1 Introduction

Harvesting energy from the wind is considered one of the most viable sources of clean energy (Ramlee et al. 2020). Wind turbines are classified into vertical axis wind turbines (VAWTs) and horizontal axis wind turbines (HAWTs). Although HAWT has higher efficiency and its technology is better developed due to the benefits from the enormous investment in the last decades to overcome many deficiencies (Akhlagi et al. 2023; Paraschivoiu 2002). In contrast, there are still existing various challenges with HAWTs currently, such as noise pollution, ecological problems, and fatigue issues (Ni et al. 2021). Compared with HAWTs, VAWTs have been gaining increasing attention for several advantages, i.e., ability to withstand high turbulence and better performance in complex urban areas, omni-directional without yawing mechanism, lower cost (manufacturing, installation and maintenance) and it is designed for low wind speed. Despite the practical advantages of the VAWT, the VAWTs face some disadvantages: low power generation due to dynamic stall and blade wake interactions and difficulty to self-start (Farajyar et al. 2023; Li et al. 2017; Paraschivoiu 2002).

The phenomenon of dynamic stall refers to the boundary layer separation that occurs to the unsteady flow over aerodynamic bodies. This phenomenon appears with various current applications in aeronautics, hydrodynamics, and wind engineering, mainly on the wings and rotating rotor blades, including VAWTs. Dynamic stall occurs when VAWT blades operate in a wide range of angle of attack (AOA) periodically at different azimuth angles at low values of the tip speed ratio (TSR) of less than 4 (Asadbeigi et al. 2023). It generally depends on the airfoil configuration, Reynolds number (Re), number of blades, chord length and TSR (Hand et al. 2017; Jha et al. 2020). It significantly impacts noise levels, vibration, and power extraction. Hence, VAWT urgently requires effective and low-cost devices to increase efficiency.

Many effective techniques have been proposed for suppressing dynamic stalls and enhancing the power coefficient of turbomachinery, including the VAWT. These techniques can be divided based on active and passive flow control techniques. Active flow control methods can suppress the dynamic stall by adjusting the control parameters. However, these techniques required complex control mechanisms, algorithms, maintenance, weight, and additional energy expenditure during operation for flow structure improvements, which any benefits must outweigh (Azlan et al. 2023). By contrast, passive flow control techniques, e.g.,,, cited by Zhu et al. (2018), including; leading-edge micro cylinder, slots, Gurney flaps (GFs), thin plates at trailing edge, passive movable flaps, leading edge serrations, tilted blades, J-shaped airfoil, airfoil with a cavity, variable droop leading-edge, adaptive blades, leading edge slat, non-circular gap, flow-deflecting airfoil and vortex generators, are usually cheap, easier to implement, and no additional energy needed. The effect of dimples (Azlan et al. 2023), surface roughness (Özkan and Erkan 2022) and slots (Belamadi et al. 2022) on the blades are some of the recent investigations on passive flow-field control for performance enhancement of HAWT. GF, micro tab, vortex generator, and leading-edge slat are the most common passive flow control technology widely used in straight-bladed VAWTs (Zhong et al. 2019).

The Gurney flap is a small plate added to the airfoil's trailing edge (TE) perpendicular to the chord line. It was first proved by Liebeck (1978) after its invention by Dan Gurney in the 1970s. Liebeck found that adding GF to the symmetrical airfoil known as a Newman airfoil increased the lift at different AOAs with a penalty in drag with an optimum GF height of 1.25% of the chord length (c). He also concluded that the GF height should have remained between 1 and 2% c and kept submerged within the local boundary layer to avoid rapid increment in drag to obtain a beneficial L/D ratio, which is supported by the results of Myose et al. (1996), Giguère et al. (1997) and Li et al. (2002). Liebeck also proposed that the adding GF changed the flow structure around the TE. Since then, and with the development of computational fluid dynamics (CFD), many geometrical modifications of the GF to enhance the lift have been proposed by researchers covering several applications, such as VAWTs.

Many flow control techniques have been proposed to enhance lift to obtain a high lift-to-drag ratio; however, the drag is also increased due to downstream flow separation. The attempts to propose, study, or investigate the drag reduction devices in the literature are limited to some works (Bechert et al. 2000). Studied different GF modifications, including GF with slite and GF with holes and later by Meyer et al. (2006) and Lee (2009); the aim of these modifications is to stabilize the wake flow behind the TE by generating jet flows disrupted the periodic wake behind the flap thus, control the size and location of a von Karman vortex street to reduce the flow unsteadiness, which results in a drag reduction. Compared to solid flap, the magnitude of lift and drag coefficients decreased; however, the decrease in drag outweighed the lift loss, resulting in an improving lift-to-drag ratio.

