Abstract
In this work, the performance of new wind blade designs for small-scale horizontal axis wind turbines (HAWTs) was studied and compared with the performance of a baseline design. Three J-shaped pressure-side truncation ratios (1/3, 1/2, and 2/3) and two Kammtail Virtual Foil (KVF) truncation ratios (1/8 and 1/4) were studied. The baseline design was experimentally investigated. Output power was measured using a digital rotary torque sensor at three different wind speeds. Tip speed ratio (TSR) was calculated after measuring each wind speed's free-rotating revolutions per minute (RPM). Three wind speeds and experimental TSRs were used in three-dimensional simulations to capture the performances of the proposed cases and compare them with the baseline. The simulation investigation was carried out for lab-scale and scaled cases. The three-dimensional study found that the J-shaped blades enhanced the performance of the HAWTs for both lab-scale and scaled cases. J-shaped blades with a 1/3 opening ratio yielded an average power coefficient enhancement of around 1.56% and 4.16% for lab-scale and scaled cases, respectively. J-shaped blades with a 1/2 opening ratio yielded an average power coefficient enhancement of around 1.15% and 4.23% for lab-scale and scaled cases, respectively. On the other hand, J-shaped blades with a 2/3 opening ratio yielded an average power coefficient enhancement of around −0.12% and 2.54% for lab-scale and scaled cases, respectively. Furthermore, it was found that the KVF blades diminished the performance for both lab-scale and scaled cases.
1 Introduction
Researchers have been working on improving the aerodynamic performance of airfoils and wind turbines as a promising renewable energy solution. For two-dimensional airfoils, the aerodynamic performance and the lift-to-drag ratio were of interest to researchers, while for wind turbines, power output and starting torque were of interest to them. Wind turbines are mainly categorized based on the direction of airflow direction to the rotation axis. Vertical axis wind turbines (VAWTs) and horizontal axis wind turbines (HAWTs) are the primary wind turbine categories. Typically, HAWTs are recognized as large-scale generators used in wind farms, while VAWTs are recognized as small-scale generators used in urban areas [1]. Electricity generation by wind energy has grown significantly over the past few decades. In 2022, 10.3% of the utility electricity generation in the U.S. came from wind turbines [2]. Most renewable energy resources have intermittency as a common issue. To overcome this issue, an energy storage system, such as batteries or thermal storage, should be integrated [3,4]. Several research efforts tried to improve the aerodynamic performance of airfoils by changing their design parameters. J-shaped airfoils are formed by removing a portion of the airfoil from the suction or pressure side starting from the trailing edge. The opening ratio is between the cut length starting from the trailing edge and the chord length [5]. Chen et al. [6] studied the ratio and location of the opening on Darrieus VAWT. They found that optimal opening ratios are between 0.48 and 0.60 and 0.72 and 0.84 for inner and outer openings, respectively. Auyanet et al. [7] investigated different J-shaped designs for VAWTs. They found that outer-cut turbines outperformed internal-cut turbines. Furthermore, they found that all studied designs showed starting torque improvement. Rathod et al. [8] studied the effect of capped vents on VAWT by comparing experimentally and numerically capped and noncapped wind turbines with vent ratios between 7% and 21%. They found that rotors with capped vents deteriorate performance compared to conventional rotors. Vents disrupt pressure distribution, resulting in decreased positive torque and increased negative torque. Kammtail Virtual Foil (KVF) is an unconventional aerodynamic shape designed and introduced by Trek Bikes with a truncated tail airfoil [9]. They used this state-of-the-art design in their bike's frame to reduce the drag experienced by bike riders [10]. The KVF concept minimizes flow separation in the front portion of the airfoil while the rear portion is truncated. This truncation retains a stiff, light structure, yielding negative drag in some wind conditions. Furthermore, it reduces the turbulent energy dissipation where the airflow reconnects as a physical tail exists. Ahmed and Nabolaniwaqa [11] investigated the effect of trailing edge flaps on the aerodynamic performance of airfoils using different low Reynolds numbers and angles of attack. They found that the airfoils equipped with flaps experienced a considerably higher lift and slightly higher drag, yielding