An actuator line model simulation with optimal body force projection length scales

In recent work (Mart\'inez-Tossas et al.~``Optimal smoothing length scale for actuator line models of wind turbine blades'', preprint), an optimal body force projection length-scale for an actuator line model has been obtained. This optimization is based on 2-D aerodynamics and is done by comparing an analytical solution of inviscid linearized flow over a Gaussian body force to the potential flow solution of flow over a Joukowski airfoil. The optimization provides a non-dimensional optimal scale $\epsilon/c$ for different Joukowski airfoils, where $\epsilon$ is the width of the Gaussian kernel and $c$ is the chord. A Gaussian kernel with different widths in the chord and thickness directions can further reduce the error. The 2-D theory developed is extended by simulating a full scale rotor using the optimal body force projection length scales. Using these values, the tip losses are captured by the LES and thus, no additional explicit tip-loss correction is needed for the actuator line model. The simulation with the optimal values provides excellent agreement with Blade Element Momentum Theory.