A wedge flap (WF) that can reduce drag can act as a passive control device placed at or near the TE of the wings and rotor blades. It helps to improve the lift coefficient, reduce the drag coefficient, and improve the overall performance of an airfoil compared to the GF. The WF and the divergent trailing edge (DTE) are similar TE devices designed to increase airfoil efficiency at cruise conditions (Storms and Jang 1994). Only a few studies are concerned with deploying WFs, GF filled-in, and DTEs as flow control devices in literature, as shown in Table 1. To conclude, the working principles of DTEs and WFs are quite similar to the GFs.

Table 1 Summary of wedge flaps, divergent trailing edges and filled-in Gurney flaps that have been attached to the airfoil
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Although the literatures listed in Table 1 showed that the WF has initial promises resulted in power output exceeding GFs if properly chosen its dimensions, since it can control its lift and drag by adjusting its height and length. There are shortcomings in the study of the WF as flow control device such as most of the previous studies conducted airfoils equipped with WFs or DTEs in aircraft operation conditions and may not be viable for other applications such as VAWTs. Even in other fields, past researchers that studied WFs limited to studying few numbers of heights and their differential. However, they did not study the effect of heights in a systematic manner, for example starting from the lowest height to the maximum possible height can achieve the best performance. In addition to height, WF effectiveness influences by length, most of previous research limited to the performance at fixed length and this dimension can be studied systematically at various lengths to determine its effect on performance and its relationship to height to obtain the best length at a certain height (L/H). Furthermore, previous studies were poor in presenting a comparison of the performance of the GF Vs WF over a wide range of AOAs..

Generally, the use of different airfoil profile can change the power and momentum outputs. Symmetrical airfoils are well-known for their effectiveness with VAWTs, among them NACA0021 which is has a relatively large thickness. It is widely used for VAWT application with reasonable performance (Balduzzi et al. 2021; Du et al. 2019; Holst et al. 2019b; Mohamed 2012). However, previous studies were limited to employing asymmetrical airfoils with WF. Moreover, there is also a lack in studying the effect of the inclined WFs on the performance of the airfoil and most of past researches limited to perpendicular ones.

This paper aims to study the effects of NACA0021 airfoil equipped with WF on the aerodynamic performance and the flows over the mid-span section of airfoil blade using ANSYS FLUENT code to solve the steady Reynolds-Averaged Navier–Stokes equation (RANS) at a wide range of AOAs. The novelty of this paper will include:

  • Studying the impact of various heights of the WF added to the symmetrical airfoil NACA0021 on the airfoil's aerodynamic performance, aiming to determine systematically the optimal height at highest lift-to-drag ratio can be achieved.

  • In addition to height, the current paper will investigate systematically the effect of changing the length of WF at optimal height, aiming to obtain the best length- to-height ratio that maximizes performance.

  • The influence of the wedge angle for different cases will be studied to identify the optimal wedge angle can achieve the highest performance.

  • A comparison between present results of studying WF performance and the results of the GF performance from literature under the same conditions will be presented and discussed in this paper.

  • The effect of the flow on the trailing edge of the airfoil including streamlines, velocity profiles, and pressure contours will be studied to gain a deeper understanding of the flow behavior on an airfoil with an added WF at various AOAs, illustrating the positive impact of the WF in delaying separation point compared to the airfoil without WF.

The paper also presents flow visualizations from the simulations, including streamlines, velocity profiles, and pressure contours.

2 Methodology

In the current study, the ANSYS FLUENT (Version 2020 R1) solver based on the finite volume method is employed to predict the fluid flow phenomena by numerically solving the governing mathematical equations. The simulations are carried out in a two-dimensional manner to model the mid-span segment of the blade, with the effects of spanwise flow and tip loss are neglected. According to the literature, 2D simulations for this case are able to provide reliable data when compared to measured data, all while maintaining reasonable computational costs (Bangga et al. 2021; Florin et al. 2014; Rezaeiha et al. 2018b). An overview of the sequence steps of CFD Modeling is shown in Fig. 1.

