Study on the effects of winglets: wind turbine blades having circular arc blade section profile

Abstract

Performance enhancement of horizontal axis wind turbine with circular arc blade section has been investigated both experimentally and computationally using upstream and downstream winglet configurations. A computational study is performed for a three-blade rotor of 0.5-m-diameter in ANSYS Fluent to identify the optimum values for cant angle and twist angle. Findings from the numerical analysis are then utilized as inputs for the experimental study. The height of the winglet is selected as 6% of the rotor radius while cant angle and twist angle are 55° and 0°, respectively. Power and thrust coefficient are measured for both the upstream and downstream winglet orientations at different pitch angles ($\varphi$) and tip speed ratios (λ). Results show that upstream winglet provides 9.79% extra power in comparison with reference model at design tip speed ratio (TSR = 5) and zero pitch angle. Improved performance is obtained with downstream winglet achieving almost 15% additional power. Conversely, for all the pitch angles, power decreases as λ^0.1 beyond the design tip speed.

Introduction

With the increase of population growth and industrial revolution, the uses of energy have enhanced. However, most of the energy are induced from some conventional energy sources like coal, crude oil, or natural gases. These fossil fuels emit an enormous amount of carbon dioxide (CO₂), increasing global warming. Based on these issues, people are rethinking and moving their concern to the use of renewable energy resources like wind, solar, hydro energies. Wind force can be a great medium of extracting energy as electricity due to its availability. There has been a noticeable development in extracting energy from the wind, i.e., by using wind turbines. According to the Global Wind Energy Council, new installations capacity of wind turbines both for onshore and offshore 71 GW annually until 2024 [1].

Wind turbine efficiency and power harnessing capacity largely depend on blade geometry, i.e., blade's shape, chord length, twist angle, etc. The majority of the blade's profile are designed with airfoils. Messaoud et al. [2] studied on different airfoils shape like NACA 0012, NACA 0015, NREL S825, and NREL S833 to investigate the effectiveness of a small-scale wind turbine blades while used in low-speed regions. They found that blades having NREL S833 airfoil provide the maximum wind power. This paper investigates the performance of a horizontal axis wind turbine (HAWT) when a circular arc blade section (CABS) has been adopted as a blade profile. Reason for preferring CABS as a blade profile is that the manufacturing complexity and maintainability expenses of airfoils. Additionally, winglets are also added to both upstream and downstream sides to evaluate the performance of the turbine blades, as they tend to decrease the downwash effects at the tip of the blade.

Researchers are continually working to study the flow pattern and behavior around the wind turbines. Before the theoretical analysis or the experimental investigation, researchers worked on the available theories to determine how the forces act on the rotor of the wind turbine. Blade Element theory or the Strip theory used frequently for analyzing the performance of Horizontal axis wind turbines [3]. In this theory, it is considered that “the forces acting on the blade element are solely due to the lift and drag characteristics of the sectional profile of the element [4]”. Walker [5] developed a method for the shape of blades for extracting maximum power. He made the blades by varying the chord length and twist angle radially at different sections until the power coefficient gained maximum. This happened at the maximum lift to drag ratio of the elemental blade. Bruining et al. [6] did some experiments to predict the effects of rotation on lift and drag coefficients of a rotor blade. Before that, they did some tests on the same blade in a wind tunnel and concluded the effect of rotation with the stationary rotor blade. Based on the performance characteristics, they calculated the flow separation point more reliably. Most. Hosney Ara Begum [7] proposed a circular arc section instead of a conventional airfoil section in case of a low tip speed ratio. She made a wind turbine rotor model using a circular arc blade profile. She did some experimental and theoretical calculations to predict the performance parameters over a conventional NACA 4418 blade airfoil. She found that the starting torque distribution with a circular arc section was more prominent than that NACA 4418 blade section. She also concluded that the power coefficient at lower tip speed ratio (less than 6) was prominently enhanced compared to those NACA 4418 blade sections.

