Aeroacoustic Inversion of Noise Generated by the Interaction of an Unsteady Gust with a Rotor

An analytical approach is explored here to study the far-field aerodynamic noise generated by the interaction of an unsteady gust with the blades of a rotor. The gust is generated by the pitching motion of an airfoil present upstream of the rotor, which sheds a vortex sheet that advects downstream towards the rotor. The advection and time-varying circulation of this sheet induce a fluctuating loading force on the rotor blades, which gives rise to far-field aerodynamic noise. An inversion approach is devised to deduce the motion of the gust generator using measurements of far-field pressure fluctuations. For the forward problem, the time-varying circulation for a step change in angle of attack of the pitching airfoil is determined using the Wagner function. A blade–vortex interaction model is used to determine the loading on each rotor blade due to the step gust, and the loading for arbitrary motion of the upstream airfoil is obtained using a convolution operation. The convolution integral is discretized to obtain the inversion expression, whereby measured far-field pressure signals can be inverted to deduce the pitching motion of the upstream airfoil. This provides a non-intrusive framework for characterizing gust–blade interaction dynamics, with potential applications in aeroacoustic diagnostics and rotor noise mitigation strategies. The inversion approach is tested with various levels of Gaussian noise introduced into the far-field pressure to assess the applicability of the proposed approach under non-ideal conditions. The results indicate that the approach is capable of successfully reconstructing a variety of pitching motion profiles such as ramps, sinusoids, and more complex variations, even when moderate levels of background noise are present.