A Pareto optimal multi-objective optimization for a horizontal axiswind turbine blade airfoil sections utilizing exergy analysis andneural networks

Seyed Mehdi Mortazavi a,n, Mohammad Reza Soltani b, Hamid Motieyan c

a Department of Energy Engineering, College of Energy and Environment, Science and Research branch of Azad University, Tehran, Iranb Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iranc Collage of Surveying Engineering, Department of GIS, Khaje Nasir University of Technology, Tehran, Iran

a r t i c l e i n f o

Article history:Received 18 May 2014Received in revised form1 September 2014Accepted 13 October 2014Available online 18 November 2014

Keywords:Wind turbine airfoilsExergy analysisCFDArtificial neural networkPareto optimal set

a b s t r a c t

In this study a multi-objective genetic algorithm is utilized to obtain a Pareto optimal set of solutions forgeometrical characteristics of airfoil sections for 10-meter blades of a horizontal axis wind turbine. Theperformance of the airfoil sections during the process of energy conversion is evaluated deploying a 2Dincompressible unsteady CFD solver and the second law analysis. Artificial neural networks are trainedemploying CFD obtained data sets to represent objective functions in an algorithm which implementsexergetic performance and integrity characteristics as optimization objectives. The results show that utilizingthe second law approach along with Pareto optimality concept leads to a set of precise solutions whichrepresent minimum energy waste, maximum efficiency, and topmost stability. Furthermore, enhanced rotorperformance coefficients are observed through a BEM study which compares conventional designs with thesecond law obtained configurations. Exergy analysis is believed to be an efficient tool in the optimal design ofwind turbine blades with the capability of determining the amount of lost opportunities to do useful work.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Depleting sources of fossil fuels and the environmental issuesassociated with utilizing them have made development of alternativeand clean energy sources and their effective employment a consider-ably rapid process (IEA, 2013). Wind energy market is experiencing asignificant growth which stands out among renewable energy tech-nologies and is expected to extend even in a more substantial way.Horizontal Axis Wind Turbines (HAWTs) have been demonstrated tobe the transcendent machine tools in extracting the energy from thewind (Hau, 2006; Gipe, 2004); these machines possess a number ofadvantages when compared with Vertical Axis Wind Turbines(VAWTs), such as higher energy efficiency, more mechanical stability,less sensitiveness to off design conditions, etc. Thus, effective extrac-tion of the wind stream energy with less energy waste, obtaining acomprehensive understanding of the energy conversion phenomena,and economic analysis of these systems have become an area ofconcern for technology leaders as well as an area of interest forresearchers (Mehta et al., 2014; Arroyo et al., 2013; Castellani andVignaroli, 2013; Castellani and Garinei, 2013; McKenna et al., 2014;Jung and Kwon, 2013; Jha, 2010; Burton et al., 2011; Wood, 2011). In

this regard, optimization of geometrical properties of wind turbineblades has been investigated using various approaches. The design of aHAWT rotor blade is a complex task consisting of trade-off decisions.The objective of this procedure can usually be addressed as finding theoptimum performance for a range of specified conditions (Burton etal., 2011).

Benini and Toffolo (2002) optimized HAWT blades using theBEM theory along with an evolutionary algorithm. In their study amulti-objective optimization algorithm was employed for design-ing the blades of a stall-regulated HAWT. The BEM theory analyzedthe flow field around the airfoil while the evolutionary algorithmselected the decision variables.

Jureczko et al. (2005) used aerodynamic characteristics alongwith modifying the composite material of the blade in order tooptimize the wind turbine blade. The complexity of the problem ofdetermining the optimum shape of the blade and the best compo-site material became the incentive to use multi-criteria optimumdesign approach. The aerodynamic analysis was based on the BEMtheory and the effect of the blade material on the dynamic proper-ties was evaluated using a Finite Element Model (FEM). A geneticalgorithm was employed to conduct the optimization.

Vitale and Rossi (2008) devised a computational method for thedesign of wind turbine blades. They developed and introduced acomputer code for blade design of HAWTs with low capacities, whichprovided the possibility of obtaining optimum wind turbine blade

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Journal of Wind Engineeringand Industrial Aerodynamics

http://dx.doi.org/10.1016/j.jweia.2014.10.0090167-6105/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel: þ98 936 865 2980E-mail address: mehdimortazavi1986@gmail.com (S.M. Mortazavi).

J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72

shape. The Blade Element Momentum (BEM) theory was used in thealgorithm of fluid dynamics analysis. The software made developingvarious designs for many different conditions affordable.

Leung et al., (2010) obtained the optimum design of the rotor of asmall wind turbine by using Computational Fluid Dynamics (CFD)analysis. The objective of this study was performance evaluation ofsmall wind turbines which usually extract energy from low speedwind streams. The study investigated the variation of the performanceof micro wind turbine with different design parameters. The resultsshowed that the performance of high-solidity wind rotors is moredesirable than that consisting of low-solidity rotors.

