CFD-Based In-Depth Investigation of the Effects of the Shape and Layout of a Vortex Generator on the Aerodynamic Performance of a Multi-MW Wind Turbine

: Thick airfoils are conventionally adopted in the blade root region of a wind turbine to ensure structural safety under extreme conditions, despite the resulting power loss. To prevent this loss, a passive ﬂow control device known as a vortex generator (VG) is installed at the starting point of the stall to control the ﬂow ﬁeld near the wall of the suction surface. In this study, we used computational ﬂuid dynamics (CFD) to investigate the aerodynamic characteristics induced as a result of the shape and layout of the VG on a multi-MW wind turbine blade. The separated and vortical ﬂow behavior on the suction surface of the wind turbine blade equipped with VGs was captured by the Reynolds-averaged Navier–Stokes (RANS) steady-ﬂow simulation. The parametric sensitivity study of the VG shape parameters such as the chord-wise length, height, and interval of the fair of VGs was conducted using thick DU airfoil on the blade inboard area. Based on these results, the response surface method (RSM) was used to investigate the inﬂuence of the design parameters of the VG. Based on the CFD results, the VG design parameters were selected by considering the lift coefﬁcient and vorticity above the trailing edge. The maximum vorticity from the trailing edge of the selected VG and the lift coefﬁcient were 55.7% and 0.42% higher, respectively, than the average. The selected VG design and layout were adopted for a multi-MW wind turbine and reduced stall occurrence in the blade root area, as predicted by the simulation results. The VG improved the aerodynamic performance of the multi-MW wind turbine by 2.8% at the rated wind speed.


Introduction
Interest in improving the performance of wind turbines by optimizing the methods used for blade design and flow control devices has grown in the last few decades. In particular, several research efforts have focused on refining these methods to increase the efficiency of wind turbines [1][2][3][4][5]. Wind turbine manufacturers have attempted to increase the blade length not only to improve the annual energy production (AEP), but also to lower the cost of energy [6]. Traditionally, the wind industry has performed aerodynamic blade design and performance analysis based on Blade Element Momentum Theory (BEMT). Aerodynamic blade design methods for wind turbines were reviewed previously [7][8][9][10]. The design method based on BEMT applies various types of loss-correction models [11][12][13] to the tip and hub of the blade, where the three-dimensional flow field is dominant. However, the problem of aerodynamic reliability with high accuracy persists in the various loss-correction models based on BEMT, owing to the enlargement of the blade length and the taper of the blade tip. To overcome the reliability problem, a 3D steady-flow simulation using CFD was performed after preliminarily performing a blade design based on BEMT.
The aerodynamic performance and load of the blade, and the complex 3D viscous flow field around the blade tip and hub were evaluated using the previous simulation results [14,15].
In this study, the use of a vortex generator (VG) as a passive performance-enhancing device for a large wind turbine was studied. A VG is a passive flow control device in the form of a small vane and is mainly used to delay the stall occurrence of an airplane blade [16][17][18] or even to improve the heat transfer performance by forming longitudinal vortices [19]. In the wind energy industry, the VG has been studied to improve the aerodynamic performance of wind turbines installed on flat terrain, as well as to extend their lifespan through the wind-kinetic energy conversion of wind turbines installed on complex terrain [20]. The effectiveness of the VG has been proven through academiaindustry joint research, and it has been installed and operated in thousands of wind turbines since 2013 [21]. VGs are installed toward the root and suction surface of the blade of a wind turbine to mitigate airflow separation. Many CFD analyses and wind tunnel tests have been carried out to assess the feasibility of VG adoption with wind turbine blades. However, few CFD studies focused on full-scale wind turbines equipped with Gurney flap VGs other than airfoil base simulation and wind tunnel testing or CFD using virtual porous models [22][23][24][25][26][27]. There was a CFD analysis study of the VG-mounted wind turbine blade by RANS, SST k-omega equation, but the blade length was as short as 35 m, and a cuboid VG was investigated for the convenience of lattice formation [28]. Although there have been studies that calculate power increase via BEM using the lift and drag coefficient, calculations using BEM are less accurate than RANS CFD analysis results [29]. The aerodynamic characteristics of multi-MW horizontal-axis wind turbine blades have been analyzed using the commercial CFD software ANSYS CFX [30]. The results of the CFD analysis were validated with GH-Bladed design data [31]. These researchers optimized the shape and layout of the VG to maximize the performance of the wind turbine in terms of power generation.

