1. Introduction
In view of the swift evolution of global warming, the topic of renewable energies as potentially efficient substitutes for fossil fuels has reached the forefront of the scholarly community’s focus. Wind turbines represent harvesters that are able to convert wind energy into mechanical energy by virtue of the rotation of the blade, eventually converting the generated mechanical energy into electrical energy through the generator [
1]. Every single wind turbine is a complex system comprising various components. Wind turbine blades, in particular, are critical components of the wind turbine since they are responsible for harnessing the wind potential and driving the rotation of the rotor [
2]. Therefore, efforts ought to be concentrated on the effective design of the aerodynamics of wind turbine blades.
Generally, many investigations of the aerodynamics governing the functioning of turbine blades are carried out under the long and slender structure assumptions [
3], in which turbine blades are considered to be slender structures, where the velocity in the spanwise direction is considerably lower than in its counterpart component in the streamwise direction [
3]. Under these specific circumstances, it is acceptable in many research efforts that the flow at a specific radial position is two dimensional, where 2D airfoil analyses can be both practical and accurate, specifically for conditions characterized by low wind speed [
4,
5,
6]. However, additional intricacies should be considered when dealing with small-scale wind turbines: First, the low aspect ratio characterizing small-scale wind turbines stresses the importance of revisiting the assumptions of the infinite wing valid only for the specific case of very long blades [
7,
8,
9]; second, the apparent differences in operating environments between horizontal axis large-scale wind turbines (LSWTs) and their small-scale counterparts, namely speed of the freestream wind, air turbulence, Reynolds number, etc. accentuates the necessity of analyzing the aforementioned turbines depending on their specific operating conditions. In view of the exponential growth of wind speed as a function of height [
10], the functioning of the LSWT is characterized by speeds higher than those undergone by the SSWT, since the latter usually reach heights approximately fourteen times lower than their large-scale equivalents [
11]. Being mounted at lower altitudes, SSWTs face more turbulent winds as a result of the presence of numerous obstacles within the same height range, namely trees and buildings [
12,
13,
14,
15].
In light of all the aforementioned differences, it is of great importance to assess the performance of each of the small- and large-scale wind turbines while considering each turbine’s own proper set of operating conditions, as failing to do so might lead to deceptive outcomes and wasted efforts. It is indisputable that during recent decades, the wind energy sector has witnessed numerous advancements, especially when it comes to the industrial scale. Nevertheless, a larger room for contribution is still available from the small-scale, as the peer-reviewed literature and investigative studies dedicated to SSWTs are, by comparison, far smaller than that available for LSWTs, despite their considerable energy potential [
16].
The overall design of a wind turbine unfolds under numerous considerations, one of which is blade shape. The main objective of the optimization of a wind turbine’s blade shape is to attain maximized torque and minimized thrust. For that, turbulence is an important criterion to explore. It can be more pronounced either by a roughening in the body surface or a sharp edge on the body [
17]. Investigation of the blade’s interactions with the wind, including turbulence, is a necessary step in the aerodynamic optimization process. The power and noise produced by the turbine depend on the turbulence over the blade. Added turbulence will change the pressure profile around the airfoil and, consequently, the aerodynamic forces. In the case of a flat plate, a separation of the boundary layer is created at the sharp edges, making the drag coefficient at that specific point significantly less dependent on the Reynolds number (Re) and largely more dependent on the plate’s aspect ratio (AR). A taper in the blades is therefore introduced in order to gently minimize the pressure gradient at the tip portion of the blade, which helps produce a narrower wake as well as very low drag [
18]. Another crucial design parameter of a wind turbine blade is the twist angle. The optimal angle of attack of the airfoiled cross-section of the blade is heavily affected by the faced wind direction. Alternatively, apparent wind direction is affected by the speed of the rotating blades, even in uniform freestream wind velocity conditions. To achieve a certain rotations-per-minute rate, the tip cross-section of the blade always travels faster than the cross-section located near the rotor hub. In other words, as the wind turbine blade rotates, the tip of the blade must travel a bigger distance than the section of the blade closer to the hub in order to maintain the same rotational speed. This means that the tip of the blade must travel more quickly than the section of the blade closer to the hub in order to maintain the same rotational speed. Therefore, it seems only logical that the different cross-sections along the blade are not going to have the same optimal angle of attack. To this end, optimized designs of wind turbine blades have adopted a varying twist throughout the length of the blade in order to achieve an optimal angle of attack along the entirety of the length.
