**1. Introduction**

The use of wind power has grown rapidly over the past few decades. The aerodynamics of the wind turbine are a core subject of wind power generation. Owing to the intermittency of wind, the orientation of a wind turbine must be frequently adjusted, typically using the yaw mechanism, to ensure the rotor disk is perpendicular to the direction of the wind. Yaw control is one of the most important strategies for improving the e fficiency of wind energy conversion. Under the yawed condition, velocity component of the upstream wind is parallel to the plane of rotation. Thus, the angle of attack of airfoil along blade spanwise exhibits periodic variation in one revolution [1]. The aerodynamic performance of a wind turbine under yaw, as well as the surrounding flow, show highly unsteady characteristics, resulting in high fatigue loads that can dramatically reduce the operational life of a wind turbine. Therefore, understanding the unsteady aerodynamic characteristics of wind turbines under yaw is important for improving their design [2]. In particular, accurate predictions of unsteady aerodynamic loads under yawed conditions are important for blade design and operational control.

Knowledge of complex three-dimensional (3D) flow phenomena over wind turbine blades and near wake under the yawing condition are still lacking. Thus, improved numerical models that consider the combined effects of stall delay, unsteady flow, and other significant effects such as the retreating & advancing effect and upwind & downwind effect are needed. The aim of present paper is to further elucidate the aerodynamic and 3D flow characteristics of yawed and yawing turbines.

The aerodynamics of wind turbines under yaw have been extensively investigated using both experiments and numerical simulations. Detailed aerodynamic performance measurements along the blade in combination with 3D flow field measurements have helped further our understanding of the flow mechanism. Wind tunnel experiments performed by Hand et al. [3] on a two-blade wind turbine provide a benchmark for numerical simulations. In their study, Hand and colleagues obtained the pressure and aerodynamic force coefficients for an azimuthal distribution at different radial locations under five yawed cases: 0◦, 10◦, 30◦, 45◦, and 45◦. The angle of attack was found to vary approximately with the blade azimuth angle according to a sinusoidal function. Further to this, Schepers et al. [4] performed wind tunnel experiments on a three-bladed wind turbine, the MEXICO rotor, under three different yaw angles: 15◦, 30◦, and 45◦. They obtained sectional aerodynamic forces and torques for different azimuth angles; however, the sinusoidal variation rule did not correlate well along the inner span of the blade owing to the velocities induced by root vortices. Sant et al. [5] investigated the TUDelft reference rotor in an open jet wind tunnel under both axial and yawed conditions and assessed the blade element moment (BEM) method, which was found to be limited to the skewed wake under yawed conditions.

Based on the work of Schepers et al. [6], Micallef et al., performed stereo particle image velocimetry measurements to study the blade aerodynamic performance and near wake development. Under yaw, flow in the windward region exhibited inboard motion due to rapid motion of the tip vortices away from the blade. In field tests, Ven et al. [7] applied in-field measurements of a turbine to investigate the three dimensional stall phenomena under yawed inflow conditions. Imbalances in the crossflow fraction along the radial direction of the blade were observed between azimuth angles of 90◦ and 270◦. The phenomenon is caused by yawed inflow leading to in-wash and outwash on the blade surface. Furthermore, Dai et al. [8] provided a detailed investigation of the yaw effect based on Supervisory Control and Data Acquisition (SCADA), and presented characteristics of the power coefficient and rotor torque under yaw. Interestingly, many yaw error control solutions based on the smart prediction of the wind direction had been used to maximum power extraction of wind power [9,10]. Further to this, Saenz-Aguirre et al. [11] claim that the drawbacks of the yaw control are the very large time constant and the strict yaw angle rate owing to the high mechanical loads, resulting that yaw control is less studied in the literature than that pitch and speed control. Furthermore, Munters et al. [12] performed wind-farm control research with a new dynamic yaw control based on the large-eddy simulation, and found that with the consideration of the unsteady-control interacting with flow dynamics, dynamic yaw control for the given wind farm setup is better than induction control in the process of power extraction. In fact, the yawing operation of wind turbine is very common, and the aerodynamic characteristics of wind turbine under yaw had been extensively studied in the literature with numerical simulation.

