Flow analysis

1
FLOW ANALYSIS OVER NACA
AIRFOILS USING FLUENT
A PROJECT REPORT SUBMITTED IN PARTIAL
FULFILLMENT OF THE REQUIREMENT FOR AWARD
OF THE DEGREE
OF
BACHELOR OF TECHNOLOGY IN
MECHANICAL ENGINEERING
BY
AMIYA KUMAR SAMAL
UNDER THE GUIDANCE OF:
MR. KASHINATH DHAMUDIA
DEPARTMENT OF MECHANICAL ENGINEERING
PARALA MAHARAJA ENGINEERING COLLEGE,
BERHAMPUR, 761003, ODISHA
2016-17

2
DECLARATION
I, Amiya Kumar Samal student of Mechanical Engineering of
PARALA MAHARAJA ENGINEERING COLLEGE, Berhampur do
hereby declare that the project report on “FLOW ANALYSIS OVER
NACA AIRFOILS USING FLUENT” submitted by me is original to
the best of our knowledge and behalf.
It has been prepared by me with my own ideas and creativity under
supervision of project guide “Mr Kashinath Dhamudia”. It has not been
presented by anyone else.
Amiya Kumar Samal

3
TABLE OF CONTENTS
TITLE PAGE
NO.
CERTIFICATE
ACKNOWLEDGEMENT……………………………………………………………. i
DECLRATION………………………………………………………………………... ii
ABSTRACT…………………………………………………………………………… iii
TABLE OF CONTENTS…………………………………………………………….. iv
LIST OF FIGURES…………………………………………………………….…….. v
LIST OF TABLES……………………………………………………………….….... vi
INTRODUCTION
IMPORTANCE OF PROBLEM………………………………….. 1
PROBLEM STATEMENT………………………………………... 1
GENERAL DESCRIPTION OFAIRFOIL………………………... 2
NACA AIRFOIL…………………………………………………... 4
LTERATURE REVIEW…………………………………………………. 4
NUMERICAL PROCEDURE
GOVERNING EQUATIONS……………………………………… 6
COMPUTATIONAL DOMAIN…………………………………… 7
NUMERICAL EVALUATION
CFD……………………………………………………………….. 8
APPROACH
PREPARING GEOMETRIC MODEL……………………....... 8
GENERATE MESHING………………………………………. 9
SETTING BOUNDARY CONDITIONS……………………… 10
SETTING UP FLUENT INITIALIZING AND SOLVING…… 10
RESULTS
LIFT AND DRAG COEFFICIENT OF NACA-4412………….. 12

4
VELOCITY AND PRESSURE DISTRIBUTION OF
NACA-4412……………………………………………………. 13
LIFT AND DRAG COEFFICIENT OF NACA-6409………….. 14
VELOCITY AND PRESSURE DISTRIBUTION OF
NACA-6409…………………………………………………….. 15
EFFECT OF ANGLE OF ATTACK ON LIFT AND
DRAG COEFFICIENT ON NACA-0012 ……………………... 16
CONCLUSION………………………………………………………... 17
REFERENCE…………………………………………………………. 18
APPENDIX
AIRFOIL COORDINATES…………………………………… 19
AIRFOIL PROFILE…………………………………………… 31

5
PARALA MAHARAJA ENGINEERING COLLEGE
BERHAMPUR-761003
CERTIFICATE
This is to certify that the thesis entitled, “FLOW ANALYSIS OVER
NACA AIRFOILS USING FLUENT” submitted by Amiya Kumar
Samal in partial fulfilment of the requirements for the award of
Bachelor of Technology in Mechanical Engineering with during
session 2013-2017 in the Department of Mechanical Engineering,
Parala Maharaja Engineering College, Berhampur.
It is an authentic work carried out by him under by
supervision and guidance. To the best of my knowledge, the matter
embodied in this thesis has not been submitted to any other
university/institute for the award of any Degree or Diploma.
EXTERNAL
Dr.Trilochan Rout Guide:
HOD Mechanical Engineering Kashinath Dhamudia

