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The actuator line model (ALM) is a commonly used method to represent liftingsurfaces such as wind turbine blades within Large-Eddy Simulations (LES). Inthe ALM the lift and drag forces are replaced by an imposed body force which istypically smoothed over several grid points using a Gaussian kernel with someprescribed smoothing width $\epsilon$. To date, the choice of $\epsilon$ hasmost often been based on numerical considerations related to the grid spacingused in LES. However, especially for finely resolved LES with grid spacings onthe order of or smaller than the chord-length of the blade, the best choice of$\epsilon$ is not known. In this work, a theoretical approach is followed todetermine the most suitable value of $\epsilon$. Firstly, we develop ananalytical solution to the linearized flow response to a Gaussian lift and dragforce and use the results to establish a relationship between the local andfar-field velocity required to specify lift and drag forces. Then, focusingfirst on the lift force, we find $\epsilon$ and the force center location thatminimize the square difference between the velocity fields induced by theGaussian force and 2D potential flow over Joukowski airfoils. We find that theoptimal smoothing width $\epsilon^{\rm opt}$ is on the order of 14-25\% of thechord 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. Theseoptimal values do not depend on angle of attack and depend only weakly on thetype of lifting surface. To represent the drag force, the optimal width of thecircular Gaussian drag force field is shown to be equal to the momentumthickness of the wake.

Optimal smoothing length scale for actuator line models of wind turbine blades