Numerical methods to evaluate the aerodynamic performance of wind turbines mainly include BEM, vortex theory, and computational fluid dynamics (CFD). The most commonly used method is BEM, which is fast with low computational costs. Ryu et al. [13] developed a successive under-relaxation technique based on the classical BEM to compute specific radial locations of the blade and found that yawed inflow leads to periodic changes in the angle of attack on different spanwise sections. Jimenez et al. [14] firstly established an analytical wake model with a simple formula to predicit the wake skew effect based on the momentum conservation and top-hat model offered by Jensen [15] for the velocity deficit effect. However, the experimental validation was not sufficient as mentioned by the author and the model overestimate the wake deflection of wind turbine, owing to the inaccurate top-hat model for velocity deficit. With the goal of optimize the yaw angles of the wind turbines, Gebraad et al. [16] presented a new flow redirection and induction in steady-state model based on internal parametric model for wake effects, which demonstrate the optimization control for increasing the energy production of the wind plant. Recently, Bastankhah and Porte-Agel [17] developed a new analytical model on the assumption of the Gaussian distribution to predict the wake deflection and far wake velocity deficit, which showed a good agreemen<sup>t</sup> with the experimental data. However, some parameters of that model have not specified which is needed to be researched. Based on the works of them, Qian Guo-Wei et al. [18] presented a new analytical wake model with Gaussian distribution function of velocity deficit and momentum conservation in the lateral direction, considering the ambient turbulence intensity, thrust coefficient and yawed effect, which enables the model to have good application under various conditions. Yaw not only influences the wake flow behind the wind turbine, but also flows on the surface of the blade and 3D aerodynamic characteristics of the rotor [19]. Castellani [20] analyzed a small three-blade wind turbine and investigated the effects of large yaw angles, using numerical and experimental methods, and found that the 3P blade frequency is clearly visible. In addition, non-uniform flow around the blades was modeled using a simplified wake model modified by Prandtl's tip loss factor.

The time constant used in dynamic inflow models results in an unrealistic drop at the tip region, and therefore, cannot accurately model for the dynamic conditions of wind turbines. For instance, both the tip loss model and dynamic inflow model have several shortcomings when used for non-design load cases but can possibly be improved by free vortex methods (FVM), which combine the blade aerodynamics with wake flow computational models. Qiu et al. [21] investigated the dynamic variation of loads on a wind turbine blade during the yaw process using an improved lift line method and proposed a wake model comprised of the vortex sheet model and tip vortex model. Further, the yaw rate and dynamic wake were shown to significantly influence the shaft thrust and torque of the wind turbine. Micallef et al. [22] performed both experimental and numerical investigations based on an FVM to investigate the tip vortex generation of a horizontal-axis wind turbine (HAWT) under yaw. Vorticity on the suction side under non-yawed conditions was shown to be more concentrated than for the yawed condition, in which vorticity spreads over a small region at the tip of the turbine blade.

