Investigate aerodynamic performance of wind turbine blades with vortex generators at the transition area

Abstract

The transition area of the blade had a large relative thickness of airfoil, which was prone to the flow separation. The vortex generators (VGs) could restrain the flow separation. In this paper, the VGs were installed at the transition area of the WindPACT 1.5 MW wind turbine blades. The numerical simulation method was used to investigate the effects of the VGs on the aerodynamic performance of the blade. The high-energy vortexes were generated at the tail by the VG. It could change the energy distribution and flow characteristics of the airflow in the boundary layer. There were influences by the geometric parameters of the VGs. The VGs could change the aerodynamic performance at the transition area of the blade. A satisfactory result was obtained for reasonable geometrical parameters of the VGs. It also could restrain the flow separation of the blade surface and improve the torque.

Keywords

Transition area flow control vortex generator aerodynamic performance wind turbine

Introduction

The global energy development situation was grim. The traditional fossil energy reserves were limited (Lior, 2010). Renewable clean energy had broad development prospects. Among them, wind power had been developing rapidly due to its wide application and reliable structure. According to the 2020 IRENA’s Report (Adrian et al., 2020), the world’s capacity of wind turbines has increased from 181 GW in 2010 to 622 GW in 2019. It maintained an annual growth rate of over 9.5%. As a core component of the wind turbines, the blade was the decisive factor affecting generator power (Li et al., 2017; Tahani et al., 2017). Enlarging the swept area of the blades could improve the power generation of wind turbines. Improving the aerodynamic performances of the blades could also improve power generation.

The different shapes and geometric parameters of the wind turbine blades have been designed (Capuzzi et al., 2014; Vianna Neto et al., 2018; Wang et al., 2017). Sedighi et al. (2020) studied the effects of adding dimples on the blade surface on the aerodynamic performance of the blade. The results showed that adding dimples could increase the torque of the wind turbine. Zhang and Wu (2012) studied the effects of the sinusoidal leading-edge on the aerodynamic performance of the blade. Favier et al. (2012) investigated a modified leading-edge of the airfoil based on humpback whale flippers. The longer blades and more powerful wind turbines had been manufactured. The Haliade-X series of GE had 13MW wind power generating units (Winters and Saunders, 2018).

But when the power was higher, the blades need to withstand the large torque and thrust. Bazilevs et al. (2012) investigated the numerical simulation method for the pre-bending of the blade. Changing the material of the composite layer of the blade could increase the fatigue strength (Pawar and Ganguli, 2005). He et al. (2016) proposed a model for predicting the fatigue life of the blades in response to the problem of blade fatigue. Using materials with better performance could improve the bearing capacity of the blade. Increasing the relative thickness of the airfoil was also a means. But a larger relative thickness of the airfoil would increase the blade resistance (Fischer et al., 2014; Sharma and Visbal, 2019). It caused the formation of separation bubbles. The separation bubbles had a close relation to the flow separation at the surface (Embacher and Fasel, 2014; Marxen et al., 2013). The flow separation of the blade surface was an essential factor that limited the use of wind energy. By controlling the separation of the airflow in the boundary layer, to improve the use of wind energy. The flow separation control had a wide range of applications (Du et al., 2019; Kundu, 2020; Ma and Schröder, 2018; Tang et al., 2014). There were active control and passive control methods for the flow separation control.

Ma et al. (2019) carried on research on the effects of pulsed discharge plasma on the aerodynamic performance of the blades. When the tip speed increased, the suppression effects on the flow separation became more evident. Rezaeiha et al. (2019) applied Leading-edge slot suction of the blades. It could delay the separation of the bubble. Ebrahimi and Hajipour (2018) used the large eddy simulation (LES) method to study the control effects of the dual excitation DBD plasma actuator on the airfoil flow. The plasma driver affected the stability of the boundary layer. It ruptured the boundary layer and reduced the vortex at the tail of the blade, and increased the lift coefficient of the airfoil.

