Introduction

Using fossil fuels in order to meet the energy demand of the world has brought a lot of environmental problems such as global warming and air pollution [1, 2]. Moreover, the resources of these fuels are limited and the energy crisis has been becoming an important issue in recent decades [3]. Therefore, several strategies like using efficient hybrid energy systems or renewable energy resources should be applied to decrease the consequences of fossil fuels consumption [4, 5].

Renewable energy resources like wind and solar energy have been known as the types of energy that are clean and have the lowest impact on the environment compared to fossil fuels [6,7,8]. With the rapid advancement of wind turbine technology and its expansion in the energy production portfolio of countries, the need to study the performance of wind turbines in different climatic conditions has become very important for wind energy engineers [9]. The study of some thermodynamic variables of wind flow has not yet been fully investigated in the wind turbine’s operation. In most studies, the power factor or the wind turbine energy efficiency ratio is considered to be the ratio of the power extracted from the wind turbine to the kinetic energy of the wind that is in contact with the rotor plate (first law of thermodynamics concept). Since this assumption does not take into account the other wind flow’s characteristics such as temperature, humidity, and pressure difference, this assumption will not be accurate enough to analyze the efficiency of a wind turbine. Therefore, studying the wind turbine based on the second law of thermodynamics (exergy analysis) is an alternative way to reach a comprehensive insight into the wind turbine’s performance in different conditions.

Exergy analysis is one of the important tools for evaluating renewable energy cases and hybrid systems in different scenarios [10, 11]. This key not only gives a clear picture of the effects of each variable on the system but also is a good way to analyze the system economically in the energy markets [12,13,14,15]. For example, Chunpeng used various scenarios based on wind energy scopes to reach a sustainable and clean energy in the multigenerational systems, and it was shown the effect of wind energy on electricity price reduction [16]. Similarly, Maleki proposed a cost-effective system using wind energy and demonstrated the effect of wind in cost and efficiency of the system [17]. Barhoumi analyzed the different resources of renewable energy in Saudi Arabia and finally explained the importance of wind and solar energy in this country for the future [18]. In these studies, the importance of wind energy resources for the future of the energy market based on the exergy analysis is shown. The exergy concept can be used to analyze the wind turbine in a hybrid system. Koroneos studied the exergy efficiency of a renewable system including a wind turbine to determine the electricity production of a hybrid system [19]. He concluded that even though wind flow has much more influence on energy and exergy efficiencies, the effects of other metrological variables are important in the calculation. Khalilzadeh employed the exergy and thermoeconomic concept to assess using waste heat from a wind turbine for desalination [20]. It was shown that this idea seems to be useful as it increases the exergy efficiency of the integrated system by 7.34%. Also, regarding the cost of potable water, the average rate of return and payback period are predicted as 6.76% and 6.33 years, respectively. Similarly, Nematollahi proposed a novel method to use the heat waste of wind turbine into an organic Rankine cycle system and analyzed it based on the second law of thermodynamic [21]. Khosravi defined and assessed an off-grid hydrogen storage system combining solar panel and wind turbine, hydrogen production unit, and fuel cell. It was demonstrated that the average energy and exergy efficiencies of the wind turbine were 32% and 25%, respectively [22]. Mohammadi analyzed the exergy efficiency of a combined cooling, heating, and power system integrated with wind turbine and compressed air energy storage system [23]. The result of this study revealed that wind turbine and combustion chamber are the most important sources of the exergy destruction in this system.

In these researches, it was assumed that the wind turbine is a stable part of the systems and did not take into account the effect of the wind turbine’s fluctuations caused by metrological variables changes on the system, while it is clear that changing the metrological variables in different conditions can affect the wind turbine’s performance.