Several aerodynamic correction models have been proposed and widely used, including Pitt and Peter's yaw correction [23,24], Suzuki's dynamic inflow model [25], Prandtl's tip loss function [26], Du and Selig's 3D stall delayed model [27], and Buhl's wake correction [28]. Nonetheless, classical BEM and FWM are still not sufficiently reliable for predicting the aerodynamic load distributions on wind turbine blades, especially for the yawed and stalled rotor conditions. Investigations were performed on the complicated yaw aerodynamic problem of wind turbines using more accurate CFD simulations using detailed visualization of the 3D flow [29]. Tongchitpakdee et al. [30] investigated the aerodynamic characteristics of the National Renewable Energy Laboratory (NREL) Phase VI wind turbine modeled by an unstructured grid under different wind speeds and yaw angles using the BL model. At low wind speeds (<7 m/s) and under low yaw angles, the flow remains attached over most regions of the rotor. Further to this, Yu et al. [31] performed time-accurate aerodynamic simulations of the NREL Phase VI wind turbine under yawed flow conditions, which was also modeled with an unstructured mesh, along with the *k*-<sup>ω</sup> shear stress transport (SST) turbulent model. They found that the retreating side shown aerodynamic loads (*Cn*, *Ct*) higher magnitudes of loads than on the advancing side. However, the three-dimensional unsteady stall effect at different yaw angles was not studied. Schulz et al. [32] modeled and analyzed a generic 2.4-MW wind turbine with over-set structured grids and yaw angles ranging from −50◦ to 50◦ using the FLOWer CFD solver. The simulation was performed using a detached eddy simulation method and revealed azimuthal non-uniformity of the load variation along spanwise sections of the blade due to the retreating & advancing effects of the blade. Furthermore, the deformation characteristics of the blade were considered in the yawed case of the wind turbine simulation. Jeong et al. [33] investigated the effects of yaw errors on the aerodynamic and aeroelastic behaviors of NREL 5-MW HAWT blades, and showed how yaw misalignment adversely affects the dynamic aeroelastic stability of the blade. Dai et al. [34] performed an aeroelastic analysis on the Tjæreborg wind turbine under yaw, and found that fluid-solid coupling results in higher averaged power and thrust, as well as violent oscillation amplitudes.

Yaw is a continuous rotation process with a constant or variable velocity of rotation. Qiu et al. [21] investigated the shaft torque of the blade and instantaneous wake flow under the dynamic yawing process with a yaw rate between 5 and 20◦/s for the NREL Phase VI wind turbine. For larger wind turbines, such as the NREL 5-MW et al., these yaw rate seem to be impossible owing to the larger moment of inertia of the rotor-nacelle subsystem due to enlargement of the blade and tower length. Leble et al. [35] carried out a series of CFD simulations to investigate the performance of the DTU 10-MW wind turbine and modeled the turbine as a structured grid with moving boundaries. Simulations were performed with a yaw rate of 0.3◦/s and 3◦ yaw angle and the results showed that overall power under the dynamic yawing condition was much larger than for the yawed case. Then, Wen et al. [36] investigated the NREL 5-MW yawing dynamic sinuous motion with an averaged yaw rate of 1.2◦/s and 2.4◦/s for the case of *f* = 0.1 Hz and *f* = 0.2 Hz, respectively. The dynamic yaw motion induced the upwind & downwind yawing e ffect, which considerably influenced the AOA of blade sections. As the blade is yawing upwind, the AOA increases and vice versa. In summary, the unsteady aerodynamic characteristics of wind turbine blades under yaw considering full 3D rotational e ffects are still unclear. In the present paper, unsteady dynamic CFD simulations were performed to investigate the aerodynamic characteristics of a wind turbine blade during the rotational revolutions using a full 3D wind turbine model. With the assumption of the rigid body, the main contribution of this paper is the proposal of a new grid methodology for analyzing the overall performance using URANS simulation, aerodynamic loads, and flow field of wind turbines in the yawed and yawing processes. The method can be used to analyze interactions between transient aerodynamic phenomena associated with the wind turbine control system. The other main objective of this study was to investigate the e ffects of yaw on the dynamic output power, rotor thrust, and the blade sectional aerodynamic characteristics caused by continuous changes in the yaw angle. The main novelty of the current work is the inclusion of the dynamic yawing simulation of wind turbine with the multiple structured domain sliding mesh. The rest of this paper is organized as follows: Section 2 describes the geometry model and computational method. In Section 3, simulation results under several yaw angles are compared to experimental data to validate the model. The discussion mainly focuses on the sectional azimuthal variations of aerodynamic force coe fficients, as well as the pressure distribution on the blade. Finally, the conclusions are summarized in Section 4.

