A time-domain inverse method for the localization and quantification of unsteady rotating loading sources

Analysis of aerodynamic loading noise generated by unsteady rotating forces is of great significance in aeroacoustics research. However, it is still difficult to obtain the position and strength information of unsteady rotating loading sources in practice. In this paper, a time-domain inverse method for the localization and quantification of unsteady rotating loading sources is proposed, based on the Farassat integral solution of the Ffowcs Williams-Hawkings equation with the monopole and quadrupole source terms being neglected. In this method, the analytical direct model that relates the unsteady rotating forces to the radiated sound field is first discretized, and then the unsteady rotating forces are reconstructed from the measured pressures via a timedomain inversion procedure. Different from the previous inverse aeroacoustic methods, the proposed method can reconstruct the time histories of the three components of the unsteady rotating forces in the Cartesian coordinate system, thereby accurately locating the source positions and quantitatively estimating the source strengths in a real-time way. Numerical simulations with two unsteady rotating point forces and experiments with the rotating blades of an unmanned aerial vehicle examine the validity of the proposed method.