Aerodynamic Optimization of NACA64A410 Blade Aerofoil for...

Aerodynamic Optimization of NACA64A410 Blade Aerofoil for Small Wind Turbine Application with Ansys Fluent

Tariku AchamyelehDepartment of Mechanical Engineering,

Faculty of Technology, Debre Tabor University, Debre Tabor, Ethiopia [email protected]

Mulu Bayray

School of Mechanical and Industrial Engineering, Ethiopian Institute of Technology- Mekelle,

Mekelle University, Mekelle, Ethiopia [email protected]

Abstract—The aim of this paper is to foster wind turbine blade design optimization using Genetic Algorithm considering NACA64A410 as a case. The design optimization of turbine blades using GA with regards to different objective functions are described and found supportive one another. NACA64A410 aerofoil shape is modeled as baseline aerofoil using fifth order Bezier curve functions with acceptable error to find control points that to shape of the aerofoil. Design of Experiment is planned for eight design variables with three levels each. 27 analyses are conducted with a varying control point values using ANSYS Fluent 14.0 workbench. Lift and drag coefficients are recorded as an output for each analyses. The objective function is formulated as a minimization problem of drag-to-lift coefficient ratio subjected to bounded constraints using 8 control points’ y-coordinate values. Using MINITAB-, control point values, as an input and drag- to-lift coefficient ratio, as response, are modeled with full quadratic surface response model function which is later optimized in MATLAB GA Toolbox. The optimization showed that drag-to-lift coefficient ratio is minimized taking control points as parameters of the minimization objective function. About 16.5% drag-to-lift reduction is achieved by implementing the aerodynamic shape optimization methodology that has been used in this research. Finally, it’s recommended that one can model aerofoil using Bezier curve modeling technique and integrate it with GA for finding optimal value of objective function of any sort.

Keywords: Aerofoil, Bezier Curve, Response Surface Model, Optimization, Genetic Algorithm

I. INTRODUCTIONEnergy and global warming are one of the most challenging problems in today’s world. Fossil fuel prices are increasing day by day because of limited resources. Natural balance of earth is changing because of global warming. One of the main reasons of this change is burning too much fossil fuel. Therefore, alternative energy sources are needed. These are the reasons why wind energy becomes so important. Wind source is free and clean. Wind turbine technology is growing and wind is getting to be one of the best alternative energy sources, today. As part of this wind energy growth, Ethiopian government has given attention to this area for the cleaner energy development. Ashegoda, Adama I and II mega projects are exemplary works that show the state’s commitment towards carbon free energy source development. Such kind of national move has motivated researchers and academicians to devote their time for the enhancement of the theme. Ethiopian Institute of Technology- Mekelle is playing its role in consulting and supervising national wind power projects at Adama II wind project. Moreover, projects and researches are also being done on adoption, modification and optimization of wind energy sources by school of Mechanical and Industrial Engineering. NACA66(2)415 and NACA64A410 wind turbine blades were manufactured for small scale power generation purpose. The two successive projects have shown progressive improvements especially in the manufacturing of the blades.

Though the achievement in manufacturing of the blades is huge, a lot more is expected in optimizing aerodynamic performance of the blades. Hence, in this thesis work, it is aimed to study a small scale horizontal axis wind turbine blade through computational fluid dynamics (CFD) analysis in order to optimize aerodynamic performance by considering NACA64A410 as a case.

1426© IEOM Society International

Proceedings - International Conference on Industrial Engineering and Operations Management, Kuala Lumpur, Malaysia, March 8-10, 2016

II. LITERATURE REVIEWDesign and optimization of wind turbines are performed by several authors.

Ozge Polat and Ismail H. Tuncer [1] have tried to show that, considering three standard NACA series aerofoils, it was possible to optimize a wind turbine blade profile that increased the power generation by 10%. In the paper, the aerodynamic shape optimization of the blades was done at specific wind speed, rotor speed, rotor diameter and number of blades. The potential flow solver with a boundary layer model, XFOIL, provides aerodynamic sectional loads. The power production of the turbine which was defined as an objective function was calculated. Optimization variables were selected as the sectional chord length, the sectional twist and the blade profile at the root, mid and tip regions of the blades. The proposed geometrical model, using circular arcs and Bezier polynomials, proved to be very effective for the modeling of turbine blades.