Aghbashlo compared the different exergy analysis methods used to model the efficiency of a wind farm in Iran and propose an accurate approach to assess a wind power plant under different conditions [24]. Ahmadi conducted an exergetic analysis on a vertical-axis wind turbine [25]. He modeled the entropy generation, and observed by increasing the entropy generation in the system that the output power produced by wind turbine drops dramatically. Baskut evaluated the impacts of meteorological parameters namely temperature, pressure differences, and humidity on the exergy efficiency of a wind site in Turkey [26].

In these cases, the results of the experimental data were used to model the wind turbines based on the second law of thermodynamics. But it should be mentioned that measuring the wind speed behind the rotor plan is very important to calculate the exergy flow in research, which is mostly calculated based on the kinetic energy changes; however, it is clear that wake production and irreversibility behind the wind turbine affect the kinetic energy of the system. Therefore, using aerodynamic modeling can be a good way to model the wind turbine and calculate the wind speed in different zones. Pope uses the CFD simulation method to model 4 different wind turbines in different conditions [27]. He modeled two vertical-axis wind turbines and two horizontal-axis wind turbines and used different methods to measure the wind speed behind the wind turbines in order to show how much calculating the wind speed behind the wind turbine can affect the calculations. However, there is no experimental data for this research to validate the calculated results. Khanjari employed the blade element momentum (BEM) method to model the MEXICO wind turbine and study the effect of the yaw changes and roughness intensity [28, 29]. He demonstrated that the BEM theory is a trustable method to model a wind turbine to calculate exergy parameters. It was concluded that increasing the roughness intensity and the yaw angle will decrease the power production and the exergy efficiency dramatically. Moreover, it was shown that the effect of the pressure changes, temperature, and humidity of wind flow at the wind speed of 24 m s−1 on the exergy efficiency of the wind turbine but these effects were not fully studied in different wind speeds and pitch angles to show the effect of every single parameter on the wind turbine’s performance.

In all cases, it was shown that the wind speed has had a significant effect on the exergy efficiency compared to the other metrological variables. But it was not shown the effect of each parameter on the exergy efficiency as a comprehensive study. On the other hands, they showed the effects of the metrological parameters in a constant wind speed and pitch angle, which will not give a clear understanding about these parameters.

In this study, the BEM theory is employed to model a 150 KW horizontal-axis wind turbine and then study the effect of temperature, pressure, and relative humidity in different wind speeds and pitch angles on the wind turbine performances based on the first and second laws of thermodynamics. The aim of this study is to show how much the metrological parameters can affect the exergy efficiency of the wind turbine in different wind speeds and pitch angles.

Materials and methods

Wind turbine energy analysis

Raising the wind turbine’s efficiency is one of the hottest topics between scientists. Therefore, studying the wind turbine’s performance in different conditions is vital in order to achieve this goal [29, 30]. With this said, aero-dynamical modeling of the wind turbine can help us to achieve a profound insight into the wind blades’ reaction in different conditions before constructing them.

There are two distinct ways to simulate the wind turbine aerodynamically:

  1. 1.

    Modeling the wind turbine by using the blade element momentum (BEM) theory, this has a satisfactory prediction and needs less time to calculate the aerodynamic loads on the wind turbine compared to other methods [28, 31, 32].

  2. 2.

    Modeling of the wind turbine in computational fluid dynamics (CFD). It is governed by Navier–Stokes equations. This method is able to plot the different contours of the wind flow before and after the wind turbine but it is time-consuming. Also, the cost of wake simulation in this method is high [33,34,35].

Direct modeling (DM), which implements the exact geometry of the wind blades, is the common approach to simulate wind turbines in the CFD domain. Also, actuator disk (AD), actuator surface (AS), and actuator line (AL) are other methods in the CFD domain, coupling Navier–Stokes equations by BEM concept to eliminate the geometry of blades in the domain and decrease the time consumed by computers [33, 36, 37].

In order to apply the BEM code, airfoil characteristics are needed, which are mostly based on 2-dimensional (2D) measurements. Due to 3-dimensional (3D) effects, the BEM code will not able to predict a trustable result. Therefore, using the 3D aerofoil correction is a pivotal part of modeling [38].

