**Contents**


## **About the Editor**

**Wen Zhong Shen (Dr)** serves as Professor in Wind Energy at the College of Electrical, Energy and Power Engineering, Yangzhou University, China, since 2021. He obtained his B.Sc. degree in Mathematics at Wuhan University, China, in 1988, and M.Sc. and Ph.D. degrees in fluid mechanics at Paris-Sud University, France, in 1989 and 1993, respectively. He worked as a post-doc in LIMSI/CNRS (Centre National de la Recherche Scientifique) in 1993–1996 and subsequently held appointments as Assistant Research Professor, Associate Professor and Full Professor at the Department of Wind Energy, Technical University of Denmark (DTU), in 1996–2021. His research areas cover the fields of wind turbine aerodynamics, aero-acoustics, computational fluid dynamics, wind turbine airfoil/rotor design, and wind farm optimization.

## **Preface to "Wind Turbine Aerodynamics II"**

As the pioneer of renewable energy, wind energy is developing very quickly all over the world. To reduce the levelized cost of energy (LCOE), the size of a single wind turbine has been significantly increased and will continue to increase further in the near future. This tendency requires the further development and validation of design and simulation models. This Special Issue "Wind Turbine Aerodynamics II" is a collection comprising numerous important works addressing the aerodynamic challenges appearing in such a development.

> **Wen Zhong Shen** *Editor*

### *Editorial* **Special Issue on Wind Turbine Aerodynamics II**

**Wen Zhong Shen 1,2**


#### **1. Introduction**

To alleviate global warming and reduce air pollution, the world needs to rapidly shift towards renewable energy. As the pioneer of renewable energy, wind energy is developing very fast all over the world. In order to capture more energy from the wind and reduce the levelized cost of energy (LCOE), the size of a single wind turbine has recently increased to 16 Mega-Watt (MW) [1], and will be increased further in the near future. Big wind turbines and their associated wind farms have advantages, but also challenges in all wind energy sciences, including wind turbine aerodynamics. The typical effects are mainly related to the increases in Reynolds number, in blade flexibility, and possibly in wind turbine noise. This Special Issue collects a number of important works addressing these aerodynamic challenges. Aerodynamics of wind turbines is a classic concept, and is the key for wind energy development, as all other wind energy sciences rely on the accuracy of its aerodynamic models. There are also several Special Issues on wind turbine aerodynamics. This guest editor edited a Special Issue in Renewable Energy on aerodynamics of offshore wind energy systems and wakes in 2014 [2], which collected state-of-the-art research articles on the development of offshore wind energy, and a Special Issue in Applied Sciences on aerodynamics in 2019 [3], which collected various important aerodynamics problems.

#### **2. Current Status in Wind Turbine Aerodynamics**

In the context introduced above, this Special Issue was to collect latest research articles on various topics related to wind turbine aerodynamics, which includes Wind turbine design concepts, Tip loss correction study, Wind turbine acoustics modelling, and Vertical axis wind turbine concept. A summary of the collected papers is given below in the order mentioned above.

There are also three papers dealing with Wind turbine design concepts. Sun et al. [4] presented a coned rotor concept with different conning configurations, including special cones with three segments. The authors made the analysis based on the DTU-10 MW reference rotor [5] and found that the different force distributions of upwind and downwind coned configurations agree well with the distributions of angle of attack, which are affected by the blade tip position and the cone angle, and the most upwind and downwind cones have a thrust difference up to 8% and a torque difference of up to 5%. The coned rotor concept has potential to be used for super-large wind turbines. The influence of tilt angle on aerodynamic performance of the virtual NREL 5 MW wind turbine [6] was studied by Wang et al. [7]. It was found that the change in tilt angle results in changing the angle of attack on wind turbine blade, which affects the thrust and power of the wind turbine, and the aerodynamic performance of the wind turbine is best when the tilt angle is about 4◦. Subsequently, the effects of wind shear were also studied for the turbine with a tilt angle of 4◦, and it was found that wind shear will cause the thrust and power of the wind turbine to decrease. Yang et al. [8] experimentally studied the effect of Gurney flaps on the performance of a wind turbine airfoil (DTU-LN221 airfoil [9]) under different turbulence levels (T.I. of 0.2%, 10.5%, and 19.0%) and various flap configurations. By further changing

**Citation:** Shen, W.Z. Special Issue on Wind Turbine Aerodynamics II. *Appl. Sci.* **2021**, *11*, 8728. https://doi.org/ 10.3390/app11188728

Received: 15 September 2021 Accepted: 16 September 2021 Published: 18 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the height and the thickness of the Gurney flaps, it was found that the height of the Gurney flaps is a very important parameter, whereas the thickness parameter has little influence, and the maximum lift coefficient of the airfoil with flaps is increased by 8.47% to 13.50% under low turbulent inflow condition.

There is one paper dealing with tip loss correction study. Tip loss correction is important for predicting the aerodynamic performance of a wind turbine, and modelling the tip loss correction is essential in wind turbine aerodynamics. Zhong et al. [10] presented a tip loss correction study for actuator disc/Navier–Stokes simulations with the newly developed tip loss correction model in [11]. The study was conducted to simulate the flow past the experimental National Renewable Energy Laboratory (NREL) Phase VI wind turbine [12] and the virtual NREL 5 MW wind turbine [6]. Three different implementations of the widely used Prandtl tip loss function [13] are discussed and evaluated, together with the new tip loss correction in [10]. It was found that the performance of three different implementations [14–16] is roughly consistent with the standard Glauert correction employed in the blade element momentum theory, but they all tend to make the blade tip loads over-predicted, and the new tip loss correction shows superior performances in various flow conditions.

There is one paper dealing with the development of flow-structure-acoustics framework for predicting and controlling the noise emission from a wind turbine under wind shear and yaw [17]. A wind turbine operating under wind shear and in yaw produces periodic changes of blade loading, which intensifies the amplitude modulation (AM) of the generated noise, and thus can give more annoyance to the people living nearby. In this study, the noise emission from a wind turbine under wind shear and yaw is modelled with an advanced fluid-structure-acoustics framework, and then controlled with a pitch control strategy. The numerical tool used in this study is the coupled Navier–Stokes/Actuator Line model EllipSys3D/AL [18], structure model FLEX5 [19], and noise prediction model (Brooks, Pope, and Marcolini: BPM) [20] framework. Simulations and tests were made for the NM80 wind turbine [21] equipped with three blades made by LM Wind Power. The coupled code was first validated against field load measurements under wind shear and yaw, and a fairly good agreement was obtained. The coupled code was then used to study the noise source control of the turbine under wind shear and yaw.

There is one paper dealing with a study of orthopter-type vertical axis wind turbine (O-VAWT) concept [22]. The study by Wijayanto et al. [23] investigated the effects of horizontal shear flow on the power performance characteristics of an O-VAWT by performing wind tunnel experiments and computational fluid dynamics (CFD) simulations. A uniform flow and two types of shear flow (advancing side faster shear flow (ASF-SF) and retreating side faster shear flow (RSF-SF)) were employed as the approaching flow to the O-VAWT. The ASF-SF had a higher velocity on the advancing side of the rotor. The RSF-SF had a higher velocity on the retreating side of the rotor. It was found that the location where ASF-SFs with high shear strength dominantly occur is ideal for installing the O-VAWT.

#### **3. Future Research Need**

Although this Special Issue has been closed, more research in wind turbine aerodynamics is expected, as the goal of wind energy research is to help the technological development of new, environmentally friendly, and cost-effective large wind turbines and wind farms.

**Funding:** The special issue was funded by the key programs of the Ministry of Science and Technology, grant number 2019YFE0192600 (Research on Key Technologies of Low Noise Wind Turbine).

**Acknowledgments:** This Special Issue would not be possible without the contributions of various talented authors, professional reviewers, and the dedicated editorial team of Applied Sciences. Congratulations to all the authors. I would like to take this opportunity to record my sincere gratefulness to all the reviewers. Finally, I place my gratitude to the editorial team of Applied Sciences, and special thanks to Nicole Lian, Assistant Managing Editor from MDPI Branch Office, Beijing.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


### *Article* **Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines**

**Zhenye Sun 1, Weijun Zhu 1,\*, Wenzhong Shen 2, Qiuhan Tao 1, Jiufa Cao <sup>1</sup> and Xiaochuan Li <sup>1</sup>**


**Abstract:** In order to develop super-large wind turbines, new concepts, such as downwind loadalignment, are required. Additionally, segmented blade concepts are under investigation. As a simple example, the coned rotor needs be investigated. In this paper, different conning configurations, including special cones with three segments, are simulated and analyzed based on the DTU-10 MW reference rotor. It was found that the different force distributions of upwind and downwind coned configurations agreed well with the distributions of angle of attack, which were affected by the blade tip position and the cone angle. With the upstream coning of the blade tip, the blade sections suffered from stronger axial induction and a lower angle of attack. The downstream coning of the blade tip led to reverse variations. The cone angle determined the velocity and force projecting process from the axial to the normal direction, which also influenced the angle of attack and force, provided that correct inflow velocity decomposition occurred.

**Keywords:** coned rotor; aerodynamics; wind turbine; computational fluid dynamics

**Citation:** Sun, Z.; Zhu, W.; Shen, W.; Tao, Q.; Cao, J.; Li, X. Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines. *Appl. Sci.* **2021**, *11*, 147. https://dx.doi.org/10.3390/ app11010147

Received: 3 December 2020 Accepted: 22 December 2020 Published: 25 December 2020

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

#### **1. Introduction**

Wind turbines are increasing in size and rated power in order to meet the requirement of wind energy development and further reduce the cost of energy (COE). Commercially available wind turbines are reaching 15 MW and are expected to achieve a power levels of 20 MW with even larger rotor diameters. As the blade mass increases subcubically with the blade length [1], the mass per blade would surpass 75,000 kg for a 20 MW wind turbine [2], which will give rise to difficulties in the design and construction of such systems. Adopting carbon fiber laminates in the major load-carrying region, such as the cap, can reduce the blade mass. Smart blades with advanced control strategies, together with add-ons, such as moving trailing edge flaps, can reduce the load and cost [3]. However, the utilization of advanced materials and the smart control techniques is constrained by cost [2]. Blade structure optimization [4–6] can also reduce blade mass. An optimization study on a 5 MW wind turbine rotor [6] found that the blade-tower clearance impedes the further reduction of blade mass, which implies the importance of coned, tilted, and prebending rotors. These ideas are not new, and have already been commercially applied. The coned rotor can reduce the static and dynamic loads [7], which will greatly reduce the blade weight and cost. Prebending blades are manufactured with their stacking lines flexed toward the wind. Compared with coned and tilted rotors, prebending blades can be mounted on the nacelle without the need to modify the design of the latter.