The overall efficiency of a wind turbine might depend onseveral contributing factors, such as generator performance, theratio of the gear box system and the height of the hub from theground, which are not investigated in this study. Generally, withspecified wind distribution and at a given range for rotationalspeed of the rotor, the most important issue to address will beselection of the airfoils and their geometrical properties along theblade (Jha, 2010; Burton et al., 2011; Wood, 2011; Cengel andBoles, 2006).

Typically, common design methodologies employ the first lawof thermodynamics for wind power system analysis and design(Benini and Toffolo, 2002; Jureczko et al., 2005; Vitale and Rossi,2008; Leung et al., 2010). Through these methods a theoreticalmaximum efficiency can be predicted, but the loss of opportunitiesto produce more useful work is not evaluated. According to Dincerand Rossen (2012), to provide an efficient and effective use of theenergy sources, it is essential to consider both the quality andquantity of the energy used to achieve a given objective. In thisregard, the second law of thermodynamics deals with the qualityof energy and it simply analyzes degradation of the energy duringa process, entropy generation and the lost opportunities to dowork (Dincer and Rossen, 2012; Dincer et al., 2014). Entropy-baseddesign and exergy analysis have been shown to identify themaximum theoretical capability of energy system performance

in various applications, by employing the fact that higher levels ofentropy generation are associated with a lower level of usefulenergy (Dincer and Rossen, 2012; Dincer et al., 2014; Koroneoset al., 2003).

Therefore, exergy analysis together with stability characteris-tics can be considered as an advantageous tool for optimal designof geometrical parameters of wind turbine rotors. In this study aMmulti-objective genetic algorithm (MOGA) is utilized to obtain aPareto optimal set of solutions for chord lengths and flow anglesfor the airfoil sections of 10-meter blades of a HAWT rotor. Theobjective functions in this algorithm are exergy efficiency of thesection, loss of exergy around the airfoil, and the solidity of theairfoil section. First, performances of three different NREL DanSomers' airfoil families are evaluated using an incompressibleunsteady CFD solver and second law approach which leads toselection of an airfoil family for blade investigations. CFD simula-tions are conducted in order to evaluate exergy efficiency and theresultant dissipated exergy around the airfoil under various flowconditions of the section's radius, chord length and flow angle.Neural networks are trained in order to enable predicting thevalues of exergy efficiency and exergy loss under un-investigatedflow conditions and section radii. In the next step trained neuralnetworks along with the section's solidity are deployed as objec-tive functions in MOGA to achieve Pareto optimal sets of solutiontailored for each of the blade sections. Moreover, power coeffi-cients of the rotors designed by the second law approach arecompared with the power coefficients representing rotors des-igned utilizing conventional methods.

2. Second law analysis via CFD

CFD has emerged as an expeditious tool for apprehendingcognition of the flow field in various engineering problemsincluding wind engineering, a few exhibits are flow analysis

Nomenclature

A Area [m2]a Axial induction factora0 Tangential induction factorc Chord length [m]Cp Specific heat ½kJ=kgK�_Ex Exergy rate ½kW �F,

External body forceH EnergyI Unit tensor_m Mass flow rate ½kg=s�k Thermal conductivity ½W=m2K�P Static pressure ½Pa�Q Heat [J]r Radius [m]R Gases constant ½J=Kmol�Re Reynolds numberS Source termt Time [s]T Temperature [K]U Undisturbed velocity ½m=s�ν, Velocity component ½m=s�V Free stream velocity ½m=s�yþ Turbulence wall Y Plus

Greek Letters

α Angle of attack ½deg�β Twist angle ½deg�ε Exergy efficiencyμ Dynamic viscosity ½kg=ms�ρ Density [kg=m3]Ω Rotational speed ½rad=s�τ Shear stress ½N=m2�φ Approach (flow) angle ½deg�

Subscripts

0 Reference conditionat Atmosphere conditionD Dragdest Destructionef f Effectivein InflowL LiftLoss Lossm Massout Outflowph Physicalproduct Productsrel Relativework Workx Streamwise directiony Vertical direction

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72 63

(Jafari and Kosasih, 2014), wind farm evaluation (Choi et al., 2013),wake behavior detection (Abdesalam et al., 2014), etc. (Blocken,2014). In this study a 2D incompressible unsteady CFD solver, basedon the finite volume method is implemented to provide imperativeinformation for a second law analysis (i.e., exergy efficiency anddissipated exergy evaluation) around the airfoil in various conditionsof Reynolds number, section's radius, chord length and flow angle.The data sets achieved in CFD simulations will further be deployed inthe learning process of the artificial neural networks making itpossible to predict exergy efficiency and exergy loss for those caseswhich are not individually simulated. Note that the CFD approach ishomologous for all simulated airfoils and the same procedure ispreserved for each and every case.