Wiśniewski et al. (2020) studied the effects of Gurney flaps on the aerodynamic performance of the airfoil. Adding Gurney flaps at the tail of the airfoil could improve the aerodynamic performance of the airfoil. Martinez Suarez et al. (2016) studied the effects of the rod-shaped VGs on the airfoil. Results showed that the rod-shaped VGs could reduce the flow separation of the airfoil. Zhu et al. (2018) developed Flow-deflecting airfoil (FDA) based on NACA0015 airfoil. The gap on the Flow-deflecting airfoil could generate the reverse flow. It increased the energy of entering the boundary layer and controlled the stall phenomenon. Wang et al. (2018) installed a small cylinder on the leading edge of the blade. It increased the torque of the blade without increasing the load of the wind turbine. Wang et al. (2019) installed slat on the blade leading edge that could increase the stall angle of attack of the airfoil. The surface roughness of the blade also affected the airflow of the boundary layer. Jung and Baeder (2020) studied the effects of the surface roughness of the NERL Phase VI wind turbine blades on the airflow characteristics. Papadopoulou et al. (2020) investigated the accumulation of dust of wind turbine blades in different areas. They found that the accumulation of dust caused power dissipation.

There were a lot of researches on the numerical simulation of two-dimensional airfoil (Du et al., 2015; Genç, 2010). It was difficult to predict the three-dimensional flow at the blade root. Because of the deficiency of research on the transition area. To analyze the aerodynamic performance of the blade surface and predict the airflow on the whole blade. It was essential to conduct numerical simulation on the three-dimensional flow field.

In this paper, the VGs were installed at the transition area of the blade. The geometric parameters of the VGs (including the height, the length, and the distance) were considered. The flow field was divided into structured grids. The turbulence model was the SST k-ω model. The flow separation and the aerodynamic performance were analyzed on the blade surface. The mechanism of the control flow of the high-energy vortex was studied.

Numerical methods

To prevent blade fatigue damages and control noise, the speed of the blade needs to be limited. In rated conditions, the gas turbulence velocity at the blade tip was generally less than 100 m/s. In this paper, the Mach number was less than 0.3. The flow field could be regarded as an incompressible flow field. The airflow through the blade surface was an adiabatic process. There was no need to solve the energy equation. The airflow through the surface of the wind turbine blades was the viscous flow. Therefore, the airflow to be solved was an incompressible steady viscous flow.

Turbulence model

When the blades were rotating, the airflow at the surface changed from laminar flow to turbulent flow. In this paper, the SST k-ω model was selected. Menter (1994) improved the SST k-ω model based on the k-ω model. The differences in the flow characteristics of the near-wall and the far-wall were considered. The definition of the turbulence viscosity coefficient was revised. Tachos et al. (2010) used the Spalart-Allmaras model, the k-ε model, the RNG k-ε model, and the SST k-ω model to simulate and verify the NERL Phase II wind turbines. The numerical results showed that the degree of accuracy of the SST k-ω was the best. In addition, other studies had also revealed that the SST k-ω model had high accuracy (Rocha et al., 2014, 2016; Wang et al., 2016).

The equations of the SST k-ω modelÿ°

ρ \frac{\partial}{\partial x_{i}} (k u_{i}) = \frac{\partial}{\partial x_{j}} ((μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}) + G_{k} - ρ β^{*} f_{β^{*}} k ω + S_{k}

(1)

ρ \frac{\partial}{\partial x_{i}} (ω u_{i}) = \frac{\partial}{\partial x_{j}} ((μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial ω}{\partial x_{j}}) + \frac{ρ α}{μ_{t}} G_{k} - ρ β^{*} f_{β^{*}} ω^{2} + D_{ω} + S_{ω}

(2)

Equation (1) represents the turbulent kinetic energy. Equation (2) represents the ratio of dissipation rate.

G_{k} = \min (G_{k}, 10 ρ β^{*} f_{β^{*}} k ω)

(3)

μ_{t} = \frac{ρ k}{ω} \cdot \frac{1}{\max [\frac{1}{α^{*}}, \frac{Ω F_{2}}{α ω}]}

(4)

D_{ω} = 2 (1 - F_{1}) ρ σ_{ω, 2} \frac{1}{ω} \frac{\partial k}{\partial x_{j}} \frac{\partial ω}{\partial x_{j}}

(5)

In the SST k-ω model, α_∞ is different from the k-ω model:

α_{\infty} = F_{1} α_{\infty, 1} + (1 - F_{2}) α_{\infty, 2}

(6)

In these equations, G_k is laminar flow velocity gradient generated by the turbulent kinetic energy; μ_t is turbulent viscosity coefficient; D_ω is the orthogonal diffusion term; S_k and S_ω are the custom terms; F₁ and F₂ are the mixed constants; Ω is the absolute value of vorticity. Equation (6) is the mixed function.