Based on the ultralight, load-aligned rotor concept, a downwind design by Loth et al. [2,8] was proposed to orient the resultant force of blades along the span-wise direction. Their blades are mostly under a tensional force and suffer fewer bending moments than traditional blades. Additionally, downwind rotors have a larger tower clearance. Therefore, this load-aligned downwind design will get rid of the rotor-tower clearance constraint and

make the full use of the material strength, which allows more flexible and lighter blades to be manufactured. It was found that a two-bladed rotor following this concept leads to a mass saving around 27%, based on a 13.2 MW reference rotor [9,10]. Qin et al. [11] upscaled the load-aligned design from 13.2 MW to 25 MW. Additionally, segmented blades and outboard pitching ideas were discussed as a means of overcoming the increased edgewise loads of load-alignment. Wanke et al. [12] compared a 2.1 MW three-bladed upwind turbine with the downwind counterparts. It was concluded that downwind configurations have no clear advantage over the original upwind design. This conclusion was made on the condition that downwind rotors are not specially redesigned for downwind conditions; redesigns may yield different results. Bortolotti et al. [13] compared 10 MW upwind and downwind three-bladed rotors, with and without active cone control. They found that downwind designs, despite having reduced cantilever loadings, did not show obvious advantages over upwind designs. Ning and Petch [14] published an integrated design of 5–7 MW downwind turbines and compared it with its upwind counterparts. It was found that 25–30% of the rotor mass could be reduced at Class III wind sites. The overall cost of energy was reduced by only 1–2%, because the benefits of a reduced rotor mass are offset by a larger tower mass, required to maintain the overhang of the mass center in downwind configurations. They noted the potential to reduce the cost of energy by using downwind rotors, but also acknowledged that more studies are needed. In short, discussions on the downwind and load-alignment concepts are ongoing, and the shift to downwind designs will require more studies.

Inspired by the above studies on load-aligned or downwind concepts, the present paper puts forward a conceptual design, as shown in Figure 1. This concept actively cones the blade tip rather than the whole blade. When wind velocity increases from cut-in speed to rated speed, the blade tip cones further downwind to make the outer part of blade actively load-aligned. However, the inner part of blade is prebended to a fixed load-aligned shape and is fixed to the hub. The maximum thrust of the rotor normally appears near the rated power condition. This new concept can reduce the blade root flapwise bending moments with the alliance of a fixed load-aligned part and an actively load-aligned part. When the wind speed approaches the cut-off speed, the thrust force gradually decreases. Meanwhile, the rotor has a constant rotational speed and a constant centrifugal force, so that the blade tip can cone upwind slightly to meet the new load-aligned condition. Under extreme wind conditions such as typhoons, the blade tip will fold and pitch to a feathered state. This active tip-conning process consumes less energy than the original load-aligned concept [9,10] which cones the whole blade, and may consume a non-negligible amount of power [13]. Additionally, the new concept has a mass center closer to the tower which introduces smaller tower base moments than the original load-aligned concept; this is especially beneficial under very strong winds. Last but not least, the downwind concepts can extend the cut-off wind speed to a larger value (for example 30 m/s), as they have a larger tower-blade clearance compared to the upwind configuration.

**Figure 1.** New concept of a combination of a fixed and an active load-alignment: (**a**) blade shape under different wind conditions; (**b**) sketch of load-alignment.

The present paper mainly focuses on the aerodynamic aspects related to these designs. In [9–14], although different simulation tools were utilized, the aerodynamic computations were all based on Blade Element Momentum (BEM) theory. However, classical BEM theory is not suitable for coned rotors, especially with a large cone angle. Mikkelsen et al. [15] applied the traditional BEM method to a coned rotor. It was found that obvious errors appeared, even if a proper decomposition of the inflow velocity on coned blades was made. The inapplicability of the classical BEM method was also noted by Madsen et al. [16] and Crawford et al. [7,17]. Crawford corrected the BEM method by applying a vortex method as well as the proper decomposition of the inflow velocity in the rotor plan [17]. The conclusions in the above studies [9–14] contain strong uncertainties due to the application of classical BEM to coned rotors. So, it is of vital importance to accurately compare the aerodynamic characteristics of these designs, which is the foundation of all of these concepts. Nevertheless, aerodynamic research on coned, tilted and prebended rotors is very limited. Notably, computational fluid dynamics (CFD) methods with three dimensional (3D) body-fitted meshes are scarce. Actuator disc (AD) CFD methods are one of the commonly used numerical methodologies. Madsen and Rasmussen [18] compared four downwind rotors utilizing the AD CFD method, and found that the span-wise axial induction distributions and power coefficient were obviously influenced by the out of plane bending. With the help AD CFD, Mikkelsen et al. [15] also found a similar influence of coning on inducted velocities. It was also found that the upwind conning had a 2–3% higher power coefficient than the downwind configuration. However, AD-based methods are inherently coupled with BEM, which has some limitations. Winglets can be seen as partially coned blades. Farhan et al. [19] utilized a 3D CFD method to analyze the effect of winglets, observing that their influence extended to 30% of the radial sections. The phenomenon whereby the uncurved part of the blade was influenced by the deformed part was also observed in the study [18]. The Vortex Method (VM) can also be adopted to analyze such rotors. Chattot [20] utilized the VM method to investigate the influence of different blade tip configurations such as sweep, bending and winglets, and found that the whole blade was influenced by the curved part. Additionally, it was found that upwind prebending yielded increased power compared to the downwind configuration, which agreed with research presented in [15,18,19]. Further study is needed to understand the nonlinear behavior related to blade bending, as noted by Chattot [20]. Shen et al. [21] utilized the VM method to optimize rotor blades and found that the bended blade tip had an aerodynamic influence on the whole blade, and that this could not be accounted for using the traditional BEM method. Lastly, wind tunnel experiments could be conducted to explore these rotor concepts [22–24]. Due to their complexity, experiments to date have only investigated overall performance, such as thrust and torque, rather than span-wise force distribution. Therefore, dedicated CFD simulations are indispensable, especially on full-scale wind turbine rotors with 3D body-fitted meshes. Prebending has a continuously changing slope or cone angle, so it is hard to quantify its effects. Conning is the basis of prebending, and conning designs are suitable for parametric studies. In a previously published paper [25], the authors simulated different up/downwind conning and presented a preliminary aerodynamic analysis. The present paper will analyze the aerodynamic performance of different conning effects, such as inflow velocity decomposition and angle of attack analysis. Additionally, this paper will cover novel cones with three segments, which is a simplification and standardization of the new concepts shown in Figure 1.

The paper is organized as follows. In Section 2, the configurations of the cones and the employed numerical methods are presented. Results and discussions are given in Section 3. Finally, conclusions are drawn in Section 4.

#### **2. Modeling and Methods**

*2.1. Modelling of Different Cone Configurations*

In order to analyze the aerodynamic performance of the load-aligned concepts, different conning configurations were designed, as shown in Figures 2 and 3. These configura-

tions are transformed from the DTU-10-MW Reference Wind Turbine (RWT) [26,27] rotor, which is referred to as the baseline rotor, according to Equations (1) and (2). To focus on the effects of coning, a DTU-10-MW RWT without cone, tilt, prebend, nacelle or hub was used. At radial position *r*, coned configurations had their blade stacking lines translated out of the rotor plane with a displacement of *Zcone*.

$$Z\_{\rm cone} = \begin{cases} 0, & r \le T\_{\rm trans} R\\ (r/R - T\_{\rm trans}) R/C\_{\rm conv}, & r > T\_{\rm trans} R \end{cases} \tag{1}$$

where *R* is the rotor radius, *Ttrans* is the relative radial position where cone starts, and *Ccone* controls the slope of the stacking line. As shown in Figure 2a, *Ttrans* = 5/*R* means cone starting at 5 m, and *Ttrans* = 1/3 means cone starting at *R*/3. The cone angles are controlled by *Ccone*. When *Ccone* = ±4, ±8, the rotors have cone angles of ±14.0362◦, ±7.1250◦, respectively. A larger |*Ccone*| produces a smaller cone angle, and a positive *Zcone* makes a downwind cone. As shown in Figure 2b, several special coning configurations are shown, which are further coned at 2*R*/3. These special cone designs have an out of plane displacement of *Zcone*, as defined by Equation (2).

$$\mathbf{Z}\_{\text{conv}} = \begin{cases} 0, & r \le T\_{\text{trans}}R \\ (r/R - T\_{\text{trans}})R/\mathcal{C}\_{\text{conv}}, & T\_{\text{trans}}R < r < 2R/3 \\ (2/3 - T\_{\text{trans}})R/\mathcal{C}\_{\text{conv}}, & r \ge 2R/3, \text{ for S0} \\ (4/3 - T\_{\text{trans}} - r/R)R/\mathcal{C}\_{\text{conv}}, & r \ge 2R/3, \text{ for S1} \\ (2r/R - T\_{\text{trans}} - 2/3)R/\mathcal{C}\_{\text{conv}}, & r \ge 2R/3, \text{ for S2} \end{cases} \tag{2}$$

**Figure 2.** Conning configurations: (**a**) *Ttrans* = 5/R with *Ccone* = ±4, ±8 and *Ttrans* = 1/3 with *Ccone* = ±4; (**b**) special configurations abbreviated as C4S0, C4S1, C4S2, C4, C-4S0, C-4S1, C-4 S2 and C-4.