a higher lift-to-drag ratio. Moreover, they concluded that trailing edge flaps perform better under low wind speeds. Yan et al. [12] investigated the effect of trailing edge flaps on the performance of the NACA0018 airfoil and its H-type Darrieus VAWT. They found that the flaps increased the airfoil lift-to-drag ratio and the turbine's power coefficient at low tip speed ratios (TSRs). Other airfoil design modifications include having a leading-edge slot. Beyhaghi and Amano [13,14] studied different slot design parameters. They found that the maximum lift-to-drag improvement was 11%. Bhavsar et al. [15] studied the effect of introducing a slot to the DU-99-W-405 airfoil as a lift control device. They studied five different slot locations. They found that one of the studied locations improved the lift-to-drag ratio by 116%. The concept of ducted wind turbines was proposed by Lilley and Rainbird [16]. The concept is to increase the air mass flow through the turbine by placing a duct around it. Safford et al. [17] assessed the impact of different TSRs on ducted wind turbines. They found that ducted wind turbines outperform the open rotor by a 0.96 power coefficient increase. Hurley et al. [18] investigated the effect of active and passive air microjet application on the aerodynamic performance of utility-scale wind turbines. They found that both active and passive microjets reduced the flapwise root bending moment. Furthermore, they found that the optimum microjet location is in the third quarter of the blade span. Vortex-trapping cavity is another airfoil design modification. Qaissi et al. [19] investigated the effect of integrating a vortex-trapping cavity in the critical region of a highly twisted span blade on the suction side. They performed two- and three-dimensional studies and found that the new design improved the lift coefficient and the generated torque. Javaid et al. [20] found the optimum cavity shape using a genetic algorithm coupled with the Gaussian process regression model. They found that the optimized cavity enhanced the performance near stall conditions. Furthermore, their results showed a power enhancement over different TSRs. El-Askary et al. [21] investigated the effect of grooved linearized-chord blades in small HAWT. They found that grooves on the blade's suction side increased the power coefficient and reduced axial forces and vibrations. Abdelsalam et al. [22] studied the blade curvature effect on small-scale HAWT performance. Different curvature positions and curvature angles were studied. They found that five degrees of curvature toward upwind at a radial position of 0.9 yielded a reduced thrust and a higher power coefficient. Derakhshan et al. [23] optimized the HAWT blade shape using artificial neural networks and bee colony. They found that twist, chord, and universal optimization improved the power by 8.3%, 3.7%, and 8.6%, respectively. Difference computational fluid dynamics (CFD) turbulence models and methods were used in literature to simulate airflow over airfoils and wind turbines to predict their aerodynamic performance. Garcia-Ribeiro et al. [24] assessed the accuracy and computational cost of different turbulence models for HAWTs at moderate Reynolds numbers. They found that the shear stress transport (SST) is more accurate than the model. However, the latter estimated good results with a coarser mesh. Other efforts to improve the performance of small-scale HAWT by design modification include tip winglets, tubercles, and vortex generators. The SST turbulence model was used to predict the performance of the modified designs [25–27]. Abdelghany et al. [28] studied the effect of different winglet design parameters on the performance of HAWTs. They used the SST and the Spalart–Allmaras turbulence models for validation. They found that the SST yielded minimal errors. Many research works used the SST turbulence model and found it reliable for wind aerodynamic performance prediction [29–31]. Many studies found in the literature aimed to improve the performance of the HAWTs by introducing blade shape modifications. The use of the J-shaped and KVF concepts in HAWT has not yet been investigated in the literature. Applying these concepts to the HAWT blades will change their aerodynamic performance by changing the difference in pressure between the pressure and suction sides of the blades. The current study addresses this gap where different J-shaped truncation ratios and different KVF trailing edge truncations were investigated, initially on airfoils for the lift-to-drag ratio, then in HAWTs to assess their impact on generated power. The aerodynamic performance of modified designs was compared with an unmodified baseline.
