Optimum Rotor Performance Based on Momentum Theory

Abstract

To determine the optimum performance of a wind turbine, the Betz limit serves as a simple guideline giving an absolute maximum. However, for more complex models involving swirl, the performance depends generally on the tip speed ratio and the basic assumptions forming the various models. Therefore, different models may actually result in different optima. In the following, based on the previously derived equations, we are going to analyse and compare the optimum performance using different aerodynamics rotor models. The fact that the models may result in different optimum performance values do not necessarily imply superiority of a specific model, but merely it illustrates that some of the basic approaches may result in different more or less erroneous behaviour. Through the following analysis, we strive to elucidate the basic approximations of the various models in order to understand the shortcoming of the models, and, hopefully, to come up with the most correct model. Finally, the geometry resulting from designing optimum rotor plan forms from the various models is compared. From the comparison, it is found that the outer part of the blades is approximately the same, whereas large differences between the various optimum geometries exist at the inner part and at small tip speed ratios.