Geometrical parameters of blade and vortex generators

The WindPACT 1.5 MW wind turbine blade was designed by the American Renewable Energy Laboratory (NERL) (Dayton, 2001; Malcolm and Hansen, 2006; Smith, 2001). The distance between the tip of the blade and the axis of rotation R = 35 m. The part at r/R = 5%–7% of the blade was a cylindrical blade root. The transition area of the blade was from a circular shape to the S818 airfoil at r/R = 7%–25%. There was the largest chord length (c_max = 2.8 m) at r/R = 25% of the blade. After that, the airfoil chord length gradually decreased along the spanwise direction.

The VG was developed by Taylor (1947). The high-energy vortex was generated at the tail of VGs and could suppress the flow separation. VGs had a wide range of applications (Bagheri et al., 2021; Ramanathan et al., 2019; Rao et al., 2020; Skrzypiński et al., 2020; Zeng et al., 2019). Skrzypiński et al. (2020) analyzed the effect of the retrofitting VGs on the blades of the megawatt-sized wind turbine. Many factors affected the effects of the VGs. Such as shape, geometric parameters, installation method, and location. Figure 1 shows the installation diagram. The rectangular VGs were installed at the transition area of the suction surface. The distance from the VGs to the leading edge of the blade was S_d (S_d = 20% c). Figure 2 is a schematic diagram of the geometric parameters of the VGs. As shown in Table 1, four variables are involved in the VGs. The windward angle of the VGs were β = 18°. The interval d of the tail of the VGs was equal to the interval b between different groups. Three parameters of 0.03c_max, 0.04c_max, and 0.05c_max were set. The height of VGs was set as three parameters of 0.01c_max, 0.015c_max, and 0.02c_max. The length of VGs along the airfoil chord was set as two parameters of 0.02c_max and 0.03c_max.

Figure 1.

The installation of the VGs on the blade.

Figure 2.

The geometric parameters of the VGs (top view of the VGs).

Table 1.

Geometric parameters of the VGs, c_max = 2.8 m.

	l	h	b	d	C (deg)
Case_1	0.02 c_max	0.01 c_max	0.03 c_max	0.03 c_max	18
Case_2	0.02 c_max	0.015 c_max	0.03 c_max	0.03 c_max	18
Case_3	0.02 c_max	0.02 c_max	0.03 c_max	0.03 c_max	18
Case_4	0.03 c_max	0.015 c_max	0.03 c_max	0.03 c_max	18
Case_5	0.02 c_max	0.01 c_max	0.04 c_max	0.04 c_max	18
Case_6	0.02 c_max	0.015 c_max	0.04 c_max	0.04 c_max	18
Case_7	0.02 c_max	0.02 c_max	0.04 c_max	0.04 c_max	18
Case_8	0.02 c_max	0.01 c_max	0.05 c_max	0.05 c_max	18
Case_9	0.02 c_max	0.015 c_max	0.05 c_max	0.05 c_max	18
Case_10	0.02 c_max	0.02 c_max	0.05 c_max	0.05 c_max	18

Boundary conditions and computational mesh

The WindPACT 1.5 MW wind turbine was a three-blade horizontal axis wind turbine. The blades were uniformly distributed around the rotation axis. 1/3 of the actual flow field was selected as the computational domain. It reduced the calculation amount. The cabin, wheel hub, tower, and other components of the wind turbine were not considered.

As shown in Figure 3, 3R upstream of the blade was defined as the speed inlet. 8R downstream of the blade was defined as the pressure outlet (the absolute pressure was 0 Pa). The boundary radius was 5R. A rotating periodic boundary was used. The angular velocity of the blade rotation ω₀ = 2.14 rad/s, the inflow velocity V_∞ = 11.39 m/s. The SIMPLE method was selected for the pressure-velocity coupling. The momentum and turbulence equations adopted the second-order upwind. The computational domain was structured mesh. The surfaces of the blade and the VGs were set as rigid walls that do not slip.

