Our research focuses on assessment and use of mathematical and numerical models for the characterization of the noise source, when the noise is generated by a fluid in motion around a body. In particular, within the framework of the acoustic analogy, we first evaluate the fluid dynamic field using Large-Eddy Simulation (LES) and then we apply the Ffowcs-Williams and Hawkings (FWH) equation to reconstruct the acoustic field. First we show the conditions under which the non-linear terms of the FWH equation can be computed by direct integration neglecting the compressible delay in the volume integral terms. Successively we evaluate the noise generated by simple, still significant, geometries, and finally we consider noise propagation from a ship propeller in uniform flow. For the latter we observe the tonal signal given by the blade rotational frequency together with a high amplitude broadband noise given by the wake.