**Figure 3.** Down/upwind coned configurations with *Ccone* = ±4 and *Ttrans* = 1/3: (**a**) C4 and C-4; (**b**) C4S0 and C-4S0; (**c**) C4S1 and C-4S1; (**d**) C4S2 and C-4S2; (**e**) straight baseline.

In the rest part of the paper, a name abbreviation rule is applied for *Ttrans* = 1/3 configurations. *Ccone* = ±4 and *Ttrans* = 1/3 are named as C4 and C-4, respectively. Symbols S0, S1 and S2 are used to discriminate among the configurations at *r* > 2*R*/3. For example, the case of *Ccone* = ±4 and *Ttrans* = 1/3 followed by S2 is abbreviated as C4S2 and C-4S2, which have their blade tips farthest from the rotor plane. The symbol of S1 represents a reverse blade tip cone, such that C4S1 has its blade tip pointing to the upwind direction of a downwind cone at *r* < 2*R*/3. Lastly, the symbol S0 represents a zero cone angle at *r* > 2*R*/3. In short, C4 stands for downwind and C-4 for upwind, and S0, S1 and S2 represent blade tip configurations. For the sake of aerodynamic comparisons, all the configurations have the same projected areas and the same distribution of airfoil thickness, chord and twist. The shapes of different configurations are depicted in Figure 3, with the wind flow from the negative *Z* to the positive *Z*.

#### *2.2. Mesh Structure and CFD Method*

The baseline rotor has been studied elsewhere [26–28]; past studies provided references for the mesh configuration applied here. The mesh employed a commonly used O-O configuration with the surface mesh on one blade containing 256 points in the airfoil circumferential direction and 128 points in the span-wise direction. The volume mesh was expanded from the surface mesh to the far-field boundary (approximately 17R away) with 128 cells along the normal direction. To meet the computational requirement of Y + <2, the first cell height was 2 × <sup>10</sup>−<sup>6</sup> m. Finally, the grid was constructed with 432 blocks which contained 14.16 million structural cells in total. A similar mesh configuration is accurate enough to simulate the aerodynamic performance of the DTU 10 MW RWT rotor [26,28] which can be found on the DTU 10 MW RWT project website [27]. Such mesh settings were used for all the coned configurations in the present paper. The blade surface mesh of C4S1 is shown in Figure 4a, and the mesh distributions on two cross-sections are illustrated in Figure 4b,c.

**Figure 4.** Mesh around the blades: (**a**) blade surface mesh; (**b**) mesh on a section away from the near-blade blocks; (**c**) mesh on an airfoil cross-section in the near-blade region.

The flow state is treated as incompressible, and the turbulence flow is fully developed. The flow-field was solved by the Reynolds-Averaged Navier-Stokes (RANS) equations with the *k* − *ω* SST turbulence model [29]. The SIMPLE algorithm was utilized to couple the pressure and velocity equations. EllipSys3D, developed by the Technical University of Denmark and widely validated over the past 20 years, was used as the CFD solver. Detailed descriptions of the solver can be found in [26,30]. Additionally, detailed boundary condition descriptions and baseline rotor validation can be found in a previous publication [25], where the same numerical methods were adopted. At a wind speed of 12 m/s, few force differences appeared between steady and unsteady simulations in the root region (*r* < *R*/3) where flow separations and 3D rotational augmentations were expected [28]. The forces along the outer part of blade remained identical. In this paper, steady CFD simulations were performed to investigate the influence of coning at a wind speed of 9 m/s, i.e., at which the unsteady effects were negligible. The operational parameters of the baseline rotor, listed in Table 1, were applied for all the coned configurations.

**Table 1.** The operational parameters.


#### **3. Results and Discussions**

In this section, the aerodynamic performance of the coned DTU 10 MW rotor, coning at a blade position near the root (*Ttrans* = *5/R*), is presented. In order to explain the physics behind the coned rotor, the concept of angle of attack (AOA) on the rotor blade sections was extended to include coned rotors. The results are discussed through the concept of angle of attack.

*3.1. Four Configurations of Coning Near the Root: Ttrans = 5/R and Ccone =* ±*4,* ±*8*

#### 3.1.1. Force Performances

Firstly, the overall aerodynamic performance of the configurations presented in Figure 2a are compared. The two configurations of *Ccone* = ± 4 and *Ttrans* = 1/3 also appear in Figure 2b, where they are abbreviated as C4S2 and C-4S2. These configurations are not discussed here, and will be explored in Section 3.2. In Table 2, the thrust *T* and torque *Q* of the other four configurations in Figure 2a are listed. As high torque and low thrust are beneficial, the torque-to-thrust ratio (*QT*) was used to compare different conning configurations. The relative variations of these parameters are denoted as *δT*, *δQ* and *δQT*; for example, δ*T* means

$$\delta = \frac{|\ T \mid\_{con} - \mid T \mid\_{straight}}{|\ T \mid\_{straight}} \times 100\% \tag{3}$$


**Table 2.** Thrust and torque of different configurations (Ttrans = 5/*R*).

The most upwind-coned configuration *Ccone* = −4 gives the lowest thrust, i.e., 4.53% lower than that of the baseline without coning. Although *Ccone* = −4 reduces the torque by 1.07% compared with the baseline, it has the highest *QT* due to the obvious decline of thrust. The downwind counterpart *Ccone* = 4 produces the highest *T*, lowest *Q*, and lowest *QT*, which is unfavorable. Among the pair of *Ccone* = ±8, the upwind configuration also has a smaller *T*, a higher *Q* and a higher *QT* than the downwind counterpart.

To understand the overall performance differences shown in Table 2, the tangential and axial force per unit span length is shown in Figure 5. The axial force *Fz* is parallel to the rotor axis, and the tangential force *Ft* is perpendicular to *Fz*. The aforementioned forces are the summation of all the three blades. Near the blade tip, the upwind configurations had a larger *Ft* and *Fz* than the downwind counterparts. For example, the *Ft* and *Fz* curves of *Ccone* = −4 were higher than those of *Ccone* = 4. Towards the blade root, the situation reversed, i.e., the upwind configurations had a lower *Ft* and *Fz*. For the distribution of *Ft*, the upwind and downwind counterparts had an almost reversed *Ft* distribution of the baseline rotor with straight blades. The upwind configurations had a higher *Ft* near the blade tip, which is more beneficial to an increase of torque. As a result, the torque of *Ccone* = −4 and −8 was slightly higher than *Ccone* = 4 and 8, as listed in Table 2. However, all four coned configurations had a smaller torque than the baseline. For the distribution of *Fz*, the baseline did not lie in the middle of an up/downwind pair, especially toward the blade tip. Although upwind lines gradually surpassed their downwind counterparts and approached the baseline near the blade tip, they barely went above the baseline. The largest upwind cone *Ccone* = −4 showed the overall lowest *Fz*, which was consistent with the results shown in Table 2. It is difficult to understand why the force distribution behaved like this, so more analyses are needed.

**Figure 5.** Force distributions along radial direction: (**a**) tangential force; (**b**) axial force.

#### 3.1.2. Flow Field Analysis

Analyzing the flow field around a wind turbine, such as inflow velocity and angle of attack (AOA), may help to understand the force distributions mentioned above. The inflow velocity decomposition for the upwind and downwind coned rotors is illustrated in Figure 6. This decomposition was made in the *YZ* plane, which contained the rotor axis and the pitch axis of a blade. The unit vectors *z*, *r*, *s* and *n* were along the axial, radial, span-wise and normal directions, respectively. At a far upstream position, the axial velocity was *V0*, the normal velocity component was *V*0cos*β*, and the radial velocity was zero. Towards the rotor, the axial and normal velocity decreased and the radial velocity increased. Arriving at the rotor, the axial and normal velocity was reduced to *V*0-*Wz*, *V*0cos*β*-*Wn*, and the radial velocity increased to *Vr*. Here, *Wz* is the axial induction velocity at the aerodynamic center (AC) and *Wn* is the normal induction velocity at AC.

**Figure 6.** Inflow velocity decomposition for an upwind and a downwind coned rotor.

Due to the presence of *Vr*, the resultant velocity *Vinflow* in the *YZ* plane was not horizontal and did not equal to *V*0-*Wz*, as shown in Figure 6. The velocity decomposition was different for the upwind and downwind coned configurations. For an upwind cone configuration, projecting the resultant velocity *Vinflow* to the normal component was different to that on a downwind counterpart, as the projection angle *γ* was different. However, the radial velocity component is omitted in the traditional BEM method because there is no equation to describe the radial flow. Then, it was assumed that the inflow velocity *Vinflow* would be along the axial direction and would be equal to *V*0-*Wz*. When projecting the inflow velocity *Vinflow* to the normal component, the projection angle *γ* equaled the cone angle *β*. Thus, the upwind and downwind pair had the same value of cos*β*, *Fn* and *Fz*. In short, the traditional BEM methods cannot distinguish the upwind and downwind coning, which is clearly in contrast with reality.

Another way to analyze the flow is to use the concept of angle of attack, which is conducted on the planes perpendicular to the blade spanwise direction. At present, difficulties or uncertainties remain in the extraction of AOA from 3D CFD simulations or experiments, which is different from that in the 2D situations. There are different kinds of methods to extract AOA from CFD data, which are thoroughly discussed and compared in [31,32]. Most methods predicted similar AOA at midspan, but it should be kept in mind that the results near the blade root and tip varied from one method to another. The Average Azimuthal Technique (AAT) [31–33], proposed by Hansen et al. [33], was used in the present paper. At a given rotor radius, AAT extracts the inflow velocity on two circles which are just upstream and downstream of the rotor, as shown in Figure 7a. The number of points on a circle is 72 in the present study. AAT estimates the velocity at AC by averaging the up- and down- stream data, and then calculates AOA using Equation (4). However, Equation (4) is only applicable for straight blades without cones. A general form of AOA, which is suitable for coned rotor analyses, is Equation (5).

$$\alpha\_{z} = \tan^{-1}(\frac{Vz}{Vt}) - \theta = \tan^{-1}(\frac{V\_0 - Wz}{Vt}) - \theta \tag{4}$$

$$\alpha\_n = \tan^{-1}(\frac{Vn}{Vt}) - \theta = \tan^{-1}(\frac{V\_0 \cos \beta - Wn}{Vt}) - \theta \tag{5}$$

where *Vz* is the estimated axial velocity at AC, *Vn* is the estimated normal-wise velocity at AC, *Vt* is the estimated tangential velocity at AC, and *θ* is the local pitch angle. When applied to straight blades without a cone, Equation (5) is reduced to Equation (4), because *Vn* becomes *Vz*. As most studies available on AOA extraction are for straight blades without coning, Equation (4) is commonly used. To extract AOA, the distance from AC to the up-/down- stream annulus was set to one local chord length *C*, as shown in Figure 7b, where the axial velocity in the *YZ* plane is also illustrated.