Figure 3.

Dimension of the computational domain and boundary conditions of the flow field.

Figure 4 shows the mesh of the computational domain and the VGs. The flow field near the blade was a rotating domain, and the flow field far away was a static domain. The rotating domain and the stationary domain were connected by a sliding mesh. In this paper, the height of the first node of the blade surface was 0.15 mm, which guaranteed y⁺ < 5, and the growth ratio of the boundary layer was 1.2. The authors have verified the grid independence in the previous work (Wang et al., 2016). The number of grids of the clean blade flow field was 7.85 × 10⁶. After installed the VGs, the number of grids was between 1.07 × 10⁷ and 1.20 × 10⁷.

Figure 4.

Mesh configuration of the WindPACT 1.5 MW wind turbine blade: (a) mesh of the computational domain, (b) mesh around the blade, and (c) mesh around the VGs.

Results and discussion

The power of a wind turbine had a great relationship with the torque received by the blades. According to the Blade-element Theory, the blade could be divided into numerous blade elements. The thrust received was the sum of the blade element’s normal force. The power of the wind turbine was positively correlated with the torque of the blades. The pressure coefficient at the surface of the blade defined as:

C_{p} = \frac{p_{1} - p_{\infty}}{1 / 2 ρ [V_{\infty}^{2} + {(ω_{0} r)}^{2}]}

(7)

Where p₁ is the pressure of the surface; p_∞ is the pressure of the free flow; ρ is the density of the free flow; V_∞ is the inflow velocity; ω₀ is the angular velocity of the blade rotation.

Coefficients of normal force and tangential force:

C_{N} = \sum_{i = 1}^{N} \frac{1}{2} (C_{p}^{i} + C_{p}^{i + 1}) (x_{i + 1} - x_{i})

(8)

C_{T} = \sum_{i = 1}^{N} \frac{1}{2} (C_{p}^{i} + C_{p}^{i + 1}) (z_{i + 1} - z_{i})

(9)

Where x_i and z_i are the dimensionless coordinates of the airfoil chord.

Thrust and torque coefficients:

C_{Thrust} = C_{N} \cos (φ) + C_{T} \sin (φ)

(10)

C_{Torque} = C_{N} \sin (φ) + C_{T} \cos (φ)

(11)

dT = \frac{1}{2} B ρ {cV}_{0}^{2} C_{Thrust} dr

(12)

dM = \frac{1}{2} B ρ {cV}_{0}^{2} C_{Torque} rdr

(13)

Where φ is the twist of the blade; B is the number of blades; V₀ is the inflow velocity at the blade element.

Pressure coefficients

Figure 5 shows the effects of the VGs on the pressure coefficients at r/R = 25% of the blade. The pressure distribution at the surface of the blade was changed with the VGs. There was a more significant effect at the suction surface. In Case_2, Case_5, and Case_8, the pressure values were increased at the suction surface. The area enclosed by the pressure coefficient curve was increased. But the effects of the VGs on the pressure distribution at the blade surface may also lead to undesirable results. In Case_1, Case_4, and Case_9, the difference of pressure on the leading edge was decreased. The decline was significant. Subsequently, the pressure coefficient curves tended to be horizontal. According to the flow theory of the boundary layer, the air at the suction surface was separate. The integral areas of the pressure coefficient were reduced. But the pressure difference at the tail section of the blade was increased compared with Clean (without VGs). Figure 6 shows the pressure coefficients at r/R = 30% of the blade. The pressure coefficient curves moved closer to the curve corresponding to Clean. The effects of the VGs were reduced. In Case_4 and Case_9, the pressure value of the suction surface was still significantly decreased. The VGs had a more extensive range of effects.

Figure 5.

The pressure coefficients at r/R = 25% of the blade. (a–c) h with different parameters (with b and d as variables, divided into three groups). (d) l with different parameters.

Figure 6.

The pressure coefficients at r/R = 30% of the blade. The pressure coefficient curves moved closer to the curve corresponding to clean. (a–c) h with different parameters (with b and d as variables, divided into three groups). (d) l with different parameters.

