Generalised grid requirements minimizing the actuator line angle-of-attack error

The actuator line (AL) is a lifting line (LL) representation of aerodynamic surfaces in computational fluid dynamics (CFD) applications. The AL blade forces are computed from 2D airfoil polars and the CFD velocity vector extracted at the line position, as the self-induction at the very centre of the bound vortex should, following vortex theory, be nil. Yet, this is not the case in CFD, which leads to errors in the angle-of-attack computation. We derive an expression for the error in the lift force from vortex considerations and show it to be a function of chord, the smearing length scale used in distributing the AL forces over the numerical domain and the number of grid cells per smearing length scale. Thereby demonstrating that the required number of grid cells-contrary to current belief-needs to grow faster than the inverse of the smearing length scale refinement to maintain the error level. We additionally show that the error can be large for the commonly used ratio of 2 grid cells per length scale, especially if the latter is relatively small with respect to the rotor radius. Ultimately, the recommendation is to always run with the largest smearing length scale possible for the specific application in conjunction with a smearing correction, as this minimizes the error in the blade forces whilst reducing the computational resources required.