Tip loss effects are significant criteria for predicting wind turbines performance while using the conventional blade element theory. Prandtl tip loss function which is generally used for calculating the tip loss effect. Shen et al. [8] proposed a new tip loss correction factor to predict the inconsistency concerning the available models at the tip region. He concluded the experimental results with the existing model and the new model. The proposed model could be used to find better predictions in the tip region. Winglet, as an extension of a blade, reduces the tip vortices, which has a similar cross-sectional area as the root of the blade. The vortices are generated due to the downwash effect at the blade. Incorporating the winglet at the tip helps to extract more wind energy and provides a considerable influence in fluid flow. The effectiveness of the wind turbine increases by adding wingtips, and this is done by shifting the vortices away from the rotor region. Thus, the effects of the downwash dwindled and also the induced drag [9]. Maughmer [10] designed some winglet configurations for the high-performance sailplanes for enhancing the effectiveness of the sailplanes. He mentioned that factors like planform shape, winglet length, winglet height, cant angles, twist angles, toe angles should be considered while investigating the performance criteria of the wind machines. He also mentioned that the plan form shape would be employed to control the span-wise flow to reduce the induced drag.

Johansen et al. [11] pursued some numerical investigation on the wind turbine blades with winglet configurations using computational fluid dynamics. He investigated five winglets with camber airfoil and varying in twist angles. He found that incorporating winglets at the tip of the blades, increased the force distribution on the outer portion around 14%. That, in turn, enhanced the power generation of around 0.6–1.4% for wind speed higher than 6%. Furthermore, he concluded that thrust increased by about 1–1.6%. Wang et al. [12] accomplished some numerical simulation on a wind turbine with a tip vane to observe the effects and pressure distribution over the blade surface. While doing this, he selected an airfoil section of FX74C16140 along with a 1.16-m-diameter of a wind turbine. The blade length, tip chord length, and tip vane dimensions were 0.5 m, 0.1 m, and (8.8 cm × 8 cm). Using the ANSYS Fluent as the solver, he found that “the pressure difference between the suction and pressure surface of the blade increases the force which helps the blade to absorb more wind energy.” Thus, the wind turbine power output is enhanced. Gertz et al. [13] investigated two different types of winglet incorporating at the tip of a 3.3–m-diameter wind turbine. He kept the cant angle the same but varied the twist and toe angles. The distribution of load is varied due to the winglet twist and sweep angles. Meanwhile, the toe angle influences the aerodynamic effect on the winglet. Further, the cant angle affects the upwards and downwards flow direction along the wing. The experimental analysis conducted and a comparison made between with and without winglets ranging the tip speed ratio from 0 to 12. An increase of around 2–8% of the power coefficient was found for both the models. They also mentioned that the accuracy of predicted results was found at tip speed ratios greater than 6.5. Saravanan et al. [14] studied four different winglet configurations, fabricated with Glass Fibre Reinforced Plastic materials, to investigate the performance for a rotor model with and without load conditions. The maximum power coefficient for a particular winglet configuration was about 0.43. He mentioned that, at a low wind speed region, wind turbines with winglets work most accurately. He concluded that with a small curvature radius along with an optimum winglet height, blades capture a more significant amount of wind energy compared to without winglets. Monier Elfarra et al. [15] investigated the aerodynamic characteristics of horizontal-axis wind turbines by using CFD and four different winglet configurations. He utilized and optimized the twist and cant angles to observe the effects on the wind turbine's performance. He found that performance enhanced by 9% while using a winglet with a 1.5% extension of blade length and faced in the suction side having 45 and 2 ° cant and twist angles, respectively.

Ostovan and Uzol [16] studied two interfacing similar horizontal axis model wind turbines to examine the effects of one another. Both winglets and tip-extensions incorporated separately on the wind turbine and compared with the base model. Winglets had a remarkable increment in the power coefficient as well as the thrust coefficient. But while the second turbine was located at the downstream position in line with the upwind turbine having winglets produced less quantity of power for the downward direction turbine. Ostovan et al. [17] analyzed the winglet's impact at the vicinity of the wake flow tip area and the characteristics of the tip vortex of a three-bladed HAWT at a distance of 0.94–m-diameter downstream by using practical image velocimetry. Vortex core size, Vortex convection, core expansion, and the resultant induced drag on the rotor were investigated. They found that vorticity and turbulent kinetic energy substantially decreased across the wake boundary, which moved radially outwards. The quantity of turbulent kinetic energy and vorticity lessened over 50%. Finally, around 15% of induced drag reduced due to the addition of winglets. Zahle et al. [18] worked on the existing wind turbine blade and redesigned a new blade tip to enhance the energy harnessing processes. He modified the twist, chord, and blade length extension to give a new winglet. They adopted CFD methods to make a surrogate model, which tip section modified numerically to various geometric and load-based limitations. They concluded that about 2.6% of power augmentation was due to the winglet addition, whereas an increase of only 0.76% for the straight blade extension. Furthermore, winglets didn't increase the bending moment in the direction of the flap at a 90% radius. Hernan et al. [19] presented various tip devices to observe the induced drag generated at the tip of the blade by using computational analysis. He studied different types of tip vanes like winglets, split types, and tip-tanks to improve the aerodynamic characteristics. He found that around 4.6% of enhancement in power generation was there when used winglets compared to 3.5% for split types. Furthermore, not an admirable improvement was there for tip-tank configuration.

