J. Fluid Mech. (1999), vol. 383, pp. 113–142. Printed in the United Kingdom c  1999 Cambridge University Press 113 Direct computation of the sound generated by vortex pairing in an axisymmetric jet By BRIAN E. MITCHELL†, SANJIVA K. LELE‡ AND PARVIZ MOIN§ Department of Mechanical Engineering, Stanford University Stanford, CA 94305, USA (Received 29 August 1997 and in revised form 14 October 1998) 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 ◦ –70 ◦ 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. 1. Introduction The use of numerical tools for acoustic predictions, e.g. computational aeroacoustics (CAA), typically relies on various assumptions beyond mere numerical issues. Primary amongst these is the assumption that an aeroacoustic theory such as Lighthill’s equation can yield accurate far-field predictions given detailed, but inexact, near- field information. The performance of such predictive methods needs to be carefully considered and validated in flows of interest. For example, it is important to recognize the spatial non-compactness of the acoustic sources and careful consideration is required to model flow–acoustic interaction effects. In the present study, direct numerical simulations (DNS) are used to directly compute the sound radiated by vortex pairing in the shear layers of axisymmetric round jets. These calculations directly solve the compressible Navier–Stokes equations on a computational domain that includes the near field and a portion of the far field. This type of DNS provides a complete description of the flow field, i.e. both the near-field acoustic source region and the radiated sound are captured in the same computation. † Present address: General Electric Corporate Research and Development Center, PO Box 8, Schenectady, NY 12301, USA. ‡ Also with the Department of Aeronautics and Astronautics. § Also with the NASA-Ames Research Center.