Aeolian tones of a plate in a channel

Abstract

The conditions of the onset of aeroacoustic resonance phenomena near a plate in a gas flow in a rectangular channel are studied theoretically and ezperimentally in a two-dimensional formulation. The eigenfrequency as a function of the plate's chord and its position in the channel, the shape of the eigenfunctions, and the effect of the Mach number of the basic gas flow versus the eigenfrequencies and ei#enfunctions and the mechanism of self-ezcited oscillations are determined. A mathematical model by means of which the dependence of the resonance phenomena on the geometrical parameters of the structure were performed is proposed and substantiated.Introduction. The investigation of self-excited acoustic oscillations in a rectangular channel with a plate --the simplest model of the periodic lattice of plates --is of importance, because this shape of an unbounded region is typical and occurs frequently in engineering. Self-excited oscillations that are generated in real structures are, as a rule, caused by the interaction of the eigenoscillations of an infinite region with nonlinear sources: the formation of coherent structures in a flow, unsteady combustion, etc. The important conditions of the onset of intense auto-oscillations are the coincidence of the frequency of an oscillation source with the acoustic eigenfrequency of an open infinite region and the nonorthogonality of the function that describes the source-generated acoustic waves and the eigenfunction.The first studies of self-excited oscillations near a symmetric lattice of plates in a rectangular channel were performed by Parker [1], who showed that self-excited oscillations are purely acoustic, are not connected with plate vibrations, and are caused by coherent structures in the wake behind the plates. Usually, these oscillations are called a vortex sound or aeolian tones (Aeolus is the Greek god of the winds). Aeolian tones near a plate in a channel or near a regular grid of plates were studied theoretically and experimentally in [2][3][4][5][6][7][8][9]. In a two-dimensional formulation, self-excited vibrations near a plate in a rectangular channel in a two-dimensional formulation were treated by Sukhinin in [10]. He proposed and substantiated a mathematical model of eigenoscillations and investigated numerically the dependence of the eigenfrequendes of oscillations on the geometrical parameters of the plate in the channel.Theoretical and experimental investigations of acoustic oscillations near a plate in a channel can be grouped as follows:9 Studying Resonance Properties of Unbounded Media. The existence of the acoustic resonance, the shape of self-excited oscillations (auto-oscillations), the dependence of resonant (eigen) frequencies on the geometrical parameters and the main gas flow. Mathematical simulation, numerical and experimental studies of self-excited acoustic vibrations in unbounded and semi-bounded regions.9 Studying the Nature of a Source of Auto-Oscillations. Formation and development of coherent structures in the wake behind a plate i...

Excitation of subharmonic oscillations in an axisymmetric flow with coherent structures in the regime of aeroacoustic resonance

“…A qualitative comparison with the experimental and mnnerical data of [10,11] obtained for planar models shows that the dependence of tile frequency on tile dimensionless length of the model for the planar and axisymmetric cases is described by similar curves. Probably, with an appropriate normalization, the acoustic resonant frequencies for axisymmetric and l)lanar models ma.v be describe(l 173" identical dependences.…”

“…The me~usurements were conducted in velocity ranges where resonant acoustic oscillatious are excited in an axisymmetric case (similar to that made in [10,11] for flat plates). However, in contrast to these works, it was not possible to perfbrm detailed me~tsurements of the distributions of the amplitude of acoustic oscillations near the model because of the specific features of the traversing gear.…”

“…The hot-wire signal was fed through a GW Instruments MacADIOS-Adio analog-to-digital converter to a Macintosh personal computer where it was processed in digital form. The details of signal processing on a computer can be found in [10,11]. Tile spectral analysis was performed in a narrow frequency band of 4 Hz.…”

“…The measurements were performed with fiat plates mounted in the square test section of the wind tunnel; these I)lates were used in [10,11], and their thickness was equal to the thickness of the walls of axisymmetric models. It was found that the sound was louder in experiments with an axisymmetric model.…”

“…The f'requency and amplitude of oscillations corresponding to these structures can be controlled by means of" an external acoustic action. Sukhinin an(l Bardakhanov [10,11] proposed a conlplete inatheniatical model for deternlining the acoustic eigenfrequencies of resoImnt volmnes and compared the calculated frequencies with experiinental (late for the case of fiat plates. At the same time,…”