Performance analysis of a small horizontal axis wind turbine under the use of linear/nonlinear distributions for the chord and twist angle

Highlights

• Nonlinear/linear distributions of the chord and twist are analyzed for small blades.

• Optimization method utilizes the output power and starting performances as criteria.

• Linear distributions for both chord and twist are recommended in low-wind areas.

• Nonlinear distributions for both chord and twist are suggested in windy regions.

Abstract

The increase in efficiency, decrease in starting time, and ease in manufacturing of rotor blades are the most desirable aims of research in the design of small-scale wind turbines. A multi-objective optimization study is carried out to analyze the performance of a small horizontal axis wind turbine in terms of the output power and the starting time for four possible combinations of linear/nonlinear distributions of the chord length and twist angle along one-meter timber blades. The blade-element momentum theory is adopted for the calculation of the power coefficient and the starting time. The optimization is achieved through a genetic algorithm which simultaneously maximized the power coefficient and minimized the starting time. The most important contribution of this paper is the in-depth comparison of the linear and the nonlinear distributions for chord and twist angle subjected to the aforementioned optimization, which is not available in the existing literature in such detail. Results show that although the linear distributions have more deviation from the so-called ideal distributions, however, the output power performance of the blades with linear distributions is competitive with that of the nonlinear ones. Moreover, the results establish that the use of linear distribution can improve the starting performance at a lesser compromise of output power. This is of paramount importance, particularly to promote harnessing the wind energy in developing countries, as simpler distributions could facilitate the manufacturing of wind turbine blades. Apart from using the linear or nonlinear distributions for both the chord and the twist angle, two other cases are also investigated including the linear distribution for the chord and the nonlinear one for the twist and vice versa. The analysis of these cases shows that choosing the nonlinear distribution for the chord would improve the starting while using the linear one would lead to more powerful blades.

Introduction

In the modern world, the access to reliable and affordable energy has become a basic human right (Hughes, 2018). The lack thereof in the developing nations implies that a large portion of population in such countries cannot be provided with the basic necessities. Consequently, such countries score quite low on Human Development Index (HDI) which strongly correlates with the per capita energy use of that country (United Nations Development Programme, 2019). Realizing such global dilemma, the United Nations General Assembly in 2015 laid down the famous Sustainable Development Goals in which one of the main goals is to achieve the access to clean energy in developing nations by the year 2030 (United Nations General Assembly, 2015). A report by International Renewable Energy Agency (IRENA) sheds light on the possible solution in this regard (Lucas et al., 2012). According to Lucas et al. (2012), the developing nations must resort to stand-alone micro grids, to enable the additional generation needed in developing countries for complete access to electricity by 2030. Renewable energy sources have the cardinal role to play in such micro grids for the electrification of remote communities. In the developing nations, however, the penetration of renewable energy, especially the wind energy, is severely limited due to its non-trivial manufacturing, high cost and low efficiency; despite the fact that there is a huge potential for wind energy generation in countries like Iran (Fazelpour et al., 2017) and Pakistan (Ashfaq & Ianakiev, 2018). Usually large-scale wind farms are installed to harness the wind energy, for instance 61 MW Siahpoush wind farm in Iran and 50 MW in Jhimpir Pakistan. However, the process of expansion and duplication of such large-scale systems is quite slow owing to the cost of specialized technology and required land, as well as the tedious governmental procedures involved from planning to commissioning of such projects. The small-scale wind energy system, which is the focus of the present paper, is a viable alternative for rapid access to wind energy right at the point of use.

The geometry of a solid wind turbine blade is primarily defined by three important parameters: i) the blade profile (airfoil), ii) distribution of the chord which determines how a blade is tapered from the root to the tip, iii) and finally the distribution of the twist angle i.e. the angle between the plane of rotation and the chord line (Hau, 2013; Manwell et al., 2010; Wood, 2011).

Generally, in a large blade, a number of airfoils are employed at different positions and each of them has its own task. While the structurally sound airfoils are used at the root of a large blade, the more aerodynamic ones are adopted near the blade tip where a substantial portion of the total aerodynamic torque is generated. Small blades, however, use the same airfoil, mainly to bring down the total cost; the airfoil in such case is usually selected in the conceptual design before finding the distributions of the chord length and the twist angle (Wood, 2011).

