Abstract
A model for the aeroacoustic resonance effects (aeolian tones) excited around a plate cascade in a gas flow is suggested. Methods of calculating the frequencies of natural acoustic oscillations near the cascade are developed. The effect of the cascade geometry and the Mach number of the main flow on the frequencies, abundance, and modes of the natural oscillations is investigated. Anomalous acoustic oscillations near a cyclic plate cascade are shown to exist and are studied. It is shown that there always exist no less than two natural oscillation frequencies in the gas flow near any nontrivial cyclic plate cascade. It has been found that the natural oscillation frequencies can be combined in bundles such that in the case where the number of plates in a period is large the frequencies pertaining to each bundle occupy a certain interval with arbitrary density. The natural oscillations are classified with respect to the form of the eigenfunctions; the classification is based on the theory of representations of groups of locally plane symmetries of the cyclic plate cascade in the solution space. The correctness of the proposed model of the aeroacoustic resonance effects (aeolian tones) excited near a plate cascade in a gas flow is supported by a comparison with the available experimental and theoretical data. On the basis of the investigation performed, some previously unknown physical phenomena are predicted. Thus, the existence of frequency zones or main-flow Mach number ranges on which aeroacoustic resonance phenomena exist near a cyclic cascade with a large number of plates in a period is proved; it is shown that for certain frequencies of the natural oscillations near the cyclic plate cascade the resonance oscillations may be localized in the vicinity of the source; and the existence of narrow-band wave packets slowly propagating along the cascade is demonstrated.
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References
R. Parker, "Resonance effects in wake shedding from parallel plates: some experimental observations,"J. Sound Vibr.,4, 62 (1966).
R. Parker, "Resonance effects in wake shedding from parallel plates: calculation of resonant frequencies,"J. Sound Vibr.,5, 330 (1967).
D. I. Blokhintsev,Acoustics of Inhomogeneous Moving Media [in Russian], Nauka, Moscow (1981).
S. V. Sukhinin and S. P. Bardakhanov, "Aeolian tones of a plate in a duct,"Zh. Prikl. Mekh. Tekhn. Fiz.,39, No. 2, 69 (1998).
S. V. Sukhinin, "Natural oscillations near a plate in a duct,"Zh. Prikl. Mekh. Tekhn. Fiz.,39, No. 2, 78 (1998).
V. B. Kurzin, "Natural oscillations in a gas flow around a plate cascade,"Zh. Prikl. Mekh. Tekhn. Fiz., No. 5, 68 (1969).
V. B. Kurzin, "The damped natural oscillations of a gas flowing past a cascade of flat plates,"Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 84 (1970).
D. N. Gorelov, V. B. Kurzin, and V. É. Saren,Aerodynamics of Cascades in an Unsteady Flow [in Russian], Novosibirsk, Nauka (1971).
W. Koch, "Resonant acoustic frequencies of flat plate cascade,"J. Sound Vibr.,88, 233 (1983).
S. V. Sukhinin, "Validation of a model of the oscillations in the gas flow around a plate cascade," in:Continuum Dynamics, No. 56 [in Russian], Siberian Branch of the USSR Academy of Sciences, Institute of Hydrodynamics, Novosibirsk (1982), p. 152.
L. I. Sedov,Two-Dimensional Problems of Hydrodynamics and Aerodynamics [in Russian], Nauka, Moscow (1966).
L. Brillouin and M. Parodi,Propagation des ondes dans les milieux périodiques, Masson & Dunod, Paris (1956).
R. Mittra and S. W. Lee,Analytical Techniques in the Theory of Guided Waves, Macmillan, New York (1971).
S. V. Sukhinin, "Waveguide, cyclic, and anomalous properties of the oscillations near a plate cascade," Siberian Branch of the USSR Academy of Sciences, Institute of Hydrodynamics, Preprint No. 2-98, Novosibirsk (1998).
S. V. Sukhinin, "Waveguide and anomalous properties of a periodic knife cascade,"Zh. Prikl. Mekh. Tekhn. Fiz.,39, No. 6, 46 (1998).
S. V. Sukhinin, "Waveguide, anomalous, and whispering properties of a periodic chain of obstacles,"Sib. Zh. Industr. Mat.,1, 175 (1998).
D. G. Crighton, "Acoustics as a branch of fluid mechanics,"J. Fluid Mech.,106, 261 (1981).
M. E. Goldstein,Aeroacoustics, McGraw-Hill, New York (1976).
M. S. Howe, "A review of the theory of trailing edge noise,"J. Sound Vibr.,61, 437 (1978).
V. V. Nikulin and I. R. Shafarevich,Geometries and Groups [in Russian], Nauka, Moscow (1983).
G. Ya. Lubarskii,Group Theory and Its Physical Applications [in Russian], Fizmatgiz, Moscow (1958).
V. P. Mikhailov,Partial Differential Equations [in Russian], Nauka, Moscow (1984).
J. P. Gostelow,Cascade Aerodynamics, Pergamon Press, Oxford (1984).
N. A. Cumpsty and D. S. Whitehead, "The excitation of acoustic resonances by vortex shedding,"J. Sound Vibr.,18, 353 (1971).
M. A. Il’chenko, A. N. Rudenko, and V. L. Épshtein, "Study of vortex sound generation in the flow past an airfoil in a duct,"Akust. Zh.,26, 708 (1980).
M. A. Il’chenko, A. N. Rudenko, and N. I. Selin, "Study of some peculiarities in the excitation of oscillations in the flow around an airfoil in a duct,"Akust. Zh.,28, 224 (1982).
F. S. Archibald, "Self-excitation of an acoustic resonance by vortex shedding,"J. Sound Vibr.,38, 81 (1975).
R. Parker and D. C. Pryce, "Wake excited resonances in an annular cascade: an experimental investigation,"J. Sound Vibr.,37, 247 (1974).
S. V. Sukhinin, "The waveguide effect,"Zh. Prikl. Mekh. Tekhn. Fiz., No. 2, 92 (1989).
E. Sanchez-Palencia,Non-Homogeneous Media and Vibration, Springer, Berlin (1980).
Additional information
Novosibirsk, e-mail: sukhinin@hydro.nsc.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–186, March–April, 2000.
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Sukhinin, S.V. Aeolian tones of a plate cascade. Fluid Dyn 35, 297–309 (2000). https://doi.org/10.1007/BF02831439
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DOI: https://doi.org/10.1007/BF02831439