隨著風機效能地持續提升導致其衍生噪音也不斷增加，而風機所產生的特徵頻率噪音十分尖銳，係由葉輪旋轉衝擊氣體所造成，因此降低風機特徵頻率噪音即成為本研究重點；在此結合透過數值模擬以及實驗驗證方式，系統地評估三種常用風機之性能及噪音，並透過加裝亥姆霍茲共振器來降低風機所產生之特徵頻率噪音。本論文首先依據各式風機原型之幾何參數建模，並利用CFD 模擬軟體進行數值分析，透過穩態流場之可視化及暫態聲場模擬分析，探討流場與噪音之關連以找出風機噪音源，再藉由加裝亥姆霍茲共振器以期對風機所產生特徵頻噪音有所改善，最後整合比較各式風機有/無加裝共振器之效果；實驗部分則透過 CNC 加工技術製作共振器，以及利用3D 列印進行複雜的風機葉輪與外殼製作，接著搭配各式基準風扇進行相關之性能實驗，透過量測結果驗證數值模擬準確度。
模擬結果彙整顯示，於軸流風機上，針對第一特徵頻設計的共振器降低目標特徵頻噪音11~19 dB，而目標第二特徵頻率的共振器則降低第二特徵頻噪音20~23 dB；而在斜流風機模擬結果，針對第一特徵頻設計的共振器約降低此特徵頻噪音2~7 dB，而目標為第二特徵頻的共振器能降低此特徵頻噪音4~9 dB；至於在離心風機上，以第一特徵頻設計之兩種共振器則分別可降低此特徵頻噪音3.3 dB及4.6 dB。至於實驗測試部分，軸流風機設計之共振器，所呈現之減噪效果最好，於第二特徵頻率可降噪20 dB，而整體噪音也降1.0 dB；實驗結果與模擬趨勢相符，但減噪量仍有所誤差，至於共振器應用於斜流風機上，針對兩種頻率的共振器設計之測試發現，最佳效果令兩個頻率下降5.4與6.9 dB；而於離心風機針對第一特徵頻所設計的兩共振器，能有效降低此特徵頻1.5~1.9 dB。綜整本研究所建立之數值模擬與實驗驗證方式，已建立一套共振器應用於風機噪音改良與評估之系統，能提供完整且可靠的設計系統以有效地降低風機的特徵頻噪音問題。

This study intends to apply Helmholtz resonator on the axial-flow, the mix-flow, and the centrifugal fans for improving their narrow-band noises by an integrated effort of numerical simulation, mockup fabrication, and experimental test. At first, the cascade and design theories are utilized to generate the three-dimensional configuration of each fan type for serving as the reference basis. Next, the flow fields and the acoustic features associated with these fans are simulated and evaluated systematically with the aids of the commercial CFD software Fluent. Subsequently, the thorough understanding on the flow and acoustic features of these fans can be attained and utilized to design proper Helmholtz resonators, which are manufactured via CNC technology and installed on the appropriate location for assessing the associated noise-reduction outcomes via both CFD and experimental techniques. For the axial-flow fan, CFD simulation indicates that the noise reductions caused by resonators designed for the 1st and 2nd harmonic frequencies are 11-19 dB and 20-23 dB on their target frequencies, respectively. Also, the experiments present that resonator designed for the first characteristic frequency has the best noise-reduction effects, which are 20.0 and 1.0 dB on the 2nd harmonics and the overall noise, respectively.
Regarding the mix-flow fan, numerical calculation predicts that the noise reductions caused by Helmholtz resonators designed for the 1st and the 2nd harmonic frequencies are 2-7 dB and 4-9 dB on their target frequencies, respectively. Also, the experiments illustrate the best noise-reduction effects on the 1st and the 2nd harmonics are 5.4 and 6.9 dB, which are not deviated too much from CFD result. However, the application of resonator on the centrifugal fan is not as effective as the above two fan types. CFD outcomes show that the noise decreases of 3.3 dB and 4.6 dB are achieved on the 1st characteristic frequency by the installation of two resonator designs aimed at the first harmonics. In addition. the smaller noise -reduction effects are found as 1.5 dB and 1.9 dB via the acoustic test inside a semi-anechoic chamber. Generally, the trend and deviation between CFD and test results are correlated and within an acceptable range. In conclusion, the accomplishment of this study provides a systematic design scheme for the application of Helmholtz resonator on three common-used fan types. Several design parameters and installation locations of Helmholtz resonator are analyzed and discussed in a rigorous manner here.