Figure 1 Blade geometry before (Top) and after optimization (Bottom)[1]

Shen M. et al [2] have defined a two dimensional multiple-peak contour using Genetic Algorithm to search for maximum value of the problem. With two different Mach numbers, the optimization method was used to modify the blade mentioned before at the cases of design condition: Mach 1 = 0.828 and a transonic condition: Mach 2 = 1.06. Comparisons between original and modified blade shapes are given in Figure 2 (a) and (b). The loss coefficient was decreased from 0.0359 to 0.0275 at the case of Mach=0.828, and decreased from 0.515 to 0.231 at the case of Mach = 1.06.

(a) (b)

Figure 2 Blade shape comparison, design (a) and transonic condition (b) [2]

G.B. Eke and J.I. Onyewudiala [3] studied the role of a well-designed turbine blade for having an aerodynamically efficient rotor. The study tried to minimize the cost of energy of a wind turbine rotor by 1.9 % by considering weight of the rotor, chord length, cross-section, and mass of blade as parameters though the Annual Energy Production of the optimized rotor is reduced by about 0.8%. The trade-off has shown a total reduction of cost of energy by 1.8%.

Giannakoglou K. C [4] has validated that a wind turbine blade can be optimized with the help of GA representing the parent aerofoil using 17 parametric geometric coding and fourth order spline curves. In the paper, it was found that surface pressure distribution was as close as possible to the targeted value after thirty generation. The modeling and the optimal solution are shown in the figure below.



(a) (b)

Figure 3 Model of initial aerofoil (a) and optimized aerofoil (b) [4]

In the paper of Chong P. and Cheong G. [5], the approximation of aerofoil shape in cubic Bezier curve and quintic Bezier curve in manual method are discussed. Both the cubic and quintic Bezier curves approximations are able to satisfy the tolerance of 0.1 mm. However, cubic Bezier curve does not have sufficient degree of freedom to capture the shape of highly curve region. Quintic Bezier curve provides second derivative control, whereby the shape of highly curve region can be captured.

Optimization study was conducted with the aim of producing at least two distinct optimized wind turbine rotors for a 1.5 MW wind turbine, where the shape of the rotor was given as much freedom as possible. In the course of the study, conclusion have been reached that Genetic Algorithm utilizing a partially constrained Bezier curve model that still allowed for large variability in aerofoil shape was successful in producing unconventional rotor configurations and aerofoil designs which still resulted in excellent predicted performance.[ 6]

According to Grin D. A. [7], BEM method and Genetic Algorithm are used for design of ART-2B Rotor Blades. Three different aerofoil families in NREL S-Series aerofoils are used separately for design and only chord and twist is optimized. In reference [8], blade design trade-offs are studied for aerofoils with different stall characteristics by using BEM method and genetic algorithm. In this study, cost is also included to the design as a constraint into optimization. Different than these approaches, design is performed by cost optimization as in reference [9], including structural constraints in reference [10] and control in reference [11].

Site specific wind turbine design studies are performed including almost all subjects of the wind turbine design process as it is described in reference [12]. This study is one of the most detailed wind turbine design process studies. The optimization is aimed to produce as much power as possible with minimum cost of energy.

III. RESEARCH METHDOLOGIES

The methodology used in this research has followed the following basic three steps. These are: existing aerofoil modeling, analysis, and optimization and validating the model.

A. Modeling of the Parent Aerofoil Since the optimization process starts from the existing aerofoil i.e. NACA64A410, the aerofoil will be represented with Bezier curve representation methods. The parent aerofoil, NACA64A410, coordinates are generated from aerofoil plotter websites [13]. The two sides of the aerofoil are represented with 50 points i.e. 26 points for upper and lower sides. Starting and end points for both upper and lower curves are fixed and shared. The 26 clouds of points in each side are converted to 6 control points that can approximate each side of the parent aerofoil. The initial and end control points are fixed to specify the chord length.

