zbMATH — the first resource for mathematics

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.

76Q05 Hydro- and aero-acoustics
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.