Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free-vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradient evaluation for gradient-based optimisation in an economic model-predictive control algorithm. Initial results are presented for mean power maximisation in a two-turbine case study. An induction control signal is found using the 2D model that is roughly periodic and supports previous results on dynamic induction control to stimulate wake mixing. The 3D model formulation effectively models a curled wake under yaw misalignment. Under time-varying wind direction, the optimisation finds solutions demonstrating both wake steering and a smooth transition to greedy control. The free-vortex wake model with gradient information shows potential for efficient optimisation and provides a promising way to further explore dynamic wind farm flow control.

Vortex generators (VGs) have proven their capabilities in wind turbine applications to delay stall in steady flow conditions. However, their behaviour in unsteady conditions is insufficiently understood. This paper presents an experimental study that demonstrates the effect of VGs in unsteady flow, including controlling and suppressing the dynamic stall process. An airfoil, particularly designed for a vertical-axis wind turbine, has been tested in a wind tunnel in steady flow and unsteady flow caused by a sinusoidal pitching motion. The steady and unsteady pressure distributions, lift, drag and moment were measured for a range of cases. The cases vary in motion (mean angle of attack, frequency, amplitude) and VG configuration. VGs have shown to delay or even suppress dynamic stall depending on the VG configuration, with particularly important factors being VG height and VG mounting position. The VGs promote a later dynamic stall onset and reduce the hysteresis loop. As soon as the VG's effectiveness vanishes, the configurations with VGs show a severe loss in normal coefficient, larger than in the case of the clear airfoil. However, the flow reattaches quicker and the airfoil recovers easier from the deep-stall conditions. The experimental results demonstrate that the use of VGs significantly changes the unsteady aerodynamic loads. This experimental database can serve for validation purposes to evaluate whether current modelling strategies in unsteady conditions are sufficient for blades equipped with VGs.

This paper deals with the 3D effects of a vertical-axis wind turbine caused by the tip vortices. In this study, the VAWT rotor is simplified by the infinitely bladed actuator cylinder concept. The loads are prescribed to be uniform and normal to the surface and are distributed between the upwind and downwind half. Depending on the load configuration, the tip vortices are shed at different locations. This causes the wake induction field and the induction at the rotor to be significantly different. The 3D effects cause a power loss that may go up to 15% depending on the load configuration and aspect ratio. Starting from an aspect ratio of 5, the rotor induction and power is approaching 2D results.

In this paper, the actuator-in-actuator cylinder (AC-squared) model is presented. This model is an extension of the original actuator cylinder model of Madsen and is capable of modelling the effect of a two concentric actuation surfaces in 2D. The induced velocity at every point in the 2D field is affected by the force field acting on the two actuator cylinders. The equations are derived, and a model verification is performed using analytical solutions of flows, proof of flow equivalence, and using OpenFOAM calculations. Finally, the model is applied to different case studies, and the results are compared with a time-dependent free wake vortex method.