Energy and exergy efciency comparison of horizontal and vertical axis

wind turbines

K. Pope, I. Dincer, G.F. Naterer*

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, Canada L1H 7K4

a r t i c l e i n f o

Article history:

Received 11 February 2009

Accepted 14 February 2010

Available online 25 March 2010

Keywords:

Wind turbine

Exergy

Energy

Efciency

a b s t r a c t

In this paper, an energy and exergy analysis is performed on four different wind power systems,

including both horizontal and vertical axis wind turbines. Signicant variability in turbine designs and

operating parameters are encompassed through the selection of systems. In particular, two airfoils (NACA

63(2)-215 and FX 63-137) commonly used in horizontal axis wind turbines are compared with two

vertical axis wind turbines (VAWTs). A Savonius design and Zephyr VAWT benet from operational

attributes in wind conditions that are unsuitable for airfoil type designs. This paper analyzes each system

with respect to both the rst and second laws of thermodynamics. The aerodynamic performance of each

system is numerically analyzed by computational uid dynamics software, FLUENT. A difference in rst

and second law efciencies of between 50 and 53% is predicted for the airfoil systems, whereas 44e55%

differences are predicted for the VAWT systems. Key design variables are analyzed and the predicted

results are discussed. The exergetic efciency of each wind turbine is studied for different geometries,

design parameters and operating conditions. It is shown that the second law provides unique insight

beyond a rst law analysis, thereby providing a useful design tool for wind power development.

! 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Wind power systems have achieved signicant improvement in

operating efciencies, making them more economically competi-

tive with other energy generation techniques. Along with the need

for increased sustainability in the energy sector, wind energy

systems are increasing their market share faster than any other

renewable energy system [1]. Horizontal axis wind turbines

(HAWTs) have emerged as the dominant technology in modern

wind energy technologies. In comparison to a vertical axis wind

turbine (VAWT), a HAWT can achieve higher energy efciencies,

thereby increasing the power production and reducing system

expense per kW of power generated. But as the opportunity to

expand wind capacity increases, it is important that all aspects of

this sustainable and environmentally benign technology are fully

developed. VAWTs have demonstrated an ability to fulll certain

energy generation requirements that cannot be fullled by HAWTs.

A HAWT can achieve higher efciencies, but only if the energy

quality of the wind is high. High wind turbulence, wind uctua-

tions, and high directional variability can cause signicant prob-

lems for a HAWT, whereas VAWTs can operate well.

Local or distributed power generation has attracted signicant

attention in recent years. The resurgence of this old technology is

partly attributed to the need for environmentally benign and

sustainable energy systems in smaller communities. This includes

diversifying the generation techniques and increasing the system

efciencies, while minimizing the environmental impact. Onsite

power generation can overcome transmission losses and land costs.

However, densely populated locations and urban centers generally

coincide with a low quality of wind source, including high turbu-

lence, uctuations in intensity, and highly variable direction of the

ow streams [2]. Variable pitch blades can improve turbine

performance by varying the angle of attack to coincide with the

various wind conditions, but this approach is generally not

economically practical for small installations [3]. Fluctuating winds

can greatly reduce a HAWT's performance as long as idling periods

are experienced at start-up when the rotor accelerates slowly. For

a small HAWT, a past study reported it to be 50 s at a wind speed of

8 m/s [4]. Certain VAWT designs have the ability to operate in these

harsh operating conditions. However, there is no clear method to

compare these different turbine designs in various wind conditions

that are inherent to the different operating regions.

Typical design methodologies employ the rst law of thermo-

dynamics for wind power system analysis and design. Empirical

tests and experience must often be used to improve system

performance and implementation. The process irreversibilities are

* Corresponding author.

E-mail addresses: kevin.pope@mycampus.uoit.ca (K. Pope), ibrahim.dincer@

uoit.ca (I. Dincer), greg.naterer@uoit.ca (G.F. Naterer).