It is known that, Bezier curve of order 5 can be expressed as

B(t) = (1-t)5*P0 + 5(1-t)4*t*P1 + 10(1-t)3*t2*P2+ 10(1-t)2*t3*P3 + 5(1-t)*t4*P4 + t5*P5 (1)



B. Aerodynamic Performance Analysis of Aerofoils From an aerodynamic shape optimization point of view, the system is basically the aerofoil geometry that has to be optimized for a specific operating condition. The design points are the design variables that completely define the aerofoil geometry. As discussed above, the design variables constitute the y-ordinates of the 8 Bezier control points that control the shape of the upper and lower surfaces of the aerofoil, and the angle of attack.

The design space is the region bounded by the upper and lower limits of the design variables. This implies that the design variables are allowed to vary only within the limits defined by the design space. It is defined such that, overly unusual or unrealistic shapes are not attained.

The design matrix is formed by concatenating the values of the design variables at all levels. In order to do so, the design space needs to be discretized into levels which are equal to the desired number of computer simulations to be performed. The design space as described above is the region bounded by the upper and lower limits of the design variables. These are the y-ordinates of the 8 control points (four control points for each surface) and the angle of attack.CPs, 2 through 5, control the upper surface while CPs, 8 through 11, control the lower surface of the aerofoil.

For this, the lower and upper limits for each of the 8 control points and the angle of attack are defined. The lower limit of the control points is taken to be 25% of the baseline values and the upper limit is taken to be 25% above the baseline values. The lower and upper limits of the angle of attack are case dependent varying between -1 and 1oas the theoretical minimum Cd/Cl of approximated NACA64A410 aerofoil is at angle of attack of 0o.

The range of each of the design variables DVRange (the design space) is the difference between the upper, DVUpper, and lower limits, DVLower, of the design variable. This range is discretized into equal number of levels which is equivalent to the number of experiments to be performed. Using MINITAB DoE creation capability, the minimum number of experimental runs needed for 9 factors with 3 levels each is 27. Hence DoE is generated considering eight design variables, i.e. eight control points and three levels of the design matrix i.e. lower limit, baseline and upper limit.

27 aerofoil profiles are created using the control points and modeled in CATIA. NACA64A410 aerofoil will also be created as a baseline aerofoil using cloud of points extracted from aerofoil plotter websites. In ANSYS-Fluent workbench 14.0, CATIA file is exported and a simulation model will be created on ANSYS FLUENT. Computational parameters such as simulation type, turbulent model type, fluid media, temperature, kinematic viscosity, Reynolds number, density, pressure and wind speed will be specified.

C. Optimizing using Genetic Algorithm

Aerofoil generation process and the search for the optimal aerofoil design towards the predetermined objective function should be backed up with an algorithm which will go for the best solution generation after generation.

Drag-to-lift coefficient ratio maximization objective function found from response surface model, constraints and numberof generations are specified and run with MATLAB GA Toolbox for searching the optimal parametric values.

The optimized aerofoil parameters will be specified and once again will be analyzed with ANSYS FLUENT for validation.

IV. RESULT AND DISCUSSION

A. Modeling of the Existing Aerofoil

It is known that the root of wind turbine blade has structural strength than its aerodynamic importance. For aerodynamic analysis purpose NACA64A410 was examined at its 70% of the rotor radius. At 70% of the rotor diameter, the chord length is 77mm. Hence, from aerofoil plotter, the cloud of points of NACA64A410 was generated with a chord length of 77mm [15].

The generated upper and lower curves’ clouds of points are shown in Table 1. Total number of generating points in the output of the plotter is 26 points for each upper and lower curve.



In representing a curve with 5th order Bezier curve, we need to find the control points i.e. p1, p2, p3 and p4 from calculated cloud of points (calculated cloud of points are usually 0 < t < 1).

From Table 1, we need to pick only six clouds of points at equidistance out of the 26 points of both upper and lower side of the aerofoil profile.

