A 3-D modal stochastic jet noise source model

In previous work the jet mixing noise model of Tam & Auriault was realized as a time marching method in 2-D using a stochastic sound source, generated by means of the RPM (Random Particle M esh) method. The generated stochastic sound sources closely realize the two-point cross-correlation function proposed by Tam & Auriault to describe the statistics of a fine-scale jet mixing noise source. In a first attempt to extend the prediction capability to 3-D, a simplified radial scaling function was introduced to use the 2-D sound sources for axisymmetric computations of azimuthal mode order m=0. In the current work a strictly derived 3-D stochastic noise source is introduced, based on an azimuthal mode decomposition. For azimuthal mode order m=0 clear differences to the previously used simplified scaling model are obtained for sources with small relative distance to the jet axis. The azimuthally decomposed 3-D stochastic noise sources are shown to be generated by mutually uncorrelated 2-D stochastic sources for each mode order. Since for jet noise only the first few azimuthal modes are essential to describe the acoustic far-field radiation, a highly efficient 3-D broadband jet noise model for jet mixing noise is obtained at the computational price of a 2-D computation. For a 2-D simulation the capability of RPM to properly prescribe sound spectra is verified with an analytical solution. Sample results that highlight the proper functioning of the 3-D modal source model are presented.