1. Introduction
To achieve sustainability and mitigate the effects of global warming, countries worldwide are beginning to use green energy as a substitute for traditional fossil fuel energy. Wind energy is a crucial source of green energy, because this energy is renewable and inexhaustible. Horizontal-axis wind turbines (HAWTs) are frequently used to capture wind energy and convert it into electricity. Numerous scholars have attempted to optimize wind turbine design to improve the efficiency with which this conversion is achieved. The performance of wind turbines can be improved through various methods, such as utilizing efficient airfoils, optimizing blade design, incorporating ducted wind turbines, and so on [
1,
2,
3]. Using efficient airfoils and blade design optimization is a conventional technique for improving wind turbine efficiency, because the blades are the most crucial parts of a wind turbine. The aerodynamics of airfoils and blades, the rotor solidity and number of blades, and the angle of attack and pitch angle of blades are crucial in wind turbine performance. Much of the previous literature often analyzed the effects of parameters on rotor performance using one-factor-at-a-time investigations. However, this approach may introduce bias, as conclusions are drawn under specific experimental conditions, resulting in varying conclusions drawn under different experimental conditions. The present study used the Taguchi method to systematically optimize the rotor blade geometry, including the rotor solidity, number of blades, and blade pitch angle, of a ducted micro HAWT to improve its rotor performance. In addition, the airflow aerodynamic characteristics were investigated.
To obtain a better rotor performance, the airfoil of a turbine blade with a high lift-to-drag ratio (LDR) should be chosen. Chaudhry and Prakash [
4] proposed six novel airfoils for the design of micro horizontal-axis wind turbines operating at low wind speeds. It was seen that the aerodynamic performance of NAF-Series airfoils was better than SG6043 and NACA4415 airfoils at a low Reynolds number, and NAF 4923 airfoil was the best candidate airfoil among others. Yossri et al. [
5] numerically evaluated the aerodynamic performance of NACA0012, NACA4412, NACA0015, and NACA4415 airfoils with three rotor diameter sizes. The findings showed that the NACA 4412 airfoil yields the highest LDR of 26. The study conducted by Mostafa et al. [
6] revealed that the SG6043 wind turbine blade has better aerodynamic performance, producing 2.5% more power than the NACA4412 blade under the same operating conditions. Suresh et al. [
7] evaluated the aerodynamic performance of ten airfoils to examine the suitability of low-Reynolds-number airfoils for the design of a small-scale wind turbine at low wind conditions. The result revealed that the SG6043 airfoil had a maximum LDR of 56.40 at an eight-degree angle of attack. However, among these airfoils, the SD7080 airfoil was selected for the design of a wind turbine blade that can operate at low wind speed conditions. Abdelghany et al. [
8] added a winglet at the blade tip to improve the aerodynamic characteristics of wind turbines. The results illustrate that the lift-to-drag ratio coefficient and power coefficient increase related to the blade without winglet by about 11.6% and 6.9%, respectively, at optimum winglet height lengths per blade radius of 0.042. Roy et al. [
9] investigated the rotor performance and observed the flow characteristics around the NACA 4415 airfoils with protrusions in the leading edge on a horizontal-axis wind turbine. The results indicated that the best flow-controlling measures were achieved by using the spherical leading-edge protrusion (SLEP) model. The HAWT with SLEP exhibited an 8.2% greater power coefficient than that without leading-edge protrusion.
