] Horváth, C. and Vad, J., "Broadband Noise Source Model Acoustical Investigation on Unskewed and Skewed Axial Flow Fan Cascades," Vol. 9, pp. 682-689, 2009.
[10] Longhouse, R. E., "Vortex Shedding Noise of Low Tip Speed, Axial Flow Fans," Journal of Sound and Vibration, Vol. 53, No. 1, pp. 25-46, 1977.
[11] Avallone, F., Van Der Velden, W. C. P., Ragni, D., and Casalino, D., "Noise Reduction Mechanisms of Sawtooth and Combed-Sawtooth Trailing-Edge Serrations," Journal of Fluid Mechanics Vol. 848, pp. 560-591, 2018.
[12] Avallone, F., Van Der Velden, W. C. P., Ragni, D., "Benefits of Curved Serrations on Broadband Trailing-Edge Noise Reduction," Journal of Sound and Vibration, Vol. 400, pp. 167-177, 2017.
[13] Zeller, W. and Stang, H., “Predetermination of Axial-Flow Fans,” Heizung-Luftung-Haustchnik, Vol. 9, No. 12, pp. 345-357, 1957.
[14] Zeller, W., “Concerning Mathematical Treatment of Noise Behaviour in Fans for Air Conditioning Plants,” VID-Berichte, No. 38, 1959.
[15] Schlichting, H., “Application of the Boundary Layer Theory to Flow Problems of Turbo Machines,” Simens-Zeitschrift, Vol. 33, No. 7, pp. 74-82, 1959.
[16] Powell, A., “Theory of Vortex Sound,” The Journal of the Acoustical Society of America, Vol. 36, pp. 177-195, 1964.
[17] 陳文雄，“田口法應用在水冷電源供應器之數值分析”，國立台灣科技大學機械工程學系碩士論文，2007年。
[18] 李灃哲，“提高軸流式風扇的效率與降低其氣動噪音之最佳化分析”，國立台北科技大學機械工程學系碩士論文，2017年。
[19] 陳源樹，“灰關聯分析應用於薄膜製程最佳化之研究”，逢甲大學工業工程系統管理學系碩士論文，2006年。
[20] 陳毓良，陳世銘，蔡錦銘，蔡兆胤，方信雄，劉森源，孫睿鴻，"應用反應曲面法探討柴油引擎添用生質柴油最適摻混比例之研究" 農業機械學刊，20卷，2期，pp: 45-58，2011。
[21] Lighthill, M. J., “On Sound Generation Aerodynamically-I. General Theory,” Proc. Roy. Soc. London, Vol. 211, pp. 564-587, 1952.
[22] Arone, A., “Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method,” Journal of Turbomachinery, Vol. 116, No. 3, pp. 435-445, 1994.
[23] Amano, R. S. and Cheng, X. C., “Aerodynamic Blade Optimal Design of Turbomachinery,” Proceedings of the International Gas Turbine Congress, Tokyo, November 2-7, 2003.
[24] Suhas, V. P., Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, 1980.
[25] Yang, L., "Study Tip Leakage Vortex of CPU Fan with Skewed Rotors," Unifying Electrical Engineering and Electronics Engineering, Proceedings of the 2012 International Conference on Electrical and Electronics Engineering, New York, Springer New York, 2013.
[26] Krömer, F. J., Sound Emission of Low-Pressure Axial Fans under Distorted Inflow Conditions. FAU University Press, 2018.
[27] Launder, Brian Edward and Spalding, Dudley Brian., "Lectures in Mathematical Models of Turbulence," 1972.
[28] Wilcox, D. C., "Reassessment of the Scale-Determining Equation for Advanced Turbulence Models," AIAA Journal, Vol. 26, No. 11, pp. 1299-1310, 1988.
[29] Menter, F., "Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows," 23rd fluid dynamics, plasmadynamics, and lasers conference, 1993.
[30] 蔡明倫，“風扇性能評估與設計方法之整合研究”，國立台灣科技大學機械工程學系博士論文，2010年。
[31] Fluent Inc., Fluent Theory Guide, Fluent Inc., 2013.
[32] Ffowcs Williams, J. E., and David, L. H., "Sound Generation by Turbulence and Surfaces in Arbitrary Motion," Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, Vol. 231, pp. 321-342, 1969.
[33] Curle, N., "The Influence of Solid Boundaries upon Aerodynamic Sound," Proceedings of the Royal Society A: Mathmatical, Physical and Engineering Sciences, Vol. 231, pp. 505-514, 1955.
[34] Box, G. E. P. and Wilson, K. B., "On the Experimental Designs for Exploring Response Surfaces," Ann Math Stat, Vol. 13, pp. 1~45, 1951.
[35] Hill, W. J. and Hunter, W. G., "A Review of Response Surface Methodology: A Literature Survey," Technometrics, Vol. 8, No. 4, pp. 571-590, 1966.
[36] Harrington, E. C., "The Desirability Function," Industrial Quality Control, Vol. 21, No. 10, pp. 494-498, 1965.