Inverse method predicting spinning modes radiated by a ducted fan from free-field measurements

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Abstract
In the study the inverse problem of deducing the modal structure of the acoustic field generated by a ducted turbofan is addressed using conventional farfield directivity measurements. The final objective is to make input data available for predicting noise radiation in other configurations that would not have been tested. The present paper is devoted to the analytical part of that study. The proposed method is based on the equations governing ducted sound propagation and free-field radiation. It leads to fast computations checked on Rolls-Royce tests made in the framework of previous European projects. Results seem to be reliable although the system of equations to be solved is generally underdetermined (more propagating modes than acoustic measurements). A limited number of modes are thus selected according to any a priori knowledge of the sources. A first guess of the source amplitudes is obtained by adjusting the calculated maximum of radiation of each mode to the measured sound pressure level at the same angle. A least squares fitting gives the final solution. A simple correction can be made to take account of the mean flow velocity inside the nacelle which shifts the directivity patterns. It consists of modifying the actual frequency to keep the cut-off ratios unchanged.

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