Verifying the Blade Element Momentum Method in unsteady, radially varied, axisymmetric loading using a vortex ring model.

Abstract

Although the Blade Element Momentum method has been derived for the steady conditions, it is used for unsteady conditions by using corrections of engineering dynamic inflow models. Its applicability in these cases is not yet fully verified. In this paper, the validity of the assumptions of quasi-steady state and annuli independence of the blade element momentum theory for unsteady, radially varied, axi-symmetric load cases is investigated. Firstly, a free wake model that combines a vortex ring model with a semi-infinite cylindrical vortex tube was developed and applied to an actuator disc in three load cases: (i) steady uniform and radially varied, (ii) two types of unsteady uniform load and (iii) unsteady radially varied load. Results from the three cases were compared with Momentum Theory and also with two widely used engineering dynamic inflow models—the Pitt-Peters and the Øye for the unsteady load cases. For unsteady load, the free wake vortex ring model predicts different hysteresis loops of the velocity at the disc or local annuli, and different aerodynamic work from the engineering dynamic inflow models. Given that the free wake vortex ring model is more physically representative, the results indicate that the engineering dynamic inflow models should be improved for unsteady loaded rotor, especially for radially varied unsteady loads.