Investigating Rotating Noise Sources Using Uniform Circular Arrays: Theoretical Limits and Self-similar Beamforming Maps

Abstract

Phased microphone array measurements combined with beamforming signal processing is a widely used approach for localizing and quantifying noise sources, which can be used for turbomachinery applications. Among the various array configurations, uniform circular arrays (UCAs) are frequently employed for rotating sources due to their geometric simplicity and the practical advantage that they can be installed around a free jet or a duct without disturbing the flow. The present article investigates this array design with the aim of providing guidelines for planning proper measurement setups. Particular attention is given to two interdependent parameters: the array diameter and the measurement distance. For a simplified turbomachinery test case, a suitable measurement range is defined within the parameter plane spanned by these variables. The lower and upper bounds of this range are established through the constraints of achieving sufficient spatial resolution and avoiding spatial aliasing, for the estimation of which straightforward formulas are derived herein. Furthermore, it is shown that the parameter plane defined by array diameter and measurement distance can be regarded as the extrusion of one of its cross-sections along specific curves, referred to herein as self-similar curves, as the beamforming maps along these curves are self-similar. This property is advantageous, as conclusions can easily be drawn for the entire parameter space under investigation by carrying out a few simple calculations that utilize the formulas derived herein.