6
ACKNOWLEDEMENT
It is my esteemed pleasure to present my project topic on “FLOW ANALYSIS
OVER NACA AIRFOILS USING FLUENT”.
It would be a great pleasure to write a few words, which would although not
suffice as the acknowledgement of this long cherished effort, but in the absence
of which this report would necessarily be incomplete. So these words of
acknowledgement come as a small gesture of gratitude towards all those without
whom the successful completion of this report would not have been possible.
I would like to express deep gratitude towards Mr. Kashinath Dhamudia (Asst.
ProfessorofMechanical Engineering Department PMEC, Berhampur) who gave
us his valuable suggestions, motivation and the direction to proceed at every
stage. They are like a beam of light for us. His kind guidance showed us the path
of life and is unforgettable. He extended his valuable guidance, indispensable
help and inspiration at times, in appreciation we offer him our heartfelt thanks.
Last butnot least I would like to thank Dr. Ranjan Kumar Swain, Principal, Parala
Maharaja Engineering College; Dr. Trilochan Rout, HOD, Department of
Mechanical Engineering for providing us their valuable guidance & prompt
cooperation without which It would be difficult for us to complete it.
AMIYA KUMAR SAMAL
PARALA MAHARAJA ENGG. COLLEGE
MECHANICAL ENGINEERING
ABSTRACT

7
In this work, flow analysis of two airfoils (NACA 6409 and NACA 4412) and
effect of angle of attack on airfoil (NACA 0012) was investigated. Drag force,
lift force as well as the overall pressure distribution over the airfoil were also
analyzed. The outcome of this investigation was shown and computed by using
ANSYS workbench 15. The pressure distributions as well as coefficient of lift to
coefficient of drag ratio of these two airfoil were visualized and compared. From
this result, we compared the better airfoil between these two airfoils. The whole
analysis is solely based on the principle of finite element method and
computational fluid dynamics (CFD). Finally, by comparing different properties
i.e. drag and lift coefficients, pressure distribution over the airfoil; it was found
that NACA 4412 airfoil is more efficient for practical applications than NACA
6409 airfoil & with increase in angle of attack, lift and drag coefficient could
increase until certain angle. After certain angle, the lift coefficient was decreasing
whereas; drag coefficient increased.

8
LIST OF FIGURES
FIG. NO. TITLE PAGE
FIG1 SCHEMATIC VIEW OF AIRFOIL…………………………… 2
FIG2 GEOMETRY OF AIRFOIL AND DOMAIN…………………. 9
FIG3 VIEW OF MESHING………………………………………….. 9
FIG4 AIRFOIL PROFILE AND VIEW OF DIFFERENT
BOUNDARY CONDITIONS…………………………………. 10
FIG5 LIFT COEFFICIENT OF NACA 4412……………................... 12
FIG 6 DRAG COEFFICIENT OF NACA 4412……………………… 12
FIG 7 VELOCITY DISTRIBUTION OF NACA 4412……………… 13
FIG 8 PRESSURE DISTRIBUTIUON OF NACA 4412……………. 13
FIG9 LIFT COEFFICIENT OF NACA 6409………………………. 14
FIG10 DRAG COEFFICIENT OF NACA 6409…………………….. 14
FIG11 VELOCITY DISTRIBUTION OF NACA 6409……………… 15
FIG12 PRESSURE DISTRIBUTION OF NACA 6409……………… 15
FIG13 EFFECT OF LIFT AND DRAG COEFFICIENT ON
NACA-0012 PROFILE………………………………………… 16

9
LIST OF TABLES
TABLE NO. TITLE PAGE
TABLE 1 TYPE OF BOUNDARY CONDITION…………... 10
TABLE 2 CL AND CD RATIO……………………………….16
TABLE 3 NACA-6409 COORDINATES…………………....19