Fig. 1
figure 1

Flow chart of CFD Modeling

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2.1 Airfoil Geometry and Test Plane

The symmetric 4-digit NACA series is the most widely used for VAWT applications. It has a relatively large thickness and improves turbine performance. Mohamed (2012) studied the performance H-rotor Darrieus turbine using the symmetric and non-symmetric NACA airfoils through CFD simulation. Its results show that NACA0021 gives the highest performance at low TSR < 4 among the symmetric NACA00xx series. Du et al. (2019) tested experimentally three‐bladed H‐Darrieus turbine with different airfoil profiles. Their study showed that the NACA0021 profile improves self-starting capability, enhancing power at low TSR. In the present study, 4-digit NACA0021 (Fig. 2) was selected with 140 mm chord length (c), which has been studied by some researchers in different works (Holst et al. 2019a; b; Balduzzi et al. 2021).

Fig. 2
figure 2

Airfoil geometry of NACA0021

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The effect of different WF dimensions (height and length) and the mounting angles were simulated and compared to the clean airfoil. The geometry of the NACA0021 airfoil equipped with WF is shown in Fig. 3, where H refers to the height of WF perpendicular to the chord line, L is the length of WF extended upstream on the lower airfoil surface, and γ is the mounting angle between the WF and the chord line of the airfoil. In this case, the dimensions of WF selected to be at the same length L = H or L/H ratio = 1.

Fig. 3
figure 3

Geometry of NACA0021 with WF

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Various wing flap (WF) heights were studied, and the lift coefficient (CL) and drag coefficient (CD) were assessed to reach the optimal lift-to-drag ratio (CL/CD). The coefficients acting on the airfoil were calculated using Eqs. 1 and 2. The flap's height (H) and length (L) were relatively defined to the chord length. Then, the influence of different mounting angles of 90° and 45° has been studied at different heights, reaching the optimum flap angle. Finally, the influence of different L/H ratios with various mounting angles and optimum fixed heights on the aerodynamic performance of static NACA0021 has been investigated.

$${C}_{{\text{L}}}=\frac{{F}_{{\text{L}}}}{0.5\rho S{U}^{2}}$$
(1)
$${C}_{{\text{D}}}=\frac{{F}_{{\text{D}}}}{0.5\rho S{U}^{2}}$$
(2)

where FL and FD are the lift and drag forces acting on the blade section, ρ is the air density, S is the area, and U is the air speed.

2.2 Governing Equations and Numerical Solutions

The governing equations of CFD are the Reynolds-averaged Navier–Stoke (RANS) equations derived from the conversation law of the physical properties of working fluid: mass, energy, and momentum. The RANS equations for the two-dimensional steady incompressible flow can be written in a conservative form continuity equation and a momentum equation, as shown below (Anderson et al. 2016; White and Xue 2021):

$$\text{Continuity equation},\quad \frac{\partial {\overline{u}}_{i}}{\partial {x}_{i}}=0$$
(3)
$$\text{Momentum equation},\quad \rho \frac{\partial {\overline{u} }_{i }{\overline{u}}_{j}}{\partial {x}_{j}}=-\frac{\partial \overline{p}}{\partial {x }_{i}}+\frac{\partial }{\partial {x}_{j}}\left(\mu \frac{\partial {\overline{u} }_{i }}{\partial {x}_{j}}-\rho \overline{{\acute{u}}_{i}{\acute{u}}_{j}}\right)+{S}_{i}$$
(4)

where the instantaneous value of velocity, u is expressed by the sum of its mean and the fluctuating part \({\overline{u}}_{i}\) and \({\acute{u}_{i}}\) of i direction, respectively, as: \(u={\overline{u}}_{i}\)+\({\acute{u}_{i} },\) \(\overline{p}\) is the mean pressure, μ is the dynamic viscosity coefficient, ρ is the density, \(\rho \overline{{\acute{u}}_{i}{\acute{u}}_{j}}\) is the Reynolds stress, and the generalized source term \({S}_{i}\) is the body force term. The energy equation requires heat transfer or high-speed flows where the velocity exceeds a critical limit, and the flow is assumed to be compressible. For the present case, the Mach number was less than 0.3, and the flow could be considered incompressible with constant viscosity; therefore, the energy equations were not solved.