[1] Zeller, W. and Stang, H., “Predetermination of the Axial-Flow Fans,” Heizung-Luftung-Haustchnik, Vol. 9, No. 12, pp. 10-20, 1957.
[2] Hüebner, G., “Noise Generated by Centrifugal Fans,” Siemens-Zeitschrift, Vol. 8, pp. 145-155, 1959.
[3] Embleton, T. F. W., “Experimental Study of Noise Reduction in Centrifugal Blowers,” The Journal of the Acoustical Society of America, Vol. 35, No. 5, pp. 700–705, 1963.
[4] Schlichting, H., “Application of the Boundary Layer Theory to Flow Problems of Turbo Machines,” Siemens-Zeitschrift, Vol. 33, No. 7, pp. 74-82, 1959.
[5] Neise, W., “Noise Reduction in Centrifugal Fans: a Literature Survey,” Journal of Sound and Viberation, Vol. 45, No. 3, pp. 375-403, 1976.
[6] Fukano, T. and Takamatsu, Y., “The Effects of Tip Clearance on the Noise of Low Pressure Axial and Mixed Flow Fans,” Journal of Sound and Vibration, Vol. 105, No. 2, pp. 291-308, 1986.
[7] Ohta, Y., Outa, E., and Tajima, K., “Evaluation and Prediction of Blade Passing Frequency Noise Generated by a Centrifugal Blower,” Journal of Turbomachinery, Vol. 118, pp. 597-605, 1996.
[8] Fehse, K. R. and Neise, W., “Generation Mechanisms of Low-Frequency Centrifugal Fan Noise,” American Institute of Aeronautics and Astronautics, Vol. 37, pp. 1173-1179, 1999.
[9] Fukano, T. and Jang, C. M., “Tip Clearance Noise of Axial-Flow Fans Operating at Design and Off-Design Conditions,” Journal of Sound and Vibration, Vol. 275, No. 3-5, pp. 1027-1050, 2004.
[10] Patankar, S. V. and Spalding, D. B., “A Calculation Procedure for Heat Mass and Momentum Transfer in Three-Dimensional Parabolic Flows,” International Journal of Heat Mass Transfer, Vol. 15, pp. 1787-1806, 1972.
[11] Su, M. M., Gu, C. A., and Miao, Y. M., “Numerical Study of Viscous Flow Field in Mixed-Flow Fan,” Journal of Xi’an Jiaotong University, Vol. 30, No. 10, pp. 55-63, 1996.

[12] Armone, A., “Viscous Analysis of Three-Dimensional Rotor Flows Using a Multigrid Method,” NASA TM-106266, 1993.
[13] Kokturk, T., Design and Performance Analysis of a Reversible Axial Flow Fan, Master’s Thesis, Middle East Technical University, February, 2005.
[14] Lin, S. C. and Huang, C. L., “An Integrated Experimental and Numerical Study of Forward-Curved Centrifugal Fan,” Experimental Thermal and Fluid Science, Vol. 26, pp. 421-434, 2002.
[15] Lighthill, M. J., “On Sound Generation Aerodynamically I. General Theory,” Proceedings of the Royal Society, London, Vol. 211, pp. 564-587, 1952.
[16] 周志成，新型離心式風扇數值與實驗整合研究，國立台灣科技大學機械工程系碩士論文，台北市，2006。
[17] Liu, Q., Qi, D., and Mao, Y., “Numerical Calculation of Centrifugal Fan Noise,” Proceedings of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol. 220, No. 8, pp. 1167-1177, 2006.
[18] Lu, H. Z., Huang, L., So, R. M. C., and Wang, J., “A Computational Study of the Interaction Noise from a Small Axial-Flow Fan,” The Journal of the Acoustical Society of America, Vol. 122, No. 3, pp.1404-1415, 2007.
[19] 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系博士論文，台北市，2010。
[20] Lin, S. C. and Tsai, M. L., “An Integrated Performance Analysis for a Small Axial-Flow Fan,” Proceedings of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol. 224, No. 9, pp. 1989-1996, 2010.
[21] Lin, S. C. and Tsai, M. L., “An Integrated Study of the Design Method for Small Axial-Flow Fans, Based on the Airfoil Theory,” Proceedings of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol. 225, No. 4, pp. 885-895, 2011.
[22] Lin, S. C. and Tsai, M. L., “An Integrated Performance Analysis for a Backward-Inclined Centrifugal Fan,” Computers & Fluids, Vol. 56, pp. 24-38, 2012.

