The filtered lifting line theory presents a continuous form of the inviscid momentum equations of flow over a lifting device, such as a wing or rotor blade, using body forces without mathematical singularities. This theory is also consistent with an actuator line representation of a lifting device. In this work, we present a reformulation of the equations in terms of the local flow angle along the line, which allows solving the stand-alone equations using multivariate root-finding algorithms. This approach can be used to obtain a fast, computationally inexpensive solution of the loading distribution along a wing without the need to perform computational fluid dynamic simulations. We study the requirements in terms of resolution in the spanwise direction and establish the criteria for spacing and minimum amount of points required along the blade to obtain converged solutions. The solutions are compared to results from large-eddy simulations, and we observed excellent agreement with less than a percent difference in quantities along the blade between the methods.

The actuator line model (ALM) is an approach commonly used to represent lifting and dragging devices like wings and blades in large-eddy simulations (LES). The crux of the ALM is the projection of the actuator point forces onto the LES grid by means of a Gaussian regularisation kernel. The minimum width of the kernel is constrained by the grid size; however, for most practical applications like LES of wind turbines, this value is an order of magnitude larger than the optimal value that maximises accuracy. This discrepancy motivated the development of corrections for the actuator line, which, however, neglect the effect of unsteady spanwise shed vorticity. In this work we develop a model for the impact of spanwise shed vorticity on the unsteady loading of an aerofoil modelled as a Gaussian body force distribution, where the model is applicable within the regime of unsteady attached flow. The model solution is derived both in the time and frequency domain and features an explicit dependence on the Gaussian kernel width. We verify the model with ALM-LES for both pitch steps and periodic pitching. The model solution is compared withTheodorsen theory and validated with both computational fluid dynamics using body fitted grids and experiment. It is concluded that the optimal kernel width for unsteady aerodynamics is approximately 40 % of the chord. The ALM is able to predict the magnitude of the unsteady loading up to a reduced frequency of k ≈ 0.2.

The development of new wind farm control strategies can benefit from combined analysis of flow dynamics in the farm and the behavior of individual turbines within one simulation environment. In this work, we present such an environment by developing a new coupling between the large-eddy simulation (LES) code GRASP and the multiphysics wind turbine simulation tool OpenFAST via an actuator line model (ALM). In addition, the implementation of the recently proposed filtered actuator line model (FALM) within the coupling is described. The new ALM implementation is cross-verified with results from four other commonly used research LES codes. The results for the blade loads and the near wake obtained with the new coupling are consistent with the other codes. Deviations are observed in the far wake. The results further indicate that the FALM is able to reduce the lift and power overprediction from which the traditional ALM suffers on coarse LES grids. This new simulation environment paves the way for future wind farm simulations under realistic weather conditions by leveraging GRASP's ability to impose data from large-scale meteorological models as boundary conditions.