Variational optimization of hydrokinetic turbines and propellers operating in a non-uniform flow field

The purpose of this paper is to provide a correction for the optimum distribution of circulation of propellers and turbines, though its effect is more noticeable in turbines. The correction is related to the fact that, when looking for the optimum, the induced speeds are derived with respect to the circulation, but the component associated to the change in direction of the free vortices has been traditionally neglected. The main result is thus a new expression for the derivatives of the induced velocities obtained by including the effect produced by a change in wake pitch due to an infinitesimal change of the circulation. The net contribution of this paper is an improved method for hydrokinetic turbine optimization, built upon the propeller vortex lattice framework, which is consistent with prior optimization methods for propellers but improves upon prior optimization methods for turbines. The result extends the theory to non-uniform axisymmetric flows. Further analysis of Lerbs/Munk original theory is provided. Example propeller and turbine designs demonstrate the utility of the Present method.