International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 4, April 2015
ISSN 2319 - 4847
An Analysis of Lift and Drag Forces of NACA
Airfoils Using Python
2
1.
3
4
Tarun B Patel, Sandip T Patel , Divyesh T Patel , Maulik Bhensdadiya
1
M E scholar Government Engineering College, Valsad, Gujarat, INDIA
2
Prof. in Mechanical Engineering Department, Government Engineering College, Valsad, Gujarat, INDIA
3
M E scholar Government Engineering College, Valsad, Gujarat, INDIA
4
M E scholar Government Engineering College, Valsad, Gujarat, INDIA
ABSTRACT
The aerodynamic Airfoils of wind turbine blades have crucial influence on aerodynamic efficiency of wind turbine. This
involves the selection of a suitable Airfoil section for the proposed wind turbine blade. Lift and Drag forces along with the
angle of attack are the important parameters in a wind turbine system. These parameters decide the efficiency of the wind
turbine. In this paper an attempt is made to study the Lift and Drag forces in a wind turbine blade for NACA0012, NACA4412
& NACA6412 Airfoil profile is considered for analysis. Data for the Angle of Attack, Co efficient of Lift and Drag of NACA
Airfoil taken from NACA Airfoil Tool. Lift and Drag Forces analysis for different parameters is carried out using
PYTHON(x,y) 2.7.9.0 programming. xlrd library used to read the Airfoil data from excel file.
Keywords: Lift forces, Drag forces, NACA Airfoils, Python.
1.INTRODUCTION
One of the most important parameter of wind turbines is wing because wind hits to the wings and energy of wind is
transformed into the mechanical energy by wings. In the literature, wings profiles are called as Airfoils. Airfoil profile
is the important parameter for wing design because wing efficiency increases depending on Airfoil profile, so there are
a lot of studies over the Airfoil profile as numerical and experimental in the literature [1]. Airfoil information is used
explicitly in the optimization process. Wind tunnel test data of several Airfoils which are publicly available are
collected and stored as an Airfoil database. This database includes Lift, Drag and Angle of Attack data of many Airfoils
developed for or used in wind turbine applications [1,2].
2.NOMECLATURE
ΑOA
Angle of attack
Cd
Drag coefficient
Cl
Lift coefficient
Fd
Drag force
Fl
Lift force
V
Wind velocity
Vrel
Relative velocity
tpr
Tip Speed Ratio
c
Chord Length
l
Blade element length
rho
Air density
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 4, April 2015
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3. AIRFOIL
Airfoils are structures with specific geometric shapes that are used to generate mechanical forces due to the relative
motion of the Airfoil and a surrounding fluid. Wind turbine blades use Airfoils to develop mechanical power. The
cross-sections of wind turbine blades have the shape of Airfoils. The width and length of the blade are functions of the
desired aerodynamic
performance, the maximum desired rotor power, the assumed Airfoil properties, and strength considerations.
Fig 1- Terminology of Airfoil.
Terminology of Airfoil shows in Fig 1.Air flow over an Airfoil produces a distribution of forces over the Airfoil surface.
The flow velocity over Airfoils increases over the convex surface resulting in lower average pressure on the ‘suction’
side of the Airfoil compared with the concave or ‘pressure’ side of the Airfoil. Meanwhile, viscous friction between the
air and the Airfoil surface slows the air flow to some extent next to the surface.
Lift force – defined to be perpendicular to direction of the oncoming air flow. The lift force is a consequence of the
unequal pressure on the upper and lower Airfoil surfaces.
Drag force – defined to be parallel to the direction of the oncoming air flow. The drag force is due both to viscous
friction forces at the surface of the Airfoil and to unequal pressure on the Airfoil surfaces facing toward and away from
the oncoming flow. Fig 2 shows the Lift and Drag Forces on Airfoil.
Fig 2- Lift and Drag forces.
The lift and drag forces are calculated by the following formula.
Lift = (1/2)*rho* CL*c*l*Vrel²
Drag = (1/2)*ρ* CD*c*l*Vrel²
Where rho – density of air - 1.2 kg/m³
c – Chord length in meter
l – Length of the blade element
Vrel – relative velocity of air in m/s
= V (1+ (tpr) ²)0.5
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 4, April 2015
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4.NACA AIRFOIL
The NACA Airfoils are Airfoil shapes for aircraft wings developed by the National Advisory Committee for
Aeronautics (NACA). The shape of the NACA Airfoils is described using a series of digits following the word
“NACA”. The parameters in the numerical code can be entered into equations to precisely generate the cross-section of
the Airfoil and calculate its properties.
4.1NACA 4 digit Airfoil specification
This NACA Airfoil series is controlled by 4 digits e.g. NACA 2412, which designate the camber, position of the
maximum camber and thickness. If an Airfoil number is
NACA
e.g
NACA 2412
MPXX
 M is the maximum camber divided by 100. In the example M=2 so the camber is 0.02 or 2% of the chord
 P is the position of the maximum camber divided by 10. In the example P=4 so the maximum camber is at 0.4 or
40% of the chord.