2.1. Governing equations

2.1.1. Navire–Stokes equationsThe mathematical model for the study of fluid dynamics

problems is based on the fundamental mass, momentum andenergy conversion principles. The approach used in this study iscalled Reynolds Averaged Navire–Stokes (RANS) modeling. Theseequations govern transport of the averaged flow quantities, andcan be used for the entire flow field.

∂ρ∂t

þ∇: ρν,� �

¼ Sm ð1Þ

∂∂t

ρν,� �

þ∇: ρν,ν,� �

¼ �∇:pþ∇: τ� �þρg

,þF,

ð2Þ

∂∂t

ρH� �þ∇: ν, ρHþp

� �� �¼∇: kef f∇T

� �þS ð3Þ

τ¼ μ ∇ν,þ∇ν,T

� �� 2∇

3

� �:ν,I

� ð4Þ

For pertinent prediction of external flow properties, differentturbulence models have been developed. In this study the shearstress transport k�ω model is employed, which is highly recom-mended for modeling flows with considerable adverse pressure.The detailed descriptions of these turbulence models are given inWilcox (1993) and Menter (1994).

2.1.2. Exergy balance for flow around airfoilGenerally, the exergy efficiency associated with energy conver-

sion processes can be evaluated from the exergy balance relation.In this case, the exergy balance equation can be expressed as

_Exin ¼ _Exworkþ _Exoutþ _Exdestþ _Exloss ð5Þwhere _Exin and _Exout represent the exergy of the incoming andoutgoing flows respectively, _Exwork is the available energy withinthe work done in the process, and _Exdestþ _Exloss stands for theamount of exergy which is destructed and lost in the conversionprocedure (Dincer and Rossen, 2012).

The exergy of a flow with a temperature of T, a pressure equalto P, and a velocity of V, deviating from a reference environmentwith properties of T0,P0, and V0 includes two terms: physical andkinetic exergy. The kinetic term of exergy is equivalent of kineticenergy of the flow while the physical term is described as

_Exph ¼ _m Cp T�T0ð ÞþTat Cp lnTT0

� ��Rln

PP0

� ��Qloss

Tat

� �� ð6Þ

In Eq. (6), P ¼ Pat7 ðρ=2ÞV2, also T is determined through thewind chill temperature, based on a model developed by Zecher(1999). In this study the velocity of the outgoing flow is obtainedat a length equal to one chord of the airfoil after the airfoil itself,providing a consistent manner for assessing the exergy associatedwith the downstream flow. The exergy efficiency can be calculated

from the following equation:

ε¼_Exproduct

_Exin� _Exoutð7Þ

Definition of _Exproduct can be deemed as a pivotal task of thesecond law analysis since description of a convenient productdirectly pertains to the quality and feasibility of the second lawmethod. Based on the aerodynamic ground, the instrumentalproduct of this process would be the resultant lift force actingperpendicular to the surface of the airfoil; therefore, the exergy ofthe lift force could be an expeditious demonstration of the exergyof the products. The exergy of the lift force is given by

Exlif t ¼ FL � ðVy�Vy0Þ ð8ÞObviously, determining a legitimate dead state vertical vel-

ocity,Vy0, is vital for the effective evaluation of _Exlif t . The referencecondition in the energy conversion process of an airfoil can bereferred to as a condition in which there are no vertical orhorizontal velocities neither are there any exergy destructions,which will lead to all the available incoming energy converting touseful work. In such a condition, the airfoil experiences a state offloatation leading to equality of the forces of lift and gravity actingon the airfoil (FL ¼mg). Therefore, for every Reynolds number aVy0 exists so that

_Exin ¼ FLð0�Vy0Þ ð9ÞEq. (9) expresses the condition in which the exergy of the inflow isthoroughly converted to the exergy of the product with nodestruction. Note that if Vy0 was set to be zero, the connotationwould be that the exergy required for achieving and maintainingthe lift is zero, which is not applicable for airfoil application.

Vy is evaluated through CFD analysis, utilizing imaginary lineswhich are literally generated according to airfoil's surface shapeand placed 10�7 meters above the upper surface and below thelower surface of the airfoil. Utilizing this method will lead toobtaining velocity values on the airfoils surface acceptably sincedue to the no slip condition deployed on the surfaces, the solverassumes that these values are zero on the actual airfoil surfaces.Thus, Vy is computed by averaging the node values on theimaginary lines.

With the exergy efficiency evaluated using the discussedapproach, the summation of exergy destruction and exergy lossfor each flow condition will be determined using Eq. (5), thissummation will be referred to as ‘dissipated exergy’ in thismanuscript. Note that dissipated exergy would represent lossesfrom the viscous dissipation phenomenon and the accompaniedparasitic drag force acting on the airfoil's surface. The ‘ViscousDissipation’ term is the destruction of fluctuating velocity gradi-ents by the action of viscous stresses. With this approach, an uttercognition of the lost energy conversion opportunities will beprovided which can be perceived as the unique advantage of thesecond law method.