Zhu et al. [20] focused on the directions of winglet attachment, including suction side, pressure side, and both sides of the primary blade to investigate their effects in wind turbines. They showed that the power generation enhanced for fusion winglets with increasing the tip speed ratio to raise a peak of the power of about 3.9. Khalafallah et al. [21] studied on straight blades as well as sweep blade winglets to enhance the performance of HAWT's. They considered both the upward and downward facing of winglets of the blades with other parameters like cant and twist angles. Using ANSYS Fluent, they found an augmentation of power coefficient of about 4.39% at design TSR while incorporating the tip extensions. This improvement happened when the swept blade with winglets direction was in the upstream position. Khaled et al. [22] considered two winglet parameters, namely winglet height, and cant angle to present the effectiveness in HAWT performance. They used CFD methods and artificial neural networks and varied the winglet height ranging from 1 to 7% of the rotor radius and cant angle ranging from 15° to 90°. They concluded an admirable increment of about 8.787% in both power, and thrust coefficient was there because of the winglets. The best configuration was, having a cant angle of 48.3° and a winglet length of around 6.30%. Zhang et al. [23] studied Vertical axis wind turbines (VAWTs) as they are very potential in harnessing wind energy. They focused on the aerodynamic effects of those blades due to tip vortex. They considered the orthogonal experimental design (OED) method to measure the different performance parameters. Their results showed that the twist angle in the winglet provides the best possible output power. An increase of about 31% in power coefficient was there due to the incorporation of winglets at TSR of 2.19 compared to without winglet models.

As winglets work as a driving force for diminishing the tip vortices as well as induced drag, Mourad et al. [24] focused on these effects. They considered the winglet height and toe angle as the performance criteria and took a three-bladed rotor with SD8000 airfoil as the prototype model. They kept toe angle constant at 0° and chose four types of winglet height. A height of 0.8%R showed the best performance and enhanced power of about 2.4% at TSR 7. Furthermore, the power coefficient increased with the increment of toe angle in upwind up to 20° with all tip speed ratio values. By using an optimum winglet height and toe angle, the power coefficient can be raised almost 6% compared to without winglets. Franz et al. [25] investigated the near wake behind the wind turbine model with two different wingtip configurations. They found that winglets not only enhance the power coefficients but also alleviate the wake losses. Winglets increased the power extraction at the tip region and also affected the wake's mean kinetic energy recovery by stimulating a faster tip vortex interaction.

Depending on the literature review, it is evident that researchers are trying to optimize the blade and modify the winglet geometry. So, this paper aims to study HAWT effectiveness with the CABS profile with lower tip-speed ratio. In addition, the impacts of winglets' direction on the turbine blades performance with circular arc blade section (CABS) are still required to analyse. Winglets' parameters like cant and twist angle are determined through computational analysis. So the objectives of this paper are listed below:

• 1. Computational study of the performance of a small HAWT model having circular arc blade section (CABS) with and without winglets. Winglets are attached both on the upstream and downstream sides to measure the efficiencies and to conclude which one provides better performance.

• 2. Verifying the findings of the computational study with the experimental output for the reference model.

• 3. Comparing and analyzing the performance parameters for each direction of winglets and without winglet.

Numerical modeling

Horizontal axis wind turbine rotor

The reference horizontal axis wind turbine model was designed using the Blade Element Momentum Theory (BEMT) [26]. The wind turbine model’s radius was 250 mm, hub radius 30 mm, the number of blades three with a design wind speed of 8 m/s.

Winglets design parameters

Winglets are incorporated at the turbine blades or aircraft's wing to enhance the performance more exactly efficiency by reducing the tip vortices and downwash effect without increasing the projected area. This is done by moving the vortices from the pressure side of the surface, which reduces the induced drag, thus, in turn, increasing the lift production capability. Additionally, winglets transform some of the waste energy to some sort of perceptible thrust [27].