Contents lists available at ScienceDirect

Renewable Energy

journal homepage: www.elsevier .com/locate/renene

0960-1481/$ e see front matter ! 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.renene.2010.02.013

Renewable Energy 35 (2010) 2102e2113

not represented in the analysis [5]. A theoretical maximum ef-

ciency can be predicted, but irreversibilities are not identied.With

a rst law methodology, the designer includes a predetermined

design factor to account for the irreversibilities. Past experimental

data reported that actual ow across a wind turbine rotor is about

20% slower than the ideal ow [6]. Predicting turbine performance

with complicated variations in operating demands and design

congurations reveal the deciencies with this strategy [7]. In

contrast, the second law denes a quality of energy and quantity of

irreversibility or loss associated with the thermodynamic process.

In this paper, the concept of entropy generation will be used to

describe the magnitude of energy dissipation. Higher levels of

entropy generation are associated with a lower level of useful

energy. The second law requires that the amount of entropy in an

isolated system will always increase [8]. This principle can be

applied to a variety of engineering applications.

Entropy-based design and exergy analysis have been shown to

identify the maximum theoretical capability of energy system

performance in various applications. For example, it can provide

component-level energy management to improve diffuser perfor-

mance [9] and reduce voltage losses within a fuel cell [10]. Exergy

analysis has been used to diagnose inefciencies of power plants

[11], minimize the carryover leakage irreversibilities in a power

plant regenerative air heater [12], and many other power plant

associated applications. These studies have shown exergy analysis

to be very useful for improving a wide range of thermo uid

systems. Exergy analysis also provides a design tool for increased

accuracy and more efcient performance.

However, there are few examples in past literature that pertain

to wind exergy. Through an energy and exergy analysis of the

characteristics of wind energy, it was found that differences

between energy and exergy efciencies are approximately 20e24%

at lowwind speeds and approximately 10e15% at high wind speeds

[13]. Sahin et al. [14] developed a useful exergetic analysis tech-

nique for determining the exergetic efciency of a wind turbine.

The technique utilizes the wind chill temperature associated with

wind velocity to predict the entropy generation of the process.

Better turbine design and location selection can be achieved with

the aid of such exergy analysis.

In this paper, a comparison of second law efciencies for four

different wind power systems will be presented. The analysis is

intended to compare turbines that have different performance

advantages in various operating conditions. A parametric study

investigates the selection and associated predictions of key variables

foreach system.Thispaperwill developa second lawanalysisofwind

power for potentially valuable utility in the wind energy industry.

2. Wind energy system description

Four systems will be investigated in this paper: two airfoils

commonly used for horizontal axis wind turbines [15,16] and two

VAWTs (Savonius and Zephyr) operating under low quality wind

properties (see Figs. 1 and 2). These include (i) a NACA 63(2)-215

airfoil developed by the National Advisory Committee for Aero-

nautics (NACA) and (ii) the Wortmann FX 63-137. The VAWTs

include (iii) a conventional Savonius design and (iv) a more

complex Zephyr VAWT prototype. A numerical model for each

system is developed for the uid ow analysis. Computational Fluid

Dynamics software, FLUENT [17], is used to predict the operation of

each system. These numerical models will offer insight into the

uid ow characteristics for each of the different turbines. Data

gained from the numerical predictions will be used to examine the

second law efciencies of wind power systems.

2.1. System 1: NACA 63(2)-215 airfoil

As presented in Fig. 3a, the NACA 63(2)-215 airfoil is a conven-

tional design that creates lift with low wind speeds, making it

suitable for use in wind turbine blades [15,16]. Throughout the

following analysis, the approach angle (4) is estimated to be 10!. The

incomingcomponentsof velocityareVx9.85m/s andVy1.74m/s.

The X and Y force vectors for the lift and drag components become

XL #sin(10!) #0.174, YL cos(10

!) 0.985, XD cos

(10!) 0.985, and YD sin(10!) 0.174, respectively. Table 1

summarizes the systemassumptions used in the numerical analysis.