The proposed SST k–ω turbulence model considers the effect of turbulent shear stress transportation and has better computational accuracy in capturing the adverse pressure gradient flows. The SST k–ω transport equations are shown below:

$$\frac{\partial }{\partial {x}_{i}}\left(\rho k{u}_{i}\right)=\frac{\partial }{\partial {x}_{j}}\left({\Gamma }_{k}\frac{\partial k}{{\partial x}_{j}}\right)+{G}_{k}-{Y}_{k}+{S}_{k}$$
(5)

and

$$\frac{\partial }{\partial {x}_{j}}\left(\rho \omega {u}_{j}\right)=\frac{\partial }{\partial {x}_{j}}\left({\Gamma }_{\omega }\frac{\partial \omega }{{\partial x}_{j}}\right)+{G}_{\omega }-{Y}_{\omega }+{S}_{\omega }$$
(6)

where k is the turbulence kinetic energy. ω the specific dissipation rate. Gk is the turbulence kinetic energy (KE) due to mean velocity gradients. Gω is the production of the dissipation rate. Γk and Γω are the effective diffusivity of k and ω, respectively. Yk and Yω are the dissipation of k and ω, respectively, due to turbulence. Sk and Sω are user-defined source terms.

The previous research (Wang et al. 2010) Investigated the ability of the standard k–ω and the SST k–ω models to correctly simulate the dynamic stall in VAWTs at the low Reynolds number regime. The results concluded that the SST k–ω could predict the experimental data sets with reasonable accuracy and the dynamic stall characteristics well captured. Rezaeiha et al. (2019) compared seven different turbulence models commonly used to optimize the most accurate model for CFD simulations of VAWTs. The extensive analysis concluded that only the SST models, including SST k–ω, can exhibit reasonable agreement with all the experimental data and predict the power coefficient more accurately with a wide range of TSR. Daróczy et al. (2015) compared five turbulent models widely used in simulations of VAWTs employing two-dimensional versus different experimental works to identify the most suitable model. The results revealed that the k–ω SST model agreed well with the experiments.

Thus, the turbulence model employed in this study is the shear stress transport (SST) k–ω. Also, the transition from laminar to turbulent flow transitional (SST) k–ω model was adopted to simulate the flow during and after stall angle at different AOAs for accurate results. In this study, numerical simulations were performed using ANSYS FLUENT commercial CFD software. The numerical constants and solution methods in this study are stabulated in Table 2.

Table 2 Numerical constants and solution methods
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2.3 Computational Domain and Boundary Conditions

In the simulation of a static aerofoil, the chord length (c) is 0.14 m. The Re (Eq. 7) is 1.8 × 105, and the Mach number is 0.06, i.e., thus, the flow is incompressible. The air temperature is 20 oC, while density (ρ) and dynamic viscosity (μ) are 1.204 kg/m3 and 1.855 × 10–5 kg/m s, respectively. Such conditions represent small to medium-scale urban VAWTs (Rezaeiha et al. 2018a).

$${\text{Re}}= \frac{c\rho U}{\mu }$$
(7)

The computational domain size in the range of 10–20 length /chord has been adopted by many researchers, such as Wang et al. (2017), Yan et al. (2020), Michna et al. (2021). Their results show that this range is sufficient to obtain accurate aerodynamic results. The distance of the inlet and outlet boundaries away from the 1/4 of the airfoil chord length is 12.5c and 22.5c, respectively, and the top and bottom boundaries are 21.75c away from the TE. Figure 4 illustrates the computational domain size adopted and the boundary conditions in the present study, while the values are tabulated in Table 3.

Fig. 4
figure 4

Computational domain dimensions and boundary conditions

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Table 3 Boundary conditions for CFD simulations
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2.4 Mesh Generation and Dependency Test

Michna et al. (2021) studied extensively different mesh properties and their impacts on the prediction of the accuracy of solutions. Different mesh properties contribute together to improve the mesh quality, increasing the accuracy of calculation results and avoiding the waste of computational time. In the present study, a C-type structured grid was adopted, and the grid distribution near the wall where the boundary layer is located is refined to capture the physics of the flow around the airfoil. Typically, there are 100 layers with a first layer height of 0.016 and a growth rate of 1.097. For the trailing edge, there are 140 layers, and the first layer height and growth rate are 0.015 mm and 1.068, respectively. Figure 5 shows the whole computational domain and a zoomed view of the leading and TEs.

Fig. 5
figure 5

Details of the computational grid. a Airfoil, b C-mesh computational domain (overall mesh), c near the leading edge, d near the TE around WF

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Four types of grids are used in the current simulation to check the dependency of the results on the grids. The details of the grids studied at Re = 1.8 × 105 are shown in Table 4. Figure 6 shows the CL and lift-to-drag ratio (CL/CD) variations with a range of AOAs for different grid distributions G1 to G4. The lift coefficient increases with grid refinement from G1 to G3, and G4 shows no more gains in the lift with high mesh density, indicating that the simulation results are independent of the grid numbers selected.

