Performance improvements of vertical axis wind turbines with modified gurney flaps

Plain Gurney flap (PGF), as a passive flow control method, is widely used to improve the aerodynamic performance. Due to the drag penalty, a novel serrated Gurney flap (SGF) is proposed. The numerical simulation is carried out to investigate the effects of GFs on the aerodynamic performance of the NACA0018 airfoil and an associated two-blade rotor of a H-type Vertical Axis Wind Turbine (VAWT). The height of GF ranges from 1.5% to 6% of the airfoil chord length. The results show that the SGF doesn’t exhibit the same lift enhancement as PGF, but lower drag. When the flap height reaches 6% c, the SGF airfoil has the higher lift-to-drag ratio. The 3%-chord-length height of GFs is employed on the rotor and it implies that both PGF and SGF can enhance the output power of VAWT. SGF has superior performance than GF, especially at the TSR>2.5 conditions. At the optimal TSR=3.0, the output power of SGF turbine is 2.7% higher than that of PGF one. The highest improvement of power can reach 13.3% at TSR=4.0.


Introduction
Wind power stands as a highly favored clean and renewable resource, possessing substantial developmental potential due to its widespread distribution across the globe.The vertical axis wind turbine (VAWT), envisioned as a potential cornerstone of distributed wind energy [1], exhibits lower power coefficients than horizontal axis wind turbine (HAWT), which curtails their utility [2].Consequently, the application of effective flow control methodologies becomes pivotal to augment the lift force exerted on VAWT blades.
Liebeck [3] discovered that a Gurney flap, referred to as the Plain Gurney flap (PGF), with a height equivalent to 2% of the chord length, can yield an approximate 30% increase in airfoil lift.Owing to its straightforward implementation and notable efficiency, the PGF has found extensive utilization in VAWT.Ismail and Vijayaraghavan [4] optimized the integration of the PGF with a semi-circular inward dimple on a VAWT blade, resulting in an approximate 35% rise in averaged tangential force under steady-state conditions and a 40% enhancement in oscillating scenarios.Xie et al [5] applied the PGF to the NACA0012 airfoil, leading to a 22% increase in maximum energy capture and a 15% boost in efficiency within a specific range of reduced frequency.Ni et al [6] examined the influences of Gurney flaps and the solidity parameter on VAWT performance.Installing Gurney flaps on the upstream pairs of VAWT can lead to elevated flow velocities, thereby enhancing the power output of the downstream rotor, with a potential peak average torque of 36.5%.Yan et al [7] explored the effects of Gurney flaps on the aerodynamic performance of an isolated NACA0018 airfoil, subsequently leading to a substantial enhancement in the power coefficient of a three-blade VAWT rotor at a low tip speed ratio (TSR).Yang et al [8] developed an active flow control method involving flapped airfoils for VAWT.The manipulation of the trailing edge flap angle was employed to mitigate trailing edge wake separation and defer dynamic stall.
In addressing the issue of drag penalty, numerous endeavors have been undertaken to mitigate the adverse effects of flaps.Meyer et al [9] explored the utilization of slotted flaps to diminish both lift and drag, simultaneously enhancing the lift-to-drag ratio.Alterations in the three-dimensional configuration of Gurney flaps were observed to influence the wake's two-dimensionality, culminating in a 12% reduction in drag.Lee [10] examined the implementation of perforated flaps, leading to a reduction in drag alongside a modest decrease in lift.Li et al [11] conducted an experimental wind tunnel study to assess the impact of serrated Gurney flaps on a 40-degree cropped nonslender delta wing.Gai and Palfrey [12] outfitted a NACA0012 airfoil with flaps of equivalent height, and the findings affirmed that the serrated flap (SGF) exhibited marginally reduced drag compared to the solid flap (PGF).Von Dam et al [13] demonstrated that while serrated Gurney flaps yield a smaller lift coefficient increment than plain Gurney flaps, they are capable of elevating the lift-to-drag ratio.This phenomenon arises from SGF's capacity to postpone boundary layer separation on the suction surface of an airfoil, achieved by generating near-streamwise vortices that undergo elongation and assimilation within the Von Karman vortex street situated behind the flap [14].Additionally, Garry and Couthier [15] documented that a serrated Gurney flap comprising 90-degree segments, resulting in a projected frontal area merely 50% of that of a plain flap, exhibits greater effectiveness in terms of the lift-to-drag ratio.
To advance the existing knowledge and attain a more profound comprehension of the flow characteristics encompassing a symmetric NACA0018 airfoil equipped with SGF, an allencompassing investigation has been systematically undertaken in this study.It delves into the aerodynamic performance, wake evolution behind the flapped trailing edge, near-wake flow structure, and turbulence patterns.Moreover, an elevation of 3% of the chord length has been selected to assess the influence of both PGF and SGF on the performance of VAWT across a range of tip speed ratios.Additionally, an evaluation of the prospective utilization of serrated flaps in vertical axis wind turbines is carried out, accentuating their potential to enhance turbine performance.

