Wake redirection is a promising approach designed to mitigate turbine–wake interactions which have a negative impact on the performance and lifetime of wind farms.
It has recently been found that substantial power gains can be obtained by tilting the rotors of spanwise-periodic wind-turbine arrays. Rotor tilt is associated with the generation of coherent streamwise vortices which deflect wakes towards the ground and, by exploiting the vertical wind shear, replace them with higher-momentum fluid (high-speed streaks).
The objective of this work is to evaluate power gains that can be obtained by tilting rotors in spanwise-periodic wind-turbine arrays immersed in the atmospheric boundary layer and, in particular, to analyze the influence of the rotor size on power gains in the case where the turbines emerge from the atmospheric surface layer.
We show that, for the case of wind-aligned arrays, large power gains can be obtained for positive tilt angles of the order of

An unavoidable byproduct of wind-turbine operation is the generation of wakes containing the low-speed, highly turbulent fluid from which mechanical power has been extracted.
As in wind farms the streamwise distance between wind turbines is typically much shorter than the distance required for the wake to diffuse and recover the incoming wind speed, wind-farm interior turbines experience large reductions of their power production and significant unsteady loads when they are shadowed by wakes of upstream turbines

In addition to yaw control, where wakes are deflected horizontally, it has been more recently proposed to deflect wakes in the vertical direction by acting on the rotor-tilt angle

Global power gains are achievable also for tilt control despite the power losses experienced by tilted-rotor upstream turbines

In C2020 it was found that significant improvements of the global power production can be obtained by operating tilted-rotor turbines at higher induction (higher thrust coefficient) to compensate for the reduction of the normal velocity component.
It was also shown that those power gains could be further improved when considering higher values of the

The results of C2020, nevertheless, call for confirmation in the high-

The questions in which we are interested are the following: What are the typical power gains that can be obtained by tilt control in the ABL? How do they compare to those found in the PBL? How do these power gains depend on the relative rotor size, especially in the case of large rotors? To answer these questions, we use large-eddy simulations (LESs) to simulate neutral atmospheric boundary layers with capping inversions in the presence of wind-turbine arrays in wind-aligned configurations which are the worst case for turbine–wake interactions. The turbines are modeled with the actuator-disk method and are assumed to operate at constant thrust coefficient in order to obtain generic results which do not depend of the specificity of particular control laws chosen for turbine operation. The effect of tilt angle, induction factor and rotor size on the global power production will be studied with respect to reference configurations where the turbines are operated in standard mode.

The paper is organized as follows:
the problem formulation is introduced in Sect.

We consider the flow developing on wind-turbine arrays immersed in the atmospheric boundary layer.
The flow is computed by means of large-eddy simulations implemented in SOWFA, the NREL's Simulator for On/Offshore Wind Farm Applications which solves the filtered Navier–Stokes equations

Preliminary “precursor” simulations of the atmospheric boundary layer in the absence of wind turbines are run with periodic boundary conditions enforced also in the streamwise direction (with

The actuator-disk model is used to approximate the forces exerted by wind turbines on the fluid and the power produced by the turbines.
This model has been shown to provide reliable results for the characteristics of turbine wakes except in the wake formation region

The power produced by each turbine is modeled, for all the results shown, as

We will consider the effect of rotor tilt in arrays composed of three rows of wind turbines aligned with the mean wind and spaced by

In the precursor simulations we consider neutral atmospheric boundary layers (ABL) at latitude

Characteristics of the considered atmospheric boundary layers and of their capping inversions.

The flow is simulated in two sets of domains: the first extending 3 km

The mean-wind profiles obtained for the three selected

Mean-wind profiles obtained in the precursor simulations along the

We first consider the effect of tilt on wind turbines with rotor diameter

First, a reference case is simulated in the ABL with

The ratios of the global power produced in the controlled case to the global power produced in the reference case are reported in Fig.

Influence of the tilt angle

Time-averaged streamwise velocity fields

Following C2020, the simulations are repeated operating tilted-rotor turbines at higher

From Fig.

Time-averaged streamwise (color scale) and cross-stream (arrows) velocity fields in the cross-stream plane at

These results, obtained in the ABL, are consistent with those found in the pressure boundary layer (PBL), as could be expected because for the considered

In C2020, for the case of the pressure boundary layer (PBL), increasing power gains were found for increasing

We begin by considering the effect of reducing

Dependence of power gains on tilt angles

To better explore the high-

Also for the

To better appreciate the influence of

Power gains versus turbine-diameter-to-boundary-layer-height ratio

The saturation of power gains at sufficiently large

From Fig.

Power gains versus the ratio

In this study we have evaluated the gains of global extracted wind power that can be obtained by tilting rotors in wind-turbine arrays immersed in neutral atmospheric boundary layers with capping inversions.
In particular, we have considered spanwise-periodic arrays with three turbine rows where rotors of the two upwind rows are all tilted by the same angle

It is found that significant power gains can be obtained.
For all the considered combinations of turbine rotors diameters (

The influence of rotor size on power gains has also been investigated for ratios

Following the rationale of

Additional final evidence is, nonetheless, needed to confirm the relation between streak amplification and tilt-induced power gains in the ABL by comparing streamwise vortices forced by tilted rotors to the optimal perturbations leading to maximum large-scale streak amplification in the ABL and in particular their optimal spanwise spacing.
Optimal perturbations and energy amplifications in the ABL are, however, currently unknown

It is also important to emphasize that a non-negligible part of the obtained power gains is associated with the operation of tilted-rotor turbines at higher induction rates.
In the present study and in the previous related one of

One limitation of the present study resides in the used highly idealized actuator-disk model for the turbines which are assumed to operate at constant

Finally, it is important to note that this study has dealt only with the fluid dynamics of tilt control without addressing issues such as the level of structural loads that turbines would experience when tilted by angles as large as

The filtered Navier–Stokes equations, including the effect of Coriolis acceleration, with Boussinesq fluid model and the

Numerical simulations have been performed in numerical domains of streamwise length

In order to enforce the turbine response to depend only on

Influence of

Power gains versus the ratio

In Sect.

In Fig.

Finally, Fig.

These additional results therefore show that
(a) non-negligible power gains are obtained by tilt control operating the turbines at the usual induction (

Data can be obtained from the author upon request.

The author declares that there is no conflict of interest.

The author gratefully acknowledges the use of the Simulator for On/Offshore Wind Farm Applications (SOWFA) developed at NREL

This paper was edited by Raúl Bayoán Cal and reviewed by two anonymous referees.