In the studies of blade design optimization, Duquette and Visser [
10] numerically examined the effect of rotor solidity and the number of blades on the aerodynamic performance of a small HAWT. Their results indicated that under fixed rotor solidity, an increase in the number of blades leads to an increase in the maximum power coefficient of the rotor. Moreover, they found that an increase in rotor solidity from 5–7% to 15–25% causes an increase in
CP,max and a reduction in the tip speed ratio (TSR). The TSR corresponding to
CP,max varies considerably and marginally with a change in rotor solidity and the number of blades, respectively. Duquette et al. [
11] experimentally evaluated the effects of rotor solidity and the number of blades on rotor performance. Their results indicated that
CP increased when the rotor solidity was increased from 7% to 27%; however, an increase in the number of blades did not result in a notable increase in
CP. For the optimum design of the three-blade rotor, an increase in solidity resulted in an increase in
CP,max but a decrease in the TSR. At a fixed solidity of 10%, the aerodynamic efficiency and power sharply decreased when the number of blades was increased to 12. Leung et al. [
12] numerically evaluated the performance of micro wind turbines with different design parameters. Their results indicated that high-solidity wind rotors outperformed low-solidity ones. The micro wind turbine with rotor solidity of more than 50% outperformed the other micro wind turbines. A multi-blade system is preferable for a micro wind turbine. Bourhis et al. [
13] investigated the effect of blade solidity on micro-scale and low tip-speed ratio wind turbines. They varied the solidity by varying the blade chord length rather than the number of blades. To conclude, the best compromise between the maximum power coefficient, the cut-in wind speed, the mass of filament, and the stability of the wake is achieved for the rotor with a blade solidity of 1.25. Birajdar et al. [
14] studied the effects of the TSR, angle of attack, rotor solidity, and number of blades on the aerodynamic performance of a small wind turbine. Their results indicated that
CP,max was 0.5 at the optimum TSR and angle of attack of 7 and 4.5°, respectively. Moreover, the turbine with three blades had the optimal rotor solidity. Sudarma et al. [
15] experimentally and numerically investigated the effect of the number of blades on the performance of a small HAWT with winglet blade tips. An increase in the number of blades was found to cause increases in the torque and output power. The presence of winglets increased the pressure on the blade surface and caused the concentration of wind flow at the blade tips, which resulted in improved rotor performance. Eltayesh et al. [
16] investigated the effect of the number of blades on the performance of a small HAWT. They found that compared with a five-blade configuration and a six-blade configuration, a three-blade configuration resulted in 2% and 4% higher
CP,max values, respectively. An increase in the number of blades caused an increase in the torque and enabled the turbine to operate at a lower TSR. Zawadzki et al. [
17] examined the effect of rotor solidity on the performance of a small HAWT. An increase in rotor solidity was discovered to lead to an increase in
CP,max but a slight decrease in the TSR. Chaudhary and Prakash [
18] explored the effects of rotor solidity (ranging from 0.055 to 0.207) and the number of blades (ranging from 3 to 7) on rotor performance. They found that
CP,max increased with the number of blades, and that favorable performance was achieved only when rotor solidity was 0.055–0.085. Porto et al. [
19] conducted experiments to investigate the effect of the number of blades on the performance of a HAWT. Their results indicated that a five-blade rotor outperformed a three-blade one; the five-blade rotor had higher static torque, which resulted in a shorter starting time and a higher
CP value (39%). Chaudhary and Roy [
20] optimized the number of blades, rotor solidity, and TSR on the basis of blade element momentum theory. They found that
CP,max varied strongly with a change in the rotor solidity but weakly with a change in the number of blades. They concluded that a rotor with five blades and solidity of 5–10% would achieve
CP of 0.5 at a blade pitch angle of 3°. Vashkevitch et al. [
21] obtained experimental data on the performance of a novel HAWT under various blade incidence angles. They found that the developed turbine exhibited high efficiency at the optimum blade incidence angle of 7.5°, with
CP,max being 0.538. Mayer et al. [
22] investigated the starting performance of a HAWT under blade pitch angles of 0°–35°. Their results revealed that (1) the turbine exhibited
CP,max at a blade pitch angle of 0°, (2) the starting process of the turbine was characterized by a long idling period, and (3) the turbine’s startup was best for a blade pitch angle of 20°. Kriswanto et al. [
23] adopted the Taguchi method to optimize the performance of a HAWT. Their analysis of variance (ANOVA) results indicated that of all the investigated parameters, the airfoil had the strongest influence on the rotor power of the HAWT. The highest lift coefficient and lift-to-drag ratio were achieved with the SD7080 airfoil under angles of attack ranging from 0° to 20°. Although the blade pitch angle can affect the performance of a HAWT, its effect may be weaker than those of the airfoil and angle of attack. Kaya et al. [
24] numerically studied the aerodynamic effects of the blade pitch angle on the performance of small HAWTs at different TSRs. Their results indicated that at low TSRs, a more downward blade pitch angle resulted in a higher
CP and a smaller thrust coefficient (
CT); however, at high TSRs, the effect of the blade pitch angle on
CP was the reverse. At low TSRs, a higher blade pitch angle resulted in the flow separation location being closer to the leading edge of the blade and the tip vortices being stronger.