Thrust and torque coefficients

The thrust coefficients and the torque coefficients of the blade were related to the pressure distribution. The area enclosed by the pressure coefficient curve increased with the VGs. The thrust coefficients and torque coefficients were increased correspondingly. Figure 7 shows the distribution of the thrust coefficients along the spanwise direction of the blade. Figure 8 shows the distribution of the torque coefficients. The geometric parameters of the VGs had significant effects. In the region of r/R ≤ 0.4, the phenomena were even more evident. Except for Case_1, Case_4, and Case_9, the thrust coefficients and the torque coefficients were increased for other cases. Besides, the thrust coefficients and the torque coefficients had the same changing trend. Contrast Figures 7 and 8, the VGs had more evident effects on the thrust coefficients on the blade. Figure 9 shows the total thrust and the change rate of the blade. Figure 10 shows the total torque and the change rate of the blade. In Case_5, the torque increased by 0.70% at the highest, but the thrust increased by 1.33%. In Case_4, the thrust decreased by 0.14%, but the torque decreased by 1.86%. When the VGs increased the torque of the blade, the increased ratio of the thrust was more evident. When the thrust was reducing, the torque of the blade decreased more obviously.

Figure 7.

Comparison of the thrust coefficients in different cases. In the region at r/R ≤ 0.4, the thrust coefficients changed evidently. (a–c) h with different parameters (with b and d as variables, divided into three groups). (d) l with different parameters.

Figure 8.

Comparison of the torque coefficient in different cases. (a–c) h with different parameters (with b and d as variables, divided into three groups). (d) l with different parameters.

Figure 9.

Comparison of the total thrust on a single blade in different cases.

Figure 10.

Comparison of the total torque of a single blade in different cases.

Flow separation of the blade

Figure 11 shows the limiting streamlines and the pressure distribution around the blade in the different cases. The flow separation occurred at the tail of the blade. There was a large flow separation zone at the transition area of the blade, which was the reason for the poor aerodynamic performance of the blade. In Case_2, Case_5, and Case_8, the flow separation area at the blade surface was reduced significantly. The VGs could delay the flow separation. The overall pressure differences of the blade were increased. It showed that the aerodynamic performance had improved.

Figure 11.

The limiting streamlines and the static pressure distribution at the suction surface.

In Case_1, Case_4, and Case_9, the large separation vortices were generated at the blade surface. The backflow phenomenon occurred on the side of the vortex close to the tip of the blade. It increased the flow separation area at the blade surface. The separation vortex at the surface took away a lot of energy, which affected the aerodynamic performance at the surface. Because of the separation vortex, the increased pressure at the surface occurred earlier. The static pressure value stabilized at 300–400 Pa in a larger area. It could improve the aerodynamic characteristics of the trailing edge of the blade. But the overall differences in the static pressure were reduced.

The tail vortex of the vortex generators

The VG generated the high-energy vortexes at the tail. The vortex could increase the energy entering the boundary layer. It changed the energy distribution and flow characteristics of the boundary layer. Whether the flow separation occurred had a great relationship with the flow state. When the energy of the boundary layer decreased to a particular value, the flow instability would increase. The flow separation would occur. The energy entering the boundary layer had a relationship with the characteristics of the vortex. Figure 12 shows the distribution of turbulence energy (m2/s2) at the tail of the VGs. In Case_2 and Case_4, the VGs had different lengths along the chord line. The area along the chord line would increase. The vortex could get more energy from the airflow flowing through the VGs. The internal turbulent flow energy would increase. In Case_4, the volume of the vortex increased, the internal high-energy area was increased. The high-energy vortex developed backward and transferred its energy to the boundary layer. The energy of entering the boundary layer was increased. The flow left the boundary layer to produce the separation bubbles, which took away the boundary layer energy. It changed the aerodynamic performance at the blade surface.

Figure 12.

Comparison of the turbulent kinetic energy distribution at the tail of the VGs. Case_2 and Case_4, which were different from l; Case_5–7 were different from h.

In Case_5, Case_6, and Case_7, the height of the VGs was different. The height of the VGs would affect the energy and position distribution of the tail vortex. The height of the VGs increased, and the volume of the vortex generating area increased. The amount of air flowing through the VGs was increased. The vortex obtained higher energy from the airflow. As the height of the VGs grew, the vortex at the tail of the VGs moved upward. The upward movement of the tail vortex has increased the thickness of the boundary layer. At the same time, the energy entering the boundary layer was increased. The flow was easier to fall off the boundary layer. The aerodynamic performance at the blade surface would reduce.

