A Unified Analysis of Fan Stator Noise

Abstract

A theory is developed for axial flow fans which predicts the harmonic and broad-band acoustic radiation from the stator due to interaction with rotor viscous wakes. Both the harmonic and broad-band spectrum components are calculated from a unified model using methodology from the theory of random pulse modulation. The stator is modeled as a circular array of pulsed dipoles. The amplitude and arrival time of each pulse are random variables whose means correspond to the values calculated for harmonic rotor-stator interaction theory. The standard deviations of these random variables are measures of the turbulence level in the blade wakes. For the model proposed, the solution is exact and the results are instructive: when pulse amplitude modulation (PAM) is imposed on a periodic stator source, new broad-band energy is generated whose spectrum shape is similar to the envelope of harmonics at high frequencies. The harmonic radiation is unchanged. When pulse position modulation (PPM) occurs, new broad-band energy is radiated but at the expense of harmonic energy. The theoretical results are discussed with reference to directivity patterns and radiation efficiency, and the harmonic component is compared with the previous Lowson and Embleton/Theissen analyses. The transfer of harmonic to random energy through PPM is discussed. At frequencies significantly above duct cutoff, it is shown for a fixed stator solidity that the spectrum is essentially independent of the number of stator vanes. In order to show the capabilities of this new theory, calculations are compared in detail with experimental data and modulation levels are discussed.