Table 1 CURVE PROFILE COORDINATES

Above curve profile Lower Curve profile X Y t X Y t C0=P0 0 0 0 C6=P0 77 0.01617 0

0.2695 0.69454 0.04 73.10919 -0.03696 0.04 0.44814 0.85624 0.08 69.21992 -0.05852 0.08 0.81543 1.11727 0.12 65.33604 -0.10164 0.12 1.75252 1.61315 0.16 61.48373 -0.17633 0.16

C1= f 3.65673 2.33618 0.2 C7 = f 57.65298 -0.3542 0.2 5.5671 2.97605 0.24 53.81684 -0.5852 0.24 7.49749 3.3726 0.28 49.98455 -0.83622 0.28 11.356 4.13182 0.32 46.15611 -1.09186 0.32 15.2229 4.71702 0.36 42.33075 -1.33672 0.36

C2= g 19.096 5.16285 0.4 C8=g 38.50847 -1.55848 0.4 22.9722 5.49087 0.44 34.6885 -1.74482 0.44 26.8507 5.70878 0.48 30.8693 -1.87572 0.48 30.7307 5.81504 0.52 27.04933 -1.93886 0.52 34.6115 5.79194 0.56 23.22782 -1.95349 0.56

C3= h 38.4915 5.65488 0.6 C9=h 19.404 -1.92423 0.6 42.3693 5.4208 0.64 15.5771 -1.85262 0.64 46.2439 5.10048 0.68 11.74404 -1.72788 0.68 50.1155 4.70162 0.72 7.90251 -1.53692 0.72 53.9832 4.2196 0.76 5.9829 -1.47763 0.76

C4= j 57.847 3.6806 0.8 C10=k 4.04327 -1.22584 0.8 61.7163 3.05459 0.84 2.09748 -0.96327 0.84 65.564 2.32386 0.88 1.10957 -0.74613 0.88 69.3801 1.56926 0.92 0.70686 -0.61292 0.92 73.1908 0.79156 0.96 0.5005 -0.52206 0.96

C5= P5 77 0.01617 1 C0=P5 0 0 1

Picked six clouds of points with t division are:

Table 2 PICKED UPPER SIDE POINTS

X Y t C0 = P0 0 0 0 C1 = f 3.65673 2.33618 0.2 u C2 = g 19.096 5.16285 0.4 v C3 = h 38.4915 5.65488 0.6 w C4 = j 57.847 3.6806 0.8 r C5 = P5 77 0.01617 1

Table 3 PICKED LOWER SIDE POINTS

X Y t C6 = P0 77 0.01617 0 C7 = f 57.653 -0.3542 0.2 u C8 = g 38.5085 -1.55848 0.4 v C9 = h 19.404 -1.92423 0.6 w C10 = j 4.04327 -1.22584 0.8 r C11= P5 0 0 1

By now, all input data are created for our fifth order Bezier curve formula. In Bezier, the control points are the driving points to create a curve [14]. We need control points of the upper and lower aerofoil profile to create an aerofoil in CATIA which later will be used as design parameters in the optimization process.

The transformed matrix of equation (1) is:



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Where, c = 5(1-u)4*u*P1 + 10(1-u)3*u2*P2 + 10(1-u)2*u3*P3 + 5(1-u)*u4*P4

d = 5(1-v)4*v*P1 + 10(1-v)3*v2*P2 + 10(1-v)2*v3*P3 + 5(1-v)*v4*P4

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k = 5(1-r)4*r*P1 + 10(1-r)3*r2*P2 + 10(1-r)2*r3*P3 + 5(1-r)*r4*P4

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The corrected aerofoil coordinate values of upper and lower curve are presented below on Table 4and 5, respectively.

Table 4 CORRECTED CONTROL POINTS FOR UPPER PROFILE

Des. CP X Y ZP0 CP1 0 0 0 P1 CP2 0 2.8 0 P2 CP3 17.2946112 8.5 0 P3 CP4 41.0282425 6.6 0 P4 CP5 57.0427492 4.5 0 P5 CP6 77 0.016170 0

Table 5 CORRECTED CONTROL POINTS FOR LOWER PROFILE

Des. CP X Y Z P6 CP7 77 0.01617 0 P7 CP8 56.531795 1.12 0 P8 CP9 40.94579 -3.28 0 P9 CP10 17.83576 -2.78 0 P10 CP11 0 -2.1 0 P11 CP12 0 0 0

B. Aerodynamic Performance Analysis The parameterization of the aerofoil was carried out using Bezier control points. The y-ordinates of the control points 2 through 5 and 8 through 11 form the vector of design variables.