2 Materials and Methods
2.1 Problem Description.
Researchers have developed methods and designs to enhance airfoils' aerodynamic performance and HAWTs' power coefficient as a promising renewable energy solution. In this research, new designs for truncation on the blades were studied and investigated for airfoils and HAWTs. Material truncation would increase the lift-to-drag ratio for airfoils by increasing the pressure gradient between the pressure and suction sides. For instance, the pressure-side J-shaped truncations will yield a sudden expansion in the flow and, consequently, a pressure increase, which will eventually increase the pressure difference between the suction and pressure sides on the blade. It would also increase the generated power for HAWT due to enhanced aerodynamic performance and reduced inertia. Many airfoil designs have been studied in the literature. However, the KVF and J-shaped designs have not yet been investigated for HAWTs. The goal of this work is to examine the proposed designs for both two-dimensional airfoils and three-dimensional HAWTs.
2.2 Two-Dimensional Study.
After conducting a mesh independence study, the airflow over J-shaped and KVF airfoils was simulated using the Siemens starccm+ CFD package. Two wind speeds (5 m/s and 10 m/s) yielding (1.6 × 105 and 8.0 × 104) Reynolds numbers, respectively, were used. The angle of attack (AoA) was varied between 0 deg and 20 deg by a step of 5 deg. Lift and drag forces were calculated and used to calculate the lift-to-drag ratios for each case.
2.2.1 Meshing.
To decide on a reasonable mesh size, a mesh independence study used NACA4412 as a baseline airfoil of 0.254 m chord and 0.762 m span. Polyhedral mesh with prism layers and volumetric controls was used. The airfoil was subjected to 10 m/s airflow with 0 deg AoA. Mesh count varied between 1 × 106 and 25 × 106 cells, as shown in Fig. 1. It was decided to use a 6 M cell mesh throughout the two-dimensional study as the values started to converge beyond this point.
2.2.2 Physical Model.
Turbulent, steady-state, segregated flow of a constant density, velocity inlet, atmospheric pressure outlet, nonslip wall condition, and SST turbulence model (gamma transition and all y+ wall treatment) were used. For each case, the airflow of two wind speeds (5 m/s and 10 m/s) was simulated for different AoAs (0–20 deg by a step of 5 deg). The stopping criterion was set as the maximum step number. The solution started to converge around 500 iterations. However, 2000 iterations were used, and output values were averaged for the last 10% of the 2000 iterations.
2.2.3 Studied Cases.
A baseline NACA4412, three J-shaped, and two KVF cases were studied. Baseline and studied J-shaped cases of 1/3, 1/2, and 2/3 pressure-side truncation ratios are shown in Fig. 2, while studied KVF cases of 1/8 and 1/4 trailing edge truncations are shown in Fig. 3.
2.3 Three-Dimensional Study.
A baseline lab-scale NACA4412 HAWT was experimentally tested using three wind speeds (8 m/s, 10 m/s, and 12 m/s). The generated power was measured using a digital rotary torque sensor. The TSR was calculated after measuring the free-rotating speed for each wind speed. Three wind speeds and experimental TSRs were used in the Siemens starccm+ CFD package. After carrying out a mesh independence study, CFD techniques were used to investigate the proposed cases and compare their performance with the baseline case. Furthermore, scaled models were investigated using CFD to study the performance of the proposed cases under realistic Reynolds number ranges without changing the TSR values.