Materials and Methods
Considering the aerodynamics and structural aspects of the blade, the airfoils shown in Figure 1 are extended in the span direction as shown in Figure 2. Figure 3 schematically shows the main parameters and layout of the VG. The distance between the VG pairs (λ) and the angle of attack (α) of the VG were specified as 6 • and 11 • for efficiency. The recommended λ/h investigated through a flat-plane CFD analysis study is 5 [32]. The VGs are installed on the suction surface and at the root of the blade to enhance the aerodynamic performance. Table 1 presents the wind turbine specification and Table 2 the shape parameters of the VG normalized by the chord length.
3D viscous flow field around the blade tip and hub were evaluated using the previ simulation results [14,15].
In this study, the use of a vortex generator (VG) as a passive performance-enhanc device for a large wind turbine was studied. A VG is a passive flow control device in form of a small vane and is mainly used to delay the stall occurrence of an airplane bl [16][17][18] or even to improve the heat transfer performance by forming longitudinal vorti [19]. In the wind energy industry, the VG has been studied to improve the aerodyna performance of wind turbines installed on flat terrain, as well as to extend their lifesp through the wind-kinetic energy conversion of wind turbines installed on complex terr [20]. The effectiveness of the VG has been proven through academia-industry joint search, and it has been installed and operated in thousands of wind turbines since 2 [21]. VGs are installed toward the root and suction surface of the blade of a wind turb to mitigate airflow separation. Many CFD analyses and wind tunnel tests have been c ried out to assess the feasibility of VG adoption with wind turbine blades. However, f CFD studies focused on full-scale wind turbines equipped with Gurney flap VGs ot than airfoil base simulation and wind tunnel testing or CFD using virtual porous mod [22][23][24][25][26][27]. There was a CFD analysis study of the VG-mounted wind turbine blade by RA SST k-omega equation, but the blade length was as short as 35 m, and a cuboid VG w investigated for the convenience of lattice formation [28]. Although there have been st ies that calculate power increase via BEM using the lift and drag coefficient, calculati using BEM are less accurate than RANS CFD analysis results [29]. The aerodynamic ch acteristics of multi-MW horizontal-axis wind turbine blades have been analyzed using commercial CFD software ANSYS CFX [30]. The results of the CFD analysis were v dated with GH-Bladed design data [31]. These researchers optimized the shape and lay of the VG to maximize the performance of the wind turbine in terms of power generati

Materials and Methods
Considering the aerodynamics and structural aspects of the blade, the airfoils sho in Figure 1 are extended in the span direction as shown in Figure 2. Figure 3 schematica shows the main parameters and layout of the VG. The distance between the VG pairs and the angle of attack (α) of the VG were specified as 6° and 11° for efficiency. The r ommended λ/h investigated through a flat-plane CFD analysis study is 5 [32]. The V are installed on the suction surface and at the root of the blade to enhance the aerodyna performance. Table 1 presents the wind turbine specification and Table 2 the shape rameters of the VG normalized by the chord length.

