Control of tonal noise from subsonic axial fan. Part 1: reconstruction of aeroacoustic sources from far-field sound pressure

An inverse method is investigated to evaluate the unsteady rotating forces (dipole strength distribution) acting by the fan on the fluid from far-field acoustic pressure measurements. A development based on the tonal noise generated by a propeller is used to derive a discretized form of the direct problem. The inversion of this direct problem is ill-posed and requires optimization technique to stabilize the solution for small perturbations in the measured acoustic input data. The reconstruction reveals that the conditioning of the inverse model depends on the aeroacoustic source and far-field sensor locations as well as on the frequency under investigation. Simulations show that an adequate choice of a regularization parameter leads to a satisfactory reconstruction of imposed unsteady rotating forces in the presence of measurement noise, and a correct localization of acoustic “hot spots” on the radiation surface. Preliminary experimental results also show the ability to extrapolate the radiated sound field at blade passage frequency (BPF), and harmonics, from the reconstructed forces. These data are exploited in the second part of this paper to evaluate various active control strategies for tonal fan noise.