2.3.1 Experimental Setup.
The baseline design of 0.55 m diameter was generated using the blade element momentum theory using NACA4412 to get the optimum twisted blade. It was three-dimesional (3D) printed and tested at the University of Wisconsin-Milwaukee wind tunnel facility. The wind tunnel is a suction type with a test section of (1.2 m × 1.2 m × 2.4 m). The baseline blade design and wind speed control are explained in Ref. [32]. A digital rotary torque sensor [33] was used to measure the generated power for validation using 8 m/s wind speed and the free-rotating speeds for all studied airflows. The digital rotary torque sensor precision is (RPM) and (N·m) for the rotation speed and torque, respectively. Experimental TSRs were calculated and used to simulate lab-scale and scaled HAWTs. Figure 4 shows the experimental setup and the wind tunnel facility. The reported turbulence intensity in the empty tunnel was measured at 0.32% [34]. In the experimental part, the test was repeated three times at 100 s a time for each data point, then data were exported as a spreadsheet, and the values were averaged to reduce errors. It is worth noting that the wind tunnel facility is temperature-controlled, which reduces temperature variations and, consequently, air properties during testing.
2.3.2 Meshing.
A mesh independence study was conducted to determine a reasonable mesh size and validate the CFD formulation using the baseline case subjected to 8 m/s airflow. Polyhedral mesh with prism layers and volumetric controls was used. Mesh size varied between 5 × 106 and 35 × 106 cells, with around 85% of the mesh cells near the rotor. Mesh independence study and validation results are shown in Fig. 5. A 26 × 106 cell mesh was used throughout the study as the power output started to converge beyond this point with a reasonable computational effort.
2.3.3 Physical Model.
Turbulent, steady-state, segregated flow of a constant density, velocity inlet, atmospheric pressure outlet, nonslip wall condition, and SST turbulence model (gamma transition and all y+ wall treatment) were used. The stopping criterion was set as the maximum step number. The solution started to converge around 400 iterations. However, 3000 iterations were used, and output values were averaged for the last 10% of the 3000 iterations. Each case was simulated using experimental angular velocities and their associated wind speeds. The generated power from each simulation was used to calculate the power coefficient.
Figure 6 shows the computational domain regions and boundary conditions underlined.
The relative velocity and the near wake region affect the power extraction from wind turbines. Unsteady simulations better capture the wakes compared to time-averaged, steady ones. Hence, the baseline case was investigated using steady and unsteady simulations applying the same mesh, physics, and turbulence model. Only the stopping criterion was changed in the implicit unsteady case. The time-step was set to 1 × 10−4 s with 1 s maximum physical time and five maximum inner iterations, yielding a total of 50,000 iterations. After averaging the generated power of the last 10% of the 50,000 iterations, results showed less than a 1% difference in generated wind power compared to a steady model. Unsteady simulations required costly computational power. Therefore, it was decided to proceed with steady simulations for further study simulations. Relative velocity scenes explained some of the studied cases behavior in the results section. The core flow eddies were captured and represented using the Q-criterion as a scalar quantity that estimates the difference between spin and strain rates to show the complexity of the flow downstream of the wind turbine. Figure 7 shows the wake region downstream of the baseline wind turbine based on a Q-criterion higher than zero. This figure shows that the correlation curves drop nearly monotonically with the increasing separation. The correlation in the turbine wake becomes lower than in the freestream flow. Near the X/D = 1, it is observed that the faster the turbine rotation, the smaller the correlation effect becomes. With the increase in X/D, this phenomenon gradually disappears. Moreover, it is clearly demonstrated that the wake structure starts to corrupt around 3D downstream from the turbine.
2.3.4 Studied Cases.
Lab-scale HAWTs of 0.55 m diameter for all proposed cases (1/3, 1/2, and 2/3 J-shaped pressure-side truncation ratios, and 1/8 and 1/4 truncated KVF cases) were simulated using the experimental angular velocities and their associated wind speeds to get the generated power and calculate the power coefficient. The performance of each studied case was compared to the baseline's performance.
To study the performance of the proposed cases under realistic Reynolds numbers, angular velocities, mesh, and all models were scaled by a 25-factor, keeping constant TSR values to imitate a small-scale HAWT (SWP-25-14TG20) [35]. Studied Reynolds numbers and TSRs are listed in Table 1.