 XX is the thickness divided by 100. In the example XX=12 so the thickness is 0.12 or 12% of the chord.
5.ANALYSIS USING PYTHON
Python is a widely used general-purpose, high-level programming language. Its design philosophy emphasizes
code readability, and its syntax allows programmers to express concepts in fewer lines of code than would be possible in
languages such as C++ or Java. The language provides constructs intended to enable clear programs on both a small
and large scale.
Python(x,y)2.7.9.0 is used for the programming. xlrd library used for the read the excel file which contain data for
different NACA Airfoils.
The Airfoil profiles selected for the analysis are NACA0012, NACA4412 and NACA6412. The database contains
Airfoils that are designed or used for wind turbine applications. The lift and drag coefficients of the Airfoils, that are
based on wind tunnel test, are listed for various angles of attack and Reynolds numbers. Data are taken from the
Airfoil tool. Fig 3-5 shows the NACA profile and Table 1-3 shows the data of each.
5.1NACA001 (Max thickness 12.2% at 22.5% chord. Max camber 0% at 0% chord)
Fig 3- NACA0012 Airfoil (Source “NACA Airfoil Tool”)
Table 1- Sheet1 data NACA0012 Cl & Cd for AOA
Reynolds No = 50000
AOA
Cl
Cd
1
-0.017
0.2162
2
0.3527
0.01992
3
0.4357
0.0225
4
0.5252
0.02594
5
0.6109
0.03079
6
0.6828
0.03762
7
0.7446
0.04637
8
0.7173
0.06535
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5.2NACA4412 (Max thickness 12% at 30% chord. Max camber 4% at 40% chord)
Fig-4 NACA4412 Airfoil (Source “NACA Airfoil Tool”)
Table 2- Sheet2 data NACA4412 Cl & Cd for AOA
Reynolds No = 50000
AOA
Cl
1
0.3166
2
0.4299
3
0.5279
4
0.635
5
0.7094
6
0.7723
7
0.843
8
0.9309
9
1.2725
10
1.3248
11
1.3527
12
1.4092
13
1.381
14
1.2403
Cd
0.03657
0.04014
0.04426
0.04832
0.05375
0.06012
0.07193
0.04155
0.03991
0.03091
0.04742
0.05796
0.07194
0.09792
5.3NACA6412 (Max thickness 12% at 30.1% chord. Max camber 6% at 39.6% chord)
Fig-5 NACA6412 Airfoil (Source “NACA Airfoil Tool”)
Table 3- Sheet3 data NACA6412 Cl & Cd for AOA
Reynolds No = 50000
AOA
Cl
1
0.3871
2
0.4843
3
0.5632
4
0.6138
5
0.6602
6
0.7021
7
0.6765
8
0.721
9
0.7932
10
0.8434
Volume 4, Issue 4, April 2015
Cd
0.04738
0.05252
0.05831
0.06554
0.07377
0.08387
0.09828
0.10767
0.11926
0.13017
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5.4Python Programme to find the Lift and drag forces for NACA Airfoils.
Fig 6 shows the screen layout of Python(x,y) 2.7.9.0 programming and its output. Excel file read by the xlrd package
for the Python.
Fig 6 - Python programming and output.
6.RESULTS
The Lift and Drag forces are find out here for different parameter which is shown in Table 4-7.There behavior shown
in Fig 7-12.
6.1Lift and Drag forces for the tpr=5, V=8m/s , c=2m & various AOA
Table 4- Lift and Drag forces for various AOA
AOA
NACA0012
NACA4412
NACA6412
Fl
Fd
Fl
Fd
Fl
Fd
1
-33.9456
431.7082
632.1869
73.02298
772.9613
94.60838
2
704.2714
39.77626
858.4243
80.15155
967.0502
104.8719
3
870.0058
44.928
1054.111
88.37837
1124.598
116.4334
4
1048.719
51.79699
1267.968
96.48538
1225.636
130.8703
5
1219.845
61.48147
1416.53
107.328
1318.287
147.3039
6
1363.415
75.11962
1542.129
120.0476
1404.953
167.4716
7
1486.817
92.59162
1683.302
143.6298
1350.835
196.2455
8
1432.305
130.4909
1858.821
82.96704
1439.693
214.9955
9
……..
……..
2540.928
79.69229
1583.862
238.1384
10
……..
……..
2645.361
61.72109
1684.101
259.9235
11
……..
……..
2701.071
94.68826
…….
…….
12
……..
……..
2813.891
115.7345
…….
…….
13
……..
……..
2757.581
143.6498
…….
…….
14
……..
……..
2476.631
195.5267
…….
…….