2.2. Computational domain

Fig. 1(a) shows the 2D computational domain; the utilized grid iscomprised of quadratic elements. A high resolution grid is employednear the airfoil surface due to the importance of this region inboundary layer modeling, the resolution of the grid decreases whenmoving far from the airfoil and near the far field boundaries to makecalculations less time consuming. Fig. 1(b) shows the fine grid aroundthe airfoil. Note that this initial grid around the airfoil will undergoadaption (refinement) in the process of the simulation, in order tomatch the convergence criteria for different flow conditions. Further-more, the total grid nodes number might not be precisely the sameafter adaption, due to preservation of the mentioned criteria for

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–7264

different cases. However, the number of total nodes for the simula-tion case consisting of a standard S814 airfoil encountering flowregime with Reynolds number equal to 106 and an angle of attack of151 emerges to be 450806 with exactly 614 nodes on the airfoil'ssurface.

2.2.1. Solving methodsDespite the problem being naturally steady-state, the flow

around the airfoil inherently tends to instabilities at high anglesof attack; thus, a transient approach has been implementedthroughout all angles of attack in order to maintain a consistentmethod of evaluation. The low Reynolds flow around the airfoilsections is considered as incompressible; as a result, the ‘pressure-based’ method is used. The pressure–velocity coupling algorithmis ‘PISO’ since the simulations are conducted in an unsteadymanner; the discretization of the convection terms in the trans-port equations is selected to be the ‘second order upwind.’ Adetailed description of these methods can be found in Ferziger andPeric (2013).

Three main criteria are majorly considered in order to guaran-tee the convergence of the solution.

1. Convergence of lift and drag coefficients on the airfoil.2. Convergence of velocity magnitude on the effective area

adjacent to the airfoil’s surface.3. Proper wall yþ .

Lift and drag coefficients are considered as substantial aero-dynamic characteristics of the flow, thus the no-fluctuationbehavior should be obtained during the solution for these para-meters. Velocity magnitude of near airfoil region represents greatimportance in evaluating Vy; therefore, this parameter should bemonitored as the solution converges. Turbulence wall yþ is afactor of correct boundary layer modeling, thus during the solutionprocess, the grid is refined to obtain yþ between 1 and 5 toguarantee the requirements for this parameter. This adaptionrepeats until yþ lies within the proper condition and there areno significant changes in other solution parameters observed. Inother words, the independency of solution to the utilized grid isobtained by changing the grid around the airfoil; with thisapproach, for each and every simulation case a distinct gridindependency study is conducted, which refines the initial generalgrid for different flow conditions (i.e., Re and AOA) and airfoilshapes to fulfill a coherent yþ requirement.

2.2.2. CFD results and airfoil selectionThe National Renewable Energy Laboratory (NREL) has devel-

oped several families of special-purpose airfoils for HAWTs (NRELAirfoil Families for HAWTs, 1995). Three airfoil families have been

considered to be evaluated for employment in the design of theblade; these families are all recommended for blade radius of 10meters. The aforementioned airfoil families are introduced inTable 1. The performances of these airfoils are evaluated throughlow Reynolds numbers and various flow angles from 01 to 201.Performance criteria are exergy efficiency and exergy dissipationas mentioned earlier.

In order to validate the transient simulation approach, thenumerically obtained lift and drag coefficients of S825 airfoil arecompared to the experimental data from NASA–Langley windtunnel test data in Fig. 2. The experimental data are availablefrom the official website of the laboratory (NREL Airfoil data,2013), the Reynolds number of the delineated simulations is106.As can be observed from Fig. 2(a), lift coefficients show greatagreement through all considered angles of attack. In addition, thebehavior of change in drag coefficient is believed to be captured inan acceptable manner when considering the fact that all CFDmodels overpredict the drag coefficient due to the implementedintegration methods.

When comparing the second law analysis results, it is observedthat the airfoil family entitled F1 transcends in both characteristicsapproximately in majority of the investigated flow conditions.However when consistency in performance is considered, theother two airfoil families (i.e., F2 and F3) show slighter magnitudesin changes of performance with probable variation in flow condi-tions. Furthermore, increase of inflow velocity in constant flowangle will lead to decline in exergy efficiency for flow angles otherthan 01 and increment in dimensionless dissipated exergy. Exam-ples of these detected tendencies are delineated in the plots ofFig. 3 while Table 2 presents more of the observed valuesdemonstrating the paradigms for different airfoils.

Note that ‘dissipated exergy’ in Fig. 3 and Table 2 is non-dimensionalized using of the term ( _mT) in order to provide thepossibility of comparison between different Reynolds numbers; asexplained earlier, ‘dissipated exergy’ demonstrates the amount oflost energy production potential.

After the above discussion, airfoil family entitled F2 is con-sidered for investigations including different chord lengths andflow conditions occurring in a HAWT blade, due to its coherence inperformance characteristics and rather acceptable exergy effi-ciency magnitudes. The schematic shapes of the selected airfoilfamily are presented in Fig. 4.