Table 4 Grid parameters of the clean static NACA0021 airfoil
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Fig. 6
figure 6

Comparison of CFD simulation for four grid distributions in the case of a clean static airfoil. a Lift, b lift-to-drag ratio

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Therefore, the G3 with the number of cells of about 10.8 × 104 for the case of clean airfoil was adopted in the present simulation. In contrast, the grid cells for the airfoil equipped with WF are about 1.16 × 105. Figure 6 shows the 800 nodes along the chord line on the upper and lower surfaces of the airfoil mesh with higher concentrations near the leading and TE regions. The non-dimensional distance y+ value of the first grid point is kept at approximately 1, which means the near-wall mesh is refined enough to resolve the viscous sublayer (Ghazali et al. 2016).

3 Results and Discussion

3.1 CFD Validation

The present CFD simulation was validated by comparing the aerodynamic characteristics of the static airfoil with measurements from wind tunnel experiments and simulations from the literature. Figure 7 compares experimental at different turbulence intensity (TI) and computational data for the NACA0021 across a wide range of AOAs at the same conditions, i.e., chord length, c = 140 mm and Re = 180K. A series of experimental works done by Holst et al. (2019a; b, c), which include the raw and corrected data were used in the validation. According to them, corrections are needed considering the airflow deflection that originated from an open jet and attributed to the lift force generated from the aerodynamic interaction between the flow and the blade surface.

Fig. 7
figure 7

Validation of static polars (NACA0021 profile) up to stall angle against literature data at Re ~ 180K. a Lift coefficient. b Drag coefficient

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From the figure, it can be observed that the maximum lift coefficient of uncorrected experimental data by Holst et al. (2019b) with TI < 0.5% shows a suitable matching to the present CFD simulation in terms of maximum lift and general behavior. Meanwhile, the corrected experimental data at a TI of 1% matches well with the simulation by Balduzzi et al. (2021). The typical stall angle of the airfoils occurred when AOA was around 15°. As shown in Fig. 7, the stall angle of the present CFD simulation occurred at 18°, while for both uncorrected experimental works, the stall occurred at AOA = 19°. Balduzzi's simulation and corrected experimental work by Holst at TI less than 1% show the same stall angle at 16°. Balduzzi's CFD work visualizes a nearly constant lift after stalling at AOAs between 16° and 20° while the present study and corrected results by Holst show constant lift at AOAs beyond 19° and 20°, respectively. This is caused by a continuous TE stall companioned with dramatic rises in drag due to separation in the boundary layer.

Figure 7b illustrates a comparison of the drag coefficient with earlier studies. The drag values from our current CFD simulation align well with literature data up to static stalling, with the exception of Holst's work. Holst's drag coefficient values exhibit underestimation in the small AOA range. This discrepancy arises because the computation of drag coefficients relies on the surface pressure distribution, wherein only pressure drag is considered. Contributions from skin friction are inherently absent, influencing the lower AOA region (Holst et al. 2019c).

Hence, the drag coefficient presented by Holst does not include the total drag, especially at low AOAs. In contrast, Balduzzi's simulation and experimental works show consistent behavior with a slight increase in the drag coefficient from the current study at AOAs less than 6°. The general behavior of the lift in the present study shows excellent agreement with the works of literature despite the lack of corrected experimental data by (Holst et al. 2019b).

3.2 Effects of the WF Height and Inclination Angle

The effect of the WF height attached to the NACA0021 airfoil and its mounting angle γ = 90° and 45° was investigated. In this section, both WF dimensions L and H are considered to have the same length. The effects on aerodynamic characteristics are discussed in the following sections:

3.2.1 Effects on Lift Coefficient

Figure 8a, d illustrate the lift coefficient increments with increasing WF heights for γ = 90° and 45°, respectively. Wedge flaps shift the maximum CL to the lift side by 2° and 3° for the cases of trailing edge wedge flap with γ = 90° (TEWF-90) and trailing edge wedge flap with γ = 45° (TEWF-45), respectively, in comparison with the clean airfoil case. The increment in maximum values of CL with WF height and angle are presented in Table 5. The value of the maximum CL increased by 25.09% at 1%c WF height to 70.19% at WF height of 5%c for the TEWF-90 case, while in the case of TEWF-45, the maximum values of CL increased from 19.19% at WF with 1%c height to the 69.15% at WF height 0f 7% of the chord length.

