Calculation of Basic Sound Radiation of Axisymmetric Jets by Direct Numerical Simulations

Abstract

The basic radiation of sound from forced laminar axisymmetric jets (ReD= 6 × 102to 1.5 × 103) is calculated by a hybrid approach, whereby the hydrodynamic field is calculated by an incompressible stream function-vorticity direct numerical simulation (DNS) and the sound field is calculated by the compact Lighthill and Möhring-Kambe formulations. It is shown that, because of the oscillatory behavior of the source as a wave packet, the acoustic results are more sensitive to numerical constraints such as the DNS box size than are the hydrodynamic results. Lighthill's formulation shows a strong sensitivity to the radial boundary condition imposed on the velocity in the DNS. A zero second-order radial derivative for the stream function behaves the best, and a zero radial velocity condition behaves the worst. The Möhring-Kambe formulation shows a strong dependence on the arbitrary location of the coordinate origin. A boundary correction developed to eliminate this dependence is shown to work well by achieving a good agreement between the two formulations in the dominant features of the sound radiation. The effects of the inflow momentum thickness and Reynolds number are investigated with reference to the directivity and frequency spectrum of the emitted sound.