## **2. Numerical Model**

The 5-MW reference wind turbine (RWT) designed by the NREL was used in this study [37]. The blade uses the Delft University (DU) airfoil family with a relative thickness ranging from 21 to 40%. The blade chord, relative thickness, and twist angle all have non-linear distributions. The rotor diameter is 126 m and the wind turbine operates at a wind speed of 11.4 m/s with a rotational velocity of 12.1 rpm, resulting in the tip speed ratio of λ = 7. The definitions of yaw angle and azimuth angle are shown in Figure 1.

**Figure 1.** Sketch of the asymmetric relative velocity under yaw.

#### *2.1. Computational Domain and Boundary Conditions*

The computational domain, as shown in Figure 2a, is a rectangular zone that is 330*D* in length and 240*D* in width, where *D* is the rotor diameter. The computational domain is made up of two main zones, the far-field zone and internal zone, as depicted in Figure 2b. The far-field is used to set the inflow conditions. The internal zone can be further subdivided into two parts: (1) cylinder yaw zone with a radius of 6*D* and a height of 7.5*D*; (2) rotor roll zone with 1.5*R* radius and 1.6-m height. The cylinder zone was used to configure the dynamic yaw motion. The distance between the inlet and rotational cylinder was 120*D*. The rotor is located at the center of the rotor roll zone.

**Figure 2.** Computational Zones: (**a**) far-field (static); (**b**) yaw zone; (**c**) rotational zone.

Figure 3 shows the boundary conditions used in the simulations. A uniform wind speed of 11.4 m/s was set at the inlet of the domain with a turbulence intensity of 5%. Boundary conditions for the up and bottom planes in the domain are free-slip and no-slip walls. The blade surface was set as a no-slip wall. The pressure outlet condition was assigned to the outlet of the domain. To simplify the static yaw simulation, the rotational axis was fixed, while the inlet velocity direction was varied to generate different angles mimicking different yaw condition. In Fluent, it is possible to select a mesh that can process non-conformal interfaces, namely boundaries interfaces between cell zones, for which the mesh node locations are not identical. In the current simulation case, the matching mesh interface option was applied to three interfaces, for example, the interface between the far-field zone and yawing zone, which is more accurate than the mapped interface option.

**Figure 3.** Boundary conditions.

## *2.2. Grid Setup*

Building multiple blocks is recommended for studying the yawing dynamics of coupled e ffects within two axes (yawing axis and rotational axis) since the relative rotation between zones can be investigated. Figure 4a,b show grids in the three di fferent zones of the turbine (far-field, yaw cylinder, and rotation) generated using the ICEM software. The NREL 5-MW rotor was modeled including the hub (without the tower) [31]. The grid number for the far-field was 3.35 million, which is enough to transition from the inflow condition to the internal zone. Dynamic yaw motion was set, along with the rotational velocity in the cylinder yaw zone, with 3.25 million grids. Figure 4a illustrates the grids of the rotor zone, generated using AutoGrid tool in the NUMECA software. The grid number for this zone was 3.76 million, the first layer wall normal distance is about 10−<sup>4</sup> m. The total grid number was about 10.27 million. The work of Tran and Kim [38] employed a 6 million-cell grid for a 5-MW wind turbine. The blade surface was resolved with 93 cells along the span. In order to resolve the boundary layer, the grids around the blades were refined to keep *y*+ less than 5 on the blade surface, which satisfies the needs of the T-SST turbulent model.

