  The blade element momentum (BEM) theory introduced by Lock et al. and
formulated in its modern form by Glauert provides a framework to model the
aerodynamic interaction between a turbine and a fluid flow. This theory is used
either to estimate turbine efficiency or as a design aid. However, a lack of
mathematical interpretation limits the understanding of some of its issues. The
aim of this paper is to propose an analysis of BEM equations. Our approach is
based on a reformulation of Glauert's model which enables us to identify
criteria to guarantee the existence of solutions, analyze the convergence of
usual and new (and more efficient) solution algorithms, and study turbine
design procedures. The mathematical analysis is completed by numerical
experiments.