Mahmoodi showed that an improved BEM model using 3D correction in the stall region has a more accurate prediction than AD simulation in the CFD domain [39]. Moreover, Kabir used the BEM method employing the 3D correction to evaluate the stall delay phenomenon for the NRELFootnote 1 Phase VI wind turbine having five radial locations. It was concluded that this has a good agreement with aerofoil characteristics distribution along the blade span and a good matching for aerodynamics load as well as power production [40]. Pinto studied the BEM theory to optimize the wind turbine’s performance aerodynamically. He demonstrated that in order to reach an optimal operating condition for a wind turbine, all sections of blades have to operate at maximum lift-to-drag ratio [41].

Arramach implemented the BEM theory coupled by brake state model for NREL wind turbine to determine the axial and tangential induction factors in different tip speed ratios and studied the effect of radial flow along the blades causing the centrifugal pumping on the wind turbine in both pre-stall and post-stall regions [42].

Another correction that has a considerable effect to reach a reliable prediction in BEM modeling is tip loss correction. Zhong implemented the tip loss correction for three wind turbines and concluded that this correction has a satisfactory agreement with experimental results in a wide range of tip speed ratios [43].

BEM theory

BEM theory combines both blade element theory and momentum theory to calculate the force on the wind turbine’s blades. At first, this theory was used by Froude [44] later refined by Glauert [45].

By assuming the wind flow around the wind turbine is incompressible and axisymmetric, BEM theory is a good tool for understanding wind turbine aerodynamics [46]. In this study, the BEM method developed and described in detail by Glauert and Hansen is implemented [45, 47]. Each blade of the wind turbine is divided into several elements, and the performance of them is deduced by applying the momentum conservation principle [44, 48, 49].

A wind turbine rotating in each angular velocity generates a wake behind itself, which has a determinable impact on the flow upstream [50, 51]. Consequently, the wind speed before touching the blades V1 will be decreased by the wake induced velocity. It will be obtained by applying the momentum theorem in the axial direction [47].

$$V_{1} = V_{0} \left( {1 - a} \right)$$
(1)

That a is the axial induction factor.

Avoiding the breaking down of the integration process, a correction is used as Eq. (2) [52]

$$a = \left\{ {\begin{array}{*{20}l} {\left( {k + 1} \right)^{ - 1} , } \hfill &\quad {a \le a_{\text{c}} } \hfill \\ {\frac{1}{2}\left( {2 + k\left( {1 - 2a_{\text{c}} } \right) - \sqrt {\left( {k\left( {1 - 2a_{\text{c}} } \right) + 2} \right)^{2} + 4\left( {k \cdot a_{\text{c}}^{2} } \right)} - 1} \right),} \hfill &\quad {a \ge a_{\text{c}} } \hfill \\ \end{array} } \right.$$
(2)
$$k = \frac{{4f\sin \phi^{2} }}{{\sigma^{{\prime }} \left( {c_{l} \cos \left( \phi \right) + c_{\text{d}} \sin \left( \phi \right)} \right)}}$$
(3)
$$\sigma^{{\prime }} = 3c/2\pi r$$
(4)

where k is an auxiliary function and ac = 0.3 is the separation point of the thrust coefficient in the high axial induction factor, Cl and Cd are the lift and drag coefficient.

Also, the tip loss correction is used in this study is defined by following equation [47, 50].

$$f = \frac{2}{\pi }{\text{arcos}}\left( {{\text{e}}^{{ - \left( {\frac{{3\left( {R - r} \right)}}{2r\sin \phi }} \right)}} } \right)$$
(5)

f is Prandtl’s tip loss correcting the turbine as a finite bladed rotor.

