Many aerodynamic predictive tools used in the wind energy industry are based on the actuator disk theory of Rankine-Froude. Some examples are the Blade Element Momentum (BEM) theory model for the turbine power prediction, the Frandsen model used in the prediction of the wake momentum deficit of wind turbines, and the Werle blockage correction model. While low-fidelity, the above models are orders of magnitude faster/cheaper than the alternatives of field/laboratory experiments and grid-based numerical simulations, and are thus expected to remain popular in the decades to come. However, the above models are only accurate at small induction factors, i.e. small turbine “loadings”, as at higher induction factors the assumptions behind the Rankine Froude theory are violated. While most large horizontal axis turbines indeed operate at low induction factors, there are cases where the permissible value is exceeded; these include vertical axis wind turbines, tidal turbines, and micro wind turbines used in urban settings. An alternative aerodynamic theory is needed there, to model the relevant flow physics.
In this talk, I will first revise the Rankine-Froude theory to extend its validity to high induction factors. I will then derive novel BEM, wake deficit and blockage models, valid at arbitrary rotor loadings. The results will be validated via a combination of laboratory and numerical experiments of wind turbines and porous plates.