Figure 13 shows the vortex equivalent distribution at the tail of the VGs. In Case_1, Case_5, and Case_8, the difference was d (the distance between the VGs) and b (the distance between different groups). In Case_1, the VGs produced a distinct separation vortex at the tail. In the case of the distance between the VGs was too short. The distance between the pair of the vortices generated at the tail would decrease. Adjacent vortices affected each other, and the degree of confusion increased. It made the boundary layer at the blade surface unstable. In the case of the distance between the VGs was too large. The area affected by the tail vortex would decrease. The total energy flowing into the boundary layer was decreased. The overall flow control capability of the VGs decreased. The characteristics of the tail vortex and the boundary layer were interrelated. To obtain the better effects of the flow control, the geometric parameters of VGs were investigated. In this paper, Case_5 had the best effect. The geometric parameters of the VGs were: l = 0.02cmax, h = 0.01 cmax, b = d = 0.04 cmax.

Figure 13.

Vorticity equivalent distribution at the tail of the VGs (Q = 1000). Case_1, Case_5, and Case_4, which were different from d and b.

To analyze the effects of the VGs on the surface flow of the blade. Case_5 (with the highest torque increase rate) and Case_4 (with the maximal reduction rate) were selected to compare with Clean. Figure 14 shows the vorticity distribution at the blade surface. In Clean, the flow separation occurred at the mid-end of the blade transition area. In Case_4, the vortex made the flow on the blade surface away from the blade root more stable. Near the root of the blade, the flow state was irregular. There were more separation vortices. At r/R = 25%, the obtained energy of the blade was reduced by a large separation vortex. In Case_5, the vortex made the airflow flow regularly in a wide range. The airflow was close to the blade surface, effectively delayed the separation of the flow. It increased the energy obtained by the blade. In part of r/R = 25%, a small separation vortex was generated at the tail of the blade, which was consistent with Figure 11.

Figure 14.

Distribution of vorticity at the blade surface: (a) vorticity around the blade surface (Q = 100) and (b) vorticity at r/R = 25% of the blade.

Conclusion

In this paper, the effects of the VGs on the aerodynamic performance of the blade were investigated. The effects of the geometric parameters of the VGs were considered. The characteristics of the airflow at the blade surface were analyzed. The pressure coefficient, the thrust coefficient, and the torque coefficient of the blade were analyzed. Moreover, the flow separation was investigated at the transition area of the blade.

The geometric parameters of the VGs had significant effects on the control of the flow separation. For Case_5, the flow separation line moved toward the trailing edge. The torque increased by 0.70%.

When the length of VGs along the airfoil chord increased, the vortex generating area would increase. The vortex could get more energy from the airflow. It enlarged the vortex’s volume and internal instability.

The height of the VGs would affect the energy and position distribution of the vortex. With the height growth, the vortex would gain higher kinetic energy. The vortex’s center would move upward, and the volume was enlarged. It increased the thickness of the boundary layer. Excessive height would cause the vortex to be unstable and the flow separation to advance.

In the case of the distance between the VGs was too small. The distance between the pair of the vortices would reduce. It would affect each other and decrease the internal stability of the boundary layer. When the space was too large, the area was affected by the tail vortex. The energy transferred to the boundary layer would decrease. It could reduce the control effect of the flow separation.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Foundation of Jiangxi Educational Committee, China (grant number GJJ200822), Doctor Foundation of Jiangxi University of Science and Technology, China (grant number 205200100080) and Natural Science Foundation of Jiangxi Province, China (grant number 20171BAB206024).

ORCID iD

Haipeng Wang

References

Adrian

Sonia

Dennis

, et al. (2020) Renewable capacity statistics 2020. Technical report, International Renewable Energy Agency, Masdar, UAE,.

Bagheri

Mirjalily

SAA

Oloomi

SAA

, et al. (2021) Effects of micro-vortex generators on shock wave structure in a low aspect ratio duct, numerical investigation. Acta Astronautica 178: 616–624.