2.2.3. Blade 2D investigation approachAs wind stream osculates the rotary blade of a wind turbine, it

is assumed that an incident ensuing velocity acts on each of thecross-sectional blade elements. This velocity is a result of the windundistributed velocity and the rotational speed of the blade itself(Jha, 2010; Burton et al., 2011; Wood, 2011). In this assumption

Fig. 1. Computational domain around the airfoil: (a) complete grid and (b) fine grid around airfoil.

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72 65

three-dimensional effects are ignored; Fig. 5 shows the bladeelement velocities.

tan φ¼ U1 1�að ÞΩr 1þa0ð Þ ð10Þ

φ¼ αþβ ð11Þ

In Eqs. (10) and (11) Ω stands for the rotational speed of therotor, r represents the radius of the section, and a and a0 are theinduction factors. Also φ is the flow angle and α and β representthe angles of attack and twist of the section, respectively. If thetangential and radial forces acting on an airfoil are known, areverse method can be utilized in which the induction factors canbe calculated using correction Eqs. (10) and (11). As a result, whena CFD simulation is conducted for a known resultant velocity,radius of the section, chord length and flow angle, it is possible toevaluate in what combination of wind free stream velocity androtational speed, the assumed, initial resultant velocity and flowangle occur. Hence, it is feasible to approximately investigate thereal conditions of a wind turbine blade. In this study, based on trialand error and utilizing the discussed reverse method, resultantfree stream velocities and flow angles are employed so that theyrepresent different wind free stream velocities equal to 5, 10, 15,and 20 ½m=s� and the various rotational rates of the rotor including30, 60, 100, and 140½rpm�. Further, for every considered airfoilsection and radius, various flow conditions are investigatedaccording to common restrictions on chord length and flow anglefor a 10-meters blade. It can be observed from these simulationsthat at a constant inflow velocity and flow angle, exergy efficiencyand dissipated exergy both behave proportional to chord length ofthe section, which is considered to be quite sensible since the liftforce, parasitic drag force, and viscous dissipation all tend to growas a result of that altercation.

3. Artificial neural networks (ANNs)

An artificial neural network (ANN) is a mathematical modelinspired by the structure and function of biological neural networksin the brain. ANNs consist of a number of non-linear processing units(i.e., neurons) which are connected to each other by means of weights.ANNs can learn a specified task by adjusting the mentioned weightsand are demonstrated to be able to represent complex non-linearbehaviors if they are trained expeditiously (Krose and Smagt, 1996).Through the training process, a network learns general properties ofthe relationship between inputs and output of a system by comparinggenerated output to target value within a back propagation rule(Kumar, 2004; Schalkoff, 1997). In this study neural networks areutilized in order to predict values of exergy efficiency and dissipatedexergy around the airfoil surface for section radii, chord lengths, andflow conditions which are not numerically evaluated.

Multi-layer perceptron (MLP) neural networks are feed-forw-ard networks extremely capable of recognizing any type of rela-tionship between input and output data (Fausett, 1993). Two MLPnetworks are trained for prediction of the relationship betweengeometrical characteristics of the airfoil sections and flow condi-tions as inputs, and exergy efficiency and dissipated exergy aroundairfoil surface as output. Data sets for training these MLPs areprovided by numerical simulations of flow osculating the airfoils,which are explained in the previous sections.

According to Krose and Smagt (1996), the situations in whichthe performance of the MLP improves with a second (or third, etc.)hidden layer are quite rare, thus one hidden layer would besufficient for the large majority of problems. In this study in orderto detect the efficient number of neurons in the hidden layer, atrial and error method has been utilized. Based on this approach,the number of neurons changes in an ascending order until theperformance of the MLP tends to degrade; this method is imple-mented based on the idea that additional nodes provide additionalweights to store or release signals to the network during iteration.Furthermore, since the MLP is meant to detect a nonlinearbehavior, continuous Log–Sigmoid function is used for transferpurpose between the layers. The Sigmoid function introduces non-linearity in the network, it is differentiable and its derivatives arefast to compute (Schalkoff, 1997; Fausett, 1993), therefore thisfunction is deemed expeditious for employment in this study.

Five different section radii (i.e., 2, 4, 6, 8, and 10m) are consideredto train the required MLPs, for each section of the blade there are 480data sets with different wind stream velocities, blade rotational rate,chord length, and flow conditions, thus with employing a total of 2400data sets the MLPs are trained. The networks are sensitive to changes

Table 1NREL airfoil families under study.

Airfoil family Root Medial Tip

F1 S814 S825 S826F2 S815 S812 S813F3 S811 S809 S810

Fig. 2. Comparison of CFD results for S825 with wind tunnel test data, Re¼ 106. (a) Lift coefficient and (b) drag coefficient.

