BEM theory: How to take into account the radial flow inside of a 1-D numerical code

Abstract

Blade Element Momentum (BEM) theory based numerical codes are employed, both in the scientific and industrial field, for designing wind turbines and appraising their performance. Using BEM theory, mono-dimensional mathematical codes can be created. They have very short processing times and high reliability. However, this is related to the solution of a few problems peculiar to these mathematical models. The problems of these numerical codes are well known in scientific literature: the impossibility of describing inside the mono-dimensional code the three-dimensional radial flow along the blades; the possibility of running into numerical instabilities which prevent the code from converging on the correct solution. In this work the author will show how to mathematically describe lift coefficients so as to eliminate the lack of description for centrifugal pumping. Finally, to ascertain the accuracy of numerical results, these will be compared to experimental data taken from scientific literature. In particular, simulated numerical code data will be compared with the experimental data for the power and efficiency curves of NREL Phase II and NREL Phase VI wind turbines.