Multipole Expansion Approach for Rotor Noise Prediction

This paper presents a frequency-domain model of rotor tonal noise, based on a multipole expansion of the radiated field. The expressions for loading and thickness noise are derived in hovering condition, employing the results of compressible thin airfoil theory. The multipole coefficients are obtained as integrals of the boundary conditions in the plane of rotation, by considering the symmetry properties of the Green’s function. The terms of the expansion are independent of the observer point. As a result, once calculated, they allow for the solution to be obtained at any desired point in the field. This characteristic is not present in the main theories developed in the literature, and it allows for computational advantages. It is shown how the derived expressions can be traced back to Hanson’s helicoidal surface theory, which is used to validate the implementation. It results that even a single term in the expansion is capable of yielding accurate results in the far field. Conversely, the near field requires several coefficients of the series to achieve convergence, unless the low-frequency assumption is met. The chordwise compactness hypothesis is examined and a simplified model for preliminary calculations is proposed.