Moreover, there is a similar equation for the rotational speed [47, 50].

$$a^{\prime } = \frac{{w_{{{\text{i}}2}} }}{\varOmega }$$
(6)

where wi2 is the tangential induced velocity at the plane just before the rotor and a′ is the tangential induction factor.

Other parameters like the angle of flow (ϕ) and the angle of attack (α) are followed by Eqs. 6 and 7 [47].

$$\phi = a\tan \left( {\frac{{V_{0} \left( {1 - a} \right)}}{{r\varOmega (1 + a^{{\prime }} )}}} \right)$$
(7)
$$\alpha = \phi - \beta$$
(8)

Regarding Fig. 1, in order to calculate the power produced by wind turbine, the axial and tangential forces on a blade element should be:

Fig. 1
figure 1

Arrangement of how to analyze the blade elements

Full size image

In Fig. 1, \(V_{\text{o}}\) is incoming wind speed, Ω is angular velocity of the blade, r is local radius of the element, W is relative velocity, β is pitch angle, ϕ is flow angle, L and D are the induced lift and drag forces per blade length, respectively [47].

$$W = \sqrt {V_{\text{o}}^{2} \left( {1 - a} \right)^{2} + \varOmega^{2} r^{2} \left( {1 + a^{{\prime }} } \right)^{2} }$$
(9)
$$L = \frac{1}{2}\rho W^{2} C_{\text{l}} c,\quad C_{\text{l}} = f\left( {r,\alpha } \right)$$
(10)
$$D = \frac{1}{2}\rho W^{2} C_{\text{d}} c,\quad C_{\text{d}} = g\left( {r,\alpha } \right)$$
(11)
$${\text{d}}F_{\text{ax}} = L \cdot \cos \left( \phi \right) + D \cdot \sin \left( \phi \right)$$
(12)
$${\text{d}}F_{\tan } = L \cdot \sin \left( \phi \right) - D \cdot \cos \left( \phi \right)$$
(13)
$${\text{Power}}\, = \,\varOmega \mathop \int \limits_{{r_{\text{hub}} }}^{R} {\text{d}}F_{\tan } r {\text{d}}r$$
(14)
$${\text{TSR}} = \frac{\varOmega R}{{V_{\text{o}} }}$$
(15)

c is chord length in Eqs. (10) and (11), \({\text{d}}F_{\text{ax}}\) and \({\text{d}}F_{\tan }\) are axial and tangential induced forces on the element length in Eqs. (12) and (13) respectively, R and \(r_{\text{hub}}\) are tip and hub radius of the rotor in Eq. (14), Power is output power generated by the rotor in Eq. (14), and TSR is tip speed ratio of the rotor in Eq. (15).

3D modeling for the stall region

The BEM theory is a 1D code, which is not able to take into account the 3D flows effect aerodynamics of blades. An aerofoil data correction described by [47] was used in this study to convert lift confident of aerofoil data from two dimensions to three dimensions.

$$C_{{{\text{l}},3{\text{D}}}} = C_{{{\text{l}},2{\text{D}}}} + x\left( {\frac{c}{r}} \right)^{\rm{y}} \cos^{4} \left( \phi \right)\left( {C_{\text{l, inv}} - C_{\text{l, 2D}} } \right)$$
(16)

Figure 2 describes how to alter the lift coefficients. By extending the linear part of the origin curve (in viscid part), the stall region will be covered. The difference between two curves ΔCl= Cl,inv − Cl,2D is multiplied by x(c/r)y, where x = 2.2 and y = 1 according to [39].

Fig. 2
figure 2

The preparation of lift coefficients for 3D conversion

Full size image

Methodology

As it shown in Fig. 3, the following steps are taken to obtain the output results of BEM based on C programming.