**Figure 7.** Sketch of points used by AAT to extract AOA: (**a**) straight baseline; (**b**) coned rotor.

The streamlines in the *YZ* plane of the two coned configurations are drawn in Figure 8, where the axial velocity contour is also shown. The streamlines of the downwind coned case in Figure 8b were more up-pointing than those of the upwind coned case in Figure 8a. Especially near the blade tip, the upwind cone had a smaller projection angle *γ* and had streamlines which were more perpendicular to the blade. When projecting the real inflow velocity *Vinflow* in direction *n*, the upwind coned rotor had a smaller *Vn* value, even if with the same *Vinflow* value. Therefore, it is more straight forward to analyze *αn*, which reveals the inflow condition in the normal-wise *Xn* plane.

**Figure 8.** Streamlines in the YZ plane with axial velocity contours for the two coned configurations: (**a**) upwind coned rotor of *Ttrans* = 5/*R*, *Ccone* = −4; (**b**) downwind coned rotor of *Ttrans* = 5/*R*, *Ccone* = 4.

To explore the mechanism behind the interesting force distributions shown in Figure 5, the distribution of *α<sup>z</sup>* and *α<sup>n</sup>* are compared in Figure 9. It was found that the *α<sup>z</sup>* of an upwind cone is always smaller than its downwind counterpart, which is not consistent with the force distributions. Interestingly, the *α<sup>n</sup>* curve of the upwind cone intersected with its downwind counterpart. Near the blade root, downwind configurations had a larger *α<sup>n</sup>* than their upwind counterparts, which indicated larger thrust and tangential force. Towards the blade tip, the downwind coning made the *α<sup>n</sup>* gradually decrease below that of upwind cone, which was consistent with the force distribution. Additionally, as shown in Figure 5, there was a phenomenon whereby an up/downwind pair had an almost reversed *Ft* distribution relative to the baseline, but had a less symmetric distribution of *Fz* curves, especially towards the tip. A reasonable explanation is given below. The upwind cone had

a slightly larger *α<sup>n</sup>* than the straight baseline toward the blade tip, and therefore, also had a larger *Fn*, which is the normal force parallel to *n*, as shown in Figure 6. But the force *Fz* in Figure 5b was along the axial direction, which has a relationship with *Fn* as follows:

$$Fz \cdot dr = Fn \cdot \cos \beta \cdot dr \tag{6}$$

͕

where the force along the span-wise direction is usually small and thus neglected. Although *Fn* of the upwind coning was slightly larger than the baseline near the tip, after projecting *Fn* to *Fz*, the *Fz* may have been smaller than the baseline, as shown in Figure 5. It is known that a cone angle always leads to a cos*β* which is smaller than one; however, there is no projection process for the tangential force *Ft*. Therefore, the *Ft* curves of the upwind cone shown in Figure 5 could be higher than the baseline curves, which follow the *α<sup>n</sup>* curves more closely. Lastly, uncertainties still lie in the extraction of AOA, especially near the blade tip [31,32], but it is clear that this provides a view to explain the force distribution shown in Figure 5.

**Figure 9.** Distributions of angle of attack: (**a**) *αz*; (**b**) *αn*.

To validate the extracted *α<sup>n</sup>* in Figure 9, streamlines and pressure plots around the normal blade section at *r* = 77.59 m are shown in Figure 10. This slice was normalcutting, which was parallel to the normal-wise *Xn* plane. It was found that the three airfoil sections were all in an attached flow condition. The *α<sup>n</sup>* of these three configurations could be approximately compared by analyzing the slopes of the streamlines ahead of the leading edge. As the slopes of the streamlines in Figure 10a–c only had minor differences, representative streamlines near the stagnation point were extracted from Figure 10a–c and compared in Figure 10d. It is shown that the upwind coning had a slightly larger *α<sup>n</sup>* than the downwind counterpart, which was consistent with the findings shown Figure 9b; meanwhile, the straight baseline lies in the middle. Additionally, it was clear that the upwind configuration had a lower pressure on the suction-side leading edge than its downwind counterpart, which was in agreement with the larger force of the upwind coning described in Figure 5.

**Figure 10.** Streamlines and pressure on *r* = 77.59 m normal-cut plane: (**a**) upwind coning of *Ttrans* = 5/*R*, *Ccone* = −4; (**b**) straight baseline; (**c**) downwind coning of *Ttrans* = 5/*R*, *Ccone* = 4; (**d**) comparisons of streamlines near stagnation points.

*3.2. Special Coned Configurations: C4S0, C4S1, C4S2, C4, C-4S0, C-4S1, C-4 S2 and C-4*

#### 3.2.1. Overall Force Performance

Configuration C-4S2 gives the lowest thrust among the cases listed in Table 3, i.e., 7.30% lower than the baseline rotor. C-4S2 had the largest blade tip offset among the upwind configurations. Although C-4S2 reduced the torque by 1.96%, it still had the largest torque-to-thrust ratio *QT* due to the large reduction of thrust. The downwind counterpart C4S2 produced the lowest *Q* and the lowest *QT*, which was unfavorable. The upwind configuration surpassed its downwind counterpart, as also revealed in the pairs of C4 and C-4, C4S0 and C-4S0. For these pairs, the upwind coned rotors had a smaller *T*, a larger *Q* and a higher *QT* than their downwind coned counterparts. However, for the pairs C4S1 and C-4S1, the downwind configuration C4S1 had a higher *QT*. Interestingly, the blade tip of the downwind configuration C4S1 was pointing upwind, which may be the reason why C4S1 had a higher *QT*. Lastly, it should also be noted that the radial velocity component is omitted in the traditional BEM method. Therefore, the same results will be obtained for an upwind configuration and its downwind counterpart, such as C4S2 and C-4S2, which is clearly in contrast with reality. In Table 3, it may be seen that the thrust discrepancy between C4S2 and C-4S2 reached nearly 8%. The torque discrepancy was approximately 5%. These results reveal that the inaccuracies of traditional BEM methods are not negligible, making the conclusions from [9–14] in Section 1 disputable.

**Table 3.** Thrust and torque of different configurations.


3.2.2. Distributed Force Performances

The axial force *Fz* and tangential force *Ft* per unit length are compared in Figure 11. Figure 2b is redrawn in Figure 11a, where the upwind configurations are denoted by the dashed lines and downwind by the dotted lines. Clearly, C4S0 and C-4S0 had the same configuration as the straight baseline when *r* > 2*R*/3, or in other words, without coning. As a result, the *Ft* and *Fz* curves of C4S0, C-4S0 and the straight baseline were very close. In the same spanwise range, C4 and C-4S1 had the same cone angle, as did C-4 and C4S1. Correspondingly, the same cone angle led to close *Ft* and *Fz* curves. The discrepancy between the close curves increased towards *r* = 2*R*/3, because the coning point at *r* = 2*R*/3 distorted the nearby flow. In short, the same cone angle near the tip will lead to close force distribution.

**Figure 11.** Comparison of special coning: (**a**) redrawn of special cone configurations; (**b**) tangential force; (**c**) axial force; (**d**) zoomed view of axial force.

When *R*/3 < *r* < *2R/3*, the four configurations C4S2, C4, C4S0, C4S1 had the same cone angle as shown in Figure 11a. Additionally, their counterparts C-4S2, C-4, C-4S0, C-4S1 had the same cone angle as well. However, none of the *Ft* and *Fz* curves coincided, even if the same cone angles existed, as shown in Figure 11b,c, which indicated that the cone effect in this range was not solely controlled by the cone angle itself. Additionally, traditional BEM methods will predict the same force distribution under the same cone

angle, which implies that such an approach is not applicable here. When *r* < *R*/3, all the cone configurations coincided with the straight baseline. However, only C4S1 and C-4S1 had close force distributions comparable to the straight baseline. The force distribution of C ± 4S2, C ± 4 and C4 ± S0 varied from configuration to configuration. It was found that C4S1 and C-4S1 were totally different cone configurations at *r* > *R*/3, but that they had the same blade tip position as the straight baseline. This implies that the influence of the coned part on the straight part is mostly determined by the blade tip position. Traditional BEM will predict the same force distribution again, or fail at *r* < *R*/3, even if all the configurations have a zero cone angle.

There are many interesting phenomena between the curves in Figure 11. Looking closely at group C4S2, C4, C4S0, and C4S1, the *Ft* and *Fz* curves (especially *Ft* lines) are nearly parallel with each other in the range of *R*/3 < *r*< 2*R*/3. The case C4S2 had the highest force curves, and C4, C4S0, and C4S1 had successively lower forces. Coincidently, this was consistent with the successively upstream-moving of the tip positions from *Z* = 3*Ztip* to 2*Ztip*, *Ztip* and 0 m (*Ztip* = 7.4292 m). If the blade tip is located at a more upstream position, it will cause the blade sections to be further immersed in the wake, which will lead to a stronger axial induction velocity *Wz*, a smaller axial inflow velocity, and a lower *α<sup>z</sup>* and *αn*. The variation of *α<sup>z</sup>* and *α<sup>n</sup>* will be validated later in Section 3.2.3. In short, the upwind transformation of the blade tip is consistent with the successive reduction of the *Fz* and *Ft* curves. Focusing on the four counterparts, C-4S2, C-4, C-4S0, and C-4S1, the curves were nearly parallel and successively ascending with the downstream-moving of the blade tips. Transforming the blade tip into a further downstream position, the blade sections immerse less heavily into the tip vortex trace, leading to a smaller *Wz* and a higher *αn*. Additionally, the nearly parallel curves of C4S2, C4, C4S0, and C4S1 had different slopes compared with those of C-4S2, C-4, C-4S0, and C-4S1, and apparently different slopes compared with the baseline rotor.

