Reconstruction of the unsteady rotating forces of fan’s blade from far-field sound pressure

The aim of this paper is to investigate an inverse method used to evaluate the unsteady rotating forces acting on the fluid by the fan’s blade. A simple model based on the tonal noise produced by an axial fan and validated with a directivity experience is used to derive a discretized form of the direct problem and to simulate acoustic pressures at known spatial positions in the radiated field. The inversion of this direct problem is ill-conditioned and requires a regularization technique to stabilize the solution for small perturbations in the measured acoustic pressures. The reconstruction reveals that the conditioning of the inverse problem depends on the aeroacoustic source and the far-field microphones number as well as on the studied frequency. Tikhonov regularization can provide an appropriate regularization parameter leading to an accurate reconstruction of imposed unsteady rotating forces even with the presence of measurement noise.