Comparative analysis of the theoretical models of ideal propulsor, ideal fluid brake, ideal screw propeller and ideal axial wind turbine

Abstract

The article presents a detailed discussion of the theoretical models of four different fluid dynamic devices: an ideal propulsor, an ideal fluid brake, an ideal screw propeller and an ideal turbine. The four models are presented with all relevant mathematical formulae regarding the forces, the power and the efficiency. It is demonstrated that the application of the model of an ideal optimum fluid brake according to the Betz theorem for determination of the maximum effectiveness coefficient of an axial wind turbine is not correct. In the case of a turbine the inclusion of important rotational flow losses may increase the maximum value of the turbine effectiveness coefficient above the level defined by Betz. Therefore the model of an ideal turbine should be an inversion of the model of an ideal screw propeller. This conclusion is supported by numerical calculations. It may influence the design procedures of wind turbines and may lead to increase in their efficiency.