Inverse design-momentum, a method for the preliminary design of horizontal axis wind turbines

Wind turbine rotor prediction methods based on generalized momentum theory BEM routinely used in industry and vortex wake methods demand the use of airfoil tabulated data and geometrical specifications such as the blade spanwise chord distribution. They belong to the category of "direct design" methods. When, on the other hand, the geometry is deduced from some design objective, we refer to "inverse design" methods. This paper presents a method for the preliminary design of wind turbine rotors based on an inverse design approach. For this purpose, a generalized theory was developed without using classical tools such as BEM. Instead, it uses a simplified meridional flow analysis of axial turbomachines and is based on the assumption that knowing the vortex distribution and appropriate boundary conditions is tantamount to knowing the velocity distribution. The simple conservation properties of the vortex components consistently cope with the forces and specific work exchange expressions through the rotor. The method allows for rotor arbitrarily radial load distribution and includes the wake rotation and expansion. Radial pressure gradient is considered in the wake. The capability of the model is demonstrated first by a comparison with the classical actuator disk theory in investigating the consistency of the flow field, then the model is used to predict the blade planform of a commercial wind turbine. Based on these validations, the authors postulate the use of a different vortex distribution (i.e. not-uniform loading) for blade design and discuss the effect of such choices on blade chord and twist, force distribution and power coefficient. In addition to the method's straightforward application to the pre-design phase, the model clearly shows the link between blade geometry and performance allowing quick preliminary evaluation of non uniform loading on blade structural characteristics.