10
INTRODUCTION
IMPORTANCE OF PROBLEM
Aerodynamics is a branch of science that deals with the analysis of flow over a
body. Therapid evolution ofCFD has been driven for faster and accurate method
for solving problems related to aerodynamics. The flow of air over the airfoils is
the most important thing that has to be considered during designing an aircraft,
missile, sportvehicles or any other aerodynamic objects. By using ANSYS, flow
analysis becomes more effective as it investigates everything thoroughly.
Computational fluid dynamics provides a qualitative and quantitative prediction
of fluid flow by means of mathematical modelling, numerical method and
software tools. CFD analysis enables an engineer to compute the flow
numerically in a ‘virtual flow laboratory’. The analysis consists of several steps
such as: problem statement, mathematical modeling, mesh generation, space
discretization, time discretization, iterative solver, simulation run, post
processing, and verification.
ANSYS is a vast computational software that enables researchers to analyze the
problems related to different engineering sectors. It is used to solve problems
related to heat transfer, fluid flow, turbulence, industrial machineries, explicit
dynamics, and structural analysis with the assistance of numerical analysis.
Airfoils and aerodynamic shaped objects are extensively used in all types of air
vehicles forexample spaceshuttle, aircrafts, helicopters and even in various types
of missiles Besides, when it comes to fluid machineries such as pump, turbine,
windmill, the shape of impeller, propeller is very important. All the parameters
which are important to express the characteristics of airfoils must be inspected
with high precision. That’s why analysis of flow over airfoils is very important.
PROBLEM STATEMENT
In this simulation and analysis, pressure and velocity distribution, were analyzed
along with coefficient of lift and coefficient of drag of three particular NACA
airfoils. Later, coefficient of lift to coefficient of drag ratio was compared
between these airfoils to find out the more accurate results. Also along with
coefficient of drag, coefficient of lift and angle of attack is varied for a profile.
GENERAL DESCRIPTION OFAIRFOIL

11
An aero-foil or airfoil is the shape of a wing blade (of propeller, rotor or turbine)
or sail. An airfoil shaped body moved through a fluid produces an aerodynamic
force. The component of this force perpendicular to the direction of motion is
called lift. The component parallel of the direction of motion is called drag.
Subsonic flight airfoils have a characteristics shape with a rounded loading edge,
followed by a shape trailing edge, often with asymmetric camber. The following
airfoil figure shows the different parameters of the airfoil.
FIG1: AIRFOIL SCHEMATIC VIEW
AIRFOIL TERMINOLOGY
The geometry of the airfoil is described with a variety of terms:
Chord Length: The chord length is a straight line connecting the leading and
trailing edges of the airfoil. That is the reference dimension of the airfoil section.
Leading Edge: The leading edge is the part of the airfoil that first contacts the
air. Alternatively it is the foremost edge of an airfoil section. At this point airfoil
that has maximum curvature (minimum radius).
Trailing Edge: the trailing edge of an aerodynamic surface such as wing is its
rear edge, where the airfoil separated by the leading edge rejoins. At this point
airfoil has minimum curvature at the rear of the airfoil.
Angle of Attack: Angle of attack (AOA,α) is a term used in fluid dynamics to
describe the angle between a reference line on a lifting body (often called the
chord line of an airfoil).

12
The various terms related to airfoils are defined below:
Suction Surface: The suction surface (a.k.a. upper surface) is generally
associated with higher velocity and lower static pressure.
Pressure Surface: The pressure surface (a.k.a. lower surface) has a
comparatively higher static pressure than the suction surface. The pressure
gradient between these two surfaces contributes to the lift force generated for a
given airfoil.
The shape of the airfoil is defined using the following geometrical parameters:
Mean Camber Line: The mean camber line or mean line is the locus of points
midway between the upperand lower surfaces. Its shapedepends onthe thickness
distribution along the chord;
Thickness:Thethickness of an airfoil varies along the chord. Itmay be measured
in either of two ways:
 Thickness measured perpendicular to the camber line. This is sometimes
described as the "American convention";
 Thickness measured perpendicular to the chord line. This is sometimes
described as the "British convention".
The forces that act on airfoil structures are listed below:
Aerodynamic Force: The lift on an airfoil is primarily the result of its angle of
attack and shape. When oriented at a suitable angle, the airfoil deflects the
oncoming air, resulting in a force on the airfoil in the direction opposite to the
deflection. This force is known as aerodynamic force and can be resolved into
two components: Lift and drag.
Most foil shapes require a positive angle of attack of generates lift, but
cambered lift, but cambered airfoils can generate lift at zero angle of attack. The
“turning” of the air in the vicinity of the airfoil creates curved streamlines which
results in lower pressure on one side and higher on the other. This pressure
difference is accompanied by a velocity difference, via. Bernoulli’s principle, so
this resulting flow field about the airfoil has a higher average velocity on the
upper surface than on the lower surface. The lift force can be related directly to
the average top/bottom velocity difference without computing the pressure by
using the concept of circulation and Kutta-Joukowski theorem.
NACA AIRFOIL

