Prediction of aerodynamic sound from circular rods via spanwise statistical modelling

The Ffowcs Williams and Hawkings’ acoustic analogy is combined in the time domain with a statistical model in order to take into account the three-dimensional character of the vortex shedding process from a rod in a uniform stream. By applying the model to a two-dimensional unsteady Reynolds averaged Navier–Stokes flow computation, it is shown that the three-dimensional effects, like spectral broadening around the shedding frequency, are partially recovered. The ad hoc statistical model relates a spanwise random distribution of the vortex shedding phase and wall pressure modulations to an arbitrary spanwise correlations. The phase distribution is applied to the tonal pressure signals of the computation and the resulting ad hoc signals are fed into the acoustic analogy. The study is carried out for a rod based Reynolds number of 2.2×104 for which the rod wake is turbulent. Numerical results compare favourably to those of an accompanying experiment.