Studied Reynolds numbers and TSRs for lab-scale and scaled cases
Size | Lab-scale | Scaled | |
---|---|---|---|
Wind speed | Diameter (m) | 0.55 | 13.75 |
8 m/s | TSR | 4.700 | |
RPM | 1315 | 52.60 | |
ReD | 280,864 | 7,021,611 | |
10 m/s | TSR | 5.195 | |
RPM | 1817 | 72.68 | |
ReD | 351,081 | 8,777,014 | |
12 m/s | TSR | 5.683 | |
RPM | 2385 | 95.40 | |
ReD | 421,297 | 10,532,416 |
Size | Lab-scale | Scaled | |
---|---|---|---|
Wind speed | Diameter (m) | 0.55 | 13.75 |
8 m/s | TSR | 4.700 | |
RPM | 1315 | 52.60 | |
ReD | 280,864 | 7,021,611 | |
10 m/s | TSR | 5.195 | |
RPM | 1817 | 72.68 | |
ReD | 351,081 | 8,777,014 | |
12 m/s | TSR | 5.683 | |
RPM | 2385 | 95.40 | |
ReD | 421,297 | 10,532,416 |
3 Results and Discussion
The results of the two-dimensional and three-dimensional studies are listed below. The lift-to-drag ratio was the key parameter for the two-dimensional study, while the power coefficient was the key parameter for the three-dimensional study. The effect of the proposed designs on the lift-to-drag ratio and the power coefficient for airfoils and HAWTs was studied and documented.
3.1 Two-Dimensional Study Results.
Airflows of two velocities (5 m/s and 10 m/s) over a NACA4412 baseline airfoil (0.254 m chord and 0.762 m span), three J-shaped airfoils with pressure-side truncation ratios (1/3, 1/2, and 2/3), and two KVF airfoils with truncation ratios (1/8, and 1/4) were simulated while varying the AoA between 0 deg and 20 deg by a step of 5 deg. Lift and drag forces were calculated and used to calculate the lift-to-drag ratios for each case. Figures 8 and 9 show the lift-to-drag ratio enhancement for J-shaped airfoils compared to the NACA4412 baseline airfoils for 5 m/s and 10 m/s airflows, respectively. J-shaped cases enhanced the lift-to-drag ratio with higher AoAs for 5 m/s wind speed. J-shaped airfoils experienced an increased lift at all studied AoAs, as shown in Figs. 10 and 11, for 5 m/s and 10 m/s airflows, respectively. It is noticed that introducing truncations in the pressure side of J-shaped airfoils reduces the lift-to-drag ratio for smaller AoAs compared with the baseline case. However, moving toward higher AoAs boosts aerodynamic performance. It is also noticed that lower velocity yielded better performance for J-shaped airfoils.
Figures 12 and 13 show the lift-to-drag ratio enhancement for KVF airfoils compared to the NACA4412 baseline airfoils for 5 m/s and 10 m/s airflows, respectively. KVF cases enhanced the lift-to-drag ratio, especially with higher AoAs. However, the enhancement was not because of an increased lift but rather because of reduced drag.
Relative velocity scenes for the baseline, J(1/2), and KVF(1/4) at 15 deg AoA subjected to 5 m/s airflow are shown in Fig. 14. The positive impact of the J-shaped truncation is evident on the pressure side, where the decrease in relative velocity results in an augmented pressure difference between the airfoil sides, consequently boosting lift. Conversely, the KVF truncation extends the wakes behind the trailing edge, causing an increase in induced drag.

Relative velocity scenes of baseline, J(1/2), and KVF(1/4) at mid cross section (5 m/s at 15 deg AoA)
3.2 Lab-Scale Three-Dimensional Study Results.
Three wind speeds (8 m/s, 10 m/s, and 12 m/s) corresponding to (4.700, 5.195, and 5.683) experimental TSRs, respectively, were used to simulate the 0.55 m diameter lab-scale HAWT baseline case and the proposed cases (1/3, 1/2, and 2/3 J-shaped pressure-side truncation ratios, and 1/8 and 1/4 KVF truncations). Experimental angular velocities associated with studied wind speeds were used. The generated power was calculated and used to calculate the power coefficient for each studied case. The performance of each studied case was compared to the baseline's performance. Figures 15 and 16 show the power coefficient versus TSR for the lab-scale baseline case and studied J-shaped and KVF cases, respectively. The J-shaped cases outperformed the baseline case for all studied wind speeds except for the J(2/3) case at higher speeds. Moreover, it is demonstrated that all studied KVF cases diminished the performance.
