Noise produced by turbulent flow into a propeller or helicopter rotor

TLDR: In this article, the authors considered the presence of blade-to-blad e correlation and showed that if a turbulent eddy is chopped by more than one rotor blade, the blade-toblade correlation leads to narrow-band noise peaked around the rotor harmonics.

Abstract: than can be applied to calculate the instantaneous sound spectrum produced by the rotor at each azimuthal rotor position, and this instantaneous spectrum can be averaged over the azimuthal rotor position to find an averaged far-field sound spectrum. In taking this average, account must be taken of the different amount of retarded time that the rotor spends at each azimuthal rotor position. Further discussion of this point is given in another paper.4 A further factor taken into account in the analysis is the existence of blade-to-blad e correlation. If a given turbulent eddy is chopped by more than one rotor blade, the blade-toblade correlation leads to narrow-band noise peaked around the rotor harmonics. The far-field sound for an airfoil moving in rectilinear motion through a turbulent flow can be expressed in terms of a single wavevector component of the turbulence. The presence of blade-to-blade correlations requires that the single wavevector component be replaced by a summation over several wavevector components. This summation generally is carried out numerically for the calculations presented herein, but, if the frequency of interest is high enough, the summation can be replaced by an integral that can be evaluated in closed form; i.e., the blade-to-blade correlation becomes unimportant, and the result reduces to that for a single blade in rectilinear motion. The preceding description of the procedure for calculating the far-field sound applies to the sound produced by a spanwise segment of the rotor. This segment must have a spanwise dimension small enough so that the velocity does not vary significantly over the segment but large enough so that the loading correlation from segment to segment is not significant. This latter assumption is consistent with the highfrequency assumption mentioned previously, since high frequency corresponds to small correlation length. Thus, to find the noise contributed by the entire rotor, an integral over span must be performed.