Modelling of tonal noise control from subsonic axial fans using flow control obstructions

This paper investigates the analytical calculation of blade unsteady lift spectrum when interacting with a neighboring obstruction, designed to control tonal noise. The approach used in this paper is to add a secondary unsteady lift mode, of equal intensity but opposite in phase with the primary unsteady lift mode which radiates most of tonal noise, so that the resultant of both primary and secondary modes is null. To control one unsteady lift mode (consequently an acoustic tone) without affecting the harmonics of the controlled mode (consequently the harmonics of the acoustic tone to be controlled), it is important for the secondary unsteady lift to be harmonically selective. We have therefore evaluated the harmonic content of the blade unsteady lift generated by the proposed control obstructions. To this purpose, an original equation is derived using the infinitesimal radial strips theory coupled with the one-dimensional Sears gust analysis. The spectrum of the blade unsteady lift is then analyzed for three types of obstructions: a series of B-trapezoidal obstructions, a B-periodic sinusoidal obstruction and a series of B-rectangular obstructions (where B is the number of blades). The use of salient obstructions leads to a large unsteady lift harmonic content. An optimized wake width of the trapezoidal obstruction leads to a low harmonic content rate of 5.5%. A Gaussian approximation of the measured inflow velocity profile generated by a sinusoidal obstruction leads to a relatively low harmonic content rate of 18.8%, which indicates that most of the energy is contained in the fundamental mode of the blade unsteady lift. Finally, a rotor/rectangular interaction shows that the use of small-width rectangular obstructions leads to a higher harmonic content rate of 58.6%.