Direct computation of the sound generated by vortex pairing in an axisymmetric jet

The sound generated by vortex pairing in axisymmetric jets is determined by direct solution of the compressible Navier-Stokes equations on a computational grid that includes both the near field and a portion of the acoustic far field. At low Mach number, the far-field sound has distinct angles of extinction in the range of 60 degrees-70 degrees from the jet's downstream axis which can be understood by analogy to axisymmetric, compact quadrupoles. As the Mach number is increased, the far-field sound takes on a superdirective character with the dominant sound directed at shallow angles to the jet's downstream axis. The directly computed sound is compared to predictions obtained from Lighthill's equation and the Kirchhoff surface method. These predictions are in good agreement with the directly computed data. The Lighthill source terms have a large spatial distribution in the axial direction necessitating the introduction of a model to describe the source terms in the region downstream of the last vortex pairing. The axial non-compactness of the quadrupole sources must be adequately treated in the prediction method.