The prole of the NACA 63(2)-215 airfoil is discretized with

a structured quadrilateral cell scheme. The mesh is rened from an

average cell edge length of 260mm at the outer region, to 14 mm at

the airfoil surface. Rened to a total of 12,150 cells, with an average

cell size of 0.061 m2, produces results that are independent of

further grid renement [18]. The governing equations are the

incompressible form of NaviereStokes equations. The standard k-3

Nomenclature

A Area [m2]

B Number of blades [e]

Cp Specic heat [kJ/kg K]

Cpower Power coefcient [e]

E Energy [kJ]

ex Specic exergy [kJ/kg]_Ex Exergy rate [kW]

I Irreversibilities [kW]

KE Kinetic energy [kJ]

m Mass [kg]

P Power [kW]

R Radius [m]

t Time [s]

T Temperature [!C]

U Volume [m3]

V Velocity [m/s]

W Work [kJ]_W Work rate [W]_m Mass ow rate [kg/s]

Greek

h Energy efciency [e]

l Tip speed ratio [e]

r Air density [kg/m3]

4 Approach angle [!]

J Exergy efciency [e]

u Humidity ratio [e]

Subscripts

0 Ambient

2 Denition 2 (exergy)

B Benz limit

D Drag

dest Destruction

eff Effective

KE Kinetic energy

L Lift

ph Physical

x Horizontal vector

y Vertical vector

K. Pope et al. / Renewable Energy 35 (2010) 2102e2113 2103

model is used to simulate turbulence in the ow eld. This is

a widely used model that provides reasonable accuracy and

a robust ability to represent a wide range of ow regimes [17]. The

features of the airfoil solver are summarized below:

$ Finite volume method with a segregated solver;

$ Standard ke3 turbulence model;

$ Standard wall functions for near-wall treatment;

$ Air density is constant, 1.225 kg/m3;

$ Air viscosity is constant, 1.7894 % 10#5 kg/m s;

$ Backow turbulence intensity, 12%;

$ Velocity-inlet e velocity specication method;

$ Inlet x-velocity, 9.85 m/s;

$ Inlet y-velocity, 1.74 m/s;

$ Airfoil roughness height, 500 mm;

$ Pressureevelocity coupling e SIMPLE;

$ Turbulence kinetic energy e second order upwind; and

$ Turbulence dissipation rate e second order upwind.

2.2. System 2: FX 63-137 airfoil

This airfoil has been examined widely in past literature. Its

characteristics will be used to investigate the aerodynamic behav-

iour of wind turbines [15,16]. In comparison to other commonwind

turbine airfoil proles, this design provides a relatively complex

conguration. The pronounced tail curvature provides a substantial

contrast to System 1 that will be evaluated (see Fig. 3b).

The same solver features, including the governing and turbu-

lence equations, as with System 1 e NACA 63(2)-215 ewill be used

for this system. Variations in airfoil surface roughness are pre-

sented in Fig. 4. Convergence in both lift and drag coefcients are

Fig. 1. Zephyr vertical axis wind turbine (a) illustration and (b) geometrical variables.

Fig. 2. Sample mesh discretization of VAWT e a) rotor, b) stator and surrounding sub-

domain. Fig. 3. Velocity contours (m/s) for (a) NACA 63(2)-215 and (b) FX 63-137 airfoils.

K. Pope et al. / Renewable Energy 35 (2010) 2102e21132104

evident after 250 mm. For both airfoils, a CL/CD ratio will be used for

the power coefcient predictions from a roughness height of

500 mm. The mesh is rened from an average of 289 mm at the

outer region, to 0.014 mm at the airfoil surface. It is rened to

12,195 cells, with an average cell size of 0.061 m2.

2.3. System 3: savonius VAWT

The Savonius VAWT is a common design that is capable of

reaching substantial efciencies. There is signicant past literature

on this design. For example, extensive experiments were per-

formed by Saha [19], whereby 16 Savonius models with identical

aspect ratios were compared in wind tunnel tests. The study

included an investigation of the optimum number of rotor blades

(two or three), number of stages (one, two, or three), and the best

blade shape (twisted or semicircular). The author found that a two-

stage design, with two twisted rotor blades, preformed the best,

achieving a maximum power coefcient of 0.32. Biswas et al. [20]

investigated experimentally the overlap effect of rotors on a Savo-

nius wind turbine. The authors achieved a power coefcient of 0.37.

A hybrid Savonius e Darrieus turbine achieved a maximum Cpowerof 0.51, in a comparative study described by Gupta et al. [21]. In the

current paper, a basic semicircular design will be used, with a 10%

overlap (see Fig. 5a).