#### 3.2.3. Flow Field Analysis

To understand the force characteristics presented in Section 3.2.2, further flow field analyses were carried out. Firstly, the streamline and the axial velocity contour in the *YZ* plane of C ± 4S2, C ± 4S0, and C ± 4S1 are shown in Figure 12. In the range of *R*/3 < *r* < 2*R*/3, the downwind cone C4S2 shown in Figure 12a had obviously lower velocity in the near wake region than that of C-4S2 shown in Figure 12b. This revealed that more energy was extracted by C4S2, which is consistent with the higher thrust force in Figure 11. Additionally, the downwind C4S2 had slightly larger wake expansion, which means a larger radial velocity. If the three figures on the left hand side are compared, the wake deficit is weaker and weaker when the blade tip is successively moving upstream from Figure 12a to Figure 12c,e. This means that the energy extracted by the rotor was progressively smaller, which is in agreement with the successive decline in the *Ft* and *Fz* curves in the range *R*/3 < *r* < 2*R*/3 in Figure 11. If the right hand side figures are compared, the wake deficit becomes stronger when the blade tip transforms downstream. This also confirms the successive increases in the *Ft* and *Fz* curves from C-4S2 to C-4S0 and then C-4S1. In the range *r* > 2*R*/3, the streamlines of C4S1 and C4S2 were the most and the least perpendicular streamlines *w.r.t.* to the blade, respectively, which led to the largest and smallest *Fn*. But, as shown in Equation (6), the large cone angle *β* reduces the value of *Fz*, which causes the *Fz* of C4S1 to barely surpass the baseline.

Utilizing the AAT AOA-extraction method introduced in Section 3.1.2, the *α<sup>z</sup>* and *α<sup>n</sup>* at different radial positions are compared in Figure 13. In the range of *r* > 2*R*/3, the *α<sup>z</sup>* and *α<sup>n</sup>* of C4S0 and C-4S0 nearly coincided with the straight baseline, which was consistent with the close *Ft* and *Fz* curves, as shown in Figure 11. This was because the three configurations were all without coning. What is more, C4 and C-4S1 had the same cone angle, which led to close *α<sup>n</sup>* distributions. Similarly, C-4 and C4S1 also had close *α<sup>n</sup>* distributions. In the range of *R*/3 < *r* < *2R/3*, the four configurations, C4S2, C4, C4S0 and C4S1, had nearly parallel *α<sup>n</sup>* curves. The *α<sup>n</sup>* line of C4S2 was the highest, and C4, C4S0 and C4S1 had successively lower curves, which matched the successive decreases of the *Ft* and *Fz* curves in Figure 11. As discussed in Section 3.2.2, this was caused by the upstream movement of the tip positions, which made caused the blade sections to be further immersed into the wake, leading to decreases in *α<sup>z</sup>* and *αn*. In contrast, focusing on the group C-4S2, C-4, C-4S0, and C-4S1, the *α<sup>n</sup>* curves successively ascended with the downstream movement of the blade tips. In the range of *r* < *R/3*, C4S1 and C-4S1 had similar *α<sup>z</sup>* and *α<sup>n</sup>* distributions to the straight baseline. This was because the three configurations had the same blade tip position, although distinctly different cones appeared at *r* > *R*/3. Generally speaking, the *α<sup>n</sup>* distributions matched the force distributions in Figure 11. It is clear that the *α<sup>n</sup>* distributions can reveal the mechanism of force distributions on coned sections, even if the blades are coned into three parts. Additionally, correctly commutating *α<sup>n</sup>* is of vital importance for improving the traditional BEM method, although further discussion of this is beyond the scope of this paper.

**Figure 12.** Streamline in the YZ plane with axial velocity contours: (**a**) C4S2; (**b**) C-4S2; (**c**) C4S0; (**d**) C-4S0; (**e**) C4S1; (**f**) C-4S1.

**Figure 13.** Distributions of angle of attack: (**a**) *αz*; (**b**) *αn*.

#### **4. Conclusions**

In future designs of super-large wind turbines, the question of being upwind or downwind will be an important one for the wind energy industry. The present paper put forward a conceptual design consisting of an actively load-aligned blade tip and a fixed load-aligned blade root. In order to evaluate the advantages and disadvantages of these concepts, it is of vital importance to carefully select appropriate tools. Different conning configurations, including special cones with three segments, were simulated and analyzed based on a 10 MW reference rotor. The results provide knowledge regarding the complex force distributions of these configurations, and could serve to improve the traditional BEM on traditionally or specially coned rotors.

Up- and down- wind coning approaches yield different aerodynamic performance, e.g., in their total integrated loading, distributed force, and flow fields. The force distributions and their differences may be explained by the concept of the angle of attack. It was found that parameters which have the greatest influence on the angle of attack are the position of blade tip and the cone angle. The blade tip position determines the induction velocity contour, and subsequently, the inflow velocity at the blade sections. With the upstream movement of the blade tip, blade sections away from the tip will be immersed more heavily in the tip vortex trace. Then, the blade sections will suffer from stronger axial induction, smaller axial inflow velocity, a lower angle of attack, and consequently, a lower force distribution. The downstream movement of the blade tip has the opposite effect. The cone angle determines the velocity and force projecting process from the axial to the normal direction, which influences the thrust and tangential forces in the normal and axial directions. The correct inflow velocity decomposition, which connects the axial and normal directions, is indispensable. The same relative blade tip position and cone angle will result in the same force; however, applying the same tip position or cone configuration alone does not guarantee the same aerodynamic performance.

The aerodynamic performance discrepancy between an upwind cone and its downwind counterpart is significant. In the present study, the most upwind and downwind cones had a thrust difference up to 8% and a torque difference of up to 5%. Nevertheless, the traditional BEM method could not differentiate an upwind cone from its downwind counterpart under the same chord, twist and airfoil distributions. Many studies on loadaligned concepts or comparing upwind/downwind designs have utilized tools based on traditional BEM, which arguably makes their conclusions disputable. A correction to the traditional BEM method must be made before it can be used to assess new cone concepts. Such an improved BEM should consider the influence of blade tip position and cone angle, and adopt the corrected inflow velocity decomposition. To date, debate over

up- or down-wind coning is ongoing. The design and optimization of super-large coned rotors still has a long way to go.

**Author Contributions:** Conceptualization, Z.S. and W.Z.; methodology, Z.S. and W.Z.; software, W.S. and W.Z.; validation, Z.S., W.Z. and W.S.; formal analysis, Z.S., W.Z., W.S. and Q.T.; investigation, Z.S.; resources, W.Z. and W.S.; data curation, Z.S., Q.T., J.C., X.L. and W.S.; writing—original draft preparation, Z.S., W.Z. and W.S.; writing—review and editing, Z.S., W.Z. and W.S.; visualization, Z.S.; supervision, W.Z. and W.S.; project administration, W.Z.; funding acquisition, Z.S. and W.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Nature Science Foundation of China under grant number 51905469 and 11672261; the National key research and development program of China under grant number 2019YFE0192600; the Nature Science Foundation of Yangzhou under grant number YZ2019074; an open funding from Shanxi Key Laboratory of Industrial Automation under grant number SLGPT2019KF01-13.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to restrictions eg privacy or ethical. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the large volume of CFD data.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine**

#### **Qiang Wang 1, Kangping Liao 1,\* and Qingwei Ma <sup>2</sup>**


Received: 16 May 2020; Accepted: 1 August 2020; Published: 4 August 2020

#### **Featured Application: This research has certain reference significance for improved wind turbine performance. It can also provide reference value for wind shear related study.**

**Abstract:** Aerodynamic performance of a wind turbine at different tilt angles was studied based on the commercial CFD software STAR-CCM+. Tilt angles of 0, 4, 8 and 12◦ were investigated based on uniform wind speed and wind shear. In CFD simulation, the rotating motion of blade was based on a sliding mesh. The thrust, power, lift and drag of the blade section airfoil at different tilt angles have been widely investigated herein. Meanwhile, the tip vortices and velocity profiles at different tilt angles were physically observed. In addition, the influence of the wind shear exponents and the expected value of turbulence intensity on the aerodynamic performance of the wind turbine is also further discussed. The results indicate that the change in tilt angle changes the angle of attack of the airfoil section of the wind turbine blade, which affects the thrust and power of the wind turbine. The aerodynamic performance of the wind turbine is better when the tilt angle is about 4◦. Wind shear will cause the thrust and power of the wind turbine to decrease, and the effect of the wind shear exponents on the aerodynamic performance of the wind turbine is significantly greater than the expected effect of the turbulence intensity. The main purpose of the paper was to study the effect of tilt angle on the aerodynamic performance of a fixed wind turbine.

**Keywords:** wind turbine; tilt angle; unsteady aerodynamics; computational fluid dynamics

#### **1. Introduction**

The use of wind energy has increased over the past few decades. Today, wind energy is the fastest growing renewable energy source in the world [1]. Despite the amazing growth in the installed capacity of wind turbines in recent years, engineering and science challenges still exist [2]. The main goals in wind turbine optimization are to improve wind turbine performance and to make them more competitive on the market. Studies have shown that the wind turbine tilt angle affects the shear force and bending moment at the tower top and the blade root [3], and the interaction between the blade and the tower also affects the aerodynamic performance of the wind turbine [4]. Therefore, it is necessary to study the effect of tilt angle on wind turbine performance and analyze the characteristics of blade–tower interaction, aiming to improve the wind turbine performance.