Numerical Analysis Methodology
Three major numerical analysis techniques, namely, direct numerical simulation (DNS) [33], large eddy simulation (LES) [34], and RANS simulation, can be used to analyze turbulent flow fields. To analyze the general vortex behavior precisely in a turbulent

Numerical Analysis Methodology
Three major numerical analysis techniques, namely, direct numerical simulation (DNS) [33], large eddy simulation (LES) [34], and RANS simulation, can be used to analyze turbulent flow fields. To analyze the general vortex behavior precisely in a turbulent

Numerical Analysis Methodology
Three major numerical analysis techniques, namely, direct numerical simulation (DNS) [33], large eddy simulation (LES) [34], and RANS simulation, can be used to analyze turbulent flow fields. To analyze the general vortex behavior precisely in a turbulent flow field containing vortices of various scales, the calculation grid size must be smaller than the minimum space scale of the vortex structure and the time interval should be less than the minimum time scale of the vortex variation. LES uses the spatially averaged Navier-Stokes equations, which directly calculate vortices greater than the grid scale and indirectly refer to the subgrid-scale model for vortices smaller than the grid scale. DNS and LES require extensive resources for their calculations, making them unfeasible in practical engineering applications. In comparison, RANS uses the time-based ensemble-averaged Navier-Stokes equations and models all of the effects caused by turbulence. Although RANS yields a lower resolution analysis than DNS or LES, it is widely used in engineering applications because it does not require high-resolution calculation grids. RANS uses the following equations: ∂ρ ∂t Turbulence models that are widely used for RANS numerical analysis in engineering include k-ε, k-ω, and SST. The k-ε turbulence model [35] precisely analyzes the turbulence behavior in free-stream regions with small pressure gradients; however, it inaccurately estimates the boundary layer separation in viscous sub-layer regions. Although the k-ω turbulence model, which was developed by Wilcox [36], accurately analyzes the separation caused by adverse pressure gradients, it is sensitive to the free-stream region. Menter [37] combined the advantages of the k-ε and k-ω models and proposed the SST turbulence model. Simulation of the wind turbine flow generally involves the use of CFD to analyze the performance of the cross-sectional airfoil of the blade, and the numerical analysis and experimental results are often in agreement [38,39]. The complete formulation of the SST model is given by: The blending function F 1 is defined by: , 10 −10 and y is the distance to the nearest wall. The turbulent eddy viscosity is defined as follows: The second blending function F 2 is defined by: Appl. Sci. 2021, 11, 10764

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A production limiter is used in the SST model to prevent the build-up of turbulence in stagnation regions:

Implementation of Vortex Generators on a Wind Turbine Blade
To accurately calculate ω (specific dissipation) in the viscous sub-layer region using RANS simulation with the SST turbulence model, the minimum grid size must satisfy y+ < 1 in the viscous sub-layer simulation [40]. Figure 4 shows the blade calculation area. In the calculation domain, a spatial resolution of 7 times the rotor radius in the inflow direction, 10 times the wake direction, and 10 times the radial direction was configured. A no-slip condition was applied to the blade surface equipped with the VG, and a freestream condition was applied to the inlet. The flow field of the wind turbine blade was simulated by applying a 120 • periodic boundary condition in the direction of rotation. The interface between the rotating and fixed parts was analyzed by applying the frozen interface condition.

Implementation of Vortex Generators on a Wind Turbine Blade
To accurately calculate ω (specific dissipation) in the viscous sub-layer region RANS simulation with the SST turbulence model, the minimum grid size must sa < 1 in the viscous sub-layer simulation [40]. Figure 4 shows the blade calculation a the calculation domain, a spatial resolution of 7 times the rotor radius in the inflow tion, 10 times the wake direction, and 10 times the radial direction was configured slip condition was applied to the blade surface equipped with the VG, and a free condition was applied to the inlet. The flow field of the wind turbine blade was sim by applying a 120° periodic boundary condition in the direction of rotation. The in between the rotating and fixed parts was analyzed by applying the frozen interfa dition.