The domain is discretized into 13,693 cells with an average cell

size of 0.019 m2. The mesh is rened from 500mm at the boundary,

to 50 mm at the rotor surface. Again, the same governing and

turbulence equations, as for previous cases, will be used for this

system. However, considerable differences in some solver features

are required. A transient mesh formulation is used to simulate the

rotor motion. This allows the rotor to rotate 50 time steps per

revolution, with a time step size of 0.0209 s. The numerically pre-

dicted average moment induced on the rotor blades will be used to

determine the power coefcient. The wall roughness height is

assumed negligible, and the incoming velocity is simulated to be

Vx 10 m/s and Vy 0.

2.4. System 4: Zephyr VAWT

As illustrated in Figs. 1, 2 and 5b, the Zephyr turbine represents

a more complex VAWT. The features of this turbine allow it to

perform in both low wind and high turbulence conditions. Thus,

several turbines can operate in close proximity of each other in

urban areas. The maximum power coefcient of this turbine is

relatively low, in comparison to other systems. However, it is an

ideal candidate to operate in low quality winds and offers a good

contrast to the Savonius VAWT and airfoil HAWT systems. The

stator sub-domain is discretized with an edge length of 191 mm at

the exterior, which is gradually rened to an edge length of

6.35 mm at the rotor. This yields approximately 117,000 cells, with

an average area of 217 mm2. At this resolution, the results become

independent of grid spacing [22]. The analysis of this system

employs the same solver features, including the governing and

turbulence equations, as the Savonius VAWT.

3. Formulation of rst and second law efciencies

This section will compare the rst law efciency (h) with the

second law efciency (J). The energy efciency is dened as the

ratio of useful work to the difference in kinetic energy,

Table 1

Signicant system assumptions.

V1 [m/s] Radius [m] Area [m2] Wout Wout,2

NACA 63(2)-215 airfoil 10 1 p % 12 f(CL, CD) DKE

FX 63-137 airfoil 10 1 p % 12 f(CL, CD) DKE

Savonius VAWT 10 1 2 f(T, l) DKE

Zephyr VAWT 10 0.762 0.7622 f(T, l) DKE

Fig. 4. Airfoil performance with variable surface roughness.

Fig. 5. Velocity contours (m/s) for (a) Savonius and (b) Zephyr VAWTs.

K. Pope et al. / Renewable Energy 35 (2010) 2102e2113 2105

h _WoutP

(1)

The exergy efciency refers to the ratio of useful work to the

exergy of the wind,

J _Wout

_Exflow(2)

In general, the energy balance equation for a wind turbine can

be represented by

KE1 Wout KE2 (3)

where KE is the kinetic energy of the ow stream and Wout is the

useful work produced by the turbine. The equation describes the

energy content of air as it passes through a two-dimensional plane.

It is based on the kinetic energy of wind, which is

KE 1

2mV2 (4)

where KE is energy, m is mass, and V is the wind velocity.

The mass of wind is difcult to measure, so a more convenient

variable is volume (U), as related to mass bym r U, where r is the

density of air. The volume is expressed by the product of the cross-

sectional area perpendicular to the wind (A) and the horizontal

length of incoming wind (L). The horizontal length of incoming

wind is then expressed as LU t. This re-arrangement results in the

more convenient following expression,

KE 1

2rAtV3 (5)

Since power is related to energy by P E/t, the above expression is

more commonly used in the following form,

P 1

2rAV3 (6)

where P is the magnitude of power, r is the density of air, A is the

cross-sectional area perpendicular to wind, and V is the wind

velocity. This expression describes total kinetic power of a wind

stream. It is used for the production of wind power maps that are

used for turbine placement and resource estimation. Although KE1can be readily determined from velocity measurements or predic-

tions, many problems are associatedwith determining KE2. The exit

velocity from a wind turbine is extremely difcult to measure, as it

is highly variable and it quickly dissipates in all directions. As

a result, empirical work outputs are generally required to deter-

mine the wind turbine efciency (h).

Methods for describing the independent variables in the energy

analysis are relatively straightforward. The density of air is most

affected by temperature and relative humidity of the air. Temper-

ature can be readily measured and computed. As a result, density is

normally selected solely on this measure (i.e., r (T), where T air

temperature). The air moisture content (u) also affects wind

density. A more accurate measure of density is r (T, u). However,

this is not commonly modelled in practice.

