Analytical Body Forces in Actuator Disk Models of Propellers

A generalized analytical model for representing body forces in numerical actuator disk models of propellers is proposed and compared to existing designs using momentum theory. The model is an extension of a previously developed load model for wind turbines, which is extended and applied to propellers. Two different versions of the model are developed. The first is based on the rotor disk subject to a constant circulation, which is modified for tip and root effects, corresponding to an optimum operating Joukowsky rotor. By adding a parabolic circulation distribution, corresponding to a solid-body approach of the near-wake flow, it is possible to take into account losses associated to off-design loads (nonoptimum operating conditions). The second model is based on an optimum design originally proposed by Betz, who, by using a variational principle, showed that the wake formed by an optimum propeller generates a spiraling vortex structure of constant helicity. The advantage of the models is that they do not depend on any detailed knowledge of the actual propeller; they only require information on the thrust coefficient and the advance ratio. The models are validated for different propellers under a wide range of operating conditions. The comparisons show errors improved the earlier version of the model. The maximum deviation over the designed maximum is less than 6.5%; the average error is Formula: see text. For the first model, the maximum deviation is 17.5%, with an average error of Formula: see text.