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–7266

in wind free stream velocity, blade rotational rate, radius, airfoil type,flow angle, and chord length. Note that 70% of the data sets are usedfor training the network, 15% of them are employed to validate thetraining process, and the remaining 15% is applied to test the network

performance against the unseen data. The performance of the trainedMLP for predicting dissipated exergy is shown in Fig. 6.

Analogous network topology, training strategy and number ofdata sets are used to train an MLP for predicting exergy efficiency for

Fig. 3. Plots of second law performance characteristics of the understudy airfoil. (Re¼ 106).

Table 2Low Reynolds number second law performance evaluation for under study airfoils.

Reynolds number 3� 105

Performance characteristic - Exergy efficiency Dimensionless exergy dissipation

Angle of attack - 0 5 10 15 20 0 5 10 15 20

S811 0.0753 0.5395 0.5210 0.4558 0.4639 0.0205 0.0071 0.0138 0.0198 0.0166S814 0.1489 0.6687 0.6070 0.4709 0.3712 0.0133 0.0053 0.0111 0.0208 0.0273S815 0.0662 0.5806 0.5841 0.4850 0.5049 0.0190 0.0072 0.0120 0.0200 0.0159S809 0.0784 0.5590 0.4157 0.3312 0.3060 0.0106 0.0059 0.0168 0.0250 0.0204S825 0.5713 0.9284 0.7213 0.4070 0.3810 0.0044 0.0011 0.0068 0.0248 0.0188S812 0.1468 0.6473 0.4574 0.3901 0.3154 0.0102 0.0049 0.0161 0.0209 0.0202S810 0.1132 0.5517 0.3921 0.2740 0.2354 0.0092 0.0062 0.0160 0.0263 0.0205S826 0.7056 0.8835 0.7026 0.4140 0.3722 0.0027 0.0021 0.0074 0.0246 0.0187S813 0.2448 0.7025 0.4865 0.3759 0.2799 0.0079 0.0039 0.0135 0.0210 0.0202

Reynolds Number 6.5�105

Performance characteristic - Exergy efficiency Dimensionless exergy dissipation

Angle of attack - 0 5 10 15 20 0 5 10 15 20

S811 0.0296 0.2699 0.2667 0.2466 0.2417 0.0647 0.0485 0.0793 0.1382 0.1195S814 0.1039 0.2923 0.3596 0.2602 0.2599 0.0558 0.0505 0.0749 0.1449 0.1220S815 0.0581 0.3069 0.3353 0.2632 0.2660 0.0671 0.0519 0.0799 0.1425 0.1206S809 0.0359 0.2443 0.2529 0.1928 0.1567 0.0486 0.0441 0.0885 0.1377 0.1280S825 0.2507 0.3885 0.3672 0.2087 0.2015 0.0345 0.0379 0.0681 0.1650 0.1289S812 0.0667 0.2300 0.2603 0.1953 0.1808 0.0498 0.0472 0.0892 0.1393 0.1265S810 0.0439 0.2395 0.1954 0.1381 0.0685 0.0469 0.0446 0.0938 0.1388 0.1294S826 0.2899 0.4410 0.3509 0.1968 0.1637 0.0298 0.0322 0.0699 0.1682 0.1297S813 0.0991 0.3182 0.2511 0.1812 0.1285 0.0414 0.0373 0.0853 0.1380 0.1267

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72 67

different possible un-investigated cases. Table 3 summarizes thenetwork characteristics for each MLP. In this table MSE refers toMean Square Error, closer to zero values of which indicate highernetwork performance in behavior modeling; regression values arealso included, closer to one values of which demonstrate thenetwork's more precise output predicting capability. Further andcomplementary information about ANNs, different network topolo-gies, various training strategies, and the methods of performanceevaluation can be found in Krose and Smagt (1996), Kumar (2004),Schalkoff (1997) and Fausett (1993).

4. Multi-objective optimization methodology

4.1. Pareto optimality concept

As mentioned earlier, the objective of this study is to determinethe geometrical properties of airfoil sections of wind turbine bladein a manner that exergy dissipation around the airfoil is mini-mized while exergy efficiency along with solidity of the airfoil ismaximized. CFD simulation revealed that exergy efficiency andexergy dissipation around the airfoil do not mandatorily showsatisfying behaviors simultaneously. For instance, in some flowconditions if the dissipated exergy is to be at its minimum possiblevalue, exergy efficiency will suffer degradation. To address thisissue of optimization, it is usually convenient to introduce a set of

solutions as possible optimum solutions rather than sticking tomerely one solution as the most valuable (Zhou et al., 2011). As aresult, the scope of the method is to achieve the best trade-offperformance between two main objectives: lower dissipation ofexergy and higher exergy efficiency plus higher solidity.