Simulation setup
2.1.Isolated airfoil 2.1.1.Isolated airfoil model.Figure 1 depicts the baseline NACA0018 airfoil fitted with a Gurney flap characterized by height H, serrated angle θ, and thickness W. The computations are executed at a Reynolds number of 1.6×10 5 , predicated upon the airfoil chord length c=80 mm.The flap heights encompass 1.5%, 3%, and 6% c.Both PGF and SGF share the identical height H, while the thickness W is maintained at 1%c.The flap is oriented perpendicularly to the local airfoil surface at the trailing edge.In the case of SGF, the serrations manifest as full-depth cut-outs with a serration angle θ of 60 degrees.2.1.2.Mesh distribution.The computational domain extends 15c in the streamwise direction and 20c in the crossflow direction, as depicted in figure 2. Consistent with the insights of Kinzel et al [16] maintaining a minimum distance of 10c between the airfoil and the inlet/outlet surface is essential to ensure precise outcomes for the isolated airfoil's calculations.At the inlet, a prescribed free stream velocity of 25.2 m/s is employed, while the outlet is characterized by ambient pressure conditions.The domain exhibits a spanwise thickness equivalent to three sawtooth pitches.Both the airfoil and flap surfaces are designated as non-slip walls.Employing periodic boundary conditions on the streamnormal side surfaces serves to alleviate interference within the boundary and the fluid dynamics system.The meshing of the GF is depicted in figure 3. To enable precise examination of flow phenomena in the vicinity of the airfoil, the circular region encompassing the airfoil with a diameter of 3c is subjected to refinement.The mesh size in the immediate vicinity of the airfoil surface is 7 × 10 -6 m for the first layer, accompanied by a mesh growth rate of 1.1, yielding 33 boundary layers to ensure the requirement of y+ ≤ 1 in the boundary layer.The computational domain integrates a prismatic boundary layer grid oriented perpendicularly to the airfoil surface, while other areas employ unstructured polyhedron grids to ensure adaptability and efficacious solutions [17].
The lift and drag coefficients of an airfoil are defined by Where   and   are the lift and drag,  is the projected area of the airfoil.

Numerical solver and simulation validation.
To ensure both feasibility and accuracy, the Improved Delayed Detached Eddy Simulation (IDDES) method was embraced as the turbulence model.This approach amalgamates the delayed-DES (DDES) model with the improved RANS-LES hybrid model [18].The selection of the modified Menter's k-ω shear-stress transport (SST) twoequation turbulence model within the IDDES framework was based on its demonstrated ability to reliably predict aerodynamic forces and flow separation in the presence of adverse pressure gradients [19].IDDES has been utilized in various studies, such as Zhao et al [20], who performed IDDES simulations of flows past a wind turbine airfoil NACA634-021 for mild separation and dynamic stall and Benim et al [21], who predicted the aerodynamics of a small horizontal axis wind turbine using IDDES and obtained good agreement between numerical and experimental pressure coefficient data.
Employing a transient formulation, a bounded second-order implicit scheme with a time step of ∆t=5.0×10 - s was employed.The simulation's validity was established through a comparison with existing experimental measurements of the baseline airfoil conducted by Jacobs and Sherman [22].The comparison of lift and drag coefficients for the baseline airfoil across various attack angles is depicted in figure 4. The current predictions demonstrate a satisfactory agreement.Notably, for angles of attack within the range of 6°<α<13°, the predicted lift and drag coefficients closely align with the experimentally measured data.The TSR defined as  = / ∞ , encompasses these blade velocities.Notably, the rotor's forward movement is primarily driven by the tangential force (  ) exerted on the struts, while the normal force (  ) directed inward towards the struts serves a minimal purpose beyond generating structural stresses.A comprehensive overview of the rotor's attributes is presented in table 1.
As the blade undergoes its rotational cycle, the angle of attack (AoA, ) experiences periodic variation corresponding to changes in the azimuth angle ().The arrangement of the azimuth angle () is depicted in the velocity triangle on the blade in figure 5.When considering a specific tip speed ratio λ,  becomes a function of both  and λ, represented as follows: sin tan cos  The Shear Stress Transport (SST) k-ω turbulence model was chosen for equation closure, given its established capacity to yield accurate flow predictions within VAWT.This model is acknowledged for precisely representing boundary layer (BL) and stall phenomena around airfoil profiles during each rotation cycle [23].To couple the pressure-velocity field, the SIMPLE scheme was implemented, accompanied by second-order discretization in both temporal and spatial domains.
The simulation commenced with a steady Reynolds-Averaged Navier-Stokes (RANS) calculation to establish a fully developed initial flow field for subsequent unsteady computations.For enhanced accuracy, a revolution count of 22 was implemented, following the recommendation by Rezaeiha et al. [24].In the initial 20 revolutions, a time step of 1° was utilized, while in the subsequent revolutions, the time step was reduced to 0.2°.The aerodynamic performance was assessed using stable data extracted from the 22 nd revolution.
A mesh sensitivity analysis was conducted on the baseline model prior to incorporating GFs to ascertain an appropriate mesh resolution for the simulation.The computational grids were generated at three different densities, each corresponding to the minimum cell size on the blade, to assess whether the employed mesh adequately captured the dominant flow features.The arrangement of meshes between the rotating grid and the outer grid is illustrated in figure 7. A refined rectangular mesh area of size 12D × 8D was introduced to ensure a seamless transition to the external flow field.Additionally, a dedicated boundary layer grid was designed for the blade surface, where the initial grid layer's height was set to 7 × 10 -6 m with a growth rate of 1.1, maintaining the blade surface y+ value close to 1.The turbine power coefficient (  ) and the instantaneous moment coefficient (  ) are employed to quantify the mesh convergence.They are defined as follows: Where T is the torque generated from the rotor blades,  is the air density, and  is the crosssectional area of the turbine, computed as the product of the rotor diameter and blade height.
The turbine power coefficient (  ) for three mesh densities is presented in table 2. It is evident from the table that the medium and fine mesh resolutions yield very similar results, while the coarse mesh produces significantly lower values.This observation suggests that the medium mesh density is sufficient for capturing the dominant flow characteristics in VAWT simulations.Therefore, the medium mesh was employed in the subsequent simulations.