Bazilevs

Hsu

Kiendl

, et al. (2012) A computational procedure for prebending of wind turbine blades. International Journal for Numerical Methods in Engineering 89(3): 323–336.

Capuzzi

Pirrera

Weaver

(2014) A novel adaptive blade concept for large-scale wind turbines. Part II: Structural design and power performance. Energy 73: 25–32.

Dayton

(2001) WindPACT turbine design scaling studies technical area 1–composite blades for 80-to 120-meter rotor. Technical report, National Renewable Energy Lab, Golden, USA.

, et al. (2019) Performance enhancement of industrial high loaded gas compressor using Coanda jet flap. Energy 172: 618–629.

Berson

Dominy

(2015) Aerofoil behaviour at high angles of attack and at Reynolds numbers appropriate for small wind turbines. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 229(11): 2007–2022.

Ebrahimi

Hajipour

(2018) Flow separation control over an airfoil using dual excitation of DBD plasma actuators. Aerospace Science and Technology 79: 658–668.

Embacher

Fasel

(2014) Direct numerical simulations of laminar separation bubbles: Investigation of absolute instability and active flow control of transition to turbulence. Journal of Fluid Mechanics 747: 141–185.

10.

Favier

Pinelli

Piomelli

(2012) Control of the separated flow around an airfoil using a wavy leading edge inspired by humpback whale flippers. Comptes Rendus Mecanique 340(1-2): 107–114.

11.

Fischer

Kipouros

Savill

(2014) Multi-objective optimisation of horizontal axis wind turbine structure and energy production using aerofoil and blade properties as design variables. Renewable Energy 62: 506–515.

12.

Genç

(2010) Numerical simulation of flow over a thin aerofoil at a high Reynolds number using a transition model. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 224(10): 2155–2164.

13.

Soady

Mellor

, et al. (2016) Fatigue crack growth behaviour in the LCF regime in a shot peened steam turbine blade material. International Journal of Fatigue 82: 280–291.

14.

Jung

Baeder

(2020) Simulations for effect of surface roughness on wind turbine aerodynamic performance. Journal of Physics Conference Series1452: 012055.

15.

Kundu

(2020) Effects of circular trailing edge with the dimple on flow separation of NACA S1210 hydrofoil. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 234(18): 3600–3613.

16.

Lior

(2010) Sustainable energy development: The present (2009) situation and possible paths to the future. Energy 35(10): 3976–3994.

17.

Maeda

Kamada

, et al. (2017) Effect of rotor aspect ratio and solidity on a straight-bladed vertical axis wind turbine in three-dimensional analysis by the panel method. Energy 121: 1–9.

18.

Wang

Zhu

, et al. (2019) Dynamic stall of a vertical-axis wind turbine and its control using plasma actuation. Energies 12(19): 3738–3755.

19.

Malcolm

Hansen

(2006) WindPACT turbine rotor design study. Technical report, National Renewable Energy Lab, Golden, USA.

20.

Martinez Suarez

Flaszyński

Doerffer

(2016) Streamwise vortex generator for separation reduction on wind turbine profile. Journal of Physics Conference Series760: 012018.

21.

Marxen

Lang

Rist

(2013) Vortex formation and vortex breakup in a laminar separation bubble. Journal of Fluid Mechanics 728: 58–90.

22.

Schröder

(2018) Reduced-order coherent structures in active flow separation control using a bio-inspired flapping actuator. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 232(14): 2536–2545.

23.

Menter

(1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8): 1598–1605.

24.

Papadopoulou

Alasis

Xydis

(2020) On the wind blade’s surface roughness due to dust accumulation and its impact on the wind turbine’s performance: A heuristic QBlade-based modeling assessment. Environmental Progress & Sustainable Energy 39(1): 13296.

25.

Pawar

Ganguli

(2005) Modeling multi-layer matrix cracking in thin walled composite rotor blades. Journal of the American Helicopter Society 50(4): 354–366.

26.

Ramanathan

Thansekhar

Kanna

, et al. (2019) A new method of enhancing heat transfer in sudden expansion channel using vortex generators with toe-out and toe-in configurations by acquiring perquisites of recirculation and secondary vortex flow. Journal of Mechanical Science and Technology 33(8): 3913–3925.

