Optimal Smoothing Length Scale for Actuator Line Models of Wind Turbine Blades Based on Gaussian Body Force Distribution

The actuator line model (ALM) is a commonly used method to represent lifting surfaces such as wind turbine blades within large-eddy simulations (LES). In the ALM, the lift and drag forces are replaced by an imposed body force that is typically smoothed over several grid points using a Gaussian kernel with some prescribed smoothing width ε. To date, the choice of ε has most often been based on numerical considerations related to the grid spacing used in LES. However, especially for finely resolved LES with grid spacings on the order of or smaller than the chord length of the blade, the best choice of ε is not known. In this work, a theoretical approach is followed to determine the most suitable value of ε, based on an analytical solution to the linearized inviscid flow response to a Gaussian force. We find that the optimal smoothing width ε^opt is on the order of 14%-25% of the chord length of the blade, and the center of force is located at about 13%-26% downstream of the leading edge of the blade for the cases considered. These optimal values do not depend on angle of attack and depend only weakly on the type of lifting surface. It is then shown that an even more realistic velocity field can be induced by a 2-D elliptical Gaussian lift-force kernel. Some results are also provided regarding drag force representation.