Figures 17 and 18 show the power coefficient enhancement versus TSR for the lab-scale J-shaped and KVF cases studied, respectively. The J(1/3), J(1/2), and J(2/3) yielded an average power coefficient enhancement of 1.56%, 1.15%, and −0.12%, respectively. The power coefficient was improved in lab-scale J-shaped cases, except for the J(2/3) at higher TSRs. In contrast, the KVF cases significantly reduced the power coefficient for all TSRs.
3.3 Scaled Three-Dimensional Study Results.
To study the effect of the proposed cases under realistic Reynolds numbers, all parameters were scaled by a factor of 25, keeping the TSR constant, as explained in Sec. 2.3.4 and Table 1. Three wind speeds (8 m/s, 10 m/s, and 12 m/s) corresponding to (4.700, 5.195, and 5.683) experimental TSRs, respectively, were used to simulate the scaled HAWT baseline case and the proposed scaled cases (1/3, 1/2, and 2/3 J-shaped pressure-side truncation ratios, and 1/8 and 1/4 KVF truncations). Scaled experimental angular velocities associated with studied wind speeds were used. The generated power was calculated and used to calculate the power coefficient for each studied case. The performance of each studied case was compared to the baseline's performance. Figures 19 and 20 show the power coefficient versus TSR for the scaled baseline case and studied J-shaped and KVF cases, respectively. It can be observed that for all studied wind speeds, the J-shaped cases outperformed the baseline case. On the other hand, all studied KVF cases diminished the performance. Figures 21 and 22 show the power coefficient enhancement versus TSR for studied scaled J-shaped and KVF cases, respectively. The J(1/3), J(1/2), and J(2/3) yielded an average power coefficient enhancement of 4.16%, 4.23%, and 2.54%, respectively.
3.4 Summary of Three-Dimensional Study Results.
To follow the discussion and compare the results for the studied J-shaped HAWT cases, the three-dimensional study power coefficient enhancement results are summarized in Tables 2 and 3 for both lab-scale and scaled J-shaped HAWT cases, respectively.
Summary of three-dimensional study results for lab-scale J-shaped HAWTs
Lab-scale power coefficient enhancement (%) | |||
---|---|---|---|
TSR | J(1/3) | J(1/2) | J(2/3) |
4.700 | 1.82 | 2.08 | 0.75 |
5.195 | 1.36 | 0.63 | −0.90 |
5.683 | 1.51 | 0.76 | −0.20 |
Average | 1.56 | 1.15 | −0.12 |
Lab-scale power coefficient enhancement (%) | |||
---|---|---|---|
TSR | J(1/3) | J(1/2) | J(2/3) |
4.700 | 1.82 | 2.08 | 0.75 |
5.195 | 1.36 | 0.63 | −0.90 |
5.683 | 1.51 | 0.76 | −0.20 |
Average | 1.56 | 1.15 | −0.12 |
Summary of three-dimensional study results for scaled J-shaped HAWTs
Scaled power coefficient enhancement (%) | |||
---|---|---|---|
TSR | J(1/3) | J(1/2) | J(2/3) |
4.700 | 3.43 | 4.42 | 1.87 |
5.195 | 4.64 | 4.07 | 2.70 |
5.683 | 4.40 | 4.22 | 3.04 |
Average | 4.16 | 4.23 | 2.54 |
Scaled power coefficient enhancement (%) | |||
---|---|---|---|
TSR | J(1/3) | J(1/2) | J(2/3) |
4.700 | 3.43 | 4.42 | 1.87 |
5.195 | 4.64 | 4.07 | 2.70 |
5.683 | 4.40 | 4.22 | 3.04 |
Average | 4.16 | 4.23 | 2.54 |
At a given TSR, power coefficient enhancement shows the same trend for both lab-scale and scaled cases. For higher TSRs, the J-shaped truncation reduced the relative velocity at the truncation position on the pressure side of the blades, which increased the pressure difference between the blade sides; hence, a higher lift was generated. This increase was more pronounced for smaller truncations. To explain that, relative velocity scenes at the midspanwise radial position of the lab-scale baseline and J-shaped models were extracted for the highest TSR, as shown in Fig. 23. The truncations on the pressure side negatively affect the separation point location and the reversed flow region size on the suction side. However, high relative velocities at high TSRs help suppress the spread of the reversed flow region, ensuring that it does not counteract the power enhancement achieved through truncations.

