On the modelling of unsteady flows for efficient prediction of the interaction tones of coaxial counter-rotating rotors

Abstract

This paper proposes a prediction model of the unsteady flows induced by the coaxial counter-rotating rotors for the efficient computation of tonal noise. Based on the mean aerodynamic distributions, which can be obtained by the rapid blade element momentum theory, we can evaluate the strengths of the bound vortex and tip vortex. Then, the sectional blades are unwrapped into the 2D domain as two arrays of point vortexes. Particularly, the equivalent point vortexes are assumed to be located on arcs of a sector region since the mutual interaction is unnecessary to take place between sectional blades at the same radii, unlike the previous studies in which the resulting cascades are placed on two parallel straight lines. A conformal mapping is performed to estimate the induced unsteady velocities due to the equivalent bound vortex. Moreover, the influence of the tip vortex on the induced flow and the noise radiation is included. We compare the prediction results with the experimental tests in the anechoic chamber, and fairly good agreements are obtained. Based on a parametric study, we explore the dependence of overall sound pressure based on the predicted multiple tones on the rotating speeds. A scaling law in the form of $p^2\sim {(({\mathrm{RPS}}_1+{\mathrm{RPS}}_2)/2)}^{\lambda }$ is obtained. The predicted value of $\lambda$ is about 5.7, close to a set of available experimental data at some observer angles. However, at observers on the rotating plane and in the downstream direction, there is a clear difference in the experimental and prediction data, suggesting that other mechanisms could contribute to the sound levels at these locations, which should be identified and modelled in future studies.