In order to address the above-mentioned crucial design parameters, numerous research efforts were dedicated to exploring several blade shapes and twist angle configurations, with the shared objective of achieving an aerodynamically efficient design for a wind turbine to reach the maximum attainable power adequate for a selected set of environmental operating conditions. For instance, a study by Rahgozar et al. [
19] assessed the performance of a small horizontal axis wind turbine with regard to the output power and the starting time for four different combinations of linear/nonlinear distributions of the chord length and twist angle along one-meter timber blades. The results of this study show that, even though the linear distributions deviate more from the ideal distributions compared to the nonlinear distributions, they still perform similarly in terms of generating power output. Xudong et al. [
20] aimed at optimizing the blade shape for 2 MW and 5 MW turbine rotors. Their effort was based on the blade element momentum (BEM) theory with a refined tip-loss correction; their work showed that the optimization model indeed reduced the energy cost in the case of the studied rotors. Tenguria et al. [
21] also used the BEM theory to identify the best combination of multiple design parameters, namely the chord, thickness, and twist distribution, basing the blade’s cross-section on two selected NACA airfoil profiles. The BEM method was also the foundation of a research effort by Tahani et al. [
22], where the goal was obtaining the maximum power coefficient for linearized chord and twist distributions. Similarly, The BEM theory was used in various studies dedicated to improving LSWT designs [
23,
24,
25,
26,
27,
28]. On the other hand, the latter theory was also relied on in several small-scale optimization studies. Tahani et al. [
29] created an optimization code for the SSWT case and provided validation of the experimental data for a specific case of operating conditions. Additionally, Chaudhary et al. [
30] conducted a study in which the BEM theory was utilized in order to optimize the blades’ number and the selection of tip speed ratio. The BEM method was also utilized in a research effort by Tahani et al. [
31]. The aim of this research study was proposing a new approach to introducing chord and twist distributions through fitting various types of functions on them. To this end, 48 functions were chosen, based on their resemblance to the classical distributions, as potential distributions for chord and twist angle profiles. Several functions were proposed, with the aim of maximizing the power coefficient. In other efforts led by Pourrajabian et al. [
32,
33], the objective was to design a fast-starting blade where the starting time was combined with the output power towards an objective function, while the blade’s tolerable stress was considered as the system’s constraint value and the BEM theory was considered the basis of the optimization code, as was the case for numerous other studies dedicated to improving the performance of SSWTs [
34,
35,
36,
37,
38], some of which were very recently published.
The BEM theory is not exempted from a set of assumptions that make it unable to provide real-time intricate information that may be important; for instance, a lack of accuracy in flow representation due to a disregard for wake expansion and tip losses, which can have significant effects, especially in fluid–structure interaction analyses. In fact, many research efforts have attempted to solve this issue by providing several corrections to the original theory [
39,
40,
41,
42]. Additionally, the BEM theory necessitates non-turbulent air movement for the equations to be calculated. This is problematic since, in the case of the SSWTs especially, the flow is characterized by a high turbulence induced by same-height-range obstacles, as discussed previously. This means that relying on the BEM for analysis of SSWTs will most likely generate best-case idealistic scenarios instead of realistic pictures of performance. Moreover, SSWT blades are characterized by smaller aspect ratios compared to their large-scale counterparts. For this scenario, neglecting 3D flow effects is more consequential, which makes the BEM theory more inadequate for SSWT analyses since it is based on calculating the aerodynamic forces acting on every cross-section along the blade while assuming the latter to be two-dimensional [
43].
Hence, high-fidelity analyses able to fully capture the 3D flow behavior around the three-dimensional rotating turbine are necessary, especially when investigating the efficiency of SSWTs. Several computational fluid dynamics (CFD) studies were carried out to assess industrial-scale wind turbines, leading to highly efficient designs [
44,
45,
46,
47,
48,
49,
50], while not as many peer-reviewed resources are available for their small-scale equivalents [
51,
52,
53,
54]. Additionally, the literature regarding the shape of the blade and the twist distribution specific to SSWTs still has major room for contribution.
The purpose of this study is to use a high-fidelity CFD approach to examine the effect of blade shape and twist angle on the power output of a 50 cm rotor diameter wind turbine. The analyses include a comparison of rectangular and tapered blade shapes using four airfoils with high lift-to-drag ratios via solving the full Navier–Stokes equations. Additionally, different twist configurations are evaluated, and the optimal design is selected based on torque and power computations. The numerical simulations are conducted using COMSOL Multiphysics, a finite element (FE)-based software.
5. Conclusions
In this work, the effects of different design and geometric characteristics of SSWTs on their aerodynamic performance is assessed using high-fidelity CFD analyses, where the full Navier–Stokes equations were solved and a mesh convergence analysis was conducted. Rectangular and tapered blade shapes as well as different linear and nonlinear twist angle distributions characterized by different steepness and slope traits were explored. For the studied operating and geometric conditions considered, NACA4412 yielded the highest power in comparison to the other airfoil profiles for both the tapered and rectangular blade configurations. The least power generated by the tapered blade shape configuration corresponds to the NACA4415 airfoil, while a lower power was obtained when the NACA0015 profile was used for the rectangular blade shape. For the considered flow characteristics, the power values showed that the most effective configuration is the rectangular blade shape with the NACA4412 airfoil profile, generating a power output of 2.452 W. In addition, it was revealed that while the rectangular blade shape is favorable in terms power production for the studied conditions, it nevertheless resulted in higher blade stresses. Therefore, a compromise between structural and aerodynamic blade characteristics is necessary to attain an aerodynamically effective and structurally robust SSWT design.
The twist distribution assessments suggested that the nonlinear twist distribution is advantageous in terms of power production when considering the studied cases. However, linear twist distributions can be a good option as well provided that a good distribution slope value is considered. Considering the cases in hand, steeper twist distributions resulted in higher stress values for both linear and nonlinear configurations. However, linear twists constantly yielded higher stress magnitudes for the x, y, and z directions compared to nonlinear configurations. Therefore, a favorable twist distribution can concurrently ensure high steady-state torque generation while guaranteeing reasonable load-induced stresses, and is therefore a good selection aerodynamically and structurally, as is the nonlinear twist for Fit A.