13
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.
NACA 4-digit series
 The NACA four-digit wing sections define the profile by:
 Forexample, the NACA 2412 airfoil has a maximum camberof 2% located
40% (0.4 chords)fromthe leading edge with a maximum thickness of 12%
of the chord.
LITERATURE REVIEW
Guilmineau etal. (1997) discussed thecomputation ofthe time-mean, turbulent,
two-dimensional incompressible viscous flow past an airfoil at fixed incidence.
A new physically consistentmethod is presented forthe reconstruction ofvelocity
fluxes which arise from discrete equations for the mass and momentum balance.
This closure method for fluxes makes possible the use of a cell-centered grid in
which velocity and pressure unknowns share the same location, while
circumventing the occurrence of spurious pressure modes. The influence of
several turbulent models is investigated. The models involve either an algebraic
eddy viscosity or determine the eddy viscosity from transport equations.
Calculations performed have also indicated that the grid independence should be
verified rather on velocity characteristics than on pressure data which are easily
made grid-free. The importance of grid effects, moreover, increases when the
nominal Reynolds number increases, while the transition phenomenon is the most
critical physical difficulty which prevents a fully automatic flow prediction.
S. B. Hazra et al. (1997) they optimized airfoils at ultra-low Reynolds numbers.
These investigations are carried out to understand the aerodynamic issues related
to the low speed and micro scale air vehicle design and performance. The
optimization method used is based on simultaneous pseudo-time stepping in
which stationary states are obtained by solving the preconditioned pseudo-
stationary system of equations representing the state, co state and design
equations. Design examples of airfoils of different thicknesses at Mach numbers
between the range of 0.25 to 0.3 and at Reynolds numbers below 15000 are
presented.

14
Dr.D.Ravindranetal. (2010) gives the Lift and Drag forces along with the angle
ofattack are the important parameters in a wind turbine system. Theseparameters
decide the efficiency ofthe wind turbine. In this paper an attempt is made to study
the Lift and Drag forces in a wind turbine blade at various sections and the effect
of angle of attack on these forces. In this paper NACA 4420 airfoil profile is
considered for analysis of wind turbine blade. The wind turbine blade is modeled
and several sections are created from root to tip. The Lift and Drag forces are
calculated at different sections for angle of attack from 0 to 12 for low Reynolds
number. The analysis showed that angle of attack of 5 has high Lift/Drag ratio.
The CFDanalysis is also carried out at various sections of blade at angle of attack
of 5. The pressure and velocity distributions are also plotted. The airfoil NACA
4420 is analyzed based oncomputational fluid dynamics to identify its suitability
for its application on wind turbine blades and good agreement is made between
results. The results demonstrate the pressure distribution over the airfoil. The
pressure on the lower surface of the airfoil is greater than that of the incoming
flow stream and as a result ofthat it effectively pushes the airfoil upward, normal
to the incoming flow stream. On the other hand, the components of the pressure
distribution parallel to the incoming flow stream tend to slow the velocity of the
incoming flow relative to the airfoil, as do the viscous stresses. It could be
observed that the upper surface on the airfoil experiences a higher velocity
compared to the lower surface. By increasing the velocity at higher Mach
numbers there would be a shock wave on the upper surface that could cause
discontinuity.
Ogumaa et al. (2010) performed the experiment on the flow characteristics on
and around an airfoil at moderate Reynolds number are studied to understand the
generation mechanism of tonal noise from a symmetrical airfoil in a uniform
flow. The separation and reattachment of the flow on the airfoil surface are
evaluated from the liquid-crystal visualization and the velocity fields across the
boundary layers over the airfoil are measured by particle image velocimetry
(PIV). When the airfoil is inclined at a small attack angle to meet with the
condition of tonal noise generation, the boundary layer on the pressure surface
experiences the separation along the surface and reattaches near the trailing edge
of the airfoil. Thus, the long separation bubbles are created on the airfoil and the
bubble on the pressure surface is placed downstream near the trailing edge. The
mean velocity measured by PIV indicates that the inflection in the velocity profile
is found in the separation region and the turbulence intensity increases a bit