Depending on some literature review and computational process (cant and twist angle), winglets design parameters were chosen and designed in Table 1. Figure 1 displays the blade profiles used in the computational investigation.

Table 1 Design parameters of winglets

Fig. 1

a Wind turbine blade with CABS profile, b wind turbine blade with upstream winglet, c wind turbine blade with downstream winglet

Governing equations

The three primary governing equations are conservation of mass, conservation of momentum, and conservation of energy. Additionally, there are auxiliary equations due to the velocity fluctuation over the entire domain. The differential equations for laminar flows are expressed as [28]:

$$\frac{\partial \rho }{{\partial t}} + \frac{\partial }{\partial x}(\rho u) + \frac{\partial }{\partial y}(\rho v) + \frac{\partial }{\partial z}(\rho w) = 0$$

(1)

$$\rho \frac{{{\text{D}}u}}{{{\text{D}}t}} = \frac{{\partial ( - p + \tau_{xx} )}}{\partial x} + \frac{{\partial \tau_{yx} }}{\partial y} + \frac{{\partial \tau_{zx} }}{\partial z} + S_{Mx}$$

(2)

$$\rho \frac{{{\text{D}}v}}{{{\text{D}}t}} = \frac{{\partial \tau_{xy} }}{\partial x} + \frac{{\partial ( - p + \tau_{yy} )}}{\partial y} + \frac{{\partial \tau_{zy} }}{\partial z} + S_{My}$$

(3)

$$\rho \frac{{{\text{D}}w}}{{{\text{D}}t}} = \frac{{\partial \tau_{xz} }}{\partial x} + \frac{{\partial \tau_{yz} }}{\partial y} + \frac{{\partial ( - p + \tau_{zz} )}}{\partial z} + S_{Mz}$$

(4)

Based on Reynolds’s decomposition, the additional fluctuation quantities, i.e., turbulent stresses in the Reynolds Averaged Navier Stokes (RANS) equations, can be written as

$$\frac{\partial \rho }{{\partial t}} + \frac{\partial }{{\partial x_{i} }}(\rho u_{i} ) = 0$$

(5)

$$\frac{\partial }{\partial t}(\rho u_{i} ) + \frac{\partial }{{\partial x_{j} }}(\rho u_{i} u_{j} ) = - \frac{\partial p}{{\partial x_{i} }} + \frac{\partial }{{\partial x_{j} }}\left[ {\mu \left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }} - \frac{2}{3}\delta_{ij} \frac{{\partial u_{i} }}{{\partial x_{j} }}} \right)} \right] + \frac{\partial }{{\partial x_{j} }}\left( { - \rho \overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }} } \right)$$

(6)

The selection of the appropriate turbulence model substantially affects the solution of the specific problems. Numerous studies have been done to predict the aerodynamics of wind turbine models. It was observed that the two equations Realizable k−ε turbulence model predicted the rates of round jets more accurately. Moreover, it has a great performance for flows involving rotation, separation, recirculation, and boundary layers with strong adverse pressure gradient. Based on the advantages, the Realizable k−ε turbulence model was chosen for all the computational simulations for the turbine model with and without winglets to close the RANS equations, where k is the turbulent kinetic energy, and ε is the dissipation rate.

Computational methodology

ANSYS Fluent was used to perform all the wind turbine model simulations with and without winglets. The solution convergence was established basing on the residual history, and the convergence criterion was 10^–6 for the variables. A three-dimensional computational fluid dynamics (CFD) analysis was done to determine the torque generated due to the flow driving around the wind turbine blade with and without winglets. The calculated torque was employed to find out the power production with the given equation:

$$P = T\omega \eta$$

(7)

The computational domain required for the analysis is shown in Fig. 2 with the necessary boundary conditions. A velocity inlet boundary condition was applied at the inlet section of the domain, which was situated at the 5R upstream (equal to 1.25 m ahead of the blade origin). A pressure outlet boundary condition was implemented at the outlet section of the domain, situated at the 10R downstream (equal to 2.5 m). Moving wall motion was applied to the turbine blades keeping the rotation of motion at the center. The blade and hub surfaces were considered as walls with no-slip boundary conditions.

