渦流動能的傳遞與流量的傳遞都與大尺度渦流結構相關，而離開勢位區後的大尺度渦流結構決定流場遠場區的動能傳遞，為了能控制遠場區流場的渦流結構，本篇研究為利用熱線測速儀量測流場及可視化流場觀測等實驗方法探討在低速下平面噴流在對稱、反對稱、單邊的長波激擾下之渦流結構擴散特性。擾動設備為裝置在噴嘴出口處上下兩片金屬平板，以出口風速及出口寬度為特徵速度及長度之雷諾數為7.7×103。
因長波激擾對於近場區沒有影響，近場區保留著與自然噴流相似的渦流結構，而遠場區在受到長波激擾下相干性結構的演變有著顯著的影響。因激擾頻率為自然噴流勢位區末端的顯著模態頻率的相關倍頻，所以對於遠場區影響會更為顯著，在反對稱的長波激擾下使得勢位區末端之後的擺盪特性被增強了，所以不對稱激擾噴流的擴展特性顯著提升。在對稱激擾下擴展特性明顯被抑制，而單邊擾動也增強了擴展特性但沒有不對稱擾動來的更好。
從頻譜中顯示遠場區只有激擾頻率與其倍頻具有較高能量，這表示遠場區的渦流結構為激擾頻率控制，而因三種激擾模態的不同，有著不一樣的大尺度渦流結構，因為自然噴流的渦流模態在遠場區會轉接近反對稱模態的大尺度渦流，所以人為的放大和抑制則能控制其擴散特性。
在頻譜分析及變動速度中能瞭解各渦流結構的合併及配對的位置和情形，但其頻譜因傅立葉轉換所存在的全時域與全時頻，無法得知瞬時頻率對於渦流結構的影響，所以以小波分析法進而分析瞬時頻率造成的影響。

ABSTRACT

In this paper the spreading characteristics of a low-speed plane jet under anti-symmetric, symmetric and one-side long-wave excitation are investigated experimentally by hot-wire anemometric measurements. Using the wavelet analysis analyze the measurement data. The perturbations of excitation are introduced with two oscillating strips located at the nozzle exit. The experiments were operated at Reynolds number of 7.7×103 based on the nozzle exit velocity and height.
The anti-symmetric, symmetric and one-side mode long-wave excitations of the jet flow are investigated for comparing the mixing and spreading properties after the end of potential core. The results of velocity measurements indicate that the jet flow is effectively influenced by flapping motion of the anti-symmetric mode. Meanwhile, the jet flapping is clearly en¬hanced and the jet spreads wider after the potential core. As for the symmetric mode excitation, the vortices shed downstream there spreading and the flapping motion was suppressed. It apparently demonstrates that the anti-symmetric mode excitation has better effective excitation on jet flow spreading and mixing as well.

