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Direct numerical simulation (DNS) and an acoustic analogy are used to investigate the sound generation by vortex pairing in idealized subsonic axisymmetric jets. The detailed sound source structure is provided by the DNS. The acoustic analogy is based on solving the nonlinearized Lilley's third-order wave equation in the time-spare domain. A numerical algorithm for solving Lilley's equation is developed, in which the sound field is simulated simultaneously with the source field calculation. The computational domain includes both the near field and a portion of the acoustic far field. Effects of a coaxial secondary jet stream and the jet-to-ambient temperature ratio on the sound generation from an axisymmetric jet are investigated. It is shown that the sound source has a long axial distribution in the streamwise direction with the strongest source located near the end of the jet potential core where vortex pairing/merging occurs, and the radiated sound field is highly directive. It is also found that the secondary jet stream reduces the sound source size; therefore, the sound radiation from the coaxial jets is lower than that from the single jet. The hot jet simulation shows that increasing the jet-to-ambient temperature ratio leads to a smaller and weaker sound source, but does not lead to a weaker sound field. For the sound field a reasonable agreement is observed between the predictions from the axisymmetric Lilley's equation and the DNS results.

The influence of various numerical parameters on the computation of the basic radiation of sound from force laminar axisymmetric jets has been studied. Sound radiation is determined by a hybrid method where the hydrodynamic field is derived from an incompressible stream function-vorticity direct numerical simulation. The sound field is obtained from the compact Lighthill and Mohring-Kambe formulations. Ways of improving the acoustic analogies solution are also explored. The structure of the axisymmetric source of radiation has also been investigated for various Reynolds numbers.