15
upstream of the reattachment point, which are followed by the reattachment and
the generation of turbulent boundary layer on the suction surface and the
formation of periodic vortex structure on the pressure surface near the trailing
edge of the airfoil at small attack angles.
Lee et al. (2011) worked on a low Reynolds number airfoil that was designed for
applications in small horizontal axis wind turbines to achieve better start up and
low wind speed performances. Their experiments were performed on the
improved airfoil (AF300) in an open circuit wind tunnel at Reynolds numbers of
38,000, 75,000, 128,000 and 205,000. Pressure distributions were obtained over
the surface of the airfoil and the lift and drag forces were measured with a
dynamometer at different angles of attack, α. A CFDanalysis was also performed
to get additional information on the flow characteristics. Particle Image
Velocimetry (PIV) together with smoke flow visualization were used to studythe
flow around the airfoil. At the Reynolds numbers of 75,000, 128,000 and
205,000, maximum lift coefficients of 1.72, 1.81 and 1.86 respectively were
obtained at the stall angle of 14°. The lift coefficient increased from 0.41 to 1.05
at Re = 38,000 in the range of α= 0–18°, in which no stalling was documented.
The results from PIV and smoke flow visualization showed that the flow stayed
fully attached to the airfoil surface from Re as low as 56,000 at an angle of attack
of 8° and maintained a fully attached flow up to 14° angle of attack for Re as low
as 75,000.
NUMERICAL PROCEDURE
1. GOVERNING EQUATIONS:
Continuity Equation:
𝝏𝝆
𝝏𝒕
+ 𝛁 . (𝝆𝑽) = 𝟎
Momentum Equation:
x component:
𝝏(𝝆𝒖)
𝝏𝒕
+ 𝛁 .( 𝝆𝒖𝑽) = −
𝝏𝒑
𝝏𝒙
+ ρfx
y component:

16
𝝏(𝝆𝒗)
𝝏𝒕
+ 𝛁 .( 𝝆𝒗𝑽) = −
𝝏𝒑
𝝏𝒚
+ ρfy
z component:
𝝏(𝝆𝒘)
𝝏𝒕
+ 𝛁 .( 𝝆𝒘𝑽) = −
𝝏𝒑
𝝏𝒛
+ 𝝆fz
Navier-Stokes Equation:
x component:
x
xxxx
z
x
y
x
x
x
g
z
V
y
V
x
V
x
P
z
V
V
y
V
V
x
V
V
t
V
 

































2
2
2
2
2
2
y component:
y
yyyy
z
y
y
y
x
y
g
z
V
y
V
x
V
y
P
z
V
V
y
V
V
x
V
V
t
V
 




































2
2
2
2
2
2
z component:
z
zzzz
z
z
y
z
x
z
g
z
V
y
V
x
V
z
P
z
V
V
y
V
V
x
V
V
t
V
 

































2
2
2
2
2
2
2. COMPUTATIONAL DOMAIN:
To convert the governing equations to algebraic equations that can be solved
numerically it is used as a control volume based technique that consist of:
 Division of domain into discrete control volumes using a computational
grid.
 Integration of the governing equations on the individual control volumes
to construct algebraic equations for discrete dependent variables.
 Linearization of the discretized equations and solutions of the resultant
linear equation system to yield updated values of the dependent variables.
One ofthe reasons forusing the finite volume method to solve the governing fluid
equation is that for a complicated geometry (as the geometry studied) the physical
domain is divided into small volumes and the mass, momentum and turbulence
equations are conserved when solved in integral form.
The solver ANSYS 15.0 Fluent is used to perform the numerical computation for
all the models in this thesis.