Fig. 3
figure 3

Algorithm designed for the enhanced BEM method in the current study

Full size image

Exergy modeling

The exergy concept depicts the locations of energy destruction in a process [53]. Therefore, the output result of exergy analysis can lead to enhance system operation [54]. Also, it can quantify the quality of energy in a thermodynamical process [55]. Exergy is the maximum work output generated by a system or a flow of matter or energy that has equilibrium with reference environmental conditions [56, 57]. In real process (except for ideal, or reversible processes), exergy is not subject to a conservation law and it will be consumed or destroyed, due to the irreversibilities of process [58]. In exergy analysis, the characteristics of a reference environment must be specified [59]. It can be done by specifying the variables namely pressure, relative humidity, temperature, and chemical composition of the reference environment. Therefore, the output results are rely on the specified reference environment [60].

In this section, the modeling of both energy efficiency (η) (Eq. 17) and the exergy efficiency (Ψ) (Eq. 18) for the wind turbine are described. Like the other thermodynamics systems having limitations in efficiency due to the irreversibility [61,62,63], it is not possible for the wind turbine to extract the total kinetic energy of the flow. Based on Betz’s law, wind turbines can convert less than 59% of the wind power to output power [64]. Nevertheless, in practice, their efficiency is about 40% for great wind speeds. The energy efficiency is the ratio of total useful work produced by a wind turbine to the difference in kinetic energy of wind flow. Also, the exergy efficiency is the proportion of useful work to the exergy of the wind passing through the wind turbine (see Fig. 4) [65].

Fig. 4
figure 4

The diagram of inlet and outlet parameters states in the rotor plan

Full size image
$$\eta = \frac{{W_{\text{out}} }}{{{\text{kinetic}}\,{\text{energy}}\,{\text{of}}\,{\text{wind}}}}$$
(17)
$$\varPsi = \frac{{W_{\text{out}} }}{{{\text{Ex}}_{\text{flow}} }}$$
(18)

The energy balance equation of the wind turbine is defined by [65]:

$${\text{ke}}_{1} = W_{\text{out}} + {\text{ke}}_{2}$$
(19)

where ke1,2 is the kinetic energy of wind flow before and after the wind rotor plan, respectively.

$${\text{ke}}_{1,2} = \frac{1}{2}\dot{m}v_{1,2}^{2}$$
(20)

The mass flow rate of the wind turbine can be introduced by:

$$\dot{m} = \rho \pi r^{2} v$$
(21)

The output velocity of the wind turbine can be calculated by [28]:

$$v_{2} = \sqrt[3]{{\frac{{2\left( {{\text{ke}}_{1} - W_{\text{out}} } \right)}}{{\rho \pi R^{2} t}}}}$$
(22)

The exergy balance for this model is [65]:

$${\text{Ex}}_{\text{flow}} \, = \,{\text{Ex}}_{\text{ph}} \, + \,{\text{ke}}$$
(23)
$${\text{Ex}}_{\text{ph}} = m\left[ {c_{\text{p}} \left( {T_{2} - T_{1} } \right) + T_{0} \left( {C_{\text{P}} \ln \left( {\frac{{T_{2} }}{{T_{1} }}} \right) - R\ln \left( {\frac{{P_{2} }}{{P_{1} }}} \right) - \frac{{C_{\text{P}} (T_{0} - T_{\text{avg}} )}}{{T_{0} }}} \right)} \right]$$
(24)

And the wind turbine’s destruction can be defined by [66]:

$${\text{EX}}_{\text{des}} \, = \,T_{0} \left( {C_{P} \ln \left( {\frac{{T_{2} }}{{T_{1} }}} \right) - R\ln \left( {\frac{{P_{2} }}{{P_{1} }}} \right) - \frac{{C_{\text{P}} (T_{0} - T_{\text{avg}} )}}{{T_{0} }}} \right)$$
(25)

where P1,2 = P0 ± (ρ/2)(V1,2)2. Also, the temperatures of flow in both states T1,2 are calculated through the wind chill temperature formula developed in [67].

$$T_{\text{windch}} = 13.12 + 0.6215T_{\text{at}} - 11.37V^{0.16} + 0.3965T_{\text{at}} V^{0.16}$$
(26)

