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Direct computation of the sound from a compressible co-rotating vortex pair. (English) Zbl 0848.76085
Direct computation of the far-field sound from co-rotating compressible vortices is performed by solving the Navier-Stokes equations on a grid that includes both near and far fields. The results are compared to the prediction of the acoustic analogy due to Möhring, a modified form of the analogy developed by Lighthill, and an acoustic analogy derived by Powell. Results for two cases are presented. In the first case, the vortices undergo a sudden merger after three revolutions. The far-field pressure fluctuations peak at merger and are significantly reduced afterwards. This case is acoustically compact and of low Mach number; the two-dimensional Möhring equation predicts the far-field pressure fluctuations to within 3% even at distances as close as 1/2 wavelength. The Powell’s analogy and the modified Lighthill’s analogy are also in good agreement with the simulation. The monopole contribution to the far-field pressure due to viscosity is found to be negligible.
The second cases is acoustically non-compact with increased near-field compressibility, and the vortices do not merge. The two-dimensional Möhring equation and the modified Lighthill analogy overpredict the far-field pressure by approximately 65%. The Powell’s analogy, which is solved numerically without assuming acoustical compactness, is able to predict the flow accurately. Based on these results the following conclusions are made: 1) theories of Möhring type based on moments of vorticity offer a convenient and accurate means to predict-far-field sound from compact low-Mach number flows; 2) the direct numerical solution of Power’s equation can be used to determine the far-field sound with a minimum of assumptions even if the near-field is acoustically non-compact; 3) although a conventional application of Lighthill’s equation is not appropriate for compact two-dimensional flow because of divergent integrals, the source terms can be modified in certain simple situations to yield accurate predictions.

MSC:
76Q05 Hydro- and aero-acoustics
76M20 Finite difference methods applied to problems in fluid mechanics
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References:
[1] Lyamshev, Sov. Phys. Acoust. 34 pp 447– (1988)
[2] Lighthill, Proc. R. Soc. Lond. 211 pp 564– (1952)
[3] Engquist, Commun. Pure Applied Math. 23 pp 313– (1979)
[4] Crow, Stud. Appl. Math. 49 pp 21– (1970) · Zbl 0185.54701 · doi:10.1002/sapm197049121
[5] Colonius, J. Fluid Mech. 260 pp 271– (1994)
[6] Colonius, AIAA J. 31 pp 1574– (1993)
[7] Cantwell, J. Fluid Mech. 173 pp 159– (1986)
[8] DOI: 10.1063/1.858395 · doi:10.1063/1.858395
[9] DOI: 10.1016/0021-9991(92)90324-R · Zbl 0759.65006 · doi:10.1016/0021-9991(92)90324-R
[10] Kambe, Phys. Rev. 48 pp 1866– (1993) · doi:10.1103/PhysRevE.48.1866
[11] Kambe, Proc. R. Soc. Lond. 386 pp 277– (1983)
[12] Kambe, J. Fluid Mech. 173 pp 643– (1986)
[13] DOI: 10.1016/0022-460X(84)90674-6 · Zbl 0557.76089 · doi:10.1016/0022-460X(84)90674-6
[14] Howe, J. Fluid Mech. 71 pp 625– (1975)
[15] Giles, AIAA J. 12 pp 2050– (1990)
[16] Ffowcs Williams, J. Fluid Mech. 31 pp 779– (1968)
[17] DOI: 10.1121/1.1918931 · doi:10.1121/1.1918931
[18] DOI: 10.1016/0022-460X(85)90448-1 · Zbl 0576.76063 · doi:10.1016/0022-460X(85)90448-1
[19] Möhring, J. Fluid Mech. 85 pp 685– (1978)
[20] Melander, J. Fluid Mech. 195 pp 303– (1988)
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