Theory for broadband Noise of Rotor and Stator Cascades with Inhomogeneous Inflow Turbulence Including Effects of Lean and Sweep

The problem of broadband noise generated by turbulence impinging on a downstream blade row is examined from a theoretical viewpoint. Equations are derived for sound power spectra in terms of 3 dimensional wavenumber spectra of the turbulence. Particular attention is given to issues of turbulence inhomogeneity associated with the near field of the rotor and variations through boundary layers. Lean and sweep of the rotor or stator cascade are also handled rigorously with a full derivation of the relevant geometry and definitions of lean and sweep angles. Use of the general theory is illustrated by 2 simple theoretical spectra for homogeneous turbulence. Limited comparisons are made with data from model fans designed by Pratt & Whitney, Allison, and Boeing. Parametric studies for stator noise are presented showing trends with Mach number, vane count, turbulence scale and intensity, lean, and sweep. Two conventions are presented to define lean and sweep. In the "cascade system" lean is a rotation out of its plane and sweep is a rotation of the airfoil in its plane. In the "duct system" lean is the leading edge angle viewing the fan from the front (along the fan axis) and sweep is the angle viewing the fan from the side (,perpendicular to the axis). It is shown that the governing parameter is sweep in the plane of the airfoil (which reduces the chordwise component of Mach number). Lean (out of the plane of the airfoil) has little effect. Rotor noise predictions are compared with duct turbulence/rotor interaction noise data from Boeing and variations, including blade tip sweep and turbulence axial and transverse scales are explored.