A Method for Predicting the Tone Noise Produced by an Open Rotor in a Rectangular Wind Tunnel

Abstract

This paper describes an analytical model for predicting the tonal noise produced by an open rotor situated in a rectangular wind tunnel with rigid walls. The mathematical derivation of the model makes use of Graf’s theorem to transform from Cartesian coordinates, which are useful for describing the duct geometry, to cylindrical coordinates, which are useful for describing the distribution of ‘sources’ on the rotating blades. This transformation greatly simplifies the analysis and provides a final expression which is relatively straightforward to evaluate. An interesting validation of the model is also presented where it is shown that the final expression is equivalent to that produced by an infinite series of ‘image sources’. The model is then used to compare sound pressure levels produced by an open rotor operating within a rigid walled wind tunnel to those which would be produced if the rotor was operating in a free-field environment. The motivation for this work was to assess how measurements made in a closed test section wind tunnel could be used to infer noise levels in a free-field environment.