Figure 4 Range of Bezier control points (Design variables)

In addition the angle of attack is taken as the ninth design variable. The range for each DV was obtained by defining an upper and a lower limit. These were taken as 25% above and below the baseline values respectively.

The baseline, the upper and lower limit values of the design variables are as follows:

Table 6 BASELINE AND UPPER AND LOWER LIMIT VALUES OF THE DESIGN VARIABLES DV CP Baseline Values Lower Limit Upper Limit 1 2 2.8 2.24 3.5

2 3 8.5 6.8 10.625

3 4 6.6 5.28 8.25

4 5 4.5 3.6 5.625

5 8 1.12 0.88 1.375

6 9 -3.28 -4.125 -2.64

7 10 -2.78 -3.475 -2.224

8 11 -2.1 -2.625 -1.68

As the GA will let us find the optimal design parameters 27 experiments are run with varying control point values as an input and lift coefficient, drag coefficient and drag-to-lift ratio as a response. The experimental plan is presented on Table 7.

Table 7 DESIGN OF EXPERIMENT PLAN Runs DV1 DV2 DV3 DV4 DV5 DV6 DV7 DV8

EiT-M001 2.24 6.8 5.28 3.6 0.896 -2.624 -2.224 -1.68 EiT-M002 2.24 6.8 5.28 3.6 1.12 -3.28 -2.78 -2.1 EiT-M003 2.24 6.8 5.28 3.6 1.4 -4.1 -3.475 -2.625 EiT-M004 2.24 8.5 6.6 4.5 0.896 -2.624 -2.224 -2.1 EiT-M005 2.24 8.5 6.6 4.5 1.12 -3.28 -2.78 -2.625 EiT-M006 2.24 8.5 6.6 4.5 1.4 -4.1 -3.475 -1.68 EiT-M007 2.24 10.625 8.25 5.625 0.896 -2.624 -2.224 -2.625 EiT-M008 2.24 10.625 8.25 5.625 1.12 -3.28 -2.78 -1.68 EiT-M009 2.24 10.625 8.25 5.625 1.4 -4.1 -3.475 -2.1 EiT-M010 2.8 6.8 6.6 5.625 0.896 -3.28 -3.475 -1.68 EiT-M011 2.8 6.8 6.6 5.625 1.12 -4.1 -2.224 -2.1 EiT-M012 2.8 6.8 6.6 5.625 1.4 -2.624 -2.78 -2.625 EiT-M013 2.8 8.5 8.25 3.6 0.896 -3.28 -3.475 -2.1 EiT-M014 2.8 8.5 8.25 3.6 1.12 -4.1 -2.224 -2.625 EiT-M015 2.8 8.5 8.25 3.6 1.4 -2.624 -2.78 -1.68 EiT-M016 2.8 10.625 5.28 4.5 0.896 -3.28 -3.475 -2.625 EiT-M017 2.8 10.625 5.28 4.5 1.12 -4.1 -2.224 -1.68 EiT-M018 2.8 10.625 5.28 4.5 1.4 -2.624 -2.78 -2.1 EiT-M019 3.5 6.8 8.25 4.5 0.896 -4.1 -2.78 -1.68 EiT-M020 3.5 6.8 8.25 4.5 1.12 -2.624 -3.475 -2.1 EiT-M021 3.5 6.8 8.25 4.5 1.4 -3.28 -2.224 -2.625 EiT-M022 3.5 8.5 5.28 5.625 0.896 -4.1 -2.78 -2.1 EiT-M023 3.5 8.5 5.28 5.625 1.12 -2.624 -3.475 -2.625 EiT-M024 3.5 8.5 5.28 5.625 1.4 -3.28 -2.224 -1.68 EiT-M025 3.5 10.625 6.6 3.6 0.896 -4.1 -2.78 -2.625 EiT-M026 3.5 10.625 6.6 3.6 1.12 -2.624 -3.475 -1.68 EiT-M027 3.5 10.625 6.6 3.6 1.4 -3.28 -2.224 -2.1



For ease of comparison and data modeling, the 27 aerofoils are analyzed with AoA of zero.

