Key points are not available for this paper at this time.
Phased arrays are a common tool for detecting aero-acoustical sources in closed or open jet wind tunnels. The usual design process of a phased array can be summarized to the following steps: In the first step, an sound source is assumed and the theoretical array output (point-spread function, "psf ") is calculated for a given microphone distribution. General shaping parameters for the psf are the minimal distance between microphones - limiting the upper frequency resolution - and the maximum distance between two microphones (or: aperture size) - limiting the array resolution towards low frequencies. Based on the psf a cost function can be defined in order to rate the array. Possible approaches for such a cost function are to integrate the energy of the psf, to detect the highest side lobe, or to compute the deviation to a desired psf in a frequency range. Whichever cost function is chosen, in the last step this cost function is minimized by variation of the microphone positions. The impact of a flow is usually neglected in this design process. However, due to turbulent decorrelation and/or retardation of sound waves in a shear layer and convection in the core flow, the optimum array in a case with flow might differ from an array optimised for no-flow condition. Assuming uniform flow without turbulence the sound propagation is only shifted in time due to the convective velocity. This can be included in the array design by using the convective velocity in the calculation of travel time between source and receiver as introduced by Amiet. ¹ Furthermore, on its way to the microphones, the sound wave has to pass a turbulent boundary layer in the closed test section and a turbulent shear layer in the open test section, respectively. Due to this turbulence the coherence of the sound wave at the microphone positions decreases with increasing frequency, increasing distance to other microphones and increasing turbulence level. ² The standard beamforming algorithm in the frequency domain is based on cross correlations between different microphone positions. Therefore, a low coherence results in a loss of image resolution and a modified sound in the beamforming result. In order to optimize an array pattern in terms of decorrelation, an analytical prediction of the coherence loss is required.
Ernst et al. (Thu,) studied this question.