Fig. 2

Domain with boundary conditions

Mesh generation

The solution of the CFD profoundly depends on mesh creation. The whole domain was discretized into several elements or grid cells. The unstructured mesh was generated having approximately tetrahedron grids of 430,545 and 85,442 nodes, where the mean cell size lies between 4.87 × 10⁻⁴ and 7.5 × 10⁻² m. A dense and mesh refinement was made near the vicinity of the blade and winglets. Figure 3 presents the mesh created for the rotor blade. To solve the partial differential equations near the viscous sub-layer, the first grid cell's distance from the centroid to the blade or winglet wall was adjusted with y + less than 2.

Fig. 3

a Computational domain mesh, b close view of meshing around the blades

A Grid-independency test was performed to verify the computational outcomes for all the simulations. The power coefficient was selected as the factor of judgment of the mesh validation test. Figure 4 described the results of the power coefficient vs. grid cell number. To ensure the solution's independence, the computational analysis was done for a wide range of grid cells (i.e., from 100,000 to 600,000) at TIP = 5 and $\varphi$ = 0°. It could be said that the power coefficient values were almost steady after the mesh size of 430,000 cells.

Fig. 4

Wind turbine model grid-independency test

Effects of cant and twist angle in winglets

Cant and twist angle are one of the crucial criteria for evaluating the wind turbine effectiveness. Before the experimental study, computational analysis was done with four different cant and twist angles to observe which configuration provided the best performance. The Fig. 5 showed that cant angle = 55° and Twist angle = 0° had the most significant effect on this particular CABS blades profile. These parameters were used for both the downstream and upstream winglets.

Fig. 5

Comparison of cant and twist Angles on power co-efficient having CABS profile

Experimental setup and procedure

To validate the computational results, experimental results are required to observe whether there are any discrepancies or not. The wind turbine blade and winglet's size and dimensions are kept similar for different cases. The significant segments of the turbine model are recorded below:

• 1. Hub

The hub's frontal shape is hemispherical with a radius of 30 mm (12% of rotor Radius), length of 25 mm. The hub has grooves to hold the blades and was produced from nylon. The hub of the model wind turbine was designed with zero coning angle and with the provision of changing blade-pitching angle as required for the present study.

• 2. Blades

The blades are both tapered and twisted with 220 mm in length. A circular arc blade section (CABS) was used for the blade profile. The blades were made of stainless steel.

• 3. Winglets

A similar type of profile and material was used for both the upstream and downstream winglets.

Experimental setup

A low subsonic open type wind tunnel (Model AF1300s of TQ Equipment, U.K.) facility in the Aeronautical Engineering Department, MIST, as shown in Fig. 6 was used for this experimental study. The maximum velocity of this wind tunnel is 36 m/s. This tunnel consists of a settling chamber with honeycomb, diffuser, test section, nozzle, and drive section with the motor. A flow straightener is attached at the exit of the wind tunnel drive section. The straightener's exit cross-section is 49 mm by 49 mm, and its center is above the ground by 1271 mm.

Fig. 6

Wind tunnel facility and experimental model

A circular horizontal shaft of 8-mm-diameter and length 737 mm was made to rotate the hub of the model turbine by roller bearings, in which the blades were attached. Free stream velocity at the wind turbine was estimated directly adopting a digital anemometer with an accuracy of 5%. For recording the wind turbine blade's rotational speed at different loadings, a non-contact digital tachometer (Model: DT-2234B) was used.

Experimental procedure

The wind velocity was measured at different distances from the wind tunnel exit without the model. Normally, the wind tunnel was continued running for a while to arrive at a consistent state activity. The wind turbine rotor model with three blades was mounted on the base structural frame (Fig. 7) so that the center of the rotor hub coincides with the central axis of the wind tunnel. At first, the blades were arranged for a zero pitching angle. The spring scale attachment and the loading system were placed in the proper position. The differential force was calculated from the spring deflection and applied load. From these distributions, using numerical calculation, the non-dimensional torque coefficient, power coefficient were determined. Output powers were obtained from the above readings. The total available power was equal to the summation of the output power and the loss of power due to friction. The experimental values of the power coefficients were calculated from the total available power ratio to the available theoretical power. The above experimental steps were repeated for different pitching angles for both the upstream and downstream winglets by changing the blade pitch angle.