27.

Rao

GAP

Charyulu

BVN

, et al. (2020) Numerical studies and validation of combustor and annular isolator interactions of hydrocarbon based axisymmetric dual combustion ramjet. Aerospace science and Technology 106: 106185.

28.

Rezaeiha

Montazeri

Blocken

(2019) Active flow control for power enhancement of vertical axis wind turbines: Leading-edge slot suction. Energy 189: 116131.

29.

Rocha

PAC

Rocha

HHB

Carneiro

FOM

, et al. (2014) K–ω SST (shear stress transport) turbulence model calibration: A case study on a small scale horizontal axis wind turbine. Energy 65: 412–418.

30.

Rocha

PAC

Rocha

HHB

Carneiro

FOM

, et al. (2016) A case study on the calibration of the k–ω SST (shear stress transport) turbulence model for small scale wind turbines designed with cambered and symmetrical airfoils. Energy 97: 144–150.

31.

Sedighi

Akbarzadeh

Salavatipour

(2020) Aerodynamic performance enhancement of horizontal axis wind turbines by dimples on blades: Numerical investigation. Energy 195: 117056.

32.

Sharma

Visbal

(2019) Numerical investigation of the effect of airfoil thickness on onset of dynamic stall. Journal of Fluid Mechanics 870: 870–900.

33.

Skrzypiński

Gaunaa

Bak

, et al. (2020) Increase in the annual energy production due to a retrofit of vortex generators on blades. Wind Energy 23(3): 617–626.

34.

Smith

(2001) WindPACT turbine design scaling studies technical area 2: turbine, rotor and blade logistics. Technical report, National Renewable Energy Lab, Golden, USA.

35.

Tachos

Filios

Margaris

(2010) A comparative numerical study of four turbulence models for the prediction of horizontal axis wind turbine flow. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 224(9): 1973–1979.

36.

Tahani

Kavari

Masdari

, et al. (2017) Aerodynamic design of horizontal axis wind turbine with innovative local linearization of chord and twist distributions. Energy 131: 78–91.

37.

Tang

Salunkhe

Zheng

, et al. (2014) On the use of synthetic jet actuator arrays for active flow separation control. Experimental Thermal and Fluid Science 57(9): 1–10.

38.

Taylor

(1947) The elimination of diffuser separation by vortex generators. Technical report, Aircraft Corporation, East Hartford, USA,.

39.

Vianna Neto

Guerra Junior

Moreno

, et al. (2018) Wind turbine blade geometry design based on multi-objective optimization using metaheuristics. Energy 162: 645–658.

40.

Wang

Jiang

Chao

, et al. (2019) Effects of leading edge slat on flow separation and aerodynamic performance of wind turbine. Energy 182: 988–998.

41.

Wang

Zhang

Qiu

(2016) Numerical study of the effects of wind shear coefficients on the flow characteristics of the near wake of a wind turbine blade. Proceedings of the Institution of Mechanical Engineers Part A Journal of Power and Energy 230(1): 86–98.

42.

Wang

, et al. (2017) Multi-objective differential evolution optimization based on uniform decomposition for wind turbine blade design. Energy 120: 346–361.

43.

Wang

Shen

, et al. (2018) Investigation on aerodynamic performance of horizontal axis wind turbine by setting micro-cylinder in front of the blade leading edge. Energy 143: 1107–1124.

44.

Winters

Saunders

(2018) The largest wind turbine ever. Mechanical Engineering 140(12): 31–31.

45.

Wiśniewski

Balduzzi

Buliński

, et al. (2020) Numerical analysis on the effectiveness of gurney flaps as power augmentation devices for airfoils subject to a continuous variation of the angle of attack by use of full and surrogate models. Energies 13(8): 1–25.

46.

Zeng

Wang

, et al. (2019) Combustion flow in different advanced vortex combustors with/without vortex generator. Aerospace Science and Technology 86: 640–649.

47.

Zhang

(2012) Aerodynamic characteristics of wind turbine blades with a sinusoidal leading edge. Wind Energy 15(3): 407–424.

48.

Zhu

Hao

, et al. (2018) A critical study on passive flow control techniques for straight-bladed vertical axis wind turbine. Energy 165: 12–25.