**Figure 4.** Computational mesh for NREL 5-MW wind turbine; (**a**) rotor cylinder; (**b**) blade surface mesh.

## *2.3. Numerical Methods*

The unsteady Reynolds-averaged Navier-Stokes equations (URANS) were solved in ANSYS Fluent. The *k*-<sup>ω</sup> transitional SST turbulent model was used for turbulence modeling considering both laminar and transitional e ffects at the blade surface. The sliding mesh technique was used for data exchange between the rotational zone and the stationary zone. To ensure time-accurate calculations, a dual-time implicit time integration algorithm based on linearized second-order Euler backward di fferencing was used. The time-step size was equivalent to a rotor azimuthal increment of 5◦ coupled with 20 pseudo-time sub-iterations. The residual of the continuity equation was reduced by at least three orders throughout the calculations. For comparison, BEM computations using the Fast software were also performed. Work of Tran and Kim [38] employed 2◦ increments of the azimuth angle. The yawed case was achieved by changing the inlet velocity component to implement yaw inflow.

The yaw velocity can be constant, shown as the black dashed line in Figure 5. In fact, yawing is a process that changes gradually, similar to the definition of 2-s (or 4-s) start or stop duration. The selected variation of angular velocity for studying the influence of start-stop duration on the dynamic aerodynamic characteristics under yawing is shown a solid black line in Figure 6, which can be separated into three part: 1. Start duration with sinusoidal variation law of yaw velocity, 2. the stage with constant yaw velocity of 0.3◦/s, 3. Stop duration with sinusoidal law of yaw velocity.

**Figure 5.** The sketch for start-stop yawing process.

In the present investigation, the yawing process of the NREL 5-MW turbine was calculated under two di fferent start-stop durations, 2-s and 4-s. Variation of the yaw velocity is shown in Figure 6, and changes more gradually with the 4-s duration of the start-stop process compared to the 2-s duration. During the start-stop yawing process, the sinusoidal variation of yaw velocity was applied to achieve transient yawing of the wind turbine, as follows:

$$
gammaVol(t) = rpm \times \sin(2\pi(1/(duration \times 4) \times t) \tag{1})
$$

where rpm = 0.3◦/s, according to the description of the NREL5 WM design manual [37], and duration is either 2-s or 4-s. Up to 0.3◦/s, the wind turbine changes from transient to a yaw angle of approximately 20◦ with the maximum rpm.

**Figure 6.** Variation of yaw velocity under di fferent transient start-stop processes.

#### **3. Analysis of Results**

The NREL 5-MW reference wind turbine (RWT) was studied [28]. The yawed and yawing wind turbines were considered. The parameters used in the simulation are listed in Table 1 for each case. Two of the cases assumed uniform inflow and the blades were assumed to be rigid in the model.

> Simulation cases.


**Table 1.**

Physically, the flow-field around a rotating HAWT is significantly influenced by the existence of wind shear, turbulence, gust, and yaw motion of the nacelle. For a yawing wind turbine, flow characteristics are more complex than those of a static yawed wind turbine, and the additional wind contribution e ffects transmitted to the rotor due to the nacelle motion must be considered. Therefore, accurate prediction of the unsteady aerodynamics calculated by many conventional numerical approaches is still questionable for a yawing wind turbine. In this study, unsteady CFD simulations based on the sliding structure mesh technique were performed to analyze the yawing motion of the wind turbine due to the nacelle motion. Thus, to investigate the e ffects of vortex-wake-blade interactions on the aerodynamic performance of the wind turbine, the yawing motion of the rotating turbine blades due to the nacelle motion was considered.

The CFD method was first verification with grid independence, turbulent model studies and time step studies. Then the computational results are validated using both fixed yaw and yawing of the NREL 5-MW wind turbine. The unsteady aerodynamic loads of the yawing wind turbine were more sensitive to change as the yaw angle was varied. Nine simulation conditions were performed based on a fixed yaw angle of 0◦, 5◦, 10◦, 15◦, 20◦, 25◦, and 30◦.

Next, the total aerodynamic performance, which was used to validate the results of the simulation, will be discussed. Thereafter, aerodynamic characteristics and three-dimensional stall characteristics at di fferent span sections will be investigated. Finally, the results of two separate simulations of the yawing start-stop stage will be used to examine the mechanism of the yawing e ffect.

#### *3.1. Verification of the Computational Results*