Fig. 7

Components of the experimental test-bench

CFD validation with experimental results

Figure 8 represents the power co-efficient for both the experimental and computational results: with and without winglets with the different TSR for zero degree pitch angle. The tip-speed ratio varies from 1 to 8 for both the experimental and computational studies. The computational outcomes are marginally higher than the experiment results for all the pitch angles. This is due to the manufacturing difficulties and roughness in the blade surfaces, which are negligible in the computational analysis. The following relationship defines the power-coefficient:

$$C_{{\text{P}}} = \frac{P}{{\frac{1}{2}\rho AV_{\infty }^{3} }}$$

(8)

Fig. 8

Coefficient of power at different TSR and φ= 0°

Figure 9 represents the error between the experimental and computational results regarding the power coefficient for zero degree pitch angle. The computational coefficient of power has a discrepancy of approximately ± (5–7) % from the observed coefficient of power. Experimental results of the power coefficients, torque coefficients, and thrust coefficients for horizontal axis wind turbines with a circular arc blade profile with and without winglets for different blade pitching angles were presented for the design wind speed 8 m/s in this section.

Fig. 9

Error of the experimental results w.r.t. computational predictions of wind turbine at φ= 0°

Experimental uncertainty

Experimental uncertainty analysis of the power coefficient is carried out depending on each measurement parameter through the combination of systematic error and precision error [29]. Each parameter has some degree of measurement uncertainty. Around 3.92% of the power coefficient uncertainties were measured at the design TSR and zero pitch angle, while seven samples of parameters were selected for estimating that error. Appendix A provides the details of measurement uncertainty and the variation of power coefficients as shown in Fig. 10

Fig. 10

Power coefficient at different tip-speed ratios at design TSR with uncertainties

.

Results and discussions

Effect and comparison of winglets position in power coefficient

In this section, the effects of winglet configurations and their positions, i.e., upstream and downstream side, were described. Upstream and downstream winglets were having 55° cant angle and a height of a 6% rotor radius. Figure 11a–d represented the power coefficients of with and without winglets in terms of different tip-speed ratios and pitch angles.

Fig. 11

Comparison of experimental power coefficient of winglets position at different pitch angles and TSR

As the tip-speed ratio increases, the power coefficients increase until the design tip-speed ratio (TSR = 5), which had the maximum value of C_P. After that, the values decrease with the increase of the tip-speed ratio. Furthermore, with the increment of pitch angles from 0° to 6°, the power co-efficient decreased for all three cases. The maximum power coefficient at design TSR was 0.329 for without winglet, 0.355 for upstream winglet, and 0.369 for downstream winglet for $\varphi$ = 0°. Thus, about 7.9% for upstream winglets and around 12.1% downstream winglets enhancement in power generation was gained with respect to without winglets while using a circular arc blade section profile. In all cases, it was found that blades with downstream winglets provided better performance than blades with upstream winglets. Concerning upstream winglets, the lift force from the blade's profile on the winglets acted outwards, leading to a wake contraction. In contrast, the loading on the winglets worked outwards for the downstream winglets and may lead to wake expansion.

Torque coefficient distribution for different pitch angles

When the air molecules impart wind turbine blades, the resultant forces are divided into two components: axial force and tangential force. This tangential force is the primary reason for torque generation. A comparison between torque coefficient versus tip-speed ratio and how they affect extracting energy from wind was discussed in this section.

Figure 12a–c represent the effects of pitch angles 0°, 2°, 4°, and 6° had been described for three different cases. It could be said that the maximum amount of torque produced for pitch angle zero and then decreased substantially as pitch angles increased for all the facts. As pitch angles increased, torque coefficient decreased leading to higher tip speeds at the outer portion of the blade. Due to the high tip speeds, an additional drag imposed on the blades, thus reducing the power generation, as we observed in the above section.