Computational model validation.
To assess the accuracy of the computational results, the experimental study by Castelli et al [25] was employed as a validation benchmark for the computational model.The results of the same computational investigations [24,25] were also compared, as shown in figure 8.It is evident that the current numerical findings exhibit a similar trend to the reference numerical simulation and experimental measurements.While this study slightly overestimates the power coefficient in comparison to the experimental data across all tested conditions, maintaining consistency with the CFD reference.Nevertheless, this discrepancy does not alter the trend of   variation with changing TSR, and the disparity with the CFD reference outcomes remains minor.Hence, these findings underscore the suitability of the current CFD methodology and grid configuration for accurately predicting the aerodynamic performance of the rotor model.

Effect of GFs on NACA0018 isolated airfoil 3.1.1. Aerodynamic forces and separation control.
The effects of GF height on the aerodynamic force coefficients upon NACA0018 are depicted in figure 9. P and S denote PGF and SGF, correspondingly, accompanied by numeric labels indicating distinct flap heights.As an example, P-3 signifies PGF with a 3% c flap height.Both PGF and SGF yield heightened lift coefficients (  ) as the angle of attack (AoA) increases.Moreover,   tends to escalate with greater flap heights, with PGF outperforming SGF at identical heights.Compared to the Baseline setup, the maximum lift coefficients for PGF and SGF at 6%c experienced increments of 77.3% and 57.7%, respectively.Additionally, as flap height rises, the airfoil's stall angle diminishes, leading to an earlier onset of stall, as depicted in figure 9 (a).
The PGF setup encounters a relatively smaller stall angle than SGF, with the stall angle of the 6% c PGF airfoil declining from 14 degrees to around 11 degrees.Another noteworthy observation from figure 9 (a) is that an SGF airfoil retains the flap's ability to augment the effective airfoil camber, leading to positive lift at a zero angle of attack, a phenomenon previously documented for the symmetric NACA0012 airfoil by Li [11] and the cambered NACA4412 airfoil by Jang et al [26].
While flaps enhance lift, they also generally result in higher drag coefficients for airfoils compared to the baseline, although this increase is less pronounced before  = 11°, as illustrated in figure 9 (b).SGF is believed to enhance the airfoil's lift-to-drag ratio (Cl/Cd) in comparison to PGF.Nonetheless, for flap heights below 6%c, the PGF airfoil exhibits a higher Cl/Cd than the SGF airfoil.For  > 12°, the flaps adversely impact Cl/Cd in contrast to the baseline configuration.With a flap height of H=6%c, the Cl/Cd of the SGF airfoil surpasses that of the PGF airfoil at  > 3°, suggesting that the SGF device enhances aerodynamic performance on a larger scale.
Flap affects flow separation on the airfoil surface by modifying the location of the separation point, as illustrated in figure 9 (d).The separation point exhibits a near-zero skin friction coefficient.At  = 6°, S-1.5 and P-1.5 displace the separation point towards the trailing edge by 7%c and 9%c, respectively, compared to the baseline airfoil, with negligible variations as flap height further increases.At  = 9°, P-6 and S-6 achieve a displacement of 17%, demonstrating effective flow separation inhibition by flaps.With increasing AoA, the separation point swiftly advances toward the leading edge, indicating airfoil stall.Furthermore, at identical flap heights, PGF exhibits a greater tendency to stall than SGF, consistent with observations in