A polar grid BEM implementation suited for individual pitch and dynamic pitching

Blade-element momentum (BEM) theory originally computes the rotor induction for uniform, steady conditions. While many sub-models are available to extend the validity of BEM theory to non-uniform, unsteady conditions, these models still have shortcomings [1, 2].
One way to enable computations of induction in non-uniform conditions is by placing a polar induction grid on the rotor plane, where the induction is computed in each grid point based on local inflow and blade element data [3]. One of the main advantages of this BEM implementation is the straight forward dynamic inflow modeling. However, if such a grid is to be used, it is not immediately obvious how to treat grid points that are not close to a blade in a given time step. In [3], the two closest blades to the grid point are virtually rotated onto a grid point, and the resulting induction is then computed using the azimuthally interpolated thrust coefficients corresponding to the two closest blades. This approach is illustrated in the left plot of Figure 1.
A shortcoming of this approach is illustrated in the right plot of Figure 1: If the blades are pitching cyclically between -1 and 1 degree, the pitch angle interpolated to, for example, the top grid point will vary continuously. As a result, the average pitch angle observed by the top grid point is roughly 0.68, even though a blade pointing upward always has a pitch angle of 1 degree. This is expected to result in an underestimated induction response to the cyclic pitching, which will result in an overestimated load variation for a given cyclic pitching amplitude. Further, the virtual rotation of blades into different grid points during every time step makes it very difficult to account for unsteady airfoil aerodynamics in a meaningful way. Therefore, the unsteady aerodynamics modeling is not part of the induction computation in [3], but just used in the computation of the aerodynamic blade forces afterwards.
A modification of the polar grid BEM implementation presented in [3] that addresses these shortcomings regarding cyclic pitch and unsteady airfoil aerodynamics influence is described in the present work.