An extended theoretical model, which is based on a two-scale coupled momentum conservation argument, is proposed to estimate aerodynamic effects of support structures on the performance of ideal very large wind farms. A key implication of this extended model is that the parameter (A_s /A) where A and A_s are the rotor swept area and support-structure frontal projected area, respectively, and is an effective support-structure drag coefficient, plays an important role in the design of very large wind farms. In particular, the optimal farm density tends to decrease as the normalised support-structure drag increases. To validate this extended model, Wall-Modelled Large-Eddy Simulations (WMLES) of a periodic array of actuator discs with and without support structures are conducted; results agree qualitatively with the model.

An extended theoretical model based on a two-scale coupled momentum balance method is proposed to estimate aerodynamic effects of wind turbine towers on the performance of both ideal (infinitely large) and more realistic (large but finite-size) wind farms. A key implication of the extended model is that a normalized support-structure drag, $\left(A_S/A\right)\times C_D^{*}$ , where $A$ and $A_S$ are the rotor swept area and support-structure frontal projected area, respectively, and $C_D^{*}$ is an effective support-structure drag coefficient, may play an important role in the design of future large wind farms. For the infinitely large case, the theoretical model shows that the optimal turbine spacing should increase with the value of $\left(A_S/A\right)\times C_D^{*}$ , whereas for the large finite case, this also depends on an additional parameter describing the response characteristics of the atmospheric boundary layer to the total farm drag. To validate the theoretical model for the infinitely large case, Wall-Modeled Large-Eddy Simulations of a periodic array of actuator disks with and without support structures are conducted. The results show a reasonably good agreement (within 10% in the prediction of power) with the theoretical model.

A fully resolved (FR) NREL 5 MW turbine model is employed in two unsteady Reynolds-averaged Navier–Stokes (URANS) simulations (one with and one without the turbine tower) of a periodic atmospheric boundary layer (ABL) to study the performance of an infinitely large wind farm. The results show that the power reduction due to the tower drag is about 5% under the assumption that the driving force of the ABL is unchanged. Two additional simulations using an actuator disc (AD) model are also conducted. The AD and FR results show nearly identical tower-induced reductions of the wind speed above the wind farm, supporting the argument that the AD model is sufficient to predict the wind farm blockage effect. We also investigate the feasibility of performing delayed-detached-eddy simulations (DDES) using the same FR turbine model and periodic domain setup. The results show complex turbulent flow characteristics within the farm, such as the interaction of large-scale hairpin-like vortices with smaller-scale blade-tip vortices. The computational cost of the DDES required for a given number of rotor revolutions is found to be similar to the corresponding URANS simulation, but the sampling period required to obtain meaningful time-averaged results seems much longer due to the existence of long-timescale fluctuations.