Direct computation of the sound from a compressible co-rotating vortex pair.

*(English)*Zbl 0848.76085Direct 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.

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.

Reviewer: T.Wang (Cherry Hill)

##### MSC:

76Q05 | Hydro- and aero-acoustics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

##### Keywords:

far-field sound; Navier-Stokes equations; two-dimensional Möhring equation; Powell’s analogy; modified Lighthill analogy; acoustical compactness
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\textit{B. E. Mitchell} et al., J. Fluid Mech. 285, 181--202 (1995; Zbl 0848.76085)

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