figure 9 (a).Analyzing the surface pressure coefficient distribution across the airfoil's upper and lower surfaces provides valuable insights into the fundamental physical mechanisms that underlie the observed lift enhancement resulting from the integration of trailing-edge flaps.The pressure coefficient () is defined as followed: Where  ∞ , , and  0 are the static pressure, density and velocity of freestream, respectively.Increasing the flap height results in a proportionally larger pressure differential between the airfoil's upper and lower surfaces at  = 6°, as depicted in figure 10 (a). Lee [10] has interpreted these effects as akin to elongating the airfoil and intensifying flow redirection near the trailing edge.The SGF airfoil exhibits a lower  compared to the PGF variant at identical flap heights.At  = 20°, indicative of a deep stall scenario, the flap substantially augmented the trailing load on the airfoil, leading to a notable region of flow detachment on the suction surface.This is supported by the presence of a consistent pressure zone, as depicted in figure 10 (b).Additionally, a substantial portion of the lift augmentation originates from a broad loading enhancement and an elevated peak suction.The flap broadens the wake width.The downward shift of the wake center is noticeable due to the heightened downwash caused by the presence of the flap.Both the wake width and downwash expand with escalating flap height, with the impact of PGF being more pronounced than that of SGF, as indicated in figure 12 (a).Furthermore, at equivalent heights, PGF experiences a more substantial velocity reduction compared to SGF, implying that SGF presents reduced resistance compared to PGF at  = 6°.Figure 12 (b) displays the mean velocity profiles at  = 20°, revealing notable distinctions in the wake characteristics.Firstly, the wake width notably expands, and flaps cease to induce the downwash effect on the airflow along the upper surface of the airfoil in comparison to the Baseline configuration.The effectiveness of the flap diminishes notably at higher airfoil angles of attack.

Effect of GFs on H-VAWT
A computational analysis was conducted on a two-blade vertical axis wind turbine equipped with 3% c height PGF and SGF at different TSR, which cover a range of 2.0 to 4.0.

Power and moment coefficient.
Flaps result in an augmentation of the power coefficient (  ) within the low TSR range (2 to 3), as depicted in figure 15.For TSR < 2.5,   of the VAWT equipped with PGF slightly surpasses that of SGF.Conversely, for TSR ≥ 3.0, the   of the VAWT employing PGF diminishes below that of the Baseline, while the VAWT featuring SGF maintains superior performance compared to the Baseline configuration.At TSR = 3.0,   of SGF is 2.7% higher than that of PGF and 5.7% higher than that of Baseline.At TSR = 4.0,   of SGF exceeds that of PGF by 13.3%.Additionally, the performance apex of the Baseline emerges at TSR = 3.0 , whereas the implementation of flaps shifts the   peak to around TSR = 2.75.Within the upwind domain (ψ=120°), a noticeable separation area emerges near the trailing edge on the suction surface, accompanied by a dual set of anti-vortices trailing the PGF airfoil.In contrast, a smaller vortex forms downstream of the SGF airfoil, constituting a flow pattern akin to the isolated airfoil configuration depicted in figure 13.At ψ=330°, representing the downwind sector, PGF amplifies wake instability, giving rise to the presence of alternating shedding vortices, a phenomenon relatively inconspicuous in the case of the SGF airfoil.This phenomenon may account for the superior performance of the SGF blade compared to the PGF blade within the downwind region.

