Mode detection in turbofan inlets from near field sensor arrays

Knowledge of the modal content of the sound field radiated from a turbofan inlet is important for source characterization and for helping to determine noise generation mechanisms in the engine. An inverse technique for determining the mode amplitudes at the duct outlet is proposed using pressure measurements made in the near field. The radiated sound pressure from a duct is modeled by directivity patterns of cut-on modes in the near field using a model based on the Kirchhoff approximation for flanged ducts with no flow. The resulting system of equations is ill posed and it is shown that the presence of modes with eigenvalues close to a cutoff frequency results in a poorly conditioned directivity matrix. An analysis of the conditioning of this directivity matrix is carried out to assess the inversion robustness and accuracy. A physical interpretation of the singular value decomposition is given and allows us to understand the issues of ill conditioning as well as the detection performance of the radiated sound field by a given sensor array.