Ainslie Wake Model with Forcing Term

Abstract The Ainslie Wake model, as part of the Dynamic Wake Meandering model, is the industry standard wake model for wind farm loads. Its defining set of equations is parabolic; it can be solved efficiently via a marching scheme by omitting the pressure term and using a prescribed eddy viscosity model. However, eliminating the pressure term requires generating an inflow condition for an already expanded wake some distance downstream of the rotor via wake expansion models that do not preserve the intrinsic conservation of mass and momentum for the full computational domain. Consequently, ensuring conservativeness within the Ainslie flow solver alone is insufficient to obtain a conservative wake model. The aim of this work is to reintroduce a part of the pressure term into the Ainslie wake model that can be precomputed and is compatible with a marching scheme. An efficient closed-form solution exists analogous to the vector potential of a vortex ring, which has been integrated into a Finite Volume solver for the momentum equation. The resulting solver conserves the applied thrust force in the integral momentum deficit to very small relative errors related to the truncation of the domain size. A first comparison to LES reference simulations shows a good qualitative agreement of the obtained velocity fields, though still being limited by the lack of a suitable eddy viscosity model.