A second law analysis includes the ow irreversibilities associ-

ated with the system. The exergy balance equation can be

expressed as

_Ex1 _Wout _Ex2

_Exdest (7)

where _Exdest represents the exergy destruction associated with the

process. It is a representative measure of the irreversibilities

involved with the process. This methodology offers a useful alter-

native measure of turbine efciency that includes the

irreversibilities, which were not included in the rst law analysis.

The exergy of ow, _Exflow, can be dened as the maximum attain-

able work acquired as the air ows through the turbine [7]. The

relevant terms include physical _Exph and kinetic exergy _ExKE,

_Exflow _Exph

_ExKE (8)

Physical exergy includes the enthalpy and entropy changes

associated with the turbine operation, expressed as [14]

_Exph _m

!CPT2 # T1 T0

"CPln

"T2T1

## Rln

"P2P1

#

#CP$T0 # Taverage

%T0

#&(9)

where Pi P0 ) r=2V2 and T1 and T2 are determined through the

wind chill temperature, based on a model developed by Zecher

[23]. The rst term in the square brackets represents the change in

ow enthalpy, while the second term characterizes the ow irre-

versibilities of the system. The irreversibilities associated with the

system can be determined by

I #T0DS (10)

or

I_ T0

"CPln

"T2T1

## Rln

"P2P1

##

_mCP$T0 # Taverage

%T0

#(11)

The kinetic component of the ow exergy is equivalent to the

difference of kinetic energy through the turbine (i.e., DKE. From

Eq. (3), the change in kinetic energy can also be expressed by the

work output of the turbine. This methodology offers a signicant

opportunity to improve the wind turbine design and enhance the

site selection by supplementing the information provided by the

Table 2

Signicant numerical assumptions and predictions.

l P0 [kPa] T0 [C] CL CD CM Cpower

NACA 63(2)-215 airfoil 4 101.3 25 1.15 0.0385 e 0.44

FX 63-137 airfoil 4 101.3 25 1.87 0.0357 e 0.47

Savonius VAWT 0.5 101.3 25 e e 0.0294 0.18

Zephyr VAWT 0.5 101.3 25 e e 0.0147 0.11

0

2

4

6

8

10

1 2 3 4

V2[m/s]

Definition of V2

NACA 63(2)-215 Airfoil FX 63-137 Airfoil Savonius VAWTZephyr VAWT

Fig. 6. Denitions of V2 for a variety of wind power systems.

K. Pope et al. / Renewable Energy 35 (2010) 2102e21132106

rst law analysis. The specic exergy destruction can be dened

as

exdest T0DS

rAV(12)

For the airfoils, _Wout will be determined by the model of Wilson

et al. [24]. This is an empirical technique that correlates the turbine

power coefcient with the lift (CL), drag (CD), number of blades (B),

and tip speed ratio (l).

Cpower

"16

27

#l

24l 1:32

l#820

)2B

23

35#1

#0:57l

2

CLCD

$l 12B

% (13)

The lift and drag coefcients are estimated from numerical

predications obtained at the specied tip speed ratio and blade

number. For the VAWTs, _Wout is determined from the product of

a numerically predicted torque and the simulated rotational

velocity.

Fig. 7. Energy and exergy efciencies based on (a) kinetic energy, (b) ow exergies, (c) V2 maintained constant, (d) V2/V1 maintained constant and (e) Benz efciencies.

K. Pope et al. / Renewable Energy 35 (2010) 2102e2113 2107

4. Results and discussion

In this section, the results of the rst and second law analyses

will be presented. The numerical simulations are used to obtain

performance predictions of the various wind systems and provide

useful information about the uid ow behaviour. For the airfoils,

the numerically predicted coefcients of lift and drag are used to

predict the maximum power coefcient through Eq. (12). A

numerically predicted moment coefcient is used to determine the

power coefcient of the VAWTs. The results of the numerical study

are summarized in Table 2.