In a problem with two objective functions off 1ðxÞ andf 2ðxÞ,solution x is a Pareto optimal solution if, and only if, there is noother solution x0 such that f 1ðx0ÞZ f 1ðxÞ and f 2ðx0Þg f 2ðxÞ or suchthat f 1ðx0Þg f 1ðxÞ and f 2ðx0ÞZ f 2ðxÞ. The solutions which are in thisset are called Pareto optimal set and the corresponding objectivefunction values are referred to as Pareto front (Doyle, 1985).

4.1.1. Genetic algorithmEvolutionary multi-objective algorithms have formerly been

employed in the design of wind turbine blades; studies of Beniniand Toffolo (2002) and Hu et al. (2013) can be referred to asnotable exhibits. In this study in order to obtain Pareto optimalsolutions for each section, the multi-objective algorithm is iteratedseparately for each section radius. The step-by-step process of thisalgorithm is described in this section.

4.1.2. Generating random populationPertinent to the radius of the section, the first random popula-

tion defining chord length and flow angle should be generated.There are some constraints imposed on chord length and flowangle in each section so that initial solutions are appropriate forthe associated section. The initial random solutions are presentedin the form of chromosomes each including 9 gens. The first genfrom left to right of a chromosome defines the round part of thechord length, the next three gens define the decimal part of thechord length. Gen numbers 6 and 7 describe the round part of theflow angle, and finally the next three digits represent the decimalpart of the flow angle. For each section a random population with100 solutions is generated.

4.1.3. Objective functions and parents selectionAs mentioned earlier two trained MLP networks will be serving

as objective functions in the genetic algorithm, and another

Fig. 4. Geometrical depiction of the selected airfoil family.

Fig. 5. Blade element velocities and including angles.

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–7268

objective function will be section solidity.

σ ¼ BcðrÞ2πr

ð12Þ

In Eq. (12) r defines the radius of the section, B is the number ofblades on the rotor and c expresses the chord length. Since thisobjective function is influential only when the chord lengthchanges and also since it shows the same behavior as exergyefficiency when chord length variation occurs, these two functionsare combined in order to make Pareto optimal selection a lesscomplex task. Thus, there are two main objective functions:

� Minimum exergy dissipation� Maximum exergy efficiencyþmaximum section solidity

For generating children from each population, parents with thebest characteristics need to be considered. In this study non-dominated sorting concept is employed in order to classify thesolutions of each population (Srinivas and Dep, 1994). In the firststep all the solutions of the population are compared consideringPareto optimality concept, the best individuals which are notdominated by any other individuals are selected and put into the

first layer. The next step is similar to the first one, except thesolutions of the first layer are not considered as candidates for thesecond layer. With this procedure all the individuals are sorted inlayers with a descending order for objective function merits. Thus,considering both fitness functions, solutions in the first layer aremore creditable than solutions in the second layer, and so on.

The number of parents in each population is set to be 10% of thenumber of the whole population, which leads to selecting 10parents from the initial random population. Since the best indivi-duals are meant to be selected as parents, solutions sorted in thefirst layer are considered. If there are not enough individuals in thefirst layer, solutions sorted in the second layer are considered,and so on.

4.1.4. Cross-over and mutationSince both chord length and flow angle are described with

three decimal digits and there are certain physical constraints onthe range of these numbers, the cross-over in this study will beperformed as shown in Fig. 7. As it is observed in this depiction,the child takes its chord length from one parent and its flow anglefrom the other. From each pair of parents two children are

Table 3Characteristics of the trained multi-layer perceptron networks.

Artificial Neural Network for exergyefficiency

Network type MLP with 1 hiddenlayer

Training algorithm Back propagation L-MNumber of neurons in hiddenlayer

15

MSE of training 0.0654125MSE of validation 0.0584269MSE of testing 0.0975148Regression of training 0.99954Regression of validation 0.99847Regression of testing 0.99896

Artificial Neural Network for dissipatedexergy

Network type MLP with 1 hiddenlayer

Training algorithm Back propagation L-MNumber of neurons in hiddenlayer

15

MSE of training 0.0864601MSE of validation 0.0657832MSE of testing 0.0672287Regression of training 0.99972Regression of validation 0.99979Regression of testing 0.99986

Fig. 6. The performance of the trained MLP for predicting dissipated exergy.

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72 69

generated, this approach will generate children with new proper-ties which may not be generated in the initial random population.

In the process of mutation some consideration must be made,first, the mutation in the digit of gen must be in the range ofpreviously mentioned physical constraints, moreover, the muta-tion should not take place on gens defining the second and thirddecimal digits, due to the fact that mutation on the second andthird decimal digits does not change the fitness function valuessignificantly.

4.1.5. Selecting new population and number of iterationsThe last step of every evolutionary cycle will be selecting

individuals for the next generation, to achieve this objectiveseveral approaches can be utilized. In this study a combinationof parents and children with the highest merits are selected inorder to prevent losing individuals with high values of fitnessfunction. The number of iterations for each section of blade is setto 100, which implies that after 100 iterations solutions sorted inthe first layer are presented as Pareto optimal set for each section.