Relative velocity scenes at blade midspanwise radial position of the lab-scale baseline and J-shaped cases for TSR = 5.683
On the other hand, for small TSRs, it was observed that J(1/3) yielded lower enhancement than J(1/2) for both lab-scale and scaled cases in contrast to higher TSRs. At low TSRs, the flow momentum on the suction side is low, allowing the wakes to expand in the axial direction and hindering the truncations' power improvement. Figure 24 shows that J(1/3) experienced more vortices and lower relative velocity values on the suction side compared to J(1/2); hence, lower enhancement was attained. The J(2/3) experienced premature early separation with more vortices on the suction side for both lab-scale and scaled rotors, which explains its poor performance compared to J(1/2) and J(1/3).

Relative velocity scenes at blade midspanwise radial position of the lab-scale baseline and J-shaped cases for TSR = 4.700
4 Conclusions
Among renewable energy solutions, wind energy has been evolving. It represents a promising renewable energy solution and is expected to expand in the near future. Airfoil design modifications such as introducing truncations at specific locations represent a hot research topic and can be useful in boosting the efficiency of HAWTs and the aerodynamic performance of airfoil-shaped objects.
This study found that the J-shaped and KVF airfoil cases increased the lift-to-drag ratio for some wind speeds and angles of attack. J-shaped airfoils enhanced lift over the studied wind velocities and range of AoAs. For the KVF cases, the lift-to-drag enhancement was not because of the lift improvement but rather because of reduced drag and reduced planner area. Furthermore, it was found that the studied J-shaped HAWTs showed an improvement in power coefficient for all studied lab-scale cases except for J(2/3) at higher TSRs. On the other hand, all studied scaled cases improved the power coefficient.
On the contrary, all studied KVF HAWTs diminished the generated power for both lab-scale and scaled cases. J(1/3) demonstrated an average enhancement in power coefficient of 1.56% and 4.16% for lab-scale and scaled HAWT cases, respectively. J(1/2) exhibited an average power coefficient enhancement of 1.15% and 4.23% for lab-scale and scaled HAWT cases, respectively. J(2/3) resulted in an average power coefficient enhancement of −0.12% and 2.54% for lab-scale and scaled cases, respectively.
Acknowledgment
The authors are profoundly grateful to the UWM high-performance computing facility.
Funding Data
The computation grant is funded by NSF (Award No. 2126229; Funder ID: 10.13039/100000001).
The U.S. Department of Energy funds the research (DE-EE0009728; Funder ID: 10.13039/100000015).
Data Availability Statement
The authors attest that all data for this study are included in the paper.
Nomenclature
- AoA =
angle of attack
- CD =
drag coefficient
- CL =
lift coefficient
- CP =
power coefficient
- CFD =
computational fluid dynamics
- DAQ =
data acquisition
- HAWT =
horizontal axis wind turbine
- KVF =
Kammtail Virtual Foil
- ReD =
Reynolds number based on rotor diameter
- RPM =
revolution per minute
- SST =
shear stress transport
- TSR =
tip speed ratio
- VAWT =
vertical axis wind turbine
- X/D =
downstream distance/rotor diameter