Fig. 8
figure 8

Effect of WF height and mounting angle on the aerodynamic characteristics of the NACA0021 airfoil. At the lift side with TEWF-90. a Lift. b Drag. c Lift-to-drag ratio. At the right side with TEWF-45. d Lift. e Drag. f Lift-to-drag ratio

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Table 5 Increments of the maximum value of lift coefficient for different TEWF-90 and TEWF-45 heights in comparison with the clean airfoil case
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3.2.2 Effects on the Drag Coefficient

The CD variations with AOA for different TEWF-90 and TEWF-45 heights in comparison with the airfoil baseline case are shown in Fig. 8b, e, respectively. The drag significantly increases as the wedge height increase. Obviously, as the AOA increases, the CD increases as well at the range of AOA between 0° and 10° with a small increase in drag while, the penalty of drag at AOA > 10 increases with the increase of AOA.

3.2.3 Effects on Lift-to-Drag Ratio, C L/C D

Figure 8c, f demonstrate the increases in lift-to-drag ratios with AOAs at different WF heights and with both angles 90° and 45°, respectively, compared with the airfoil without WF. At low to moderate AOAs, the lift increases with the minor penalty of drag, resulting in a significant increase in the lift-to-drag ratio. At moderate to high AOAs, a significant drag penalty decreases the lift-to-drag ratio reaching the stall angle.

  • Case of TEWF-90

As depicted in Figs. 8c and 9, the maximum lift-to-drag ratio increases with WF heights %1c, %2c, %3c and %4c. In contrast, the maximum lift-to-drag ratio at WF with five height shows a reduction in lift-to-drag ratio due to a significant penalty in drag. This might happen when the WF height exceeds the boundary layer thickness. Therefore, the optimum WF height at a 90° mounting angle is 4%c with a maximum increment in the lift-to-drag ratio of 40.80% at AOA = 7° compared to the clean airfoil case.

Fig. 9
figure 9

Increments in the values of maximum lift-to-drag ratio at different WF heights and angles compared with the clean airfoil

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  • Case of TEWF-45

Lift-to-drag ratio value increases as illustrated in Figs. 8f and 9 with WF heights of %1c, %2c, %3c, %4c, %5c and 6%c. In contrast, WF with 7%c height shows a reduction in lift-to-drag ratio due to a significant penalty in drag. The optimum WF height at 45° mounting angle is 6%c with a maximum increment in lift-to-drag ratio of 44.57% at AOA = 6° compared with the clean airfoil case. Therefore, the NACA0021 employed with a WF mounting angle of 45° provides better performance than whose WF is 90°. These results agree with the experimental work by Bloy et al. (1997). From Fig. 9, it can also be concluded that the point of intersection of TEWF-90 and TEWF-45 curves means that the increment of lift-to-drag ratio of 40.7% in comparison with clean airfoil case could be achieved for both cases using WF with the same height at about 3.55% of the chord length.

3.3 Effect of the WF Length

The effect of various WF length-to-height (L/H) ratios for TEWF-90 and TEWF-45 in comparison with optimum characteristics of WF at heights of 4%c and 6%c, respectively on the aerodynamic performance of the NACA0021 airfoil presented in Table 6, Figs. 10 and 11. In previous sections, the investigations were performed to find the optimum WF height and angle attached to the symmetrical airfoil NACA0021 at L/H = 1. In the present section, the effect of different WF lengths at an optimum fixed height (resulting from the last section) and different mounting angles on the performance of static NACA0021 will be performed. Different L/H ratios have been studied L/H < 1 and L/H > 1. The CL-AOA curves show positive increments of maximum lift at L/H < 1 for TEWF-90 and TEWF-45 cases, while at L/H > 1, the increment of maximum CL values becomes negative be due to the penalty of drag due to extending the length upstream.

Table 6 Increment in the values of the maximum lift-to-drag ratio at fixed WF height and with different WF lengths for TEWF-90 at 4%c (5.6 mm) and TEWF-45 at 6%c (8.4 mm) in comparison with the L/H = 1 case
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Fig. 10
figure 10

Effect of WF length and mounting angle on the aerodynamic characteristics of the NACA0021 airfoil. At the lift side with TEWF-90. a Lift. b Drag. c Lift-to-drag ratio. At the right side with TEWF-45. d Lift. e Drag. f Lift-to-drag ratio

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Fig. 11
figure 11

Increment in the values of maximum lift-to-drag ratio at different WF lengths and angles compared with the L/H = 1 case

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The lift coefficient curve shows a higher lift value for the TEWF-90 case at L/H = 0.125 ratio with a higher penalty of drag resulting in the low values of lift-to-drag ratio as shown in Figs. 10c and 11, and this might be happened due to the vortex tip losses occurs with thin WF. As the L/H ratio increases at the pressure side of the airfoil, the lift decreases, and the drag also decreases. Still, the lift-to-drag ratio increased, reaching the maximum value at L = H before falling again at L/H > 1.25. Therefore, the optimum lift-to-drag ratio for the TEWF-90 case was achieved at L = H.

