Filtered lifting line theory and its application to the actuator line model

In this work, a new formulation for a filtered version of Prandtl's lifting line theory is presented. In this formulation, a Gaussian filter is applied to the infinitesimally thin line of vorticity source, resulting in a volumetric distribution of vorticity along the blade. This formulation is then used to predict the induced velocity along the blade from the actuator line model. Using the new formulation, a correction is developed which allows the actuator line model to provide results independent of the smearing length scale ε. The correction is then tested on large eddy simulations of flow past a fixed wing with constant and elliptic chord distributions. Excellent agreement is found in all cases when using the correction. Finally, the correction is tested on a simulation of flow past a wind turbine.