A simple wind-speed-independent actuator disk control method is proposed that can be applied to speed up annual energy production calculations of wind farms using Reynolds-averaged Navier–Stokes simulations. The new control method allows the user to simulate the effect of different wind speeds in one simulation by scaling a calibrated thrust coefficient curve, while keeping the inflow constant. Since the global flow is not changed, only the local flow around the actuator disks need be recalculated from a previous converged result, which reduces the number of required iterations and computational effort by a factor of about 2–3.

Wind turbine wakes cause energy losses in wind farms

The wind turbines in RANS are often represented by actuator disks (ADs), where the wind turbine forces are implemented as a sink term in the momentum equations.
The Reynolds number of the RANS-AD simulations, based on a rotor diameter of 100 m, is on the order of 10

In previous work

The RANS-AD methodology used for our wind farm simulations are described in previous work

The new AD force control method is an extension of previous work

Precalculated

Prior to the wind farm simulations, a

The precalculated

Parallel and sequential simulation methodologies to calculate the AEP using 22 wind speeds (

The AEP of the

The baseline case represents 352 individual simulations, which need a total of

For RANS-AD simulations including terrain or in-homogeneous roughness lengths, it is not possible to rotate the layout while keeping the inflow direction constant.
In this case, our proposed wind-speed-independent AD control method would reduce the number of required iterations and computational effort significantly following Method II.
Note that RANS simulations of non-homogeneous terrain using a logarithmic inflow and rough wall boundary condition are also independent of the Reynolds number, for wind speeds that are relevant for wind turbines, as discussed by

The total CPU time of the fastest method (Method V) is

In the present work, we have simulated all wind speeds, also far above rated power where the wind turbines do not experience power losses. If one is only interested in the AEP, then these simulations could have been skipped once rated wind farm power is achieved. One could further reduce the computational effort of RANS-AD AEP calculations by reducing the number of wind speed and wind direction cases using statistics of the wind resources (i.e. using the Weibull and wind direction distributions), which could be investigated in future work.

Finally, these computations have been performed with an accuracy of 0.02 % for the convergence error in AEP. One could choose to relax the convergence criteria of the solutions at the expense of an higher error but with a significant reduction in the total amount of computational iterations. For instance, one could choose to accept an error of 0.5 %, which would reduce the computational effort by a factor of 18. An error of 0.5 % would presumably still be less than the uncertainty associated with, for instance, the wind rose and

A simple wind-speed-independent actuator disk control method is proposed and employed to reduce the number of iterations necessary to calculate the annual energy production from Reynolds-averaged Navier–Stokes simulations of

The numerical results are generated with proprietary software, although the data presented can be made available by contacting the corresponding author.

The Reynolds number independence of the RANS-AD simulations for a single wind turbine wake is shown in Fig.

Reynolds number independence of the streamwise velocity deficit of a single AD with a prescribed thrust coefficient

MPVDL performed the simulations, produced all figures and drafted the article. SJA and P-ER contributed to the methodology and finalization of the paper

The authors declare that they have no conflict of interest.

This paper was edited by Carlo L. Bottasso and reviewed by two anonymous referees.