Spinning modes generated by a ducted turbofan at a given frequency determine the acoustic free-field directivity. An inverse method starting from measured directivity patterns is interesting in providing information on the noise sources without requiring tedious spinning-mode experimental analyses. According to a previous article, equations are based on analytical modal splitting inside a cylindrical duct and on a Rayleigh or a Kirchhoff integral on the duct exit cross section to get far-field directivity. Equations are equal in number to free-field measurement locations and the unknowns are the propagating mode amplitudes (there are generally more unknowns than equations). A MATLAB procedure has been implemented by using either the pseudoinverse function or the backslash operator. A constraint comes from the fact that squared modal amplitudes must be positive which involves an iterative least squares fitting. Numerical simulations are discussed along with several examples based on tests performed by Rolls-Royce in the framework of a European project. It is assessed that computation is very fast and it well fits the measured directivities, but the solution depends on the method and is not unique. This means that the initial set of modes should be chosen according to any known physical property of the acoustic sources.

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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Following large efforts to reduce tone noise during the last decades in modern high-bypass ratio turbofans, fan broadband noise reduction has become now an industrial priority. A hybrid computational method providing source-to-far-field predictions of broadband noise due to rotor-stator interaction is presented. The acoustic model is based on the loading term of the FWH (Ffowcs Williams and Hawkings) equation with a modal Green's function valid for an infinite annular duct, and a Kirchhoff approximation for the free-field radiation. The aerodynamic sources on the airfoils required by the model are expected to be directly issued from a LES (Large Eddy Simulation) computation. The method is applied to a simplified configuration tested in a laboratory rig. The first part of the study is concerned with the assessment of in- duct acoustic field. Usual assumptions about coherence and energy distribution between the acoustic modes are analyzed. PSD (Power Spectrum Density) are calculated through several ways. The second part is focused on the ability to generate an equivalent PSD by means of equivalent source distributions. The purpose is to validate a practical way for coupling LES with Computational Aero-Acoustics Euler solver, in order to include realistic geometry and mean flow effects.

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