The sound generated by an acoustic source near a semi-infinite edge with uniform parameters is studied theoretically. The acoustic emission of a vortex ring passing near a semi-infinite porous or elastic edge with uniform properties is formulated as a vortex sound problem and is solved using a Green’s function approach. The time-dependent pressure signal and its directivity in the acoustic far field are determined analytically for rigid porous edges as a function of a single dimensionless porosity parameter. At large values of this dimensionless parameter, the radiated acoustic power scales on the vortex ring speed U and the nearest distance between the edge and the vortex ring L as U^6L^−5, in contrast to the U^5L^−4 scaling recovered in the impermeable edge limit for small porosity values. These analytical findings agree well with the results of a companion experimental campaign conducted at the Applied Research Laboratories (ARL) at Penn State University. A related theoretical analysis of the sound scattered by uniform, impermeable elastic edges admits analytical results in a specific asymptotic limit, in which the acoustic power scales on U^7L^−6. In complement to the analysis of vortex ring sound from edges, the acoustic scattering of a turbulent eddy near a finite edge with a graded porosity distribution is determined numerically and is validated against analytical acoustic directivity predictions from the vortex-edge model problem for a semi-infinite edge in the appropriate high frequency limit. The cardioid and dipolar acoustic directivity obtained in the vortex ring configuration for low and high dimensionless porosity parameter values, respectively, are recovered by the numerical approach. An imposed linear porosity distribution demonstrates no substantial difference in the acoustic directivity relative to the uniformly porous cases at high porosity parameter values, where the local porosity parameter value at the edge determines the scattered acoustic field. However, more modulated behavior of the acoustic directivity is found at a relatively low frequency for the case of a finite edge with small graded porosity distribution.
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Acoustic emission from one-dimensional vibrating porous panels in a single-sided flow
The acoustic far-field pressure is determined for one-dimensional finite-chord panels with uniform porosity in a single-sided uniform flow. The unsteady, non-circulatory pressure on the panel is computed using a previously established analysis method. The acoustic field is computed using the Green’s method. Results from this acoustic analysis identify the sensitivity of the far-field pressure magnitude and directivity to changes in flow Mach number, the reduced frequency of the panel vibration, and the panel porosity level characterized by a Darcy-type porosity boundary condition.
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- Award ID(s):
- 1805692
- PAR ID:
- 10091957
- Date Published:
- Journal Name:
- 2018 AIAA/CEAS Aeroacoustics Conference
- Page Range / eLocation ID:
- AIAA Paper 2018-2962
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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