Optimisation of Sensor Arrays for Radial Mode Analysis in Flow Ducts

For the assessment and improvement of noise reduction concepts and the validation of computational aero-acoustic (CAA) codes in turbomachinery applications, the detailed knowledge of the in-duct acoustic mode spectrum of tonal frequency components is of great interest. Radial mode analysis (RMA) is an experimental technique that delivers the complex amplitudes of higher order acoustic modes propagating through flow ducts. Thus, RMA enables the calculation of the acoustic power radiated in and against flow direction, though, requiring at high frequencies the acquisition of the sound field at a large number of positions in the flow duct. The quality of the analysis results is very sensitive to the arrangement of the measurement coordinates, the frequency, and the flow parameters. A simple and robust RMA realisation just consists of sensor rakes at a single duct cross section. This method, however, has the drawback of not being able to distinguish downstream and upstream propagating modes. Furthermore, the sound field as well as the flow field may be altered by the rakes. In the paper, a numerical study of RMA employing four substantially different sensor arrangements is conducted. The arrangements I and II consist of sensor rakes located at two or four axial measurement positions, respectively. Arrangement III is equipped with sensors mounted flush with the hub and the outer duct wall and in arrangement IV the sensors are mounted flush with the outer duct wall, only. The dependency of the RMA quality on the frequency, e.g. the number of cut-on modes, and on the number of axial and radial measurement positions was investigated by means of a condition analysis. Studies were carried out for the analysis of coherent modal sound fields in hard-walled cylindrical flow ducts of arbitrary hub-to-tip ratio with a constant mean axial flow profile. Additionally, the influence of a solid-body like swirl was considered. The paper reveals reasons for bad conditioning of the RMA-systems and gives guidelines for an optimum sensor separation in order to improve the overall system condition. Since the condition number is only a relative measure for the inaccuracies caused by the RMA system, simulations with synthetic sound pressure data were carried out. The RMA performance of the sensor arrangements I-IV is compared.