Array measurements in a wind tunnel are typically taken in an open, semi-anechoic facility, where the walls and the ceiling are sound absorbing and where the vehicle under test is in a flow region in the lower middle part of the facility. Arrays can then be placed outside of the core flow but as close as possible to the vehicle (and the flow) to get the highest possible resolution of sources on the vehicle.
At the array position, the average flow speed will, therefore, be low (usually less than 5 m/s), but there will be turbulence. Arrays can be placed on the sides and/or above the vehicle. Noise source localization is typically performed for each array using delay and sum (DAS) beamforming with the cross-spectral matrix (CSM) between all microphones in an array as input. The CSM has one row and one column for each microphone in the array. A selected element in the matrix contains the cross-power spectrum between the two microphones specified by the row and column indices of the selected element. The elements on the diagonal of the matrix, therefore, represent the autospectra for each one of the microphones. We now assume the following:
- The flow noise induced in one microphone is not picked up by any other microphone
- The flow-noise signals generated in different microphones are incoherent/independent
This implies that, after a sufficiently long averaging time, the flow-noise contributions will be insignificant outside the matrix diagonal while they will remain on the diagonal, that is, in the autospectra. Theory and practical experience show that the two assumptions hold true to a large extent.