The development of diffuser-augmented wind turbines (DAWTs) improving rotor performance began in the 1950s and has been a hot research topic since the Wind Energy Innovative Systems Conference of 1979. Many studies have indicated that DAWTs have advantages over other types of augmented wind turbines [
2]. A diffuser or duct can generate separation regions behind it; thus, compared with a bare wind turbine, DAWTs produce low-pressure regions that draw in more wind at higher speeds past the rotors. Because wind’s power is proportional to the cube of its speed, a slight increase in wind speed can considerably increase the power output of wind turbines. The performance of a DAWT depends on several factors, such as the diffuser shape, diffuser geometry, and rotor blade geometry. The diffuser can have different shapes, such as a nozzle or flange shape, and the geometric parameters of a diffuser include the rotor diameter, nozzle length, nozzle angle, diffuser length, diffuser angle, and flange height. Rahmatian et al. [
25,
26] optimized the design of converging-diverging ducts using the response surface method (RSM) and a genetic algorithm (GA) and investigated the effect of the duct diffuser on the aerodynamic performance of a micro HAWT. Their optimal duct design increased
CP,max by a factor of 3.94 and reduced the noise level and dynamic forces behind the turbine. Wang and Chen [
27] numerically investigated the effect of the number of blades on the performance of a converging-diverging ducted wind turbine. They found that a higher number of blades results in higher torque and a larger blade area for capturing wind energy; however, it also results in greater blockage and thus lower
CP. Therefore, using an appropriate number of blades is essential for achieving high wind turbine performance and efficiency. Asl et al. [
28] studied the effects of the number of blades, blade geometry, and angle of attack on the rotational speed of a converging-diverging ducted wind turbine. Their results indicated that the rotational speed (1) decreased with an increase in the number of blades, (2) decreased with an increase in the width of the top blades, and (3) increased with an increase in the angle of attack.
Chen et al. [
29] investigated the effect of a flanged diffuser on the rotor performance of micro wind turbines under different rotor solidity values. This study is motivated by micro-HAWTs being suitable for moving vehicle applications, because high-speed and stable wind is easily generated as the vehicle moves. The results showed that the use of a flanged diffuser resulted in a substantial enhancement of rotor performance, which was predominantly influenced by rotor solidity. Rotor solidities of 30% and 40% resulted in the highest power outputs, whereas a rotor solidity of 60% resulted in the highest torque output. The study mentioned above also revealed that the investigated wind turbine exhibited low torque and high rotor rotational speed. Chen et al. [
30] evaluated the aerodynamics of a ducted micro wind turbine with large-tip untwisted blades. Their results suggested that a rotor solidity of 60% resulted in high power and torque outputs at a relatively low rotational speed; thus, this rotor solidity value is suitable for micro wind turbines.