REFERENCES

[1] Michalke, A., 「On the inviscid instability of the hyperbolic-tangent velocity profile」, J. Fluid Mech., Vol. 22, pp. 543−556 , 1964
[2] Michalke, A., 「On spatially growing disturbances in an inviscid shear layer」, J. Fluid Mech., Vol. 23,part 3, pp. 521−544 , 1965
[3] Hussain, A. K. M. F., 「Coherent Structures – Reality and Myth,」 Phys. Fluids, Vol. 26, pp. 2816-2850, 1983.
[4] Winant, C. D. and Browand, F. K.,「Vortex pairing-the mechanism of turbulent Mixing layer growth at moderate Reynolds number」, J. Fluid Mech., Vol. 63, pp. 237-255, 1974
[5] Crow, S. C., and Champagen, F. H., 「Orderly structure in jet turbulence」, J. Fluid Mech., Vol. 48, pp. 547−591, 1970.
[6] Browand, F K., and Weidman, P. D., 「Large scales in the developing mixing layer」, J. Fluid Mech., Vol. 76, pp. 127−144, 1976.
[7] Brown, F. K. and Roshko, A., 「On the density effects and large structure in turbulent mixong layer」, J. Fluid Mech., Vol. 64, pp. 775−816, 1974.
[8] Thmoas, F. O., 「Structure of mixing layers and jets」, Appl. Mech. Rev., Vol. 44, No. 3, pp. 119-150, 1991
[9 ] Ho, C. M. and Gutmark, E., 「Prefered mode and the spreading rates of jets」, Phys. Fluids, Vol. 26, pp.2932-2938, 1983
[10] Ho, C. M. and Huerre, P., 「Perturbed free shear layer」, Ann. Rev. Fluid Mech., Vol. 16, pp.635-424, 1984
[11] Hsiao, F. B. and Huang, J. M., 「Near-field flow structures and sideband instabilities of an initially laminar plane jet」, Experiments in Fluid, Vol. 9, pp. 2-12, 1990
[12] Drazin, P. G., 「Discontinuous velocity profiles for the Orr-Sommerfeld equation」, J. Fluid Mech., Vol. 10, pp. 571−583, 1961
[13] Drazin, P. G., 「On instability of slowly-varying flow」, Quart. J. Mech. Appl. Math., Vol. 27, pp. 69-86, 1974

[14] Drazin, P. G., 「Internal gravity waves and shear instability」, pp. 61-73 of Wavea and Stability in Continuous Media, eds. A. Donato & S. Giambo(Editel, Italy), 1982
[15] Drazin, P. G., 「Nonlinear System (Cambridge University Press)」, 1992
[16] Drazin, P. G. and Reid, W. H., 「Hydrodynamic Stability (Cambridge University Press)」, 1981
[17] Goldschmidt, V. M., Moallemi, M. K. and Oler, J. W., 「Structures and flow reversal in turbulent plane jet」, Phys. Fluid, Vol. 26, pp. 428-432, 1983
[18] Hussain, A. K. M. F. and Zaman, K. B. M. Q., 「The preferred mode of the axisymmetric jet」, J. Fluid Mech., Vol. 110, pp. 39-71, 1981
[19] Hussain, A. K. M. F. and Zaman, K. B. M. Q., 「Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics」, J. Fluid Mech., Vol. 101, pp. 493-544, 1980
[20] Ho, C. M. and Hsiao, F. B., 「Evolution of coherent structures in a lip jet」, IUTAM Symposium on Structure of Complex Turbulent Shear Layers, ed. R. Dumas, L. Fulachier, pp. 121-136. Berlin, 1983
[21] Hsiao, F. B. and Huang, J. M., 「Subharmonic evolution of coherent structures in an excited plane jet」, AIAA-88-3609, presented in the 1st National Fluid Dynamics Congress, Cincinnati, Oh, 1988
[22 ] Kibens, V., 「Discrete noise spectrum generated by an acoutically excited jet」, AIAA Journal, Vol. 18, pp. 434-441, 1980
[23] Wygnanski, I. and Peterson, R. A., 「Coherent motion in excited free shear flows」, AIAA Journal, Vol. 25, pp. 201-213, 1974
[24] Husain, H., Bridges, J. E. and Hussain, F., 「Turbulence management in free shear flowss by control of coherent structures」, Transport Phenomena in Turbulent flows, pp. 111-130, 1988
[25] Hussain, A. K. M. F., 「Coherent structures and studies of perturbed and unperturbed jets」, The role of coherent structures in modeling turbulence and mixing, Lect. Notes Phys., Vol. 136, 1981
[26] Crighton, D. G., 「Jet noise and the effects of jet forcing」, The role of coherent structures in modeling turbulence and mixing, Lect. Notes Phys., Vol. 136, pp. 340-362, 1981
[27] Oster, D. and Wygnanski, I., 「The forcing mixing layer between paralle streams」, J. Fluid Mech., Vol. 123, pp. 91-130, 1982
[28] Simmons, J. M. and Lai, J. C. S., 「Jet excitation by an oscillating vane」, AIAA Journal, Vol. 19, pp. 673-676, 1981
[29] Ho, C. M. and Huang, L. S., 『Sub-harmonics and vortex merging in mixing layers」, J. Fluid Mech., Vol. 119, pp. 443-473, 1982
[30] Huang, J. M. and Hsiao, F. B., 「 On the mode development in the developing region of a plane Jet」, Phys. Fluid, Vol. 11, 7, pp. 1847-1857, 1999
[31] Hsiao, F. B., Hsu, I. C. and Huang, J. M., 「Evolution of coherent structures and feedback mechanism of the plane jet impinging on a small sylinder」, Journal of Sound and Vibration, Vol. 278, Issues 4-5, pp. 1163-1179, 2004
[32] Weisbrot, I. and Wygnanski, I., 「On coherent structures in a highly excited mixing layer」, J. Fluid Mech., Vol. 195, pp. 137-159, 1988
[33] Cervantes de Gortari, J. G. and Glodschmidt, V. M., 「The apparent flapping motion of turbulent plane jet-further experimental results」, Trans. ASME I: J. Fluids Eng., Vol. 103, pp. 119-126, 1981
[34] Goldschmidt, V. M. and Bradshaw, P., 「Flapping of a plane jet」, Phys. Fluid, Vol. 16, pp. 354-355, 1973
[35] Oler, J. W. and Goldschmidt, V. M., 「A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet」, J. Fluid Mech., Vol. 123, pp. 523-535, 1982
[36] Browne, L. W. B., Antonia, R. A. and Chambers, A. J., 「The interaction region of a turbulent plane jet」, J. Fluid Mech., Vol. 149, pp. 355-373, 1984
[37] Moallemi, K., 「Visualization and characterization of a two-dimensional turbulent jet」, Master thesis, School of Mech. Eng., Purdue University, 1998
[38] Atassi, O. V. and Lueptow, R. M., 「A model of flapping motion in a plane jet」, European Journal of Mechanics B / Fluids, 21, pp. 171-183, 2002
[39] Yeh, Y. L., Hsu, C. C., Chiang, C. H. and Hsiao, F. B., 「Vortical structure evolutions and spreading characteristics of a plane jet flow under anti-symmetric long-wave excitation」, Journal of Thermal and Fluid Science, Vol. 33, pp. 630-641, 2009

