The goal of this paper is to employ a multiobjective genetic algorithm (MOGA) to optimize the shape of a wellknown wind turbine airfoil S809 to improve its lift and drag characteristics, in particular to achieve two objectives, that is, to increase its lift and its lift to drag ratio. The commercially available software FLUENT is employed to calculate the flow field on an adaptive structured mesh using the ReynoldsAveraged NavierStokes (RANS) equations in conjunction with a twoequation
With recent emphasis on emissionfree renewable energy, wind energy has taken a center stage in recent years with exponential growth in deployment of windturbines worldwide. Among windturbines, horizontalaxiswindturbines (HAWTs) are mostly deployed for power generation in Megawatt range. It is well established that the power generated by a HAWT is a function of the number of blades, the
The present paper focuses on the optimization of most wellknown NREL airfoil, known as the S809 airfoil. This airfoil is 21% thick laminar flow airfoil whose design and experimental results are given in [
This paper presents shape optimization of S809 airfoil using a multiobjective genetic algorithm (MOGA). The commercially available software FLUENT is used for calculation of the flow field using the ReynoldsAveraged NavierStokes (RANS) equations in conjunction with a twoequation
Genetic algorithms are a class of stochastic optimization algorithms inspired by the biological evolution. In GA, a set or generation of input vectors, called
Initialization: randomly create
Evaluation: evaluate the fitness of each individual (airfoil) by calculating the fitness or objective function (e.g., lift coefficient or lift to drag ratio).
Natural selection: remove a subset of the individuals. Often the individuals that have the lowest fitness value are removed; although culling, the removing of those individuals with similar fitness is sometimes performed.
Reproduction: pick pairs of individuals to produce an offspring. This is often done by roulette wheel sampling; that is, the probability of selecting some individual
A crossover function is then performed to produce the offspring. Generally, crossover is implemented by choosing a crossover point on each individual and swapping
Mutation: randomly alter some small percentage of the population.
Check for convergence: if the solution has converged, return the best individual observed. If the solution has not yet converged, label the new generation as the current generation and go to step 2. Convergence is achieved after a certain number of generations when the fitness value does not change for a number of consecutive generations (generally 3 to 5).
Illustration of the general crossover function in GA.
For many design problems, it is desirable to achieve, if possible, simultaneous optimization of multiple objectives [
First, the population is initialized based on the constraints. The population is then sorted based on nondomination into various fronts, the first front being completely the nondominant set in the current population and the second front being dominated by the individuals in the first front only and so on for the other fronts. Individuals (airfoils) in each front are assigned rank (fitness) values based on the front to which they belong. Individuals in first front are assigned a given fitness value and individuals in the second front are assigned another fitness value and so on. In addition to the fitness value, a new parameter called
At 0th generation: a random parent population of airfoils
At
Termination: the procedure is terminated when convergence criterion is met. The convergence is considered achieved when the two objective values do not change from one generation to the other; generally, the algorithm termination condition is applied when no improvements are observed after a number of consecutive generations.
The java code package utilized in this study is called jMetal. It is a Javabased framework for multiobjective optimization using metaheuristics. It is easy to use and is flexible and extensible [
The airfoil shapes are parameterized using Bezier curves. Bezier construction is a curve fitting method for constructing freeform smooth parametric curves which are widely used in CAE design data structure modelling and computer graphics application [
Each airfoil is divided into top and bottom boundary curves by the airfoil chord joining its leading edge and trailing edge. Considering the complexity of S809 airfoil shape, 12 control points are used for parameterization. For an airfoil curve, two points are fixed since they represent the leading and trailing edge of the airfoil. The intermediate points are allowed to move within the specified boundaries. A maximum thickness constraint of 19%–22% of chord is imposed on the airfoil. The constraints applied to the Bezier control points are shown in Table
Coordinates of the control points used in airfoil parameterization.
Upper limit  Lower limit  Upper limit  Lower limit  

Top 

0.020  0.000  Bottom 

0.020  0.000 

0.065  0.025 

0.100  0.060  

0.340  0.300 

0.300  0.260  

0.400  0.360 

0.400  0.360  

0.500  0.460 

0.480  0.440  

0.850  0810 

0.770  0.730  

0.030  0.010 

−0.013  −0.025  

0.090  0.070 

−0.053  −0.065  

0.128  0.108 

−0.125  −0.145  

0.128  0.108 

−0.125  −0.145  

0.128  0.108 

−0.125  −0.145  

0.045  0.025 

0.020  0.008 
This section presents the optimization process for S809 airfoil using the multiobjective genetic algorithm (MOGA). An optimization procedure is established by coupling the MOGA code coupled with the mesh generation code “ICEM” and the CFD solver “FLUENT” as shown in Figure
Schematic of information flow in the optimization process.
The individuals in each generation of MOGA are represented by a set of control points, which generate the airfoil shape through the Bezier curve. The mesh around the airfoil shape is generated using the grid generation software ICEM, which is used to create a twodimensional structured or unstructured mesh as an input to CFD solver FLUENT. FLUENT is used to calculate the flow field for given flow conditions. Using the flow field data, FLUENT calculates the lift coefficient
NSGAII [
The multiobjective optimization algorithm is performed with two objective functions. The first objective is to minimize 10/
The commercially available software “ICEM” is used to generate a structured Cmesh around the NREL S809 airfoil. A reply file is scripted to automatically generate mesh around different airfoils in a given generation. The reply file is edited to be able to generate mesh based on different airfoil shapes. Figure
Structured Cgrid around NREL S809 airfoil: (a) entire mesh in the computational domain and (b) zoomedin view of the mesh near the airfoil.
The commercial software FLUENT is employed to calculate the lift coefficient and the drag coefficient of an individual airfoil in a generation. Because of low Mach number
Computed fully turbulent lift coefficients and the experimental lift coefficients.
AoA 
Comp. 
Exp. 