Validation of CFD Model
The results of the CFD analysis of the wind turbine blade without a VG wer pared with experimental BEMT data. The BEMT-based analysis was carried out us Bladed, which is commercial code used for wind turbine design. Figures 4 and 5 the computational grid system of the blades in the simulation, and Table 3 provi number of elements in the computational grid system used for the simulation. F and Table 4

Validation of CFD Model
The results of the CFD analysis of the wind turbine blade without a VG were compared with experimental BEMT data. The BEMT-based analysis was carried out using GH Bladed, which is commercial code used for wind turbine design. Figures 4 and 5 shows the computational grid system of the blades in the simulation, and Table 3 provides the number of elements in the computational grid system used for the simulation. Figure 6 and Table 4

Flow Behavior on the Wind Turbine Blade
The simulation was performed by specifying many grids in the wake direction of the blade tip to accurately simulate the tip vortex, and these results are shown in Figure 7. Vortex core 1 is generated in the boundary layer of the suction surface, and vortex core 2 is combined with vortex core 1 in the boundary layer of the pressure surface. Vortex core 3 is a boundary layer generated at the blade trailing edge and is swept into the tip vortex structure. As shown in Figure 8, large-scale flow separation occurred at a distance of approximately 20% of the chord length from the leading edge. The airflow characteristics on the suction surface of the blade were affected by the thickness ratio of the airfoil and the

Flow Behavior on the Wind Turbine Blade
The simulation was performed by specifying many grids in the wake direction of the blade tip to accurately simulate the tip vortex, and these results are shown in Figure 7. Vortex core 1 is generated in the boundary layer of the suction surface, and vortex core 2 is combined with vortex core 1 in the boundary layer of the pressure surface. Vortex core 3 is a boundary layer generated at the blade trailing edge and is swept into the tip vortex structure. As shown in Figure 8, large-scale flow separation occurred at a distance of ap-

Flow Behavior on the Wind Turbine Blade
The simulation was performed by specifying many grids in the wake direction of the blade tip to accurately simulate the tip vortex, and these results are shown in Figure 7. Vortex core 1 is generated in the boundary layer of the suction surface, and vortex core 2 is combined with vortex core 1 in the boundary layer of the pressure surface. Vortex core 3 is a boundary layer generated at the blade trailing edge and is swept into the tip vortex structure. As shown in Figure 8, large-scale flow separation occurred at a distance of approximately 20% of the chord length from the leading edge. The airflow characteristics on the suction surface of the blade were affected by the thickness ratio of the airfoil and the angle of attack depending on the wind speed. The flow-separated low-energy air was confirmed to flow secondarily in the tip direction along the suction surface owing to forces such as the centrifugal force, Coriolis force, and pressure difference in the radial direction of the rotor. angle of attack depending on the wind speed. The flow-separated low-energy air was confirmed to flow secondarily in the tip direction along the suction surface owing to forces such as the centrifugal force, Coriolis force, and pressure difference in the radial direction of the rotor.

Aerodynamic Characteristics of DU Airfoil with VG
Based on the results of the CFD analysis, the cross-sectional DU airfoil in the region where flow separation occurs predominantly was selected as the test airfoil for VG application analysis. Figure 9 shows the surface grid of the VG-equipped airfoil used for simulation, and Table 5 contains the number of grids that were used.
The chordwise velocity contours of the airfoil with and without the VG are shown in Figure 10a,b. The results of the CFD analysis confirm that, in the case of the airfoil without the VG, the fluid did not accelerate along the suction surface and flow separation occurred; however, in the case of the airfoil with the VG, the fluid accelerated along the suction surface and flow separation did not occur. When flow separation occurs on the suction side, a low-pressure region is formed in the wake, which lowers the lift coefficient and increases the drag coefficient. As shown in Figure 11a,b, when the VG is attached, the airfoil experienced a high lift force at an angle of attack of 5.9° or higher and a low drag force at an angle of attack of 14.8° or higher. angle of attack depending on the wind speed. The flow-separated low-energy air was confirmed to flow secondarily in the tip direction along the suction surface owing to forces such as the centrifugal force, Coriolis force, and pressure difference in the radial direction of the rotor.