[23] Lin, S. C., Shen, M. C., Li, C. M., Wang, F. Y., and Yen, H. C., “An Integrated Numerical and Experimental Investigation on Improving Acoustic and Cooling Performances of a High-Power Motor,” Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, pp. 327-336, 2017.
[24] Neise, W. and Koopman, G. H., “Reduction of Centrifugal Fan Noise by Use of Resonator,” Journal of Sound and Viberation, Vol. 72, No. 2, pp. 297-308, 1980.
[25] Neise, W. and Koopmann, G. H., “The Use of Resonators to Silence Centrifugal Blowers,” Journal of Sound and Vibration, Vol. 82, No. 1, pp. 17-27, 1982.
[26] 洪宗揚，後傾式離心風機之噪音研究，國立台灣工業技術學院機械工程系碩士論文，台北市，1996。
[27] 呂水煙，前傾式離心風機之噪音研究，國立台灣工業技術學院機械工程系碩士論文，台北市，1997。
[28] 吳御銓，λ/4減噪器應用在離心扇之數值與實務整合研究，國立台灣科技大學機械工程系碩士論文，台北市，2014。
[29] Alster, M., “Improved Calculation of Resonant Frequencies of Helmhlotz Resonantors,” Journal of Sound and Vibration, Vol. 24, No. 1, pp. 63-85, 1972.
[30] Bies, D. A. and Hansen, C. H., Engineering Noise Control: Theory and Practice. E&FN Spon, New York, USA, 1966.
[31] Kurze, U. J. and Beranck, L. L., Noise and Vibration Control. Institute of Noise Control Engineering, Washington, DC, USA, 1998.
[32] Han, M., Sound Reduction by a Helmholtz Resonator, Thesis, Lehigh University, 2008.
[33] Han, S. S. and Rhim, Y. C., “Noise-Level Reduction of a Slim-Type Optical Disk Drive Using the Idea of a Helmholtz Resonator,” Transactions on Magnetics, Vol. 45, No. 5, pp. 2217-2220, 2009.
[34] 陳彥彰，亥姆霍茲共振器應用於管路風機之實驗與模擬整合研究，國立台灣科技大學機械工程系碩士論文，台北市，2014。
[35] 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系碩士論文，台北市，2017。

[36] Li, L., Liu, Y., Zhang, F., and Sun, Z., “Several Explanations on the Theoretical Formula of Helmholtz Resonator,” Advances in Engineering Software, Vol. 114, pp. 361-371, 2017.
[37] Komkin, A. I., Mironov, M. A., and Bykov, A. I., “Sound Absorption by a Helmholtz resonator,” Acoustical Physics, Vol. 63, No. 4, pp. 385–392, 2017.
[38] Cai, C., Mak, C. M., and Shi, X., “An Extended Neck versus a Spiral Neck of the Helmholtz Resonator,” Applied Acoustics, Vol. 115, pp. 74–80, 2017.
[39] CNS 8753, “Determination of Sound Power Level of Noises for Fan, Blower, and Compressors,” Chinese National Standard, 1982.
[40] 白明憲，工程聲學，全華圖書，台北，2005。
[41] Powell, A., “Theory of Vortex Sound,” The Journal of the Acoustical Society of America, Vol. 36, No. 1, pp. 177-195, 1964.
[42] Copley, L. G., “Fundamental Results Concerning Integral Representations in Acoustic Radiation,” The Journal of the Acoustical Society of America, Vol. 44, No. 1, pp. 28-32, 1968.
[43] De Vries, M. P., Schutte, H. K., Veldman, A. E. P., and Verkerke, G. J., “Glottal Flow through a Two-Mass Model: Comparison of Navier–Stokes Solutions with Simplified Models,” The Journal of the Acoustical Society of America, Vol. 111, No. 4, pp. 1847–1853, 2002.
[44] Launder, B. E. and Spalding, D. B., Lectures in Mathematical Models of Turbulence, Academic Press, London, England, 1972.
[45] Smirnov, R., Shi, S., and Celik, I., “Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling,” Journal of Fluids Engineering, Vol. 123, pp. 359-371, 2001.
[46] Uranga, A., Persson, P., Drela, M., and Peraire, J., “Implicit Large Eddy Simulation of Transitional Flows over Airfoils and Wings,” 19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas, 2009.
[47] Ffowcs Williams, J. E. and Hawkings, D. L., “Sound Generation by Turbulence and Surface in Arbitrary Motion,” Philosophical Transactions of the Royal Society of London, Vol. 264, pp. 321-342, 1969.

[48] Curle, N., “The Influence of Solid Boundaries upon Aerodynamic Sound,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 231, pp. 505–514, 1955.
[49] CNS 8753, “Determination of Sound Power Level of Noises for Fan, Blower, and Compressors,” Chinese National Standard, 1999.
[50] ISO 3744:2010, “ Determination of Sound Power Levels and Sound Energy Levels of Noise Sources Using Sound Pressure,” International Organization for Standardization, 2010.
[51] ANSI/AMCA Standard 210-99 (ANSI/ASHRAE 51-1999), “Laboratory Method of Testing Fans for Aerodynamic Performance Rating,” Air Movement and Control Association, Inc., 1999.