A method to predict the canceling response of flow-excited resonators for the reduction of axial turbomachine noise

Flow-excited, tunable quarter-wavelength resonators can be integrated into the shrouds of ducted subsonic axial fans to generate a canceling secondary sound field. Arrays of resonators have been employed to reduce existing blade tone noise levels to within 5 dB of the broadband noise floor, for both plane wave and higher order modal propagations. In previous work, experimental methods were used to determine the optimal positioning of resonator sources to achieve maximal noise reductions for both monopole and dipole configurations of resonators. This study explores a modeling technique that was developed to analytically determine an optimal configuration of resonator sources for a given fan. A finite element method (FEM) propagation model is developed to determine the sound pressure level (SPL) at the fan's location from measurements taken upstream and downstream of the source. Once SPL is known at the source, resonator configurations can be optimized analytically to radiate anti-phase canceling tones. Flow driven response of individual resonators is modeled using a method based on transmission line theory. Sources are then superimposed in the FEM model and propagated back to the measurement location. Analytical results are compared with measurements taken at the Deutsches Zentrum Für Luft Und Raumfahrt (DLR), verifying the efficacy of the modeling technique.