Aerodynamic Characteristics of DU Airfoil with VG
Based on the results of the CFD analysis, the cross-sectional DU airfoil in the region where flow separation occurs predominantly was selected as the test airfoil for VG application analysis. Figure 9 shows the surface grid of the VG-equipped airfoil used for simulation, and Table 5 contains the number of grids that were used.
The chordwise velocity contours of the airfoil with and without the VG are shown in Figure 10a,b. The results of the CFD analysis confirm that, in the case of the airfoil without the VG, the fluid did not accelerate along the suction surface and flow separation occurred; however, in the case of the airfoil with the VG, the fluid accelerated along the suction surface and flow separation did not occur. When flow separation occurs on the suction side, a low-pressure region is formed in the wake, which lowers the lift coefficient and increases the drag coefficient. As shown in Figure 11a,b, when the VG is attached, the airfoil experienced a high lift force at an angle of attack of 5.9° or higher and a low drag force at an angle of attack of 14.8° or higher.

Aerodynamic Characteristics of DU Airfoil with VG
Based on the results of the CFD analysis, the cross-sectional DU airfoil in the region where flow separation occurs predominantly was selected as the test airfoil for VG application analysis. Figure 9 shows the surface grid of the VG-equipped airfoil used for simulation, and Table 5 contains the number of grids that were used.
The chordwise velocity contours of the airfoil with and without the VG are shown in Figure 10a,b. The results of the CFD analysis confirm that, in the case of the airfoil without the VG, the fluid did not accelerate along the suction surface and flow separation occurred; however, in the case of the airfoil with the VG, the fluid accelerated along the suction surface and flow separation did not occur. When flow separation occurs on the suction side, a low-pressure region is formed in the wake, which lowers the lift coefficient and increases the drag coefficient. As shown in Figure 11a,b, when the VG is attached, the airfoil experienced a high lift force at an angle of attack of 5.9 • or higher and a low drag force at an angle of attack of 14.8 • or higher.      Figure 9. Surface mesh of VG-mounted airfoil extruded in the span direction.

Investigation of the Influence of VG Design Parameters
The design variables and layout of the VG are shown in Figure 3, where the thickness t is fixed at 0.05 and the length of the upper section u is fixed at 0.2. A total of 27 CFD analyses were performed, and the variables used in each of these cases are listed in Table 6. In the analyses, the Reynolds number and angle of attack were set to 3.0 × 10 6 and 12 • , respectively. The results of these case studies are presented in Table 7. Figures 12 and 13 show the vorticity contours for cases 1,2,3,5,8,11, and 20 at locations 50% and 100% of the chord length from the leading edge, respectively. In Figure 13, the vorticity contour at the trailing edge can be compared when each parameter is changed based on case 2.
The response surface methodology (RSM) used a LOWESS (Locally Weighted Scatterplot Smoother) second equation to find combinations that could represent the best VG effect using the three independent design parameters, layout (L), length (l), and height (h), as shown in Figure 3 [41]. Four objective variables, C L , C D , and the maximum vorticity at the positions 50% and 100% from the leading edge to the trailing edge, were investigated. The correlation between the C L values is shown for these cases in Figure 14 as 3D surface plots. In this figure, the value calculated for C L tends to be higher as the length (L) is closer to the median value and the height (h) and layout (l) are lower. The correlation between the maximum vorticity values of the trailing edge is also shown in terms of the three parameters in Figure 15. Unlike C L , the calculated value of the maximum vorticity of the trailing edge tends to be higher for l, lower for L, and that of h is closer to the median value. The VG design parameter selection criteria, more weight assigned to the maximum vorticity at the trailing edge, and the parameters were selected as shown in Figure 3 in consideration of manufacturability.