Using the second law analyses for wind turbines requires V2. A

standard metric for nding V2 is crucial for maintaining consistent

exergetic efciency predictions for different wind turbine designs

and operating conditions. In this paper, four different denitions for

determining V2 are presented. Each denition is investigated with

respect to its reference variables and operating conditions. The

second law predictions achieved from each denition are the

compared with the rst law predictions and discussed with regards

to accuracy. The ability to represent the performance of different

turbine designs and operating conditions with a standard metric is

a signicant contribution of the second law. Each denition of V2and its ability to uphold these criteria will be identied. Four

denitions below of V2 will be used in the analysis (see Fig. 6),

$ Denition 1: Point specic, low wind velocity (measured one

chord behind the turbine);

$ Denition 2: Specic effective velocity (V2 V2,eff % Aeff/A);

$ Denition 3: Average velocity of useful area (V2 V2,useful,ave);

$ Denition 4: Average of the low velocity stream.

A parametric study of the reference conditions and operating

wind conditions will be presented for each of the four wind energy

systems. The results will be compared for each denition of V2. This

includes (i) point specic low velocity, (ii) specic effective velocity,

(iii) average velocity of useful area, and the (iv) average of the low

velocity stream.

4.1. Denition 1: point specic, low wind velocity (measured one

chord behind the turbine)

Denition 1 is advantageous because it can be determined in

a consistent manner for different designs. Also, this denition lends

itself well to physical measurements. Virtually identical values of V2are predicted for the VAWTs, with similar values also suggested for

the airfoils. The resultant airfoil second law efciencies are 15% and

17% for the NACA 63(2)-215 and FX 63-137, respectively. A 51e50%

distinction between the rst and second law efciencies is

predicted for the airfoil designs. A different trend is forecasted for

the VAWTs. The second law efciency for the Savonius VAWT is

predicted to be 17%, a 6% difference from the rst law predictions.

Comparably, a 10% exergy efciency, which is 9% different than the

rst law predictions, is forecasted for the Zephyr VAWT.

Fig. 8. Energy and exergy efciencies with varying pressure for (a) point specic low velocity, (b) specic effective velocity, (c) effective velocity and (d) average low velocity.

K. Pope et al. / Renewable Energy 35 (2010) 2102e21132108

Results of the energetic and exergetic analysis using Denition 1

for determining V2 are presented in Figs. 7e12a. Variations to the

reference conditions P0 and T0 are presented in Figs. 8a and 9a,

respectively. Theminor effects of altering P0 are included in the rst

law efciencies for the VAWTs, but they do not affect the airfoils.

The discrepancy is caused by the method of determining _Wout, or

more specically, the power coefcient. The analysis of the airfoils

uses an empirical correlation, which is independent of the refer-

ence pressure. In contrast, for the energy analysis, the VAWT

predictions include the effects of local pressure on the local wind

density, when predicting the power coefcient. The plot of varying

reference temperature includes the majority of the standard

operating conditions, with an equal distribution from 25 !C, stan-

dard reference temperature. Similar to the variable P0, it can be

observed that although the second law efciencies depend on the

choice of reference conditions, it allows different wind power

systems to be compared with one descriptive parameter.

Variations to the input velocity, V1, are presented in Figs. 10a and

11a. These gures illustrate the effects of variations of inlet velocity,

while comparing the assumptions that (a) V2 is constant, or (b) V2/

V1 is maintained constant. The rst law analysis fails to predict

changes to the system efciency when this crucial operating

condition is altered. In comparison, despite the assumption of V2,

the second law predicts an increased efciency with higher values

of V1. The linear trend displayed by V2 has a higher variability,

suggesting that this denition of V2 increases reliability with the

assumption of V1/V2 C. More importantly, the second law

efciency reveals variability in the efciency of each system for

different wind conditions. This is valuable information when

designing a turbine for a wide variety of wind conditions, or

selecting a turbine for a specic site with one of the many different

possible operating requirements.

Sahin et al. [14] proposed that the shaft work is used to estimate

the kinetic component of ow exergy. The same value is used to

represent the work output, thereby assuming that the turbine is

100% energy efcient. This paper offers two alternative methods,

using one of the proposed denitions for obtaining V2 to represent

the change in kinetic energy. This includes the effects of DKE on (a)

its inclusion in _Exflow as_ExKE, and (b) assuming DKE Wout. To

differentiate, the second law efciencies in (a) are denoted as J2.