Finally, Eq. (27) can be used for exergy of humid air [26].

$$\begin{aligned} {\text{Ex}}_{\text{ph}} & = m\left[ {\left( {c_{{{\text{p}}.{\text{a}}}} + \varpi C_{{{\text{p}}.{\text{v}}}} } \right)\left( {T - T_{0} } \right) - T_{0} \left[ {\left( {c_{{{\text{p}}.{\text{a}}}} + \varpi C_{{{\text{p}}.{\text{v}}}} } \right)\ln \left( {\frac{T}{{T_{0} }}} \right) - \left( {R_{\text{a}} + \varpi R_{\text{v}} } \right)\ln \left( {\frac{P}{{P_{0} }}} \right)} \right]} \right. \\ & \quad \left. { + T_{0} \left[ {\left( {R_{\text{a}} + \varpi R_{\text{v}} } \right)\ln \left( {\frac{{1 + 1.6078\varpi_{0} }}{1 + 1.6078\varpi }} \right) + 1 + 1.6078R_{\text{a}} \varpi \ln \left( {\frac{\varpi }{{\varpi_{0} }}} \right)} \right]} \right] \\ \end{aligned}$$
(27)

In this research, the reference pressure and temperature are taken based on the experiment environmental condition (101.3 kPa and 298 K), respectively.

Case study

A horizontal-axis and a three-bladed wind turbine with a 150 KW power output named INER-P150II is used in this study [68] (see Fig. 5). The pitch angle and chord length are varied along the wind blade with 10.8 m length. Moreover, different types of airfoil sections such as DU series, NACA0013166, and FX63-137 were used from the root to tip blade. The wind turbine specification is summarized in Table 1.

Fig. 5
figure 5

INER-P150II wind turbine

Full size image
Table 1 the specification of nominated wind turbine [68]
Full size table

Results and discussion

One important reason to implement the BEM method in this study is that to achieve clear anticipation about the power productions and power calculating the wind speed behind the rotor plan. The results of the output power under different speeds and pitch angles are presented and compared with experimental data in Fig. 6. With increasing the wind speed from 5 to 12 m s−1, the power production of the wind turbine increases steadily; however, after peaking at 12 m s−1 there is a reduction in the power production for all three modelings. Also, the results of the BEM modeling are almost in the same phase with experimental data in low wind speed under 10 m s−1. It is anticipated that the wind turbine can produce 165 KW output power under the wind speed of 12 m s−1 and pitch angle of 5°. Also, it is shown that increasing the pitch angle will decrease the power production more specificity in high wind speeds.

Fig. 6
figure 6

Comparison of output power between BEM model and experimental data under

Full size image

As seen in Fig. 7, both energy and exergy efficiencies of the wind turbine are increased by rising the wind speed from 5 to 12 m s−1 at the pitch angle of 5° and 10°, while in higher wind speeds up to 12 m s−1 the wind turbine has faced with a steady reduction in efficiency. The maximum exergy and energy efficiencies are 42.8% and 43.9% at wind speed 12 m s−1 and pitch angle 5°. Moreover, the wind turbine has had the lowest efficiency at pitch angle 20° compared to other pitch angles. Also, it should be mentioned that since the energy analysis just shows changing the kinetic energy and is not able to depict the effects of the temperature, pressure, and humidity, it predicts the higher efficiency more than the exergy efficiency.

Fig. 7
figure 7

a Exergy efficiency. b Energy efficiency of the wind turbine against the wind speed in various pitch angles

Full size image

Wind speed is the most important source of the exergy flow in the wind systems; however, the wind turbine is not able to extract all of the wind exergy and the leftover of the upcoming wind leave the rotor plan and disappear. Also, due to the wake production behind the wind blades in both laminar and turbulent flows as main sources of entropy production, the amount of the exergy destruction is shown in this study. As seen in Fig. 8, while wind speed increases, both exergy destruction and exergy flow rise continuously. By increasing the pitch angle from 5° to 20°, the wind blade will touch the higher angle of attacks, which means that the flow separation behind the blade will increase considerably. Therefore, it increases the wake production in the flow stream behind the wind turbine; consequently, the exergy destruction will increase dramatically.

