Coherence decay and its impact on sound radiation by wavepackets

2014 ◽  
Vol 748 ◽  
pp. 399-415 ◽  
Author(s):  
André V. G. Cavalieri ◽  
Anurag Agarwal
Keyword(s):  
Coherence Function ◽  
Sound Radiation ◽  
Turbulent Jets ◽  
Sufficient Condition ◽  
Far Field ◽  
Mean Flow ◽  
Spectral Densities ◽  
Flow Fluctuations ◽  
Order Of Magnitude ◽  
Field Sound

AbstractWavepackets obtained by a linear stability analysis of the turbulent mean flow were shown in recent works to agree closely with some relevant statistics of turbulent jets, such as power spectral densities and averaged phases of flow fluctuations. However, when such wavepacket models were used to calculate the far-field sound, satisfactory agreement was only obtained for flows that were supersonic relative to the ambient speed of sound; attempts with subsonic flows led to errors of more than an order of magnitude. We investigate here the reasons for such discrepancies by developing the integral solution of the Helmholtz equation in terms of the cross-spectral densities of turbulent quantities. It is shown that agreement of a statistical source, such as would be obtained by the above-mentioned wavepacket models, in averaged amplitudes and phases in the near field is not a sufficient condition for exact agreement of the far-field sound. The sufficient condition is that, in addition to the amplitudes and phases, the statistical source should also match the coherence function of the flow fluctuations. This is exemplified in a model problem, where we show that the effect of coherence decay on sound radiation is more prominent for subsonic convection velocities, and its neglect leads to discrepancies of more than an order of magnitude in the far-field sound. For supersonic flows errors are reduced for the peak noise direction, but for other angles the coherence decay is also seen to have a significant effect. Coherence decay in the model source is seen to lead to similar decays in the coherence of two points in the far acoustic field, these decays being significantly faster for higher Mach numbers. The limitations of linear wavepacket models are illustrated with another simplified problem, showing that superposition of time-periodic solutions can lead to a correlation decay between two points. However, the coherence between any pair of points in such models remains unity, and cannot thus represent the behaviour observed in turbulent flows.

scholarly journals Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

2019 ◽  
Vol 863 ◽  
pp. 969-993 ◽  
Author(s):  
Marcus H. Wong ◽  
Peter Jordan ◽  
Damon R. Honnery ◽  
Daniel Edgington-Mitchell
Keyword(s):  
Dynamic Models ◽  
Critical Role ◽  
Coherence Function ◽  
Supersonic Jets ◽  
Far Field ◽  
Shock Cell ◽  
Acoustic Spectrum ◽  
Flow Mechanisms ◽  
The Relationship ◽  
Field Sound

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

On-axis and far-field sound radiation from resilient flat and dome-shaped radiators

2009 ◽  
Vol 125 (3) ◽  
pp. 1444-1455 ◽  
Author(s):  
Ronald M. Aarts ◽  
Augustus J. E. M. Janssen
Keyword(s):  
Sound Radiation ◽  
Far Field ◽  
Field Sound

A Potential-Theoretic Method for Far-Field Sound Radiation Calculations

2000 ◽  
Vol 164 (1) ◽  
pp. 143-164 ◽  
Author(s):  
S.I. Hariharan ◽  
J.R. Scott ◽  
K.L. Kreider
Keyword(s):  
Sound Radiation ◽  
Far Field ◽  
Theoretic Method ◽  
Field Sound

scholarly journals An Analytical Solution for the Vibration and Far-Field Sound Radiation Analysis of Finite, Semisubmerged Cylindrical Shells

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wenjie Guo ◽  
Zhou Yang ◽  
Yueyang Han
Keyword(s):  
Cylindrical Shell ◽  
Free Surface ◽  
Present Method ◽  
Sound Pressure ◽  
Low Frequency ◽  
Sound Radiation ◽  
Far Field ◽  
Vibration Responses ◽  
Frequency Excitation ◽  
Field Sound

The vibration response and far-field sound radiation of a semisubmerged, finite cylindrical shell with low-frequency excitation are studied. The solution to this problem can be divided into two steps. The first step is to apply the wave propagation approach to determine the vibration response of the cylindrical shell. In the cylindrical coordinate system, the Flügge shell equations and Laplace equation are used to describe the cylindrical shell and surrounding fluid so that the vibration responses of the shell can be addressed analytically. The fluid free surface effect is taken into account by applying the sine series to force the velocity potential on the free surface to be zero. Furthermore, compared with the FEM (the finite element method), the present method is not only reliable but also effective. In the second step, the far-field sound radiation is solved by the Fourier transform technique and the stationary phase method in accordance with the vibration responses of the shell from the previous step. The boundary element method is applied to validate the reliability of the acoustical radiation calculation. The circumferential directivity of far-field sound pressure is discussed, and it is found that the maximum value of the sound pressure always appears directly under the structure when the driving frequencies are relatively low. Besides, in consideration of simplicity and less computation effort, the present method can be used for the rapid prediction of the vibration and far-field sound pressure of a semisubmerged cylindrical shell with low-frequency excitation.

Prediction of Far Field Sound Radiation from Transformers

1980 ◽  
Vol PAS-99 (1) ◽  
pp. 358-364 ◽  
Author(s):  
G. Usry ◽  
P. Saha ◽  
J. Hadden ◽  
A. Pierce
Keyword(s):  
Sound Radiation ◽  
Far Field ◽  
Field Sound

Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
High Frequency ◽  
Sound Pressure ◽  
Plate Theory ◽  
Sound Radiation ◽  
Laminated Plates ◽  
Far Field ◽  
Frequency Range ◽  
First Order ◽  
Shear Deformable ◽  
Field Sound

Sound radiation from shear deformable stiffened laminated plates with multiple compliant layers is theoretically studied. Equations of motion for the composite laminated plates are on the basis of the first-order shear deformation plate theory, and the transfer matrix method is used to describe sound transmission through compliant layers. The first and second sets of stiffeners interact with the plate through normal line forces. By using the Fourier transform and stationary phase method, the far-field sound pressure is obtained in terms of analytical expressions. Comparisons are made between the first-order shear deformation plate theory and the classical thin plate theory. Three principal conclusions are drawn in the study. (1) The transverse point force acting on the stiffeners yields lower far-field sound pressure in the middle and high frequency range. Specifically, the transverse point force exerting on the large stiffeners produces the lowest far-field sound pressure among three different reactive points at the plate, small stiffener and large stiffener. (2) The far-field sound pressure spectra are confined by an acoustic circle and remain unchanged. Lots of flexural waves in the structure cannot radiate sound into the far field. (3) The sound attenuation of stiffened plates with compliant layers is mainly caused by the sound isolation of compliant layers rather than vibrational reduction. Compliant layers can effectively reduce the radiated sound pressure in the medium and high frequency range.

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