[40] Hsiao, F. B., Lim, Y. C. and Huang, J. M., 「On the near-field flow structure and mode behaviors for the right-angle and sharp-edged orifice plane jet」, Journal of Thermal and Fluid Science, Vol. 34, 2010
[41] Morlet, J., Arens, G., Fourgeau, I. and Giard, D., 「Wave propagation and sampling theory」, Geophysics, Vol. 47, No. 2, pp. 203-236, 1982
[42] Torrence, C. and Compo, G. P., 「A practical guide to wavelet analysis」, Bulletin of the American Meteorological Society, Vol. 79, pp. 61-78, 1998
[43] Hsiao, F. B. and Huang, K. S., 「 Experimental investigation of jet flapping by long-wave excitation」, 4th International conference on heat transfer, Fluid Mechanics and Thermodynamics, Cairo, Egypt, 2005
[44] Liu, C. E. and Hsiao, F. B., 「 The vortical structure spreading characteristics on a plane jet under anti-symmetric and symmetric long-wave excitation jet 」,中華民航太學會學術研討會,中華民國,桃園市開南大學, 2010
[45] Liu, C. E. and Hsiao, F. B., 「The study of vortical structure spreading characteristics on a plane jet under long-wave excitation with wavelet analysis 」, The 8th International Conference on Heat transfer, Fluid Mechanics and Thermaldynamics, Pointe Aux Piments, Mauritius, 2011
[46] Farge, M. and Schneider, K., 「 Wavelet: Application in Turbulence 」, Encyclopedia of Mathematical Physics, Elsevier, pp. 408-420, 2006.