Broadband Noise of Fans - With Unsteady Coupling Theory to Account for Rotor and Stator Reflection/Transmission Effects

This report examines the effects on broadband noise generation of unsteady coupling between a rotor and stator in the fan stage of a turbofan engine. Whereas previous acoustic analyses treated the blade rows as isolated cascades, the present work accounts for reflection and transmission effects at both blade rows by tracking the mode and frequency scattering of pressure and vortical waves. The fan stage is modeled in rectilinear geometry to take advantage of a previously existing unsteady cascade theory for 3D perturbation waves and thereby use a realistic 3D turbulence spectrum. In the analysis, it was found that the set of participating modes divides itself naturally into "independent mode subsets" that couple only among themselves and not to the other such subsets. This principle is the basis for the analysis and considerably reduces computational effort. It also provides a simple, accurate scheme for modal averaging for further efficiency. Computed results for a coupled fan stage are compared with calculations for isolated blade rows. It is found that coupling increases downstream noise by 2 to 4 dB. Upstream noise is lower for isolated cascades and is further reduced by including coupling effects. In comparison with test data, the increase in the upstream/downstream differential indicates that broadband noise from turbulent inflow at the stator dominates downstream noise but is not a significant contributor to upstream noise.