Fig. 7a illustrates the variations in the incoming velocity, where hKEand JKE represent the rst and second law efciencies, with

DKE Wout. A high level of variability is expected with the de-

nition of V2, thereby providing signicant information about the

effects of the denition. Furthermore, these plots present the point

specic change in kinetic energy, as stated by the rst law. Fig. 7c

and d present the methods of predicted ow exergy with

a varying inlet velocity. A comparison with Figs. 10a and 11a

predicts a 50e53% difference in the rst and second law efciencies

for the airfoil systems, and 44e55% for the VAWTs, at reference

conditions.

Fig. 7e illustrates the results of a second law analysis of the Benz

limit. The theoretical maximum energy efciency is obtained with

the Benz limit. With the rst law, the Benz limit is a constant value,

Fig. 9. Energy and exergy efciencies with varying temperature for (a) point specic low velocity, (b) specic effective velocity, (c) effective velocity and (d) average low velocity.

K. Pope et al. / Renewable Energy 35 (2010) 2102e2113 2109

independent of operating conditions. However, combining the Benz

limit theory with second law analysis provides a theoretical

maximum efciency that includes the effect of irreversibilities,

resulting in a dependence on design and operating conditions.

Dening it here as 0:59 _Woutt= _Exflow, the second law Benz limit

with both methods of obtaining _Exflow (i.e., JB, and J2,B) is pre-

sented. Signicant variability between the VAWTs and the airfoils is

predicted by JB from 29% to 59%, while the range of J2,B is only

28e32%. Table 3 summarizes the rst and second law efciencies,

predicted for the reference operating conditions.

4.2. Denition 2: specic effective velocity (V2 V2,eff % Aeff/A)

This denition suggests a high level of accuracy with the second

law, as it attempts to specify the acting ow stream on the turbine.

This denition can provide a high level of comparability between

different turbine designs and congurations. However, the precision

of analysis could be a problem with this denition, as it requires

a level of intuition from the analyst. Figs. 8e12bpresent the results of

varied reference conditionsandoperatingconditions forDenition2.

A noticeable reduction in variability is experienced between the

airfoils from Denition 2. Also, the exergetic variability between the

airfoils and VAWTs is reduced. Difculties in dening the effective

area for an airfoil could be a contributing factor to this result.

In this paper, the effective area was assumed as the high speed

ow streamdirected above the airfoil, with the total area taken to be

the chord length. This denition does not fully represent the

differences in geometry between the airfoils, as the effects of tail

curvature are not fully represented. Dening the effective area for

the VAWT is comparatively straightforward. A low velocity ow

stream is evident in the locations where a signicant kinetic force is

applied. An effective area is assumed as the cross-sectional area of

this ow stream, with a total area assumed to be the turbine diam-

eter. Anotable result fromDenition2 is illustrated in Fig.11b,where

the airfoil second law efciencies exhibit a non-linear reduction in

efciency, falling rapidly after the referencewind velocity of 10m/s.

The VAWT second law efciencies display a slight linear increase.

ThehighvaluesofV2 suggested fromDenition2produce the lowest

predictions ofJ throughout the study.

4.3. Denition 3: average velocity of useful area (V2 V2,useful,ave)

Denition 3 predicts the largest range in V2, with 9.5 m/s for the

NACA 63(2)-215 airfoil, compared to 3.1 m/s for the Zephyr VAWT.

A high dependence on the streamline conguration of the turbine

is obtained by this denition. A high level of precision is attainable,

compared with Denition 2, since the value is independent of size

for the effective area. The analysis of Denition 2 reveals an output

for J that is evenly distributed at the reference conditions and

throughout most of the varied operating conditions. Similar to

Denition 2, the relatively high values of V2 for the airfoil translate

into low second law efciencies. However, the VAWTs are less

affected. From Fig. 11c, the prole of an airfoil can signicantly

affect the second law efciency. The basic prole of the NACA 63(2)-

215 exhibits only a slight reduction in second law efciency,

compared to the FX 63-137. A decreasing trend, which increases its

Fig. 10. Energy and exergy efciencies with varying V1, constant V2 for (a) point specic low velocity, (b) specic effective velocity, (c) effective velocity and (d) average low velocity.