17
NUMERICAL EVALUATION
1. CFD:
Computational Fluid Dynamics (CFD) is a numerical method used to simulate
physical problems with use of governing equations. This method can be used
to investigate design approaches without creating a physical modeland can be
a valuable tool to understand conceptual properties of new mechanical
designs. By using a simulation instead of doing lab experiments, one may
acquire results faster and with less expense. An important aspectin the use of
CFDis to understand the simplifications in software, and know the limitations
in the computed results. Though the CFDsoftware uses well known governing
equations, severe simplifications are made in terms of grid and representing
geometries.
2. APPROACH:
Following is the method employed to carry through the CFD simulation
I. Preparing geometric model
II. Generate meshing
III. Setting boundary conditions
IV. Software (Fluent) setup, initialization and solving
I. Preparing geometric model
NACA airfoil geometry was acquired as co-ordinate vertices i.e. texts file and
imported into the ANSYS FLUENT. Some adjustments were made to this to
correct the geometry and make it valid as a CFD model.
FLUENT is essential in the process of doing the CFD analysis, it creates the
working environment where the object is simulated. An important part in this is
creating the mesh surrounding the object. This needs to be extended in all
directions to get the physical properties of the surrounding fluid in this case
moving air. The mesh and edges mustalso begrouped in orderto setthe necessary
boundary conditions effectively.
Firstly we have to import the coordinates of airfoil and create the curve, the 2D
analysis type is used and launch the design modelcreated. Then we need to create
the surface to the curve then the airfoil is generated. We need to create the
meshing surface we will use once we begin to specify boundary conditions. We
will begin by creating a coordinate system at the tail of the airfoil this will help
us create the geometry for the C-mesh domain by using sketcher toolbox and
dimension tool.

18
FIG2: GEOMETRY OF AIRFOIL AND DOMAIN
II. Generate meshing
A domain consisting of a rectangular profile of15:2 is to be created having airfoil
as an interior surface. The mesh is constructed to be very fine at regions close to
the airfoil. For this airfoil a structured rectangular mesh was used. Due to
limitations in the FLUENT software, the mesh has to be fine also in certain
regions far from the airfoil.
FIG3: VIEW OF MESHING
A fine mesh implies a higher number of calculations which in turn makes the
simulation use longer time to finish For the NACA airfoils, the grid distributed
with an increasing distance between nodes, starting from very small sizes from
the leading edge. From the point of max thickness on the airfoil to the trailing
edge an even number of points are distributed and analyzed.
III. Setting boundary conditions
Giving properties to the different geometries is vital to make the simulation
work. In this case, the mesh boundaries were given set to the x and y velocity

19
components, and the end boundary the property “pressure-outlet” to simulate
the zero gauge pressure. The airfoil itself is given as interior surface.
EDGE NAME TYPES OF BOUNDARY
A Inlet Velocity
B Outlet Pressure
C Pressure side Stationary wall ,no slip
D Suction side Stationary wall ,no slip
(TABLE 1: BOUNDARY CONDITION)
FIG4: AIRFOIL PROFILEAND VIEW OF DIFFERENT BOUNDARY
IV. Setting up FLUENT (Initializing and Solving)
The geometry and mesh were imported into FLUENT, and the system and
environment properties set “Standard” and “Double precision” is selected as
system parameters, ensuring adequate accuracy. FLUENT has single precision as
default, but for these simulations an accurate solution is requested. The residuals
for the different turbulence model variables were set to 10e−6and the iteration
max count to 70. The simulation process could also be halted or stopped if the CL
or CD seemed to have stabilized properly.
Turbulent models
Considering vortex shedding and boundary layer separation for airfoils and
wings, this simulation will have to deal with turbulent flows. The chaotic nature
B
A
D
C

