本研究利用田口實驗設計法配合計算流體力學，探討噴流驅動的圓柱Helmholtz共振腔，改變噴流吹口的幾何條件，並在Helmholtz共振腔內加入不同的延伸頸長結構，觀察聲音特性的變化。選擇吹口的速度、彎曲角度、高度、寬度，延伸頸長結構的長度與傾斜角度，作為田口實驗設計法的變因。利用CFD數值模擬共振腔內部流場，釐清各種不同Helmholtz共振下流場結構對聲音特性的影響。
研究結果顯示，各控制因子對聲音強度的影響力依序為：吹嘴高度>下游延伸頸長傾斜角度>吹嘴速度>吹嘴彎曲角度>上游延伸頸長傾斜角度>上游延伸頸長長度，吹嘴寬度與下游延伸頸長長度則可忽略。各控制因子對共振頻率的影響力依序為：吹嘴高度>吹嘴速度>上游延伸頸長長度>吹嘴寬度>上游延伸頸長傾斜角度>下游延伸頸長長度，吹嘴彎曲角度與下游延伸頸長傾斜角度則可忽略。數值模擬顯示，造成Helmholtz共振腔有“強共振”與“弱共振”兩種聲音特性差別的原因，可能是因Helmholtz共振腔內部流場渦漩結構的不同。

In this thesis, both Taguchi experimental methods and Computational Fluid Dynamic(CFD) software, Fluent, are used to analyze the acoustic effects of jet-excited cylindrical Helmholtz resonators. The shape of the mouthpieces and various extended neck structures of the Helmholtz resonators are examined to observe the acoustic characteristics of Helmholtz resonators. Velocity, bending angle, width, height of mouthpiece and the length, tilt angle of extended neck are chosen as the factors of Taguchi experimental methods. Fluent software is adopted to simulate the flow field inside the Helmholtz resonator for clarify the influence of fluid structure on the acoustic effects of the Helmholtz resonator.
According to the analysis, the influence sequence of controlled parameters in order of importance on sound amplitude is height of mouthpiece >downwind length of extended neck placed >velocity of mouthpiece >bending angle of mouthpiece > upwind tilt angle of extended neck placed > upwind tilt angle of extended neck placed .The effects of width of mouthpiece and length of extended neck placed at downwind can be ignored. Influence sequence of importance of controlled parameters on resonant frequency is as follows: height of mouthpiece >velocity of mouthpiece >upwind length of extended neck placed >width of mouthpiece >upwind tilt angle of extended neck placed >downwind length of extended neck placed. The effects of bending angle of mouthpiece and tilt angle of extended neck placed at downwind can be ignored. Simulation results suggest that, “strong resonance” or “weak resonance” of Helmholtz resonance might determine the type of vortex structure inside the Helmholtz resonator.

[1] N. H. Fletcher, "Air flow and sound generation in musical wind instruments," Annual Review of Fluid Mechanics, vol. 11, p. 123, 1975.
[2] B. Fabre, J. Gilbert, A. Hirschberg, and X. Pelorson, "Aeroacoustics of musical instruments," Annual Review of Fluid Mechanics, vol. 44, pp. 1-25, 2012.
[3] R. L. Paton and J.M. Miller, "Excitation of a Helmholtz resonator by a turbulent boundary layer," Journal of the Acoustical Society of America, vol. 58, pp. 800-806, 1975.
[4] D. Rockwell and E. Naudascher, "Review—self-sustaining oscillations of flow past cavities," Journal of Fluids Engineering, vol. 100, pp. 152-165, 1978.
[5] T. Morel, "Experimental study of a jet-driven Helmholtz oscillator," American Society of Mechanical Engineers, Winter Annual Meeting, San Francisco, Calif., pp.383-390, 1978.
[6] P. A. Nelson, N.A. Halliwell, and P.E. Doak, "Fluid dynamics of a flow excited resonance. Part I: Experiment," Journal of Sound and Vibration, vol. 78, pp. 15-38, 1981.
[7] P. A. Nelson, N.A. Halliwell, and P.E. Doak, "Fluid dynamics of a flow excited resonance. Part II: Flow acoustic interaction," Journal of Sound and Vibration, vol. 91, pp. 375-402, 1983.
[8] T. D. Mast and A. D. Pierce, "Describing‐function theory for flow excitation of resonators," Journal of the Acoustical Society of America, vol. 97, pp. 163-172, 1995.
[9] R. Khosropour and P. Millet, "Excitation of a Helmholtz resonator by an air jet," Journal of the Acoustical Society of America, vol. 88, pp. 1211-1221, 1990.
[10] M. Meissner, "The Response of a Helmholtz resonator to external excitation. Part II: Flow-induced resonance," Archives of Acoustics, vol. 30, pp. 57-71, 2005.