K. Pope et al. / Renewable Energy 35 (2010) 2102e21132110

rate of reduction throughout the plot, is predicted for the more

complex FX 63-137. At the upper boundary of V1, the second law

efciency of the FX 63-137 airfoil falls below the value for the

Savonius VAWT.

4.4. Denition 4: average of the low velocity stream

This denition suggests a relatively even distribution of V2amongst the various systems. This translates into evenly distrib-

uted second law efciencies, at the given reference operating

conditions illustrated in Figs. 8e12d. Similar to the other deni-

tions, little effect is exhibited from altering the reference pressure.

This denition suggests a high variability between the airfoil

second law efciencies. Similar to Denition 3, the second law

efciency for the NACA 63(2)-215 airfoil deteriorates rapidly

throughout the range of V1, dropping below the Savonius second

law efciency within the operating velocity. The declining NACA 63

(2)-215 airfoil second law efciency suggests that this denition

can give insight into the interdependence of the geometric prole,

operating conditions, and turbine performance.

Fig. 12 compares the various denitions of V2 in terms of exdest,

assuming V2/V1 is maintained constant. Many of the previous

results can be understood through the exergy destruction. The rst

denition of V2 predicts similar exergy destruction for the airfoils

and VAWTs, respectively. It appears that this denition fails to fully

represent the differences in ow irreversibilities between all

systems. Better results would likely occur from Denitions 3 and 4,

whereby a greater range of variability is predicted between the

various systems.

These case studies have compared the rst and second law

efciencies of four wind energy systems. Difculties exhibited

with applying the exergetic analysis have been identied and

preliminary solutions were obtained. The denition of V2 has been

identied as a key component for implementing the second law in

regular wind power analysis, optimization and design. The second

law provides a valuable design tool that can help improve the

efciency and economic cost of wind power. Improvements to

system output, development and installation can contribute to

wind power systems alleviating the substantial demand from

traditional non-renewable energy sources. There is an urgent

need to alter these current consumption and production patterns.

Combustion of vast quantities of fossil fuels for power production

is responsible for numerous environmental problems. The emis-

sions from hydrocarbon combustion contain pollution agents

including NOx, SOx, CO and CO2. These chemicals are connected to

a variety of environmental degradation problems, including acid

rain, smog, and greenhouse gases that contribute to climate

change.

To ensure that wind energy capacity is fully utilized, the

turbine design must be optimized to operate in various wind

conditions. A second law analysis can contribute to improving the

wind turbine design, system efciency and power output. Signif-

icant reductions in the environmental impact of energy generation

methods can be achieved through efciency improvements via the

second law. Wind power can provide a sustainable contribution to

Fig. 11. Energy and exergy efciencies with varying V1, constant V1/V2: (a) point specic low velocity, (b) specic effective velocity, (c) effective velocity, (d) average low velocity.

K. Pope et al. / Renewable Energy 35 (2010) 2102e2113 2111

society's energy needs. The minimal impact caused by wind

turbine manufacturing, installation, maintenance, and operation

can be further reduced through efciency improvements and

enhanced design methodologies that use the second law of

thermodynamics.

5. Conclusions

In this paper, the rst and second lawswere used to compare the

performance of a variety of wind power systems. Exergy analysis

was shown to allow a diverse range of geometric and operating

designs to be compared with a commonmetric. The results indicate

a 50e53% difference in rst and second law efciencies for the

airfoil systems, and 44e55% for the VAWTs. Exergy is a useful

parameter in wind power engineering, as it can represent a wide

variety of turbine operating conditions, with a single uniedmetric.

Through exergy methods, better site selection and turbine design

can improve system efciency, decrease economic cost, and

increase capacity of wind energy systems.

Acknowledgements

The authors gratefully acknowledge the nancial support of this

research provided by Zephyr Alternative Power Inc. and the Natural

Sciences and Engineering Council of Canada.

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Table 3

Various predicted rst and second law efciencies.

h [%] J [%] J2 [%] JB [%] J2,B [%] hKE [%] JKE [%] JKE,2 [%]

NACA 63(2)-215

airfoil

44 21 22 29 30 39 19 20

FX 63-137 airfoil 47 23 22 30 28 59 29 27

Savonius VAWT 18 17 10 55 32 94 87 51

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