The lift-to-drag ratio curves for TEWF-45 Figs. 10f and 11 show higher increment at low L/H ratio with a slight degradation of maximum lift-to-drag ratio at thin WF when L/H = 0.0834 (L = 0.5%c). The increments in lift-to-drag ratio have a maximum value of 0.847% at L/H = 0.0167, where the length is 1%c, and the height is 6%c compared with TEWF-45 case at L = H = 6%c, the increments in maximum lift-to-drag ratio decrease slightly at L/H < 0.5 then, the decrement rate at L/H > 1 increased. Generally, the WFs with L/H < 1 show a slight increment in the aerodynamic performance compared with the higher decrement at L/H > 1.

3.4 Optimum Aerodynamic Characteristics for TEWF-90 and TEWF-45

Comparison of different maximum aerodynamic characteristics for TEWF-90 with 4%c height at L = H, TEWF-45 with 6%c height at L = H, and with 6%c height and 1%c length with comparison to clean airfoil case are shown in Fig. 12. As Fig. 12a presents, TEWF-45 with 6%c height and 1%c length shows a higher lift coefficient at AOA < 15° with a maximum lift force coefficient value of 1.59 at AOA = 11 with total increments value of about 71.67% in comparison to clean airfoil case, before its early stall in comparison to TEWF-90 with 4%c. The maximum lift for studied cases shifted the lift by 2° compared to the clean case. Figure 12b shows a reduction in drag of TEWF-45 cases at AOA < 10° before their increase at higher AOA compared to TEWF-90. The aerodynamic efficiency for TEWF-45 with L/H = 0.167 (L = 1%c) in Fig. 12c shows the highest values of lift-to-drag ratio at low to the medium of AOA range with a maximum increment of 45.79% at AOA = 6 compared to the clean airfoil case.

Fig. 12
figure 12

Optimum aerodynamic characteristics for TEWF-90 and TEWF-45 cases in comparison with the clean NACA0021 airfoil case. a Lift. b Drag. c Aerodynamic efficiency

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3.5 Wedge Flap Versus Gurney Flap

The length and height of WF can control the drag and lift coefficients, respectively, while the GF effectiveness depends on just height, which gives WF more advantages over GF. A comparison of the lift-to-drag ratio of NACA0021 employed with TEWF-45 with 6%c height and length of 1%c versus the same airfoil section and chord length equipped with GF with 2.5%c height from literature work by Balduzzi et al. (2021) presents in Fig. 13. At AOAs < 5, the performance of TEWF is higher than GFs, which could give the better self-starting capability to WFs over GFs, while at AOAs > 5, the GF could give higher performance before stalling at the same angle. It can also be concluded that GF with 2.5%c height can produce nearly the same effect as WF with 6%c height. The greater height of WF provides higher stability and mechanical stiffness of the blades (Bechert et al. 2000).

Fig. 13
figure 13

Comparing maximum lift-to-drag ratio TEWF-45, H = 6%c, L = 1%c and GF H = 2.5%c from literature

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3.6 Flow Control Visualizations

The effect of WF control on the flow structure could be understood through flow visualization. Figure 14 shows velocity and pressure distributions and streamlines of NACA0021 airfoil equipped to TEWF-90 with h = 4%c and TEWF-45 with h = 6%c compared with flow visualization of the clean airfoil at different AOAs. At AOA = 0°, separation bubbles can be observed at the upstream zone, while two counter-rotating vortices are presented at the downstream zone of the WFs, and the wake streamlines are deflected downward as compared to the clean airfoil case. The TEWF-90 shows higher circulation in the upstream zone than TEWF-45; this might be attributed to the higher lift and drag produced by TEWF-90, while TEWF-45 shows smooth flow deflection, leading to less lift but considerably less drag with enhancing lift-to-drag ratio over TEWF-90.

