Nonlinear analysis of pressure field upstream of transonic rotors and generation of combination tones

Abstract

Pressure field upstream of a transonic rotor with attached shock waves is determined using the rotational method of characteristic. In addition to the theoretical case of rotors with identical blades, the analysis includus the practical case of rotors with blade-to-blade variations due to manufacturing tolerances. The variations are produced in the analysis by assuming perturbations in the blade stagger angle and radius of curvature at the leading edge. Perturbation at one blade is shown to significantly modify the pressure field only at the following two blade channels. Investigations of static pressure waves upstream of the rotor with errors in neighboring blades indicate that the effects of manufacturing errors in the blades are linearly additive. Influence functions for errors in blade stagger angle have been deduced and the pressure pattern due to variety of error configurations has been obtained. Rotation of these pressure patterns results in noise spectra at blade passage frequency and multiples of the shaft rotation frequency, with the manufacturing errors inducing frequency and amplitude modulation effects. The relative intensity of the various harmonics is shown to be dependent on error configurations and the axial location upstream of the rotor. Correlated and uncorrelated error distributions are considered. Comparison with available experimental data, however, indicates that blade errors in actual rotors are essentially uncorrelated.