Baseline
With P-3 With S-3

Conclusions
To offer valuable engineering insights into the aerodynamics a compact vertical axis wind turbine utilizing PGF and SGF, numerical simulations were conducted on both the NACA0018 airfoil and an H-type Darrieus wind turbine utilizing the same airfoil profile.The reliability of the current calculations was demonstrated through an evaluation of grid sensitivity and by validating the results against experimental data.The following conclusion were derived from the present study: (1) When compared to the Baseline configuration, both PGF and SGF exhibit substantial enhancements in lift coefficient.At a flap height of 6% c, the maximum lift coefficients for PGF and SGF increase by 77.3% and 57.7%, respectively.As the flap height attains 6% c, the lift-to-drag ratio of SGF surpasses that of PGF, predominantly owing to the notable escalation in resistance linked with PGF.
(2) The serrations on SGF disturb the columnar vortex structure created by PGF, resulting in a dual vortex arrangement that envelops both sides of the triangle and rotates perpendicular to the wake flow.This disruption is the cause for the lower lift and drag coefficient of the SGF airfoil compared to the PGF airfoil.
(3) Incorporating SGF into a VAWT yields a significant augmentation in turbine performance across all evaluated tip speed ratios.For TSR ≥ 3.0, the performance of the PGF rotor lags behind that of the Baseline configuration.This discrepancy arises from the amplified wake instability induced by PGF, a phenomenon alleviated by SGF within the downwind sector.At TSR = 3.0 , the power coefficient of SGF surpasses that of PGF by 2.7%, and this improvement amplifies to 13.3% at TSR = 4.0.

Figure 2 .
Figure 2. Geometry features and main dimensions of the computational domain (not to scale).

Figure 3 .
Figure 3. Zoom view of the computational mesh of the isolated aerofoil with SGF.

Figure 4 .
Figure 4. Lift and drag coefficients variations for the baseline airfoil.

2. 2 .
The vertical axis wind turbine 2.2.1.Geometric model of VAWT.Figure 5 provides a visual representation of the H-type Darrieus wind turbine's associated two-blade rotor configuration.The rotor operates at a constant angular velocity denoted by , resulting in the blades moving with a speed of .

Figure 6 .
Figure 6.Computational domain for the VAWT (not to scale).

Figure 8 .
Figure 8.Comparison between simulation and experimental results.

Figure 9 .
Figure 9. GFs effects on airfoil aerodynamic performance with respect to the AoAs.

Figure 13 Figure 13 .
Figure 13 depicts a contrast in the time-averaged streamline distribution at the airfoil's trailing edge for  = 6°, featuring 3%c height flaps.Downstream of the PGF, two counter-rotating vortices induce downward deflection of the airflow along the airfoil's upper surface.In contrast to PGF, SGF displays a diminished occurrence of anti-vortices, leading to a relatively weaker hindrance of flow detachment on the suction surface due to the presence of the tooth gap.Consequently, the diminished pressure differential between the airfoil's upper and lower surfaces, attributed to SGF, contributes to a comparatively less pronounced lift augmentation compared to that achieved with PGF.

Figure 14 Figure 14 .
Figure 14 illustrates the instantaneous iso-surfaces (Q = 2 × 10 5 s -2 ) of P-3 and S-3, with velocity magnitude represented by colour, at  = 6°.Particularly, PGF demonstrates clear columnar vortex shedding, while SGF perturbs the columnar vortex arrangement, leading to the formation of a

Figure 15 .
Figure 15.Comparison of power coefficient of VAWTs with and without GFs.

Figure 16 Figure 16 .
Figure16presents the torque coefficient (Cm) curves for VAWT equipped with PGF and SGF across different TSR values.While the SGF blade exhibits reduced performance within the azimuth angle (ψ) range of approximately 30° to 90°, in comparison with the PGF airfoil, the subsequent section can compensate for this drawback.Specifically, it is noticeable that within the downwind sector (ψ ranging from 180° to 360°), the SGF blade demonstrates a more substantial enhancement in Cm compared to the PGF counterpart.This is the reason why Cp of the SGF can surpass that of the PGF for TSR values of 3.0 and greater.
Figure 17  showcases the relative velocity streamlines, indicated by the color-coded z vorticity contour, at azimuth angles of 120° and 330° for a TSR of 3.0.

Figure 17 .
Figure 17.Flow structure of streamline and z vorticity contour for the Baseline and GFs.

Figure 18 Figure 18 .
Figure 18 displays the  distributions at azimuth angles of 120° and 330° for a TSR of 3.0.At ψ = 120°,  distribution is similar to the findings in section 3.1.1.Within the upwind sector, the PGF turbine outperforms the SGF turbine due to the greater magnitude of the  for the PGF blade.Conversely, at ψ = 330°, owing to flow separation on the blade surface, the pressure and suction surfaces alternate at / = 0.5, 0.3, 0.4 for the baseline, PGF, and SGF configurations.Consequently, PGF displays reduced performance relative to SGF and the Baseline within the downwind region.

Table 2 .
The sensitivity test of grid size for the PGF VAWT at TSR = 3.0.