[11] R. Ma, P. E. Slaboch, and S. C. Morris, "Fluid mechanics of the flow-excited Helmholtz resonator," Journal of Fluid Mechanics, vol. 623, pp. 1-26, 2009.
[12] M. Massenzio, A. Blaise, and C. Lesueur, "Mechanisms of self-sustained oscillations induced by a flow over a cavity," Journal of Vibration and Acoustics, vol. 130, pp051001-1-17, 2008.
[13] S. Dequand, J. F. H. Willems, M. Leroux, R. Vullings, M. van Weert, C. Thieulot, "Simplified models of flue instruments: Influence of mouth geometry on the sound source," The Journal of the Acoustical Society of America, vol. 113, pp. 1724-1735, 2003.
[14] H. J. Ausserlechner, T. Trommer, J. Angster, and A. Miklos, "Experimental jet velocity and edge tone investigations on a foot model of an organ pipe," Journal of the Acoustical Society of America, vol. 126, pp. 878-886, 2009.
[15] S. Yoshikawa, H. Tashiro, and Y. Sakamoto, "Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model," Journal of Sound and Vibration, vol. 331, pp. 2558-2577, 2012.
[16] A. Selamet and I. Lee, "Helmholtz resonator with extended neck," The Journal of the Acoustical Society of America, vol. 113, pp. 1975-1985, 2003.
[17] S. K. Tang, "On Helmholtz resonators with tapered necks," Journal of Sound and Vibration, vol. 279, pp. 1085-1096, 2005.
[18] S. Caro, P. Ploumhans, X. Gallez, F. Brotz, M. Schrumpf, A. Read, "Aeroacoustic simulation of the noise radiated by an Helmholtz resonator placed in a duct," 11th AIAA/CEAS Aeroacoustic Conference, Monterey CA, USA, pp.2005-3067, 2005.
[19] S. Arunajatesan and N. Sinha, "Modeling approach for reducing Helmholtz resonance in submarine structures," 11th AIAA/CEAS Aeroacoustic Conference, Monterey CA, USA, pp.2005-2858, 2005.
[20] T. Kobayashi, T. Takami, M. Miyamoto, K. Y. Takahashi, A. Nishida, and M. Aoyagi, "3D calculation with compressible LES for sound vibration of ocarina," Open Source CFD International Conference, 2009.
[21] E. Selamet, A. Selamet, A. Iqbal, and H. Kim, "Effect of flow on Helmholtz resonator acoustics: A three-dimensional computational study vs. experiments," SAE Technical Paper, vol. 2011-01-1521, 2011.
[22] S. Dequand, X. Luo, J. Willems, and A. Hirschberg, "Helmholtz-like resonator self-sustained oscillations, part 1: Acoustical measurements and analytical models," AIAA Journal, vol. 41, pp. 408-415, 2003.
[23] S. Dequand, S. Hulshoff, H. van Kuijk, J. Willems, and A. Hirschberg, "Helmholtz-like resonator self-sustained oscillations, part 2: Detailed flow measurements and numerical simulations," AIAA Journal, vol. 41, pp. 416-423, 2003.
[24] S. Mallick, R. Shock, and V. Yakhot, "Numerical simulation of the excitation of a Helmholtz resonator by a grazing flow," The Journal of the Acoustical Society of America, vol. 114, pp. 1833-1840, 2003.
[25] G. Paál and I. Vaik, "Unsteady phenomena in the edge tone," International Journal of Heat and Fluid Flow, vol. 28, pp. 575-586, 2007.
[26] A. Powell, "On the edgetone," Journal of the Acoustical Society of America, vol. 33, pp. 395-409, 1961.
[27] K.Y. Takahashi, T. Iwasaki, T. Akamura, Y. Nagao, K. I. Nakano, T. Kobayashi, "Effective techniques and crucial problems of numerical study on flue instruments," Proceedings of Meeting on Acoustics, Montreal, Canada, vol. 19, 2013.
[28] R. L. Panton and J. M. Miller, "Resonant frequencies of cylindrical Helmholtz resonators," Journal of the Acoustical Society of America, vol. 57, pp. 1533-1535, 1975.
[29] R. C. Chanaud, "Effects of geometry on the resonance frequency of Helmholtz resonators," Journal of Sound and Vibration, vol. 178, pp. 337-348, 1994.
[30] U. Ingard, "On the theory and design of acoustic resonator," Journal of the Acoustical Society of America, vol. 25, pp. 1037-1061, 1953.
[31] 劉育政， “以三維大尺度渦流法模擬平板混合紊流場，”國立成功大學航空太空工程學系碩士學位論文，2009年。
[32] 李輝煌，“田口方法：品質設計的原理與實務，” 高立圖書有限公司出版，2011年。
[33] "Fluent 6.3 user's guide," Fluent Inc., Lebanon, 2006.