Fig. 14
figure 14figure 14

Streamlines, pressure, and velocity distributions for TEWF-90 and TEWF-45 at different AOAs in comparison with clean NACA0021 airfoil

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With increasing AOA, the first appearance of separation point at AOA = 1° for clean airfoil case starting from TE, as shown in Figs. 14 and 15, while TEWF-45 suppressed the separation points till AOA = 5°. At AOA = 7°, the separation point moves slightly forward, and the size of the vortices increases, which leads to more deflection of the flow at the TE, hence increasing the effective downwash. Therefore, the vortices in the wake region are mainly responsible for the pressure difference between suction and pressure surfaces, hence the lift enhancements. The counter-rotating pairs move up at AOA = 12°, where the lift is at its maximum value, and the separation point moves toward the leading edge. At x/c ≈ 40%c from TE, the locations of the separation points are close for the clean airfoil case and TEWF-45 case, as shown in Fig. 15. Thus, WF can increase the lift by delaying the flow separation in the TE of the airfoil.

Fig. 15
figure 15

Separation point development versus AOA along airfoil chord length for TEWF-45 compared with clean NACA0021 airfoil

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A sudden decrease in the lift indicates the occurrence of a dynamic stall with a large turbulent wake behind the TE, as shown in Fig. 14. The stall occurs at AOA 16° and 17° for TEWF-45 and TEWF-90, respectively, compared with the clean airfoil where the stall occurs at AOA = 19°. With more increasing AOA, the airfoil experiences complete flow separation.

At AOA = 0° as shown in Fig. 14, the velocity and pressure contours for clean airfoil show that the stagnation point located precisely at the leading edge of an airfoil and the airflow accelerate to go on either side symmetrically. While at the same AOA in presence of WFs the stagnation point shifted a bit toward pressure side. For AOA = 7° the stagnation point of clean airfoil shifted a bit downstream of the leading edge. While this shifting toward pressure side clearly observed in presence of WFs at AOA = 7°.

4 Conclusions

In this study, the potential of using WF as a passive flow control device equipped to the wind turbine airfoils (NACA0021) has been studied computationally using ANSYS FLUENT to explore its impact on the flow behavior and aerodynamic performance. Various cases are considered to investigate WF height's effect and (L/H) variations at angles 90° and 45°. Results showed that deploying WFs changes the Kutta condition and creates a recirculation suction region near the TE's pressure side surface. This suction region enhances the flow pattern on the airfoil; thus, the effective camber line changed, and the pressure distribution between TE upper stream and downstream was affected.

The CFD model from this study could adequately capture the aerodynamic characteristics and the flows over the modified airfoil. To conclude, the main findings are as follows:

  • The optimum WF height at a 90° mounting angle is 4%c with a maximum increment in the lift-to-drag ratio of 40.80% at AOA = 7° compared to the clean airfoil.

  • The optimum WF height at a 45° mounting angle is 6%c with a maximum increment in lift-to-drag ratio of 44.57% at AOA = 6° compared with the clean airfoil.

  • Thin WFs with L < 1%c show the highest lift coefficient but with slight degradation of the maximum glide ratio, which may be attributed to the vortex tip losses at blade tips.

  • The maximum increment value in lift-to-drag ratio due to variations of L/H is 0.847% at L/H = 0.0167, L = 1%c and the H = 6%c compared to TEWF-45 case at L = H = 6%c,

  • The WFs with L/H < 1 show a slight increment in the aerodynamic performance, while at L/H > 1 indicate a higher performance decrease compared with the L/H = 1 case.

  • The TEWF-45 with H = 6%c and L = 1%c suppressed the separation points till AOA = 5° and achieved maximum CL and CL/CD values at AOA 11° and 6° with total increment values of about 71.67% and 45.79%, respectively, in comparison with the clean airfoil case.

  • Trailing edge WF shows higher performance than GF for the same airfoil section and Re number at AOA < 5, which might give better self-starting capability to WFs than GFs.

  • It can also be concluded that Gf with 2.5%c height can produce nearly the same effect as WF with 6%c height. The greater height of WF provides higher stability and mechanical stiffness of the blade.

  • The presence of WFs at certain AOAs adds a further effect of shifting the leading-edge stagnation point on the airfoil toward the pressure side of the airfoil, which is associated with increased circulation, resulting in lift enhancement.

  • The vortices acting on the downstream face of the WF are mainly responsible for the pressure difference between suction and pressure surfaces, hence the lift enhancements.

As a passive flow control device, WF can potentially suppress the separation point and enhance aerodynamic performance. The findings of the current study help to better understand the influence of airfoils employed with WF on the aerodynamic performance of different applications, such as aeronautics and rotating rotor blades. However, the investigations were limited to Re = 180k on a symmetric airfoil section in 2D. Further studies could be done to explore the effects of different Re numbers and asymmetric airfoil sections in 3D. Moreover, the developments could consider using WFs at optimal configurations in vertical axis wind turbine design or in combination with different passive flow control techniques.