The minimum Cd/Cl values in each run are recorded and presented as follows:

Table 8 LIFT-DRAG COEFFICIENTS Runs Cl Cd Cd/Cl EiT-M001 0.024780 0.000134 0.005400 EiT-M002 0.024142 0.000134 0.005558 EiT-M003 0.023360 0.000127 0.005450 EiT-M004 0.031499 0.000138 0.004395 EiT-M005 0.030848 0.000127 0.004114 EiT-M006 0.030907 0.000122 0.003956 EiT-M007 0.040162 0.000145 0.003622 EiT-M008 0.040343 0.000134 0.003312 EiT-M009 0.039610 0.000129 0.003251 EiT-M010 0.033403 0.000141 0.004232 EiT-M011 0.033962 0.000147 0.004328 EiT-M012 0.036038 0.000157 0.004359 EiT-M013 0.028784 0.000122 0.004242 EiT-M014 0.029271 0.000133 0.004537 EiT-M015 0.032205 0.000135 0.004193 EiT-M016 0.029890 0.000124 0.004139 EiT-M017 0.031236 0.000143 0.004567 EiT-M018 0.033380 0.000134 0.004011 EiT-M019 0.031223 0.000141 0.004529 EiT-M020 0.033031 0.000139 0.004199 EiT-M021 0.033918 0.000154 0.004537 EiT-M022 0.032913 0.000141 0.004269 EiT-M023 0.034715 0.000144 0.004139 EiT-M024 0.036467 0.000156 0.004274 EiT-M025 0.028140 0.000132 0.004687 EiT-M026 0.030769 0.000143 0.004645 EiT-M027 0.031706 0.000155 0.004896

C. Optimization Using GA

From the aerodynamic shape optimization perspective with 8 design variables, the number of coefficients are = 45.

Using MINITAB 16, surface response was analyzed for the DOE presented in Table 7.

Response Surface Regression: Cd/Cl versus C1, C2, C3, C4, C5, C6, C7, and C8 Where C1 is DV1, C2 is DV2, C3 is DV3, C4 is DV4, C5 is DV5, C6 is DV6, C7 is DV7, and C8 is DV8. The data analysis on MINITAB has resulted in:

S = 0.000111495 R-Sq = 99.84% R-Sq(adj) = 95.82%

The SRM will have a quadratic function formula

y = Cd/Cl = 0.0128702 - 6.05E-04*X(1) + 0.000282908*X(2) - 0.00140171*X(3) -0.00249117*X(4) + 0.000506373*X(5) + 0.000756026*X(6) - 8.54E-04*X(7) -0.00357563*X(8) + 0.00026835*X(1)^2 + 6.29E-05*X(2)^2 - 1.02E-05*X(3)^2 + 0.000184809*X(4)^2 + 0.000498092*X(5)^2 - 9.71E-05*X(6)^2 + 0.000146412*X(7)^2 - 6.05E-04*X(8)^2 + 0.00039219*X(1)*X(8) - 5.66E-04*X(2)*X(5) + 2.17E-05*X(2)*X(6) + 0.000219137*X(2)*X(7) + 9.42E-05*X(2)*X(8) + 0.000438391*X(3)*X(5) – 2.53E-04*X(3)*X(6) + 2.18E-06*X(3)*X(8) – 1.67E-04*X(4)*X(8) In the optimization using MATLAB GA Toolbox, it is mandatory to write the objective function in an M-file so that it could be called from GA Toolbox window. The M-file is created using the surface response model function which is developed in the previous section is presented in Figure 5.

In the M-file script, function y denotes the objective function Cd/Cl, X (i) denotes DVi where i = 1, 2, 3,…, 8 and objfun is M-file function name.



