Application of spectral proper orthogonal decomposition to the analysis of sound field of aeroacoustic sources

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Spectral proper orthogonal decomposition (SPOD) is proposed for the identification of the multipole structure of aeroacoustic noise sources from far-field measurements. The method is verified via tests with point multipoles and validated using experimental data on flow-induced cylinder noise and turbulent jet noise.

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作者简介

O. Bychkov

FAU TsAGI

Email: georgefalt@rambler.ru
俄罗斯联邦, Moscow

G. Faranosov

FAU TsAGI

编辑信件的主要联系方式.
Email: georgefalt@rambler.ru
俄罗斯联邦, Moscow

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2. Fig. 1. Model sources from uncorrelated dipoles (l = 1) or quadrupoles (l = 2).

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3. Fig. 2. Radiation directions of the original dipole sources (lines) and SPOD modes (markers): 1 – axisymmetric dipole (n = 0); 2 – transverse dipole (n = 1); 3 – total noise. ○ – SPOD mode j = 1; ◊ – SPOD mode j = 2; □ – total intensity of SPOD modes. (a) – = 2, = 1, N = 10; (b) – = 1, = 2, N = 10; (c) – = 1, = 1, N = 10; (d) – = 1, = 1, N = 20.

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4. Fig. 3. Radiation directions of the original quadrupole sources (lines) and SPOD modes (markers) for (a) – N = 10 and (b) – N = 30; 1 – axisymmetric quadrupole (n = 0); 2 – quadrupole (n = 1); 3 – quadrupole (n = 2); 4 – total noise. ○ – SPOD mode j = 1; ◊ – SPOD mode j = 2; Δ – SPOD mode j = 3; □ – total intensity of SPOD modes.

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5. Fig. 4. Experimental scheme. The arrows show the orientations of the dipole moments of the flow noise around the cylinder: the lift dipole (L) and the drag dipole (D).

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6. Fig. 5. Measured noise spectra: (a) – θ=30; (b) – θ=90; ​​(c) – θ=150. 1 – cylinder in a jet; 2 – jet without a cylinder.

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7. Fig. 6. Spectra of eigenvalues ​​of the SPOD decomposition of the sound field in the presence of a cylinder in the jet.

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8. Fig. 7. Radiation directivities in frequency bands for a cylinder in a jet: (a) – St = 0.017; (b) – 0.08; (c) – 0.14; (d) – 0.2. Solid line – measurements; ○ – SPOD mode j = 1; ◊ – SPOD mode j = 2; □ – total intensity of SPOD modes.

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9. Fig. 8. Spectral densities of the radiation intensity of individual SPOD modes (1-9), calculated using formula (20), and spectral densities of the radiation of the transverse (10) and longitudinal (11) dipoles, determined using the azimuthal decomposition method [33] (data are reduced to a distance of 1 m from the source).

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10. Fig. 9. (a) – Spectra of eigenvalues ​​of the SPOD expansion of the sound field of a free jet; (b) – radiation directions of the dominant SPOD modes for Stj = 0.1; curve designations are as in Fig. 3.

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