In recent years, more and more scholars have been paying attention to the interaction between the blades and towers of wind turbines. Kim et al. [4] studied the interaction between the blade and the tower using the nonlinear vortex correction method. They concluded that as the yaw angle and wind shear exponent increase, the interaction between the blade and the tower decreases. The influence of the tower diameter on the interaction between the blades and the tower is higher than that of the tower clearance. Meanwhile, this interaction may increase the total fatigue load at low wind speed. Guo et al. [5] used blade element moment (BEM) theory to study the interaction between the blade and tower. Their results show that the blade–tower interaction is much more significant than that of the wind shear. Wang et al. [6] researched the blade–tower interaction using computational fluid dynamics (CFD). Their research shows that the influence of the tower on the total aerodynamic performance of the upwind wind turbine is small, but the rotating blade will cause an obvious periodic drop in the front pressure of the tower. At the same time, we can see the strong interaction of blade tip vortices. Narayana et al. [7] researched the gyroscopic effect of small-scale wind turbines. Their findings show that changing the tilt angle can improve the aerodynamic performance of small-scale wind turbines. Recently, Zhao et al. [3] proposed a new wind turbine control method. In their control method, tilt angle increases as wind speed increases, with the purpose of reducing the blade loading and maintaining the power of the wind turbine at high wind speeds. Their research shows that the new control method can reduce the shear force at the top and bottom of the tower when compared with the yaw control strategy.

Many researchers have studied the effect of tilt angle on the structural performance of a wind turbine. For example, Zhao et al. [8] studied the structural performance of a two-blade downwind wind turbine at different tilt angles. However, there is little research on the effect of tilt angle on the aerodynamic performance of wind turbines. In this paper, aerodynamic performance of a wind turbine at different tilt angles is studied. All simulations are performed in CFD software STAR-CCM+ 12.02. Through a comparison of aerodynamic performance of the wind turbine at different tilt angles, the effects of tilt angle on the thrust, power and wake of the wind turbine are studied.

#### **2. Numerical Modeling**

#### *2.1. Physical Model*

In this study, the governing equation uses the unsteady Reynolds-averaged Navier–Stokes equation. The *SST k* − ω turbulence model was used in current simulations. A separated flow model was used to solve the flow equation. SIMPLE solution algorithm was used for pressure correction. Convection terms used the second-order upwind scheme. In the unsteady simulation, the time discretization used the second-order central difference scheme. In addition, due to the sliding mesh approach, no hole cutting was necessary, making the calculations more efficient than with the use of an overset mesh. Thus the sliding mesh technique was used to handle rotating motion of a blade [9].

#### *2.2. Turbulence Model*

The *SST k* − ω turbulence model can consider the complex flow of the adverse pressure gradient near the wall region and the flow in the free shear region. Thus, the *SST k* − ω turbulence model is suitable for simulating the rotational motion of the blade [10]. In addition, this turbulence model can accurately capture wind turbine wake [11,12].

In the Reynolds-averaged N-S equations, τ*ij* = −ρ*u i u <sup>j</sup>* refers to the Reynolds stress tensor. Reynolds stress tensor and mean strain rate tensor (*Sij*) are related by the Boussinesq eddy viscosity assumption:

$$
\pi\_{i\bar{j}} = 2\nu\_t \mathcal{S}\_{i\bar{j}} - \frac{2}{3}\rho k \delta\_{i\bar{j}} \tag{1}
$$

where ν*<sup>t</sup>* refers to the eddy viscosity, ρ refers to the density, *k* refers to the turbulence kinetic energy and δ*ij* refers to the Kronecker delta function.

To provide closure equations, in the *SST k* − ω turbulence model, the turbulent kinetic energy (*k*) and specific dissipation of turbulent kinetic energy (ω) also need governing transport equations, which are given as follows:

$$\frac{D\rho k}{Dt} = \tau\_{ij}\frac{\partial u\_i}{\partial \mathbf{x}\_j} - \beta^\* \rho \alpha k + \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \sigma\_k \mu\_t) \frac{\partial k}{\partial \mathbf{x}\_j} \right] \tag{2}$$

$$\frac{D\rho\omega}{Dt} = \frac{\mathcal{V}}{\mathbf{v}\_{\mathrm{f}}}\tau\_{i\bar{j}}\frac{\partial\mathbf{u}\_{\mathrm{i}}}{\partial\mathbf{x}\_{\mathrm{j}}} - \beta\rho\omega^{2} + \frac{\partial}{\partial\mathbf{x}\_{\mathrm{j}}}\bigg[ (\mu + \sigma\_{w}\mu\_{\mathrm{f}})\frac{\partial\omega}{\partial\mathbf{x}\_{\mathrm{j}}} \bigg] + 2(1 - F\_{1})\rho\sigma\_{w2}\frac{1}{\omega}\frac{\partial\mathbf{k}}{\partial\mathbf{x}\_{\mathrm{i}}}\frac{\partial\omega}{\partial\mathbf{x}\_{\mathrm{j}}} \tag{3}$$

In the formulas above, the model coefficients are defined as follows:

$$
\beta^\* = F\_1 \beta\_1^\* + (1 - F\_1) \beta\_2^\* \tag{4}
$$

$$
\beta = F\_1 \beta\_1 + (1 - F\_1) \beta\_2 \tag{5}
$$

$$
\gamma = F\_1 \gamma\_1 + (1 - F\_1)\gamma\_2 \tag{6}
$$

$$
\sigma\_k = F\_1 \sigma\_{k1} + (1 - F\_1) \sigma\_{k2} \tag{7}
$$

$$
\sigma\_{\omega^{\flat}} = F\_1 \sigma\_{\omega 1} + (1 - F\_1) \sigma\_{a2} \tag{8}
$$

The blending function *F*<sup>1</sup> is defined as follows:

$$F\_1 = \tanh\left\{ \left\{ \min \left[ \max \left( \frac{\sqrt{k}}{\beta^\* \omega y}, \frac{500 \nu\_{\infty}}{y^2 \omega} \right), \frac{4 \rho \sigma\_{a2} k}{\mathrm{CD}\_{k\omega} y^2} \right] \right\}^4 \right\} \tag{9}$$

where *CDk*<sup>ω</sup> refers to the cross-diffusion term, y refers to the distance to the nearest wall and υ refers to the kinematic viscosity. *F*<sup>1</sup> is equal to zero in the region away from the wall (*k* − ε turbulence model) and one in the region near the wall (*k* − ω turbulence model).

The eddy viscosity is

$$\nu\_t = \frac{a\_1 k}{\max(a\_1 \omega, \Omega F\_2)} \tag{10}$$

where Ω is the absolute value of the vorticity and *F*<sup>2</sup> is the second blending function, defined as

$$F\_2 = \tanh\left[\max\left(\frac{2\sqrt{k}}{\beta^\*\omega y}, \frac{500\nu}{y^2\omega}\right)^2\right] \tag{11}$$

A more detailed description of the *SST k* − ω turbulence model is provided in [10]. In this study, the parameters for the *SST k* − ω turbulence model are as follows:

$$\begin{array}{ccccccccc} \sigma\_{k1} & 0.85 & \sigma\_{\omega 1} & 0.5 & \beta\_1 & 0.075 & a\_1 & 0.31 & \beta^\* & 0.081 & 0.05 & 0.05 & 0.05 \\ \sigma\_{\omega 2} & 0.856 & \beta\_2 & 0.0828 & \gamma\_1 & \frac{\beta\_1}{\beta^\*} - \frac{\varepsilon\_{\omega k} k^2}{\sqrt{\beta^\*}} & \gamma\_2 & = \frac{\beta\_2}{\beta^\*} - \frac{\varepsilon\_{\omega k} k^2}{\sqrt{\beta^\*}} & & & & & & & & & & & \end{array}$$

#### *2.3. Computational Domain*

The computational domain was divided into the rotating and outer domains, as shown in Figure 1. The size of the entire outer domain was 12D(x) × 5D(y) × 4D(z). The distance from the wind turbine to the velocity inlet was 3D, and the distance to the pressure outlet was 9D, where D is the diameter of the wind turbine. Due to the complex geometry of the blades, we used the trimmed cell mesh technology to generate high-quality meshes. In order to capture the complex flow around the blade, a fine mesh was used around the blade. A 10-layer boundary layer mesh was generated near the blade and the hub. The total thickness of the boundary layer was 0.03 m, and the growth rate was 1.2. A six-layer boundary layer mesh was generated near the tower and the nacelle. The total thickness of the boundary layer was 0.1 m, and the growth rate was 1.2. Figure 2b shows the refined sliding mesh regions around the blade. Figure 2c,d shows a close-up view of the blades and nacelle tower.

**Figure 1.** Rotating and outer domain: (**a**) rotation domain for wind turbine simulation; (**b**) entire computational domain for numerical simulation.

**Figure 2.** The computational mesh domain for the wind turbine: (**a**) full grid domain, (**b**) sliding mesh regions, (**c**) close-up view of the blade surface, (**d**) close-up view of the hub surface mesh and (**e**) close-up view of nacelle and tower.

#### *2.4. Boundary Conditions*

Figure 2a illustrates the setting of the boundary conditions in this study. In the computational domain, the inlet boundary, bottom and top surfaces were set as velocity inlets. The pressure outlet was set at the outlet boundary. The sides of the computational domain were set to the plane of symmetry. In this simulation, all of the y+ wall treatment of near-wall modeling was applied. In order to reduce

the convergence order and improve the solution accuracy, the maximum internal iterations within each time-step was 10 [13].

#### **3. Results and Discussion**

#### *3.1. Validations*

The 1/75 scale model of a DTU 10 MW reference wind turbine was used for the mesh independence test. In the numerical verification, the tilt angle of the wind turbine was not considered. The main parameters of the scale model are given in Table 1. A detailed introduction of the blade parameters at 40 different blade sections is provided by [14]. Figure 3 shows the wind turbine geometric model and the surface grid. After scaling according to the scale factor, the boundary layers near the blade and hub surface have five layers of refined grid with the total layer thickness of 0.004 m and a progression factor of 1.2.