Fig. 12

Comparison of torque coefficient at different pitch angles for with and without winglets

Effect of thrust coefficient with and without winglets

During the wind turbine model design, it is required to check structural integrity as there are numerous effects on blades, for instance, radially, aerodynamic effects, and thrust forces. Thrust loads have a significant impact on supporting tower. The thrust coefficient for the wind turbine can be calculated from the give equation below.

$$C_{{\text{T}}} = \frac{T}{{\frac{1}{2}\rho AV_{\infty }^{2} }}$$

(9)

The above equation can be used while the blade pitching angle is zero, hence directly impacting the air molecules on the blades. But in case of increasing the pitching angle at the same free stream velocity, the projected area normal to the wind speed direction reduces. The modified thrust coefficient equation can be written as below.

$$C_{{\text{T}}} = \frac{T}{{\frac{1}{2}\rho AV_{\infty }^{2} \cos \varphi }}$$

(10)

Figure 13a–c displays the effects of thrust coefficients on pitch angles 0°, 2°, 4°, and 6° that had been described for three different cases. The maximum values of the thrust coefficient were obtained for $\varphi$ = 0°, and then, there was a slight drop in the thrust coefficient for $\varphi$ = 2°, 4°, 6°, respectively, for with and without winglets. At $\varphi$ = 0° and design TSR, the coefficient of thrust raised from (0.9587) for the base model without winglets to 1.0408 having upstream winglets by about 8.6% and to 1.0636 with downstream winglets approximately 10.94%.

Fig. 13

Comparison of computational thrust coefficient at different pitch angles for with and without winglets

Coefficient of pressure distribution

To study the aerodynamic performance of the winglets in the wind turbine blades having CABS, the pressure co-efficient distributions along three different span-wise position (i.e., r/R = 50%, 75%, and 95%) on the blades at design TSR are described in this section. The equation used for determining the pressure co-efficient.

$$C_{\Pr } = \frac{{P - P_{\infty } }}{{\frac{1}{2}\rho \left( {V_{\infty }^{2} + (\omega r)^{2} } \right)}}$$

(11)

Figure 14a, b illustrates the pressure coefficient distribution along the blade chord length at three different span-wise sections (i.e., 0.5, 0.75, and 0.95 of the blade). It was found that there was little change in the pressure distribution on the pressure side, for all the cases, as winglets attached at the blade tip. Regarding the suction side, the coefficient of pressure remained almost steady near the blade rotor hub (say, for r/R = 50%, 75%) for all cases. Meanwhile, at blade tip (r/R = 95% section), the pressure distribution on the suction side was reduced due to the incorporation of winglets. Furthermore, the amount of reduction faced in downstream winglets was far more than the turbine without winglets. So, it can be said that downstream winglets are more effective as the net pressure difference is more considerable in that case.

Fig. 14

Coefficient of pressure distributions on the three span-wise sections at design TSR and φ= 0°

Pressure and velocity contours

Figure 15 showed the turbine model's static pressure and velocity contours with and without winglets at design TSR and $\varphi$ = 0°. It was evident that, by incorporating winglets at the blade tip, the maximum static pressure near the leading edge increased from (862.56 pa) for the baseline rotor to (1170.77 Pa) for the wind turbine with the downstream winglets. Furthermore, the pressure at the center part near the tip of the blades without winglets was less than that pressure at the exact location for the blades with downstream winglets. This phenomenon was helpful for smoother flow over the blades while winglets incorporated.

Fig. 15

Wind turbine model having a without winglets, b downstream winglets

The maximum velocity increased from (44.05 m/s) for the baseline rotor to (51.13 m/s) at the blade tip for the wind turbine with the downstream winglets. This means blades with downstream winglets rotate faster than the baseline rotor.

Blade tip-vortices and sectional flow streamlines

As described earlier, the primary reason for the decrement of the generation of lift and power is that the vortices created at the blade's tip. For that reason, winglets are attached at the blade's tip to overcome the downwash effects of those vortices. As shown in Fig. 16a, vortices have created at the blade's tip, while there were no winglets. The cause for that was the higher pressure side flow moves to the lower pressure side in a circular fashion, which creates a circular flow-pattern named vortex. Turning to the Fig. 16b, c, they represented that by adding the winglets, there was a reduction in tip vortices as the lift-induced drag decreased. Furthermore, the compensation occurred more by the downstream winglets than the upstream winglets.

Fig. 16

Comparison of vortices at the blade tip region between with and without winglet at TSR = 5 and φ= 0°

Figure 17 showed the cross-sectional flow and surface wall streamlines at TIP = 5 and $\varphi$ =0° on wind turbine blades and the influence winglets on them. Considering the spanwise direction and three locations, i.e., r/R = 50%, 75%, 95% were selected to analyse the flow behavior. It could be mentioned that for the first two locations, there was no significant change in flow behavior for those two configurations.