0.0  0.12529  0.07 
2.1  0.35428  0.3 
4.1  0.55472  0.55 
6.1  0.75412  0.79 
8.2  0.94169  0.9 
10.1  1.0678  0.94 
11.2  1.1046  0.93 
Computed fully turbulent drag coefficients and experimental drag coefficients.
AoA [deg.]  Comp. 
Exp. 

0.0  0.012006  0.0022 
2.1  0.012824  0.0037 
4.1  0.015248  0.005 
6.1  0.017615  0.0063 
8.2  0.021507  0.0096 
10.1  0.027757  0.0231 
11.2  0.03413  0.0236 
Variation of lift coefficient with angle of attack.
Variation of drag coefficient with angle of attack.
It can be seen from Figure
A journal file is written for autorunning of FLUENT in the optimization process. Temperature and static pressure are defined at standard sea level condition and are taken as 288.16 K and 101325 Pa, respectively. Both values are quite reasonable for a wind turbine whose maximum altitude does not exceed a few hundred meters. Density is taken as
Windturbines generate power due to rotation of the blades. Blade Element Momentum (BEM) theory is used to determine the generated power [
Velocities in the rotor plan of the wind turbine [
Using the published data in [
Effective angle of attack and relative velocity for
AoA 



0.23  4.871484  10.95754347 
0.28  5.33559  12.49505605 
0.33  5.507533  14.12325328 
0.38  5.695772  15.81257285 
0.43  5.65495  17.54835289 
0.48  5.481622  19.31840765 
0.53  5.285769  21.11286633 
0.58  5.113385  22.9245775 
0.63  4.943813  24.74883296 
0.68  4.799144  26.58353782 
0.73  4.692116  28.4262618 
0.78  4.619902  30.27473603 
0.83  4.540881  32.12794747 
0.88  4.399174  33.98431527 
0.93  4.133288  35.84205712 
0.98  3.397045  37.68558576 
As mentioned before, in the application of multiobjective genetic algorithm (MOGA), we optimize the S809 airfoil at three locations of the blade, 23%, 58%, and 98% locations from the center of the rotor which correspond to the root, mid, and tip section of the blade, respectively. We consider the free stream wind velocity of 6.7 m/s, rotational speed of 72 rpm, and pitch setting of 5 deg. We set two objectives: minimize 10/
Shape evolution of airfoil and variation in drag to lift ratio at 23% span location in various generations of MOGA.
Shape evolution of airfoil and variation in drag to lift ratio at 58% span location in various generations of MOGA.
Shape evolution of airfoil and variation in drag to lift ratio at 98% span location in various generations of MOGA.
Dominated solutions in Pareto front approximation for airfoils at 23%, 58%, and 98% span locations.
23% span airfoil
58% span airfoil
98% span airfoil
Comparison of original airfoil and optimized airfoil (23% span): (a) shape and (b) pressure distribution.
Comparison of original airfoil and optimized airfoil (58% span): (a) shape and (b) pressure distribution.
Comparison of original airfoil and optimized airfoil (98% span): (a) shape and (b) pressure distribution.
A comparison between the present optimized airfoil shapes using MOGA and those obtained by Ritlop and Nadarajah [
Comparison of
Present results at 23% span  Ritlop and Nadarajah [ 
Present results at 58% span  Ritlop and Nadarajah [ 
Present results at 98% span  Ritlop and Nadarajah [  

Original 
0.64528  0.64  0.68023  0.675  0.492  0.49 
Optimal 
0.7461  0.76  0.78274  0.78  0.63  0.68 

15.62%  18.75%  15.06%  15.55%  28.04%  38.78% 
Comparison of
Present results at 23% span  Ritlop and Nadarajah [ 
Present results at 58% span  Ritlop and Nadarajah [ 
Present results at 98% span  Ritlop and Nadarajah [  

Original 
40.17289  45.5  43.22983  47  37.77  36.2 
Optimal 
48.48394  50.8  49.01435  51.8  48.89  47 

20.688%  13%  13.38%  10%  29.44%  29.83% 
Comparison of present optimized airfoil shapes with those of Ritlop and Nadrajah [
23% span airfoil
58% span airfoil
98% span airfoil
In this paper, a multiobjective genetic algorithm (MOGA) has been employed to optimize the shape of a wellknown wind turbine airfoil S809 to improve its lift and drag characteristics, in particular to achieve two objectives, that is, to increase its lift and its lift to drag ratio. The commercially available software FLUENT is employed to calculate the flow field on an adaptive structured mesh using the ReynoldsAveraged NavierStokes (RANS) equations in conjunction with a twoequation
The authors declare that there is no conflict of interests regarding the publication of this paper.