# Numerical Study on the Yaw Control for Two Wind Turbines under Different Spacings
###### Abstract  
In this study, the large eddy simulation method and the actuator line model are used to investigate the wake redirection of two turbines. Different turbine spacings and yaw-based control of the upstream turbine are considered. The effects of yaw angle and turbine spacing on the output power of two turbines are comprehensively analyzed, and the physical mechanisms of the wake deficit, deflection and interaction are revealed from the distributions of the wake velocity, turbulence intensity and the structures of wake vortices. The results show that the overall power of two turbines is related to the yaw angle of the upstream turbine and the spacing between two turbines. We find yaw angle is the dominant factor in the total power improvement compared to turbine spacing. Still, a large yaw angle causes significant power fluctuations of the downstream turbine. The deficit of wake velocity and the change of output power are determined by the characteristics of the wake flow field, which the yaw control regulates. wind turbine wake; large eddy simulation; actuator line model; spacing effect; yaw control 202212709820221270982222127098221221222122122122222222222222222222222222222222222222222222222222222222222222222222222222222222212212212212212212221222222222222222222222  
unsteady rotating flow. [PERSON] (2008) firstly applied the actuator disk model (ADM) to the evaluation of the turbine wake, and then the large eddy simulation (LES) was combined with ADM to simulate the wake of the wind turbine ([PERSON] et al., 2010; [PERSON] et al., 2011). To improve the accuracy of ADM, [PERSON] and [PERSON] et al. (2010) proposed the actuator line model (ALM), which can consider the impact of blade geometry. Thus, ALM can be used to investigate the blade tip and root vortices. To evaluate the influence of complex inflow on the operating state of the wind turbine in actual work conditions, [PERSON] et al. (2011, 2013) developed Simulator for Wind Farm Applications (SOWFA) based on Open Field Operation And Manipulation (OpenFOAM), which was capable of studying the aerodynamic and wake characteristics of wind turbines in wind farms under the atmospheric boundary layer (ABL) with ALM. In SOWFA ([PERSON] et al., 2016), the LES method was used to simulate the ABL turbulence and analyze the wake effect of the turbine. The models of the actuator class mainly consist of the actuator disk, the actuator line and actuator surface for the high-fidelity simulation. [PERSON] and [PERSON] (2015) studied the wake effect of two turbines with different longitudinal and transverse spacings using the vorticity transport model. The downstream turbine was located entirely or partially in the wake region of the upstream turbine in their study. [PERSON] et al. (2016) combined the actuator line and CFD to study the aerodynamic output power of the wind farm and the mutual effects of the wake of three turbines in the cases that the downstream turbine is fully or partially located in the upstream turbine's wake area. These studies demonstrate that when the spacing between two wind turbines is greater than five times the rotor diameter (D), the interaction between the turbines is reduced and the overall power of the wind farm increases significantly. Similarly, [PERSON] et al. (2017) analyzed the wake effects of two turbines with different spacings at various inflow conditions using ALM and LES. It was found that when the downstream turbine operates in the wake of the upstream turbine, the average value of blade load decreases, but the standard deviation increases. The aforementioned studies analyze the impact of turbine spacing on downstream turbines and provide a clear explanation of how multi-turbine wake interference works. However, they only consider the influences of wind turbine layout without using control strategies for turbines to improve the performance of the wind farm. Many scholars have studied the mechanism of yaw control of wind turbines. [PERSON] et al.