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 4, Issue 4, April 2015
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Fig 7- NACA0012 Lift & drag forces for AOA
Fig 8–NACA4412 Lift & drag forces for AOA
Fig 9-NACA6412 Lift & drag forces for AOA
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6.2Lift and Drag forces for the tpr=5, AOA=70 and c=2m & Varying V
Table 5- Lift and Drag forces for various V
Velocity
NACA0012
NACA4412
NACA6412
Fl
Fd
Fl
Fd
Fl
Fd
5
580.78
36.1686
657.54
56.1054
527.67
76.6584
6
836.3347
52.08278
946.8576
80.79178
759.8448
110.3881
7
1138.344
70.89046
1288.778
109.9666
1034.233
150.2505
8
1486.817
92.59162
1683.302
143.6298
1350.835
196.2455
9
1881.753
117.1863
2130.43
181.7815
1709.651
248.3732
10
2323.152
144.6744
2630.16
224.4216
2110.68
306.6336
Fig 10-NACA Airfoil Lift & drag forces for Wind velocity.
6.3Lift and Drag forces for the V =5, AOA=70 and c=2m & Varying tpr.
Table 6- Lift and Drag forces for various tpr
tpr
NACA0012
NACA4412
NACA6412
Fl
Fd
Fl
Fd
Fl
Fd
5
1486.817
92.59162
1683.302
143.6298
1350.835
196.2455
6
2115.855
131.765
2395.469
204.3963
1922.342
279.2724
7
2859.264
178.0608
3237.012
276.2112
2597.76
377.3952
8
3717.043
231.479
4208.256
359.0746
3377.088
490.6138
Fig 11-NACA Airfoil Lift & drag forces for Tip speed ratio.
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6.4Lift and Drag forces for the tpr = 5 and c=2m & Varying AOA & V.
Table 7- Lift and Drag forces for Varying AOA & V
Wind
velocity
AOA
5
NACA0012
NACA4412
NACA6412
Fl
Fd
Fl
Fd
Fl
Fd
1
-13.26
168.636
246.948
28.5246
301.938
36.9564
6
2
396.1526
22.37414
482.8637
45.08525
543.9658
58.99046
7
3
666.0982
34.398
807.0535
67.66469
861.0202
89.14433
8
4
1048.719
51.79699
1267.968
96.48538
1225.636
130.8703
9
5
1543.866
77.81249
1792.796
135.837
1668.457
186.4315
10
6
2130.336
117.3744
2409.576
187.5744
2190.552
261.6744
11
7
2811.014
175.056
3182.494
271.5501
2553.923
371.0267
12
8
3222.685
293.604
4182.347
186.675
3239.308
483.739
Fig 12-NACA Airfoil Lift & drag forces for varying Wind velocity & Angle of Attack.
7.CONCLUSION
1. Python is programming tool which can be used for the analysis of wind energy.
2. Cl and Cd increased as increasing AOA up to maximum limit then after decreased.
For NACA0012 max AOA 70 NACA4412 max AOA 140 NACA6412 max AOA 100
3. Increasing wind velocity For AOA=7, tpr=5, c=2, Fl and Fd increased.
4. Increasing tpr For AOA=7, V=5, c=2, Fl and Fd increased.
5. As V and AOA increased for tpr=5 c=2, Fl and Fd increased. Maximum Lift Forces obtain for
the NACA4412.Drag forces eobtain for NACA6412 is higher than other profiles.
REFERENCES
[1] Michael S. Selig and Bryan D. McGranahan ” Wind Tunnel Aerodynamic Tests of Six Airfoils for Use on Small
Wind Turbines” January 31, 2003.
[2] Eke G.B., Onyewudiala J.I. “Optimization of Wind Turbine Blades Using Genetic Algorithm”Global Journal of
Researches in Engineering 22 Vol. 7 (Ver 1.0), December 2010.
[3] Arvind Singh Rathore, Siraj Ahmed ,“ Aerodynamic Analyses of Horizontal Axis Wind Turbine By Different
Blade Airfoil Using Computer Program”, IOSR Journal of Engineering (IOSRJEN, Vol. 2 Issue 1, Jan.2012, pp.
118-123.
[4] Dr. Eng. Ali H. Almukhtar, “Effect of drag on the performance for an efficient wind turbine blade design”, Energy
Procedia 18 ( 2012 ) 404 – 415.
[5] www.Airfoiltool.com
Volume 4, Issue 4, April 2015
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 4, Issue 4, April 2015
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AUTHOR
Tarun B Patel1 ME scholar in Energy engineering from Government engineering College, Valsad,
Lecturer in Government Polytechnic, Valsad Gujarat , B E Mechanical from SVNIT Surat year
2004, Gujarat, INDIA.
Prof. Sandip T Patel2 Professor in Mechanical Department , Government Engineering College,
Valsad, Gujarat. B E SVMIT Bharuch year 2004 , M.Tech in CAD/CAM SVNIT, Surat year 2009.
Divyesh T Patel3 ME scholar in Energy engineering from Government engineering College,
Lecturer in Government Polytechnic Valsad, B E Mechanical from LDCE Ahmedabad year 2005,
Gujarat, INDIA.
Maulik Bhensdadiya4 ME scholar in Energy engineering from Government engineering College,
Valsad, Gujarat B.Tech Mechanical from Ganpat University year 2013, Gujarat, INDIA.
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