Regardless of the blade size, the blade geometry is normally determined with the help of an optimization procedure in which the maximization of the output power is the first and the most important technical goal of the design (Pourrajabian, Amir Nazmi Afshar, Mirzaei, Ebrahimi, & Wood, 2016). Literature reports other objectives as well, such as minimization of the blade mass (Andrew Ning et al., 2014) and the generated noise (Clifton-Smith, 2010). This provides the motivation for a multi-objective optimization to find the best distribution of the chord and twist angle (Pourrajabian, Amir Nazmi Afshar, Ahmadizadeh, & Wood, 2016; Sessarego & Wood, 2015). The ideal equations for the chord (c) and the twist angle (β), neglecting the drag force and the tip losses, for a wind turbine operating at Betz – Joukowsky limit were derived in (Burton et al., 2011) as:

$$c=\frac{16\pi }{9C_l\mathit{N\lambda }\sqrt{\frac{4}{9}+{\left[{\lambda }_r+\frac{2}{\left(9{\lambda }_r\right)}\right]}^2}}$$

and

$$\beta =\phi -\alpha ,tan\phi =\frac{2}{3{\lambda }_r+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{${\lambda }_r$}\right.}$$

where C_l is the lift coefficient, N is the number of blades, λ is the tip speed ratio, λ_r is the local tip speed ratio, α is the angle of attack, and φ is the inflow angle (Wood, 2011). Using these equations can result in a power efficient wind turbine blade but not necessarily a cost efficient one in terms of manufacturing. Eqs. (1), (2) lead to large values for the chord and twist angle at the root, which adds extra mass to the blade and consequently increases the manufacturing cost and complexity (Burton et al., 2011; Wood, 2011). To address this issue, linear distributions can be fitted to the ideal equations to ease the fabrication process while keeping the output power at a reasonable level (Burton et al., 2011; Liu, Wang, & Tang, 2013; Tahani et al., 2017) (see Fig. 3.20 of Burton et al., 2011 as an example).

The performance of a wind turbine blade has also been investigated under the use of functionalized chord and twist angle distributions (Kaya & Elfarra, 2019; Tahani et al., 2017; Tahani et al., 2019). A variety of mathematical functions including triangular, exponential and logarithmic were studied in (Tahani et al., 2019). The power coefficients obtained from these distributions came out high enough to be considered for manufacturing.

Design and optimization of small wind turbine blades is performed not only for improving the power coefficient but also for accelerating the starting (Amir Nazmi Afshar et al., 2017; Pourrajabian, Ebrahimi, & Mirzaei, 2014; Sessarego & Wood, 2015; Wood, 2011). The former is the main objective of the blade design, while the latter is also important to consider because there is no pitch adjustment in small turbines which results in high angles of attack during the starting especially at the root part of the blade (Wood, 2011). This leads to a reduction in the starting aerodynamic torque which delays the power generation and consequently reduces the annual energy production (AEP) (Worasinchai et al., 2012). This issue can be addressed by redesigning the blade geometry through the multi-objective optimization. The previous studies revealed that the performance of the small wind turbines in terms of the starting and the power coefficient could be improved remarkably by changing the distributions of the chord and twist angle at the root part of the blades (Pourrajabian, Amir Nazmi Afshar, Mirzaei, et al., 2016; Pourrajabian, Mirzaei, Ebrahimi, & Wood, 2014b; Sessarego & Wood, 2015; Wood, 2011).

The nonlinear distributions for both the chord and the twist angle in small blades have been widely used by the researchers (Amir Nazmi Afshar et al., 2017; Wood, 2004, Wood, 2011). The linear distribution, however, has not been studied for simultaneously analyzing the output power and the starting performance. The use of linear distribution is deemed to ease the blade manufacturing (Tahani et al., 2019) and therefore it warrants further investigation. If the blades are made in molds, the linear distributions of the chord and the twist have no obvious benefit from manufacturing aspect but this is not necessarily the case for blades fabricated from timber; this deserves further discussion here. Firstly, it is worth noting that lower cost with suitable physical properties and sustainability of production, render the timber an appropriate material for small wind turbine blades (Astle et al., 2013; Pourrajabian, Dehghan, Javed, & Wood, 2019; Wood, 2011). Since the surface of a wind turbine blade has a complex curved shape, a computer numerical control (CNC) timber milling machine is routinely used for fabrication of timber blades. Despite the high precision of the CNC tool, the machining cost is expensive. More importantly, working with CNC machines requires specialized operators and maintenance personnel. As a low-cost alternative, a copying router can be employed for machining timber blades (Astle et al., 2013; Bralla, 2006). However, design of a copying router with acceptable tolerance is a challenging task for more complicated blade geometry (Astle et al., 2013). In this respect, the linear distributions in the chord and the twist can ease the manufacturing process, particularly as various simple mechanical mechanisms have been developed for producing linear paths (Norton, 2004). Another advantage of the copying router, contrary to the CNC machine, is its flexibility and capability for working on similar workpieces with different sizes. When it comes to the fabrication of small timber blades that are knot- and defect-free, the blade size is limited by the type of CNC machine while a copying router can be mechanically tailored for longer blades.

With these considerations in mind, the research presented in this paper investigates the performance of a small wind turbine by analyzing the combinations of linear and nonlinear distributions of the chord and the twist angle. The external geometry of a small wind turbine blade is optimized for maximizing the power coefficient and minimizing the starting time. This will be done for four possible combinations of linear/nonlinear distributions of the chord and twist angle and the effect of employing those types of distribution on the performance of a small wind turbine will be fully studied.