Aerodynamic Characteristics of Wind Turbine Blade with VG
The CFD analysis of the viscous sub-layer was precisely performed by composing the entire grid with a hexahedron. Figure 16 shows the surface grid of the VG-mounted blade used for the simulation, and the number of grids is provided in Table 8. A pair of VGs each generates a vortex in the opposite direction and a high-energy fluid flows into the boundary layer region of the low-energy flow field. Figure 17 shows the characteristics of the fluid flow and the CFD results of the structural analysis of the vortex created by the VG. The analysis confirmed that a tip vortex was generated at the tip of the VG and a horseshoe-shaped vortex formed at the lower front of the VG. Figure 18a,b shows that the flow separation is relatively reduced on the suction side compared to the baseline blade. Figure 19a,b shows that the VG forms a vortex and pushes the separation fluid to a distance of 8 m from the root, where flow separation is dominant. The shaft power was calculated by multiplying the torque and angular velocity of the simulation results. The calculated shaft power without and with the VG-mounted blade was 2365 kW and 2433 kW,

Aerodynamic Characteristics of Wind Turbine Blade with VG
The CFD analysis of the viscous sub-layer was precisely performed by composing the entire grid with a hexahedron. Figure 16 shows the surface grid of the VG-mounted blade used for the simulation, and the number of grids is provided in Table 8. A pair of VGs each generates a vortex in the opposite direction and a high-energy fluid flows into the boundary layer region of the low-energy flow field. Figure 17 shows the characteristics of the fluid flow and the CFD results of the structural analysis of the vortex created by the VG. The analysis confirmed that a tip vortex was generated at the tip of the VG and a horseshoe-shaped vortex formed at the lower front of the VG. Figure 18a,b shows that the flow separation is relatively reduced on the suction side compared to the baseline blade. Figure 19a,b shows that the VG forms a vortex and pushes the separation fluid to a distance of 8 m from the root, where flow separation is dominant. The shaft power was calculated by multiplying the torque and angular velocity of the simulation results. The calculated shaft power without and with the VG-mounted blade was 2365 kW and 2433 kW, respectively, confirming a 2.80% increase in the shaft power compared with the result before installation. respectively, confirming a 2.80% increase in the shaft power compared w before installation.    respectively, confirming a 2.80% increase in the shaft power compared with the resu before installation.

Conclusions
In this study, a CFD-based in-depth investigation was conducted to d effects of the shape of the VG and the layout of VGs on the power performa turbine. The RSM was used to investigate the influence of VG design variab plex simulations using more than 55 million elements were carried out. Ba depth investigation, the following conclusions were drawn.

Conclusions
In this study, a CFD-based in-depth investigation was conducted to determine the effects of the shape of the VG and the layout of VGs on the power performance of a wind turbine. The RSM was used to investigate the influence of VG design variables, and complex simulations using more than 55 million elements were carried out. Based on the in-depth investigation, the following conclusions were drawn.

1.
A CFD analysis of multi-MW wind turbine blades was performed, and subsequently validated by comparing the results with those obtained with the GH Bladed design values.

2.
The influence of the VG design parameters was investigated using CFD analysis, which confirmed that the VG reduced the occurrence of separation flow, increased the lift, and reduced the drag at high angles of attack.

3.
Analysis of the flow characteristics of the blade with the mounted VGs confirmed that the tip vortex generated by the VG reduced the separation area by allowing the high-energy fluid to flow to the low-energy separation area. 4.
The VGs were confirmed to play an important role by improving the aerodynamics of multi-MW wind turbines by 2.80% at the rated wind speed. This was confirmed by the simulation at the rated wind speed with more than 55 million elements.

5.
The results of this study are expected to be useful for selecting the mounting position and shape of the VG by conducting a full-scale simulation by automating the construction of the simulation environment.
The selected VG discussed in this study is currently installed in a 2.3 MW wind turbine and is being monitored using SCADA systems. The VG could also be installed on other large wind turbines by using the proposed method for constructing a computational environment.