On Open Rotor Blade-Vortex Interaction Noise

An analytical model is developed for the impingement of the tip-vortex produced by an upstream rotating blade onto the tip region of a downstream one, in a conguration representative of counter-rotating open rotor architectures. The interaction is addressed in an annular strip of limited spanwise extent bounding the impinged blade-tip segment. The unwrapped strip is described in Cartesian coordinates. Two models of cylindrical vortices are considered, for which the velocity eld is expanded into two-dimensional gusts in the reference frame of the segment. For each gust the response of the segment is derived, rst ignoring the eect of the tip, assimilating the blade to a rigid at plate, with or without sweep. The corresponding unsteady lift acts as a distribution of acoustic dipoles. The radiated sound is computed by a radiation integral over the actual extent of the segment, for vortex trajectories passing beyond, exactly at and below the tip radius, and the eects of the parameters are discussed. In a second step the same problem is readdressed accounting for the eect of span end on the aerodynamic response of the blade segment. This is achieved through a composite two-directional Schwarzschild’s technique. The modications of the distributed unsteady lift and of the radiated sound are discussed.