As mentioned above, much of the previous literature examined parameter effects on rotor performance by one-factor-at-a-time investigations, implying that the conclusions were drawn under specific experiment conditions, resulting in bias. Consequently, the conclusions could differ if the experiment conditions are different. For example, Duquette et al. [
11] found that an increase in the number of blades did not cause an improvement in rotor performance; the aerodynamic efficiency and power even decreased when the number of blades was increased to 12. However, Sudarma et al. [
15] and Porto et al. [
19] concluded that an increase in the number of blades causes an increase in the power output of a wind turbine. Similarly, scholars have obtained differing results regarding the effect of rotor solidity on rotor performance. Considerable research has discovered that an increase in rotor solidity causes a substantial improvement in rotor performance; however, Chaudhary and Prakash [
18] found that this effect was only observable under rotor solidity values of 0.005 to 0.085, with a further increase in rotor solidity resulting in a decrease in rotor performance. The differences in the conclusions of the aforementioned studies may have been caused by differences in their experimental conditions with the one-factor-at-a-time investigations. By contrast, the Taguchi method involves using an orthogonal array (OA) to design experimental conditions that enable the simultaneous systematic assessment of the effects of multiple relevant parameters on a certain quality [
31]. In this method, the signal-to-noise (
S/
N) ratio is employed to evaluate quality and to achieve optimum quality with minimal variance [
32]. Moreover, the Taguchi method is also known as robust parameter design owing to the finding of the optimum parameters, considering that quality may be affected by the design, the production, and environmental disturbance [
31]. Additional information on this method is provided in the papers of Roy [
33] and Ross [
34]. Some studies have adopted the Taguchi method to optimize wind turbine design [
23,
35,
36].
In previous studies of wind turbines installed on mobile vehicles, the rotor sizes investigated were relatively large. As a result, they needed to be installed on the vehicle’s roof or hood, causing additional resistance and fuel consumption concerns. A micro wind turbine can be installed in front of or inside the engine compartment of a car without causing additional drag. The present study focused on optimizing the blade geometrical parameters of a ducted micro HAWT based on an existing flanged duct investigated by the corresponding author of this article. The results obtained can provide guidelines for the development of a micro wind turbine suitable for installation in a mobile vehicle. In a further study, the authors will use the obtained optimal rotor blade geometrical parameters to examine the optimization of a flanged converging-diverging duct. The rest of this paper is divided into four sections.
Section 2 describes the parameter optimization process,
Section 3 details the numerical model of this study, and
Section 4 presents the numerical results. Finally,
Section 5 provides the conclusions of this study and suggestions for the design of a ducted micro HAWT.
2. Taguchi Optimization Process
In this study, the blade geometry of a ducted micro HAWT was optimized using the Taguchi method. The control factors in this study were the number of blades
n, rotor solidity
, and blade pitch angle
(
A,
B, and
C, respectively). Every control factor was set to three-level values. Wind turbines installed on vehicles must have a small rotor diameter. Therefore, a rotor diameter of 30 cm was selected in this study. Duquette and Visser [
11] and Chen et al. [
35,
36] have suggested that when the rotor diameter is small, higher rotor solidity results in a higher
CP,max value. Of the rotors studied by Chen et al. [
30], the rotor with 60% solidity exhibited the highest power. In the present study, the rotor solidity was set as 50%, 60%, and 70%. Chen et al. [
30] also found that when the rotor diameter is small, a higher number of blades results in the generation of more power. Therefore, the number of blades was set as 8, 10, and 12 in this study. In addition, the blade pitch angle was set as 25°, 30°, and 35°. The control factors and their corresponding levels are summarized in
Table 1. Given that a wind turbine may operate at various wind speeds, wind speeds of 10 and 16 m/s were regarded as noise factors to achieve a robust quality characteristic. The
CP,max value of the ducted micro HAWT was the objective quality to be maximized in this study. After determining the investigated control factors and their level numbers, the experimental conditions were arranged using an
L9(3
4) OA and carried out by numerical simulation.
The simulated wind turbine was similar to the wind turbine used in experiments by Chen et al. [
30].
