On the frequency domain formulation of the generalized sound extrapolation method

A frequency domain formulation of the generalized sound extrapolation method is proposed. The Fourier transform is performed to the flow variables to prepare the source terms as the input of the sound extrapolation solver, and the inhomogeneous convected Helmholtz equation is solved using the Green's functions in the frequency domain. The proposed formulations are applied to typical aeroacoustics problems including two dimensional (2D) and three dimensional monopoles in uniform mean flows, flat plate-gust interaction noise and the sound produced by a co-flowing jet. The formulations can yield close agreements with the predictions by the time domain solution. Substantial time saving can be achieved compared with a time domain solver, as the estimation of emission/retarded time, which needs to conduct interpolation of the time sequence of the flow variables, is not required. Also, the computation in the 2D space is much easier since the Green's function is used directly. The results suggest that the frequency formulation can potentially be used for sound projection computation in aeroacoustics.