Fig. 8
figure 8

Compression of the a exergy flow and b exergy destruction under different wind speeds

Full size image

Regarding the former figures, it is shown that wind speed has a noticeable effect on the wind turbine’s performance, but in figures from 9 to 11 it will show the effect of the other metrological parameters on the exergy efficiency in four wind speeds of 8, 10, 12, and 14 m s−1 and three pitch angles of 5°, 10° and 20°. As seen in Fig. 9 increasing the relative humidity has had a negative effect on the exergy efficiency in all three pitch angles; however, this impact on the higher wind speeds (12 and 14 m s−1) is not very sensible. By increasing the pitch angle, this amount of the reduction increases too. The higher exergy efficiency loss has occurred at the wind speed of 8 m s−1 and pitch angle 20° (near 1.76%), When the relative humidity increases from 0.001 to 0.015.

Fig. 9
figure 9

Effect of relative humidity on exergy efficiency in different wind speed. a Pitch angle 5°. b Pitch angle 10°. c Pitch angle 20°

Full size image

In Fig. 10, the relation between pressure changes (from 100 to 250 pa) and exergy efficiency is shown. Likely, changing the Δp from 100 to 240 pa has had an adverse effect on the exergy efficiency, especially at the lower speeds and pitch angle 20°. In wind speeds more than 10 m s−1, the effect of the wind speed on the wind turbine’s efficiency is dominant. Therefore, the sensibility of the system to other parameters becomes insignificant. It is shown that by increasing the pressure changes from 100 to 250 pa at the wind speed of 8 m s−1 and pitch angle of 20° the exergy efficiency will decrease 1.26%.

Fig. 10
figure 10

Effect of pressure changing on exergy efficiency in different wind speed. a Pitch angle 5°. b Pitch angle 10°. c Pitch angle 20°

Full size image

Numerical evaluation between changing the ambient temperature and exergy efficiency is depicted in Fig. 11. Compared to pressure changing and relative humidity, the temperature has a straight effect on exergy efficiency. In all three pitch angles, temperature has had the highest effect on the wind speed of 8 m s−1. It is shown that by increasing the ambient temperature from 5 to 35 °C, exergy efficiency increases from 38.1 to 40.1% in wind speed of 8 m s−1 and pitch angle 5°.

Fig. 11
figure 11

Effect of temperature on exergy efficiency in different wind speed. a Pitch angle 5°. b Pitch angle 10°. c Pitch angle 20°

Full size image

Conclusions

In this study, the wind turbine’s performance in different conditions based on the energy and exergy analysis is studied.

  • The BEM code has had a good agreement with experimental data to calculate the power production for all three pitch angles.

  • The maximum exergy and energy efficiencies are 42.8% and 43.9% at wind speed 12 m s−1 and pitch angle 5°

  • Wind speed has the highest impact on the energy and exergy efficiency of the wind turbine, compared to the temperature, pressure changes and relative humidity.

  • Temperature has a positive effect on the exergy efficiency and by increasing the temperature from 5 to 35 °C, the exergy efficiency rises 2% at the wind speed of 8 m s−1 and pitch angle of 5○,

  • Increasing the relative humidity from 0.001 to 0.015 and pressure changes from 100 to 240 pa can decrease the exergy efficiency 1.76% and 1.26% at the wind speed of 8 m s−1 and pitch angle of 20°, respectively.

  • Effects of the pressure, temperature and relative humidity in the low wind speeds (less than 10 m s−1) are more significant than the high wind speeds on the wind turbine.