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Beamforming methods for sound source localization are usually based onfree-field Green's functions to model the sound propagation between source andmicrophone. This assumption is known to be incorrect for many industrialapplications and the beamforming results can suffer from this inconsistencyregarding both, accuracy of source power estimation, and accuracy of sourcelocalisation. The aim of this paper is to investigate whether the use ofnumerically calculated Green's functions can improve the results of beamformingmeasurements.  The current test cases of numerical and experimental investigations consistsof sources placed in a short rectangular duct. The measurement is performedoutside the duct in a semi-anechoic chamber. A typical example for this kind ofinstallation is a fan with a heat exchanger.  The Green's functions for this test case are calculated numerically using theboundary element method. These tailored Green's functions are used to calculatethe corresponding beamforming steering vectors. The weighting of the Green'sfunctions in the steering vectors has a decisive influence on the beamformingresults. A generalization of the common steering vector formulations is givenbased on two scalars. It is shown that arbitrary differentiable Green'sfunctions can be used to find the correct source position or source power levelby using the appropriate steering vector formulations.  Beamforming measurements are performed using a loudspeaker as a referencesource at different positions in the heat exchanger duct. The measurements areevaluated in the frequency domain and by means of different validation criteriait can be shown that the results with the numerical calculated Green's functionare improved compared to free field beamforming especially at low frequencies.

Beamforming for measurements under disturbed propagation conditions using numerically calculated Green's functions