**Table 1.** Principal dimensions of the scale model.

**Figure 3.** Geometric model and surface grid: (**a**) the rotor geometric model; (**b**) the blade surface grid.

The blade surface mesh size includes the maximum mesh size and the minimum mesh size. The number of meshes corresponding to different mesh sizes is shown in Table 2. According to previous study, the time-step size corresponding to 1◦ increment of azimuth angle of the wind turbine per time-step was applied in all simulations [15]. Moreover, the simulation was run under unsteady conditions. The comparison of thrust and torque for different grid resolutions with the same wind speed of 5.53 m/s, rotor speed of 330 rpm and time-step size of 5 <sup>×</sup> 10−<sup>4</sup> s is presented in Tables 3 and 4. It can be observed from Tables 3 and 4 that the grid resolution of Case 3 is sufficient to solve the unsteady aerodynamics of the wind turbine. Therefore, the grid resolution of Case 3 was used in subsequent simulations.


**Table 2.** Mesh size of blade surface.

**Table 3.** Comparison of thrust between experiment and CFD simulation at different grid densities.


**Table 4.** Comparison of torque between experiment and CFD simulation at different grid densities.


Simulations at different wind speeds were performed, and the simulation results were compared with wind tunnel experiment data, as presented in Figure 4. In this paper, we always keep the pitch angle at 0◦, so we have not considered the working conditions above the rated wind speed. When the wind speed is close to the rated wind speed, the thrust and torque of the CFD simulation are lower than those of the wind tunnel experiment, but the maximum error is not more than 10%. This means that STAR-CCM+ can accurately simulate the aerodynamic performance of the wind turbine under rotating motion.

**Figure 4.** Comparison of thrust and torque between wind tunnel experiment and CFD simulation at different wind speeds (Case 3).

In order to ensure the reliability of the NREL 5 MW real-scale wind turbine simulation, the NREL 5 MW real-scale wind turbine was used for grid convergence analysis. Major properties of the NREL 5 MW reference wind turbine are given in Table 5 [16]. Figure 5 shows the blade alone geometric model and full configuration geometric model with the tower. The blade alone model was used for numerical verification, and the full configuration model was used to investigate the effect of tilt angle on the aerodynamic performance of the wind turbine. Near the wall surface of the blades and hub, the boundary layers have 10 layers of refined grid with the total layer thickness of 0.03 m and a progression factor of 1.2. The same wind speed of 11.4 m/s and rotor speed of 12.1 rpm were applied in all simulations. Meanwhile, in all simulations, the time step is the time taken by the wind turbine to increase the azimuth angle by 1◦.


**Table 5.** Principal dimensions of the NREL 5 MW reference wind turbine.

**Figure 5.** Geometric model of a 5 MW reference wind turbine: (**a**) the rotor geometric model; (**b**) the full configuration model.

The number of meshes corresponding to different mesh sizes is shown in Table 6. The comparison of power for different grid resolutions with the same wind speed of 11.4 m/s and rotor speed of 12.1 rpm is presented in Table 7. It can be observed from Table 7 that the grid resolution of Case 2 is sufficient to solve the unsteady aerodynamics of the wind turbine. Therefore, the grid of Case 2 was used for the simulation of NREL 5 MW real-scale wind turbines at different wind speeds.





Aerodynamic simulations of a wind turbine with various wind speeds were tested and compared with the FAST results. The obtained thrust and power were compared with the corresponding NREL data calculated by FAST V8, as presented in Figure 6. The power agrees well with the NREL data, but the thrust tends to be smaller than that from NREL data. The reason for the difference between the CFD method and the FAST can be summarized as follows: (a) the FAST does not consider the three-dimensional flow effects around blades; (b) in the BEM method, in order to calculate a rotor with a limited number of blades, a tip loss correction model needs to be added. The results obtained by different tip loss correction models are also quite different [17]. FAST uses a Prandtl tip loss correction model [16]. Therefore, the CFD result of the thrust is significantly lower than the FAST result. A similar phenomenon appeared in [18]. However, at the rated wind speed, compared with FAST data, the errors of the thrust and power obtained by CFD are less than 5% Through the above analysis, the grid of Case 2 can accurately simulate the aerodynamic performance of NREL 5 MW real-scale wind turbines. Therefore, the grid of Case 2 was used to simulate the effect of tilt angle on the aerodynamic performance of the wind turbine.

**Figure 6.** Comparisons of thrust and power.

#### *3.2. The E*ff*ect of the Tilt Angle on the Aerodynamic Performance of the Wind Turbine*

In this study, nacelle tilt angles of 0, 4, 8 and 12◦ were investigated. Figure 7 shows the structure of the wind turbine at different tilt angles. In the picture, β is the pre-coning angle, and γ is the shaft tilt angle. The azimuth of the rotor is defined as ψ, as presented in Figure 8. In Figure 8, the blue rotor is the initial position with the 0-azimuth angle. Subsequent analysis is based on the results after the wind turbine has stabilized. Under different tilt angles, the change in wind turbine thrust and power with the azimuth is shown in Figure 9. Comparing the no-tower curve with the other four curves, it can be seen that the thrust and power generate periodic fluctuations due to the influence of the tower. When the blades pass through the tower, the thrust and power will periodically decrease. This phenomenon is called the blade–tower interaction (BTI) [19]. The BTI effects begin at approximately 30◦ rotor azimuth and dissipate at approximately 100◦ rotor azimuth, as presented in Figure 10. This agrees with previous studies, which all show effects in approximately this same 70◦ range [19].

Figure 9 shows the difference between the thrust and power at approximately 60, 180 and 300◦ azimuth with the same nacelle tilt. This phenomenon is due to the interaction between the blade and the tower creating a random vortex. As the nacelle tilt increases, the blade and tower interactions gradually weaken. Therefore, this phenomenon becomes less important as the nacelle tilt increases. In Figure 10, when ψ is approximately 65◦, the thrust and power of the wind turbine at 4 and 8◦ nacelle tilt are higher than 0 and 12◦ nacelle tilt.

**Figure 7.** Structure of the wind turbine at different tilt angles.

**Figure 8.** Definition of the azimuth.

**Figure 9.** Comparison of thrust and power at different nacelle tilt angles.

**Figure 10.** Comparison of thrust and power at different nacelle tilt angles (partial enlargement).

The position of the blade relative to the tower with the 60◦ azimuth is shown in Figure 11. Instantaneous pressure magnitude and streamlines at blade sections r/R = 0.5, r/R = 0.7 and r/R = 0.9 (Blade 1) of the wind turbine are presented in Figures 12–14. In the low span (r/R = 0.5) suction side, the flow separation phenomenon can be observed. However, the flow remains attached for higher radial sections (r/R = 0.7 and r/R = 0.9). In addition, with the increase of the nacelle tilt, the flow separation of the low span suction side is gradually weakened. The variation of the pressure distribution around different sections airfoil with the nacelle tilt can also be observed.

**Figure 11.** Blade position (ψ = 60◦).

**Figure 12.** Instantaneous pressure magnitude and streamlines diagram (r/R = 0.5).

**Figure 13.** Instantaneous pressure magnitude and streamlines diagram (r/R = 0.7).

**Figure 14.** Instantaneous pressure magnitude and streamlines diagram (r/R = 0.9).

H. Rahimi et al. [20] studied different methods of calculating the angle of attack of the wind turbine section airfoil. However, in CFD, when considering the interaction between the blade and the tower, it is difficult to calculate the angle of attack of the blade section airfoil. Therefore, only the effect of tilt angle on the blade section airfoil load is considered in this paper. Figure 15 shows the distribution of azimuth average thrust and tangential force along the blade span. From the figure, we can see that in terms of thrust, when the tilt angle is 4◦, the distribution of the thrust along the blade span does not change much compared to the 0◦ tilt angle. However, when the tilt angle is increased to 8 and 12◦, the thrust of the section airfoil at the blade tip is lower than the values at 0 and 4◦ tilt angle. In terms of tangential force, the tangential force gradually decreases as the tilt angle increases, for up to 0.5 of the span. However, the tangential force at 4◦ tilt angle does not change much compared to 0◦ tilt angle. Figure 16 shows the distribution of thrust and tangential force along the blade span when the blade is located in front of the tower. In terms of thrust, the thrust of the section airfoil gradually increases as the tilt angle increases, for up to 0.7 of the span. Regarding the tangential force, the increase of the tilt angle also increases the tangential force, for up to 0.6 of the span. However, regardless of thrust or tangential force, the value at 8◦ of tilt does not change much compared to 12◦ of tilt. This means that the influence of the tower becomes weaker after the tilt angle exceeds 8◦.

**Figure 15.** The average thrust and average tangential force per unit of span along the blade span for Blade 1.

**Figure 16.** Thrust and tangential force per unit of span along the blade span for Blade 1.

Thrust force per unit of span along the rotor span for Blade 1 is shown in Figure 17. In the blade root, the thrust will fluctuate with the change of the azimuth angle, which is mainly caused by the three-dimensional flow of the blade root. In the middle of the blade, when the azimuth angle is 0-180◦, the thrust is the largest at 4◦ tilt angle, and the thrust is the smallest at 12◦ tilt angle. When the azimuth angle is 180-360◦, the thrust gradually decreases as the tilt angle increases. In the vicinity of the blade tip, when the azimuth angle is 0-180◦, except for the tilt angle of 0◦, the thrust has a change that increases first and then decreases with the change of the azimuth angle. When the azimuth angle is 180-360◦, the thrust curve decreases first and then increases, and the thrust gradually decreases as the

elevation angle increases. Figure 18 shows the tangential force per unit of span along the rotor span for Blade 1. We can see that in the middle of the blade and near the tip of the blade, the tangential force of the section airfoil in the 180-360◦ angle range is higher than the value in the 0–180◦ angle range, except for the case of the 0◦ tilt angle. At the same time, we found that in the middle of the blade and near the tip of the blade, when the azimuth angle is 180◦, the thrust and tangential force at 0◦ tilt are the smallest, which is mainly due to the maximum interaction between the blade and the tower at 0◦ tilt angle.

