Analysis of rotor wake stability in hovering state by Fourier method

A method of rotor wake stability analysis in hovering state by Fourier method is established. By the present method, the interval of harmonic wavelength is given when any disturbance on the rotor wake is separated into Fourier series, by which the theoretical foundation of rotor wake stability analysis is improved. Furthermore, a methodology, which can extend the stability analysis for single collocation point to the whole rotor wake by extracting and analyzing the upper and lower bound of the divergence rate relative to the vortex age, has been presented. Taking the rotor of H34 helicopter in hovering state as a numerical example, the influence of the number of wakes (blades), distribution of vortex core and distortion of wake on rotor wake stability is investigated by this method. The results show that, as for a single collocation point on the rotor wake, it is intrinsically unstable, while as for the whole rotor wake, its stability relative to the vortex age is affected by many factors and exhibits some variation characteristics. Moreover, by comparing with the experimental data of aperiodicity of the hovering rotor wake, it is proved that this method can effectively predict the growth characteristics of any disturbance on the rotor wake.