Figure 5 M-file script

In the GA Toolbox, ga- Genetic Algorithm is set as a solver. The objective function is called in the GA Toolbox as @objfun and the number of variables is set to 8.

As the design space is bounded with the lower and upper limits of the control points’ y-coordinate values, the constraining option is bounds.

Lower and upper boundaries are [2.24 6.8 5.28 3.6 0.896 -4.1 -3.475 -2.625] and [3.5 10.625 8.25 5.625 1.4 -2.624 -2.224 -1.68] respectively.

Figure 6 Problem setting up

The default optimization options are kept as it is since the surface response model function best models the input and response data.

The optimization is run to find the optimal objective function value and the optimal design points that gave the minimal Cd/Cl value in this case.

The minimum Cd/Cl value is 0.0022982 and attained at 51st generation which is roughly less than the least Cd/Cl value recorded in the analyses. The objective function value and final design points are shown in Figure 7 below.



Figure 7 Objective function value and final point

Figure 8 Convergence of objective function value

V. VALIDATION The optimal design points of 8 CPs are used to model the final optimal aerofoil in CATIA and once again analyzed using ANSYS Fluent.

After solving, the solution converged after 2487 iterations, values of the aerofoils performance is revealed at the specific angle of attack, as shown in the table below:

Table 9 CL AND CD VALUES

Coefficient of Lift (Cl) 4.18E-02 Coefficient of Drag (Cd) 1.04E-04

Using Fluent’s various capabilities; the following plots were generated at AoA of 0.1o.

Figure 9 Contours of Pressure Coefficient (in Pascal) over the entire aerofoil

Figure 10 Velocity vectors over aerofoil colored by velocity magnitude (in m/s)

Figure 9 shows that there is a region of high pressure at the LE (stagnation point) and region of low pressure on the upper and lower surfaces of the aerofoil (relatively lower pressure on upper surface). This is what was expected from analysis of the velocity vector plot. From the Bernoulli equation, it is known that whenever there is high velocity, there is low pressure, and vice versa (See Figure 10).

The following values on Table 10 compare the performance parameters (Lift coefficient, drag coefficient maximum and minimum velocity, maximum and minimum static pressure) of NACA64A410 and optimized aerofoil.



Table 10 NACA64A410 AND OPTIMIZED COMPARISON Parameters NACA64A410 Optimized Remarks Lift Coefficient, Cl 3.02E-02 4.18E-02 Drag Coefficient, Cd 8.77E-05 1.04E-04 Cd/Cl 0.002905 0.002494 16.5%↓ Cl/Cd 344.23 401.01 16.5% ↑ Maximum Velocity 8.63 9.14 Minimum Velocity 2.57 2.23 Maximum Static Pressure 22.1 25.1 Minimum Static Pressure -15.3 -21 Location of Minimum Pressure (in tenth) 0.4 0.3 Maximum Thickness 7.508 (~10% of chord) 9.392 (~12% of chord)

In Figure 11, the pressure coefficients of the two aerofoils are compared. The lower side of the curve in the figure depicts the pressure coefficient value of the upper aerofoil profiles the upper side of the curve in the figure depicts the pressure coefficient value of the lower aerofoil profile for both aerofoils.

The lower curves have a negative pressure coefficient as the pressure is lower than the reference pressure. And the value of pressure coefficient of the optimized aerofoil is relatively lower than NACA64A410 aerofoil. On the other hand, the upper curves, in the figure, have mostly positive pressure coefficient as the pressure is higher than the reference pressure. The value of pressure coefficient of the optimized aerofoil on the lower side of the aerofoil is relatively higher than NACA64A410 aerofoil.

Figure 11 Comparison of pressure coefficient

Hence, it is understood that the optimized aerofoil has a better lift and less drag than NACA64A410 aerofoil.

VI. CONCLUSION Aerofoil curves are generated based on 8 control points using the Bezier curve modeling approach. It has been shown that two control points, free to move in both x and y directions, can reproduce the leading edge more accurately than with a single control point. Most of the control points are fixed in x-direction in order to limit the number of design variables. The baseline NACA64A410 aerofoil was modeled with maximal areal geometry difference less than 3%.

