Generalized Filtered Lifting Line Theory for Arbitrary Chord Lengths and Application to Wind Turbine Blades

The filtered lifting line theory is an analytical approach to solving the equations of flow subjected to body forces with a Gaussian distribution, such as used in the actuator line model. In the original formulation 1, the changes in chord length along the blade were assumed to be small. This assumption can lead to errors in the induced velocities predicted by the theory compared to full solutions of the equations. In this work, we revisit the original derivation and provide a more general formulation, that can account for significant changes in chord along the blade. The revised formulation allows for applications to wings with significant changes in chord along the span, such as wind turbine blades.