  Beamforming methods for sound source localization are usually based on
free-field Green's functions to model the sound propagation between source and
microphone. This assumption is known to be incorrect for many industrial
applications and the beamforming results can suffer from this inconsistency
regarding both, accuracy of source power estimation, and accuracy of source
localisation. The aim of this paper is to investigate whether the use of
numerically calculated Green's functions can improve the results of beamforming
measurements.
  The current test cases of numerical and experimental investigations consists
of sources placed in a short rectangular duct. The measurement is performed
outside the duct in a semi-anechoic chamber. A typical example for this kind of
installation is a fan with a heat exchanger.
  The Green's functions for this test case are calculated numerically using the
boundary element method. These tailored Green's functions are used to calculate
the corresponding beamforming steering vectors. The weighting of the Green's
functions in the steering vectors has a decisive influence on the beamforming
results. A generalization of the common steering vector formulations is given
based on two scalars. It is shown that arbitrary differentiable Green's
functions can be used to find the correct source position or source power level
by using the appropriate steering vector formulations.
  Beamforming measurements are performed using a loudspeaker as a reference
source at different positions in the heat exchanger duct. The measurements are
evaluated in the frequency domain and by means of different validation criteria
it can be shown that the results with the numerical calculated Green's function
are improved compared to free field beamforming especially at low frequencies.