Figure 1 displays the simulated micro HAWT with a flanged diffuser system. The flanged diffuser had an inlet radius of 15 cm, a length of 10 cm, a diffusion angle of 30°, and a flange height of 3 cm [
Figure 1a]. The present study focused on the effects of blade geometry on rotor performance; therefore, the design of the flanged diffuser was not optimized. The cross-sectional profile of the rotor blade was an NACA 4415 airfoil. The blades of the simulated turbine were untwisted blades with a length of 12 cm, and
was varied from 25° to 35°; these blades were attached to a cone hub with a base diameter of 8 cm and a length of 6 cm [
Figure 1b], which resulted in a rotor diameter of 30 cm. The assembled rotor was placed in the middle of the flanged diffuser [
Figure 1c]. The required rotor solidity was achieved by adjusting the chord lengths of the blade tip and root.
Table 2 presents the chord lengths of the blade tip and root [denoted as
a and
b in
Figure 1b, respectively] for different numbers of blades and rotor solidities. The blade profiles of an eight-blade rotor with different solidities are displayed in
Figure 2.
Several dimensionless parameters discussed in subsequent sections are defined as follows. The power coefficient
CP and torque coefficient
CT of a wind turbine are expressed as follows:
where
T is the torque generated by the rotor,
ω is the rotor’s angular speed,
ρ is the wind density,
A is the rotor’s swept area,
R is the radius of the rotor, and
V is the free-stream wind speed. In addition, the TSR is expressed as follows:
The expressions for these dimensionless parameters above can be referred to [
25].
5. Conclusions
This numerical study optimized the blade geometry of a ducted micro HAWT through the Taguchi method to improve the rotor performance. The investigated rotor blades were untwisted with an NACA 4415 airfoil. Taguchi optimization can systematically and comprehensively investigate the parameter effects and avoid the bias caused by one-factor-at-a-time investigations. The numerical results were compared with the experimental results of Chen et al. [
30] to examine the reliability of the numerical model. The relative error in
CP,max was approximately 4.7%, indicating the developed model was reliable. The blade geometrical parameters investigated included the number of blades, rotor solidity, and blade pitch angle. The optimum parameter design included 8 blades, 60% solidity, and a 30° pitch angle, and the achieved
CP,max was 0.432 at a TSR of 1.2, which was 39.4% higher than that obtained with the worst blade geometry. The optimum result of a high solidity of 60% confirmed the conclusion drawn from Chen’s experiments [
30], e.g., a high rotor solidity value is suitable for micro wind turbines. Of the three control factors, the blade pitch angle was found to have the most significant effect on the rotor’s power output. In addition, strong factorial interactions were observed, implying that individually investigating wind turbine blade geometrical parameter effects potentially caused improper optimization.
The airflow aerodynamic characteristics were also discussed. After passing this wind turbine, airflow formed complex ellipsoidal vortex structures because of the rotor’s rotation. Compared to the rotor with the worst blade geometry, the optimum rotor blade geometry could draw more airflow into the duct, and its pressure difference between the windward and leeward sides of the blades was greater, exhibiting higher CP,max. In addition, the optimum blade geometry achieved a CT,max of 0.43 at a TSR of 1.2, which was 38.7% higher than the worst one. However, the untwisted blades considered in this study exhibited low torque near their tips; therefore, twisted blades should be used for further increasing the torque generated at the blade tips to achieve higher power output for the rotor.
In pursuit of sustainability and the mitigation of global warming impacts, nations across the globe are increasingly adopting green energy alternatives to conventional fossil fuels. Wind energy stands out as a pivotal component of green energy solutions due to its renewable and limitless nature. This study optimized the rotor blade geometry and provided some insight into the influence of blade geometrical parameters on rotor performance, thereby enhancing the efficiency of wind energy utilization and contributing to sustainable development goals (SDGs) like SDG 7 (affordable and clean energy).