**Figure 17.** Thrust force per unit of span along the rotor span for Blade 1.

**Figure 18.** *Cont*.

**Figure 18.** Tangential force per unit of span along the rotor span for Blade 1.

#### *3.3. The E*ff*ect of the Tilt Angle on the Wind Turbine Wake*

The instantaneous isovorticities occurring when the blade is in front of the tower are presented in Figure 19. One can clearly see that these instantaneous diagrams with nacelle tilt angle shows that there is a strong flow interaction between the wake generated by the blade root, hub and tower regions. Because of the existence of the tower, there are strong unsteady flow interactions between tower vortex and blade tip vortex during downstream propagation. This interaction caused the blade tip vortex to break behind the tower. In addition, an increase in tilt angle will cause the blade tip vortex tube to tilt.

**Figure 19.** Side-view of instantaneous isovorticity contours for different nacelle tilt angles.

The instantaneous x-vorticities at different sections in four tilt angles are presented in Figure 20. We can observe that there is a clear difference in the blade tip vortex at different tilt angles. At 0 and 4◦ tilt angles, the blade tip vortex has only negative x-vorticities. When the tilt angle is changed to 8◦, positive x-vorticity and negative x-vorticity appear in the right half of the blade tip vortex. When the tilt angle is changed to 12◦, the left part of blade tip vortex is negative and right part is positive. At the same time, it can be seen that there are slight differences in the tower-generated vortexes of the four cases. By comparison, at the positions of x/D = 0.25 and x/D = 0.5, the vortex generated by the tower behind the rotor at the tilt angle of 4◦ is slightly less than other cases. When the tilt angle reaches 12◦, the vortex generated by the tower is broken.

**Figure 20.** Instantaneous x-vorticities at different sections for four tilt angles.

The corresponding vertical x-velocity profiles are presented in Figure 21. When the tilt angle is 0◦, as the downstream distance increases, the velocity field behind the wind turbine is approximately symmetrical about the centerline and keeps a circular shape. However, as the tilt angle increases, the velocity field behind the wind turbine shows asymmetry and gradually moves to the upper right. Meanwhile, the low-velocity region at the end of the wake gradually decreases with increasing tilt angle.

**Figure 21.** Vertical section x-velocity profiles at y = 0 m.

Figure 22 shows the distribution of instantaneous axial velocity along blade span at the wind turbine downstream positions of 0.5D, 2.5D, 3.5D and 4.5D, which represent the development of the velocity in the wake. Observing the instantaneous axial velocity distribution at the position of X/D = 0.5, it can be seen that the upper half of the curve does not change much with the tilt angle, but the lower half of the curve changes significantly with the tilt angle. In addition, it can be seen that the lower half of the curve has the smallest fluctuation at the 4◦ tilt angle, which means that the interaction between the blade tip vortex downstream of the wind turbine and the tower wake vortex is the weakest at a tilt angle of 4◦. We can also observe a similar phenomenon in Figure 21. Observing the instantaneous axial velocity distribution at the positions of X/D = 2.5 and X/D = 3.5, we can see that as the tilt angle increases, the minimum velocity in the wake gradually increases and shifts upwards. However, at the position of X/D = 4.5, there is a slight decrease in the minimum velocity as the tilt angle increases. This is due to the upward shift of the wake-end deceleration zone.

**Figure 22.** *Cont*.

**Figure 22.** The distribution of instantaneous axial velocity along blade span at the wind turbine downstream positions of 0.5D, 2.5D, 3.5D and 4.5D.

#### *3.4. Wind Shear*

The change in wind speed with height was determined according to the power function given in International Electrotechnical Commission (IEC) 61400-1 [21] and presented as follows:

$$\frac{V\_Z}{V\_{Z\_r}} = \left(\frac{Z}{Z\_r}\right)^{\circ} \tag{12}$$

where *VZ* refers to the wind speed at height z, *VZr* refers to the reference wind speed at height *Zr* and γ refers to the wind shear exponent. *Zr* refers to the hub height. In this study, the reference wind speed is 11.4 m/s. In this paper, wind shear exponents are 0.09, 0.2 and 0.41. The wind shear exponent of 0.09 indicates a very unstable atmospheric state, 0.20 represents a neutral state and 0.41 represents a very stable state [4].

The turbulence intensity was calculated according to the formula in IEC 61400-1 [21] and given as follows:

$$I\_T = I\_{ref}(0.75V\_{hub} + 5.6) / V\_{hub} \tag{13}$$

where *IT* is the turbulence intensity, *Ire f* is the expected value of the turbulence intensity and *Vhub* is the reference velocity at the hub. In this paper, *Ire f* values are 0.12, 0.14 and 0.16. *Ire f* of 0.12 represents lower turbulence characteristics, 0.14 describes medium turbulence characteristics and 0.16 describes higher turbulence characteristics.

Table 8 shows the average power along one rotation of the wind turbine after it has stabilized. It can be seen from Table 8 that, compared with uniform wind, wind shear will cause the average power of the wind turbine to decrease by about 14%. At the same time, it can be found that the average power of the 4◦ tilt angle is close to that of the 0◦ tilt angle and is higher than the average power of the 8 and 12◦ tilt angles under uniform wind or wind shear conditions. The deviation (|*Pa* − *Pm*|) of the power relative to the average power at an azimuth angle of 180◦ gradually decreases as the tilt angle increases (see Figure 23, Table 8). When the tilt angle reaches 8◦ and continues to increase, |*Pa* − *Pm*| will remain unchanged. This means that as the tilt angle increases, the interaction between the blade and the tower gradually weakens. When the tilt angle exceeds 4◦, the influence of the tilt angle on the interaction between the blade and the tower can be ignored. However, when the tilt angle exceeds 4◦, it will cause a significant decrease in the average power of the wind turbine. Therefore, considering the power of the wind turbine and the interaction between the blade and the tower, it is more appropriate to set the wind turbine tilt angle to about 4◦.


**Table 8.** Power for uniform wind and wind shear flow conditions at *Vhub* = 11.4 m/s (γ = 0.2, *Ire f* = 0.14).

**Figure 23.** Thrust and power versus azimuth angle for various tilt angles at *Vhub* = 11.4 m/s (γ = 0.2, *Ire f* = 0.14).

Figure 24 describes the influence of wind shear exponents (γ) on the aerodynamic performance of the wind turbine. It can be seen from Figure 24 that the thrust and power of the wind turbine when the wind shear exponent is 0.41 are higher than the values when the wind shear exponents are 0.09 and 0.20. It can be found from Table 9 that the average thrust and power of the wind turbine under different wind shear exponents have the smallest error when the wind shear factor is 0.41 compared with the uniform wind, and the average thrust and power of the wind turbine are almost the same when the wind shear factors are 0.09 and 0.2. In Table 9, the wind shear exponent of 0.00 means uniform wind inlet conditions. In Figure 24, it can be seen that the fluctuation of the wind turbine thrust and power curve when the wind shear factor is 0.09 is significantly higher than the other two cases. This means that the wind shear exponent has an effect on the interaction between the blade and the tower.

**Figure 24.** Thrust and power versus azimuth angle for various wind shear exponents (γ) at *Vhub* = 11.4 m/s (*Ire f* = 0.14, tilt angle = 4◦).


**Table 9.** The power for various wind shear exponents (γ) at *Vhub* = 11.4 m/s (*Ire f* = 0.14, tilt angle = 4◦).

At the same time, as can be seen from Figure 25, at different turbulence intensity expectations, the thrust and power of the wind turbine are basically the same. This shows that the expected value of the turbulence intensity has little effect on the thrust and power of the wind turbine. Therefore, when using wind shear to simulate a wind turbine, it is necessary to focus on the size of the wind shear exponents according to simulated working conditions.

**Figure 25.** Thrust and power versus azimuth angle for various expected values of the turbulence intensity (*Ire f*) at *Vhub* = 11.4 m/s (γ = 0.2, tilt angle = 4◦).

#### **4. Conclusions**

The computational fluid dynamics (CFD) method was used to simulate the aerodynamic performance of a fixed wind turbine with different tilt angles. By comparing the aerodynamic performance of a wind turbine at different tilt angles, it was found the aerodynamic performance of the wind turbine is better when the tilt angle is about 4◦. The main purpose of the paper was to study the practical importance of effect of tilt angle on the aerodynamic performance of a wind turbine. The main conclusions of the paper are as follows:

1. In order to balance the power generation efficiency of the wind turbine and the interaction between the blade and the tower, the tilt angle of a wind turbine can be set at about 4◦ to obtain better aerodynamic performance.

2. The increase of the tilt angle will cause the load of the section airfoil to change, thus affecting the thrust and power of the wind turbine. When the blade is located in front of the tower, increasing the tilt angle will increase the load of the section airfoil. At the same time, after the tilt angle reaches 8◦, the change in the load of the section airfoil with the tilt angle will not be obvious.

3. Wind shear will cause the thrust and power of the wind turbine to decrease, and the effect of the wind shear exponents on the aerodynamic performance of the wind turbine is significantly greater than the expected effect of the turbulence intensity. When performing wind turbine simulations, it is recommended to use a wind shear that is closer to that found in the real environment instead of uniform wind.

In summary, in order to ensure that a fixed wind turbine has an improved aerodynamic performance, the tilt angle of the wind turbine when installed should be about 4◦. In reality, for a floating offshore wind turbine, a tilt angle of about 4◦ may not be appropriate, so the effect of tilt angle on a floating offshore wind turbine should be further studied in future works.

**Author Contributions:** Conceptualization, K.L.; Data curation, Q.W.; Formal analysis, Q.W.; Software, Q.W.; Supervision, Q.M.; Validation, Q.W.; Writing—original draft, Q.W.; Writing—review & editing, K.L. and Q.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the National Natural Science Foundation of China (Nos. 51739001, 51779049).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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#### *Article*
