Statement of the Beamforming Problem and a Method of Its Solution for the Localization of an Acoustic Source Based on Computational Experiment Data

The paper is devoted to the statement of the beamforming problem the goal of which is the determination of the continuous acoustic source function based on the analysis of time–space data obtained in computational experiments in aerodynamics and aeroacoustics problems. Here the computational experiment is a highly accurate reproduction of turbulent flow by numerical simulation, which is nowadays possible due to the use of eddy-resolving approaches, improved accuracy methods, large grids, and high-performance computers. Conditions on the parameters of discretization grids in the domain containing a monopole sound source and on the microphone grid required to ensure the validity and accuracy of the algorithm are formulated. A method for specifying the numerical parameters appearing in these conditions is proposed. The correctness of these parameters is controlled by the magnitude of the condition number of the beamforming operator. If the correctness conditions are not fulfilled, regularization of the beamforming operator with the aim of obtaining the source function with acceptable accuracy is considered. It is shown that the proposed numerical beamforming method accurately reconstructs the source function in test examples, and its application to the data obtained in computational experiments on turbulent flow around a part of wing with a high-lift device is in good agreement with the results of the acoustic field analysis of experimental data.