Fig. 17

Sectional flow streamlines at TIP = 5 and φ= 0°

Meanwhile, at r/R = 95%, blades without winglets, flow particles were detached and separated due to the vortices creation at the tip. However, for the other two configurations, flow particles were attached due to elliptical winglets introduction.

Conclusions

This present study demonstrates a small-scale horizontal axis wind turbine with a circular arc blade section designed with a blade element momentum theory with a 0.5-m-rotor diameter and design wind velocity 8 m/s. The twist angle and chord length along each section of the blade linearized to provide the blade taper and twist angle. Winglets were designed and incorporated both on the upstream and downstream side to observe the wind turbine effects. The performance characteristics of Horizontal Axis Wind Turbines having Circular Arc Blade Section, the following conclusions are drawn:

• 1. Both Power and Thrust coefficient increased while adding elliptical winglets, having Circular Arc Blade Section (CABS) profiles in wind turbine blades.

• 2. Both Power and Thrust coefficient enhanced concerning downstream winglets than the upstream winglets for the same winglet height and cant angle.

• 3. Regarding the experimental results, the maximum increment of the coefficient of power was from (0.329) for the base model to (0.355, increased by 7.91%) for upstream winglets and (0.369, increased by 12.1%) for downstream winglets at the design TSR and zero pitch angle.

• 4. Regarding the computational results, the maximum increment of the coefficient of power was from (0.3454) for the base model to (0.3792, increased by 9.79%) for upstream winglets and (0.3950, increased by 14.36%) for downstream winglets at the design TSR and zero pitch angle.

• 5. Blades having winglets, the maximum increment of the coefficient of thrust was from (0.9587) for the base model to (1.0636, increased by 10.94%) for upstream winglets and (1.0408, increased by 8.6%) for downstream winglets at the design TSR and zero pitch angle.

• 6. The coefficient of pressure at the outer portion of the blade (r/R = 95%) of the suction side dropped while winglets are attached, leading to the pressure difference increment. Thus, HAWT producing considerably more torque in the spanwise direction while winglets are added at the blade's tip. Additionally, this phenomenon was more substantial regarding the downstream winglets.

• 7. Due to this reason, downstream winglets are much effective than the upstream winglets while added in the blade tip with CABS profile.

Appendix A

The level of uncertainty can be obtained using the following equation

$$\delta R = \sqrt {\left( {\delta x_{1} \frac{\partial R}{{\partial x_{1} }}} \right)^{2} + \left( {\delta x_{2} \frac{\partial R}{{\partial x_{2} }}} \right)^{2} + \cdots + \left( {x_{n} \frac{\partial R}{{\partial x_{n} }}} \right)^{2} }$$

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Coefficient of power equation in simplified form:

$$C_{{\text{P}}} = \frac{{(F_{1} - F_{2} )R * \frac{2\pi r}{{60}}}}{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}\rho \pi r^{2} V_{\infty }^{3} }}$$

(13)

The uncertainty equation becomes:

$$\delta_{{C_{{\text{p}}} }} = \sqrt {\left( {\delta F_{1} \frac{{\partial C_{{\text{P}}} }}{{\partial F_{1} }}} \right)^{2} + \left( {\delta F_{2} \frac{{\partial C_{{\text{P}}} }}{{\partial F_{2} }}} \right)^{2} + \left( {\delta R\frac{{\partial C_{{\text{P}}} }}{\partial R}} \right)^{2} + \left( {\delta N\frac{{\partial C_{{\text{P}}} }}{\partial N}} \right)^{2} + \left( {\delta \rho \frac{{\partial C_{{\text{P}}} }}{\partial \rho }} \right)^{2} + \left( {\delta r\frac{{\partial C_{{\text{P}}} }}{\partial r}} \right)^{2} + \left( {\delta V_{\infty } \frac{{\partial C_{{\text{P}}} }}{{\partial V_{\infty } }}} \right)^{2} }$$

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$$\delta_{{C_{{\text{p}}} }} = \pm 0.0129$$

$${\text{Experimental}}\,{\text{Uncertainty}}\,{\text{at}}\,{\text{design}}\,{\text{TSR}} = \, 0.329 \pm 0.0129$$

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$$\begin{aligned} {\text{Percentage}}\,{\text{of}}\,{\text{error}} & = \frac{0.0129}{{0.329}}*100\% \\ & = 3.92\% \\ \end{aligned}$$

(16)