5. Results and discussion

Since the design of a 10 m blade usually requires more than5 blade sections, and due to the fact that ANNs and specificallyMLPs possess the possibility of rather accurate interpolation,characteristics of 10 blade sections are obtained through theMOGA. The results of the algorithm for each section of the bladeare shown in Figs. 8–12, which represent the design characteristics

tailored for a 10 m blade. Note that these plots delineate the Paretooptimal set (not the Pareto front) after 100 iterations for eachsection, and according to the Pareto optimality concept all of thesuggested combinations of flow angle and chord length are equallymeritorious. Foremost, it is observed that although all initialpopulations are generated within the specified ranges, the MOGAenforces more confined ranges for both chord length and flowangle. The next discernible point in the plots deals with the overallparadigm of the positioning of the solution sets for differentsections, since the flow properties of the radii 1 and 2, 3 and 4,5 and 6, 7 and 8, and 9 and 10 m are more likely similar, ananalogous pattern of positioning of the optimal solution points isdetectable for each mentioned pair of sections.

Moreover, in order to evaluate the performance of a rotorconsisting of blades designed through second law analysis, an opensource BEM code ‘Qblade’ is employed (⟨http://www.q-blade.org,2013⟩). The software is capable of conducting performance analysisfor various rotor configurations which provides the opportunity ofcomparison between different blade designs. ‘Qblade’ utilizes polardata profiles to investigate a rotor performance through an iterativeprocess.

Three different blade designs with capricious selection of chordlength and twist angle among the second law optimization resultsare considered to be compared with blade configurations obtainedfrom conventional design methods targeting the power coefficient.The customary methods utilized for defining the geometricalcharacteristics of the blades include linear distribution, Betzmethod, and Schmitz method for chord length determinationand linear distribution, optimal lift to drag ratio, and simultaneous

Fig. 7. The pattern of cross-over for an example of a possible solution in the form of a chromosome.

Fig. 8. The Pareto optimal set suggested by MOGA for the section positioned at r¼1and r¼2.

Fig. 9. The Pareto optimal set suggested by MOGA for the section positioned at r¼3and r¼4.

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stall for twist angle selection. Table 4 tabulates the informationabout the utilized methods in each design. Note that all the bladedesigns are conducted in a manner to achieve the best perfor-mance at a tip speed ratio equal to 6.5. Fig. 13 contains power

coefficients versus tip speed ratio for the aforementioned designedblades demonstrating the domination of the second law designs inmajority of the tip speed ratios. It is perceived that second law-based blade designs possess average advantages approximatelyequal to 8.5%, 15.4%, and 12.1% over configurations 1, 2, and 3,respectively. Furthermore, it is observed that despite the randomselection of the characteristics for second law designs, homolo-gous values of Cp are achieved via second law optimized blades,which posits the idea that employing Pareto optimal concept hasled to rather equally creditable solutions.

6. Conclusion

In this study the second law analysis of energy conversion inwind turbine airfoils is conducted deploying a 2D incompressibleunsteady CFD solver. Several NREL airfoil sections are evaluated byexergetic performance characteristics under low Reynolds numberflows, leading to selection of an airfoil family for blade investiga-tions. Each simulation case implements a distinct grid since theindependency of the solution to the grid is obtained by adaptingthe mesh around the airfoil maintaining the same yþ require-ments. Neural networks are trained to represent objective func-tions of exergy efficiency and dissipated exergy in the multi-objective genetic algorithm the results of which illustrate a moreprecise, confined expression of the combinations of geometricalcharacteristics for different sections along the blade. The Paretooptimal solution sets represent a beneficiary trade-off selectionbetween more efficiency and solidity and less waste in energyproduction opportunities. Employing a commercial open sourceBEM code further reveals the worthiness of the blades designed bythe second law analysis method in comparison with the bladeconfigurations resulting from the usual design methods. An exergyanalysis approach is believed to be a useful tool in assessing the

Fig. 10. The Pareto optimal set suggested by MOGA for the section positioned atr¼5 and r¼6.

Fig. 11. The Pareto optimal set suggested by MOGA for the section positioned atr¼7 and r¼8.

Fig. 12. The Pareto optimal set suggested by MOGA for the section positioned atr¼9 and r¼10.

Table 4Characteristics for rotor blade configurations under study.

Design name Chord distribution Twist distribution

Second Law Config.1, 2, 3 Pareto optimal sets Pareto optimal setsConfig.1 Linear distribution Linear distributionConfig.2 Betz equation Optimal lift to dragConfig.3 Schmitz equation Simultaneous stall

Fig. 13. Performance coefficients comparison between different second lawdesigned rotors and rotor designs obtained from conventional methods.

S.M. Mortazavi et al. / J. Wind Eng. Ind. Aerodyn. 136 (2015) 62–72 71

performance of wind turbine blades since it provides substantialinsights over the quality of energy conversion.

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