Design of Experiment is planned for 8 factors and three levels each using MINITAB. 27 analyses are done in ANSYS Fluent for fully modeling the input, design variables and the output response, Cd/Cl. The minimum Cd/Cl value of the analyses is recorded on 9th experiment for EiT-M009 aerofoil and is 0.003312.

Using the results obtained from ANSYS Fluent analyses, a full quadratic polynomial response surface model (RSM) is constructed. The response surface model results indicate that the model is significant and best fitted i.e. R2 and adjusted R2 are 99.84% and 95.82%, respectively).

The objective function used here is the drag-to-lift coefficient ratio minimization problem. Optimization is done using MATALAB GA Toolbox. The optimal design values gave Cd/Cl value of 0.002298 which is by far less than the least Cd/Cl value found from the experiment. Optimum aerofoil is analyzed in ANSYS for validation and Cd/Cl value has proven that the aerofoil is optimum with Cd/Cl value of 0.002494.



The Cd/Cl value of NACA64A410 using ANSYS is 0.002905. Optimized shape offers lesser drag-to-lift coefficient ratio while maintaining the desired lift force. About 16.5% drag-to-lift reduction is achieved by implementing the aerodynamic shape optimization methodology that has been used in this research. The maximum change in the geometry (from NACA64A410 to optimized) is about 0.9% increase of the upper curve and 0.22% increase of the lower curve of the aerofoil over the baseline which is relatively very small compared to the overall dimensions of the aerofoil. This implies that very little deformations are required to obtain aerodynamically efficient aerofoil, which offer significantly lesser drag-lift coefficient ratio.

VII. RECOMMENDATION The results from this research show that significant drag-to-lift coefficient ratio reduction is possible using Genetic Algorithm. This however must be weighed against the material consumption, deign for manufacturability, adapting the aerofoil, the increased cost and complexity, and the implications for safety.

VIII. FUTURE WORK There remains a lot of scope for improvement in the optimization methodology that has been employed in this research work. In particular, fifth order Bezier curve representation can be substituted with curve model having higher order than fifth order Bezier curve model. The aerofoil curve modeling can also be replaced with B-Spline and NURBS curve modeling techniques for higher accuracy and confidence of the aerofoil approximation. The flow solver and the turbulence model that has been used here can be replaced with higher-fidelity flow solvers that can predict the flow transition from laminar to turbulent more accurately. The optimization methodology can be performed on more number of analyses. This would ensure that a much accurate surface response model will be possible. In this work, the methodology has been applied for the optimization of an aerofoil which is basically a 2D shape. Even though having the right aerofoil shape is essential, the 3-dimensional shape of the aerofoil is equally crucial. A lot of other factors need to be addressed while designing the 3D shape of the blade. Thus for a full-fledged implementation of the optimization in 3D, it is necessary to extend the optimization methodology to 3D blades. Here, with an addition of a third dimension, more number of design variables will be required to completely parameterize the aerofoil. The optimization objectives can also be extended to include other performance parameters such as chord length, twist angle, rotor diameter and etc.

ACKNOLEDGMENT The authors acknowledge Fana Fili and Mewael Gebrehiwot for their valuable support towards making this paper fruitful.

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AUTHORS’ BIOGRAPHY Tariku Achamyeleh is currently a lecturer at the Department of Mechanical Engineering and a coordinator of University-Industry Linkage Office for Faculty of Technology, Debre Tabor University, Debre Tabor, Ethiopia. He received his Bachelor of Science and Master of Science degree from Mekelle University in Industrial Engineering and Product Design and Development, respectively. He has taught courses like Computer Aided Design, Materials Handling Equipment, Total Quality Management, Strength of Materials, Computational Methods with Matlab, and etc. in the undergraduate degree program.

Dr. Mulu Bayray is currently an Assistant Professor at the School of Mechanical and Industrial Engineering, EiT-M, Mekelle University, Mekelle, Ethiopia. He received his Ph.D. in Mechanical Engineering (Dr.techn.) in April 2002, Vienna University of Technology, Austria.



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