An Unsteady Lifting Surface Theory for Ducted Fan Blades

A frequency domain lifting surface theory is developed to predict the unsteady aerodynamic pressure loads on oscillating blades of a ducted subsonic fan. The steady baseline flow as observed in the rotating frame of reference is the helical flow dictated by the forward flight speed and the rotational speed of the fan. The unsteady perturbation flow, which is assumed to be potential, is determined by solving an integral equation that relates the unknown jump in perturbation velocity potential across the lifting surface to the upwash velocity distribution prescribed by the vibratory motion of the blade. Examples of unsteady pressure distributions are given to illustrate the differences between the three-dimensional lifting surface analysis and the classical two-dimensional strip analysis. The effects of blade axial bending, bowing (i.e., circumferential bending), and sweeping on the unsteady pressure load are also discussed.