Antenna geometry effect on the reconstruction of the unsteady rotating forces of axial fan blade

The aim of this paper is to investigate the influence of the geometrical arrangement of acoustic pressure measurement sensors on the reconstruction of the unsteady rotating forces acting on the fluid by the fan's blade. A development based on the tonal noise generated 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 inverse problem is usually ill-posed and requires optimization technique to stabilize the solution for small perturbations in the measured acoustic input data. The reconstruction shows that the inverse problem conditioning depends on the aeroacoustic source and the far-field sensor number and geometrical distribution as well as on the studied frequency. Tikhonov regularization can provide an appropriate regularization parameter leading to a satisfactory reconstruction of imposed unsteady rotating forces even in the presence of measurement noise. Simulations are conducted for three geometrical arrangements of microphones: line, arc of a circle and square.