20
of turbulent flow makes it very expensive to compute velocities for all points in
space. RANS (Reynolds-Averaged Navier-Stokes) is the oppositeto DNS (Direct
Navier-Stoke) which is the analytic direct simulation of the governing equations,
and use a statistical and averaged approachto find the flow behavior. The reason
for using RANS models is that small vortices in turn very expensive to solve are
removed by averaging the flow.
A crucial point is selecting a viscous model, and in FLUENT there are several
options. There are fundamental differences to the different models, and may be
used for different types of flows. In this, the viscous models Realizable (k-ε) are
2-equation models.
RESULTS
In this study, experimental and numerical analysis were performed. The
experimental are conducted at different velocity. Lift, drag coefficient and
pressure distribution of NACA airfoil profiles at different angles are analyzed.
 Case1: A comparative flow analysis of NACA-6409 and NACA-
4421 airfoil.
 Case2: Effect of angle of attack on lift coefficient and drag
coefficient on NACA-0012.
CASE 1:
Lift and Drag coefficient of NACA-4412

21
FIG5: LIFT COEFFICIENT OF NACA-4412
FIG6: DRAG COEFFICIENT OF NACA-4412
Fig: After 70 iterations, convergence was obtained and the values of CL and CD
as 3.6860e-01 and 2.4544e-02 were found respectively for 0 degree angle of
attack for NACA 4412.
Velocity and pressure distribution of NACA-4412

22
FIG7: VELOCITY DISTRIBUTION OVER NACA-4412 AIRFOIL FOR AN ANGLE OF
ATTACK 00
FIG8: PRESSURE DISTRIBUTION OVER NACA 4412 AIRFOIL FOR AN ANGLE OF
ATTACK 0 DEGREE.
Lift and drag coefficient of naca-6409

23
FIG9: LIFT COEFFICIENT OF NACA-6409
FIG10: DRAG COEFFICIENT OF NACA-6409
Fig: After 70 iterations, convergence was obtained and the values of CL and CD
as 5.9060e-01 and 4.3853e-02 were found respectively for 0 degree angle of
attack for NACA 6409.
Velocity and pressure distribution of naca-6409

24
FIG 11: VELOCITY DISTRIBUTION OVER NACA 6409 AIRFOIL FOR AN
ANGLE OF ATTACK 00
FIG 12: PRESSURE DISTRIBUTION OVER NACA 6409 AIRFOIL FOR AN
ANGLE OF ATTACK 0 DEGREE
CL/CD RATIO:

25
NACA-4412 15.017
NACA-6409 13.46
TABLE 2: CL VS CD RATIO
CASE 2:
Effect of Angle of Attack on Lift and Drag coefficient on NACA-
0012 profile.
CONCLUSION
Angle of Attack

26
After successfully completing this simulation based experiment, the
decisions were finally confined into the following points.
Case1:
 Static pressure distribution on these two airfoils was visualized. It was
found that forsame angle of attack, NACA 4412 has less negative pressure
on the upper surface than NACA 6409.
 Coefficient of drag and coefficient of lift were found for different angle of
attack from the simulation.
 Finally, lift to drag ratio for these two airfoils were compared to find out
the better airfoil. In this case, NACA 4412 is better than NACA 6409.
Case2:
 If angle of attack increased, lift and drag coefficient could increase until
certain angle. After certain angle, the lift coefficient was decreasing
whereas; drag coefficient increased. This situation is called as stall angle.
REFERENCES

27
a. www.google.co.in
b. www.wikipedia.com
c. www.youtube.com
d. www.slideshare.com
e. www.lynda.com
f. www.naca.com
g. www.quroa.com
h. ANSYS FLUENT 15, Tutorial Guide.
i. International Journal of Research in Engineering and Technology
j. International Journal of Mechanical Engineering project and Research
k. Numerical and Experimental Investigation of the Flow Field around
NACA 0012 Airfoil
APPENDIX

28
NACA-6409 COORDINATES
#group #point #x cord #y cord D
1 1 1.000185 0.000927 0
1 2 0.999944 0.001001 0
1 3 0.999219 0.001226 0
1 4 0.998011 0.001598 0
1 5 0.996322 0.002119 0
1 6 0.994153 0.002785 0
1 7 0.991506 0.003595 0
1 8 0.988382 0.004546 0
1 9 0.984785 0.005635 0
1 10 0.980718 0.006859 0
1 11 0.976184 0.008214 0
1 12 0.971188 0.009696 0
1 13 0.965732 0.0113 0
1 14 0.959823 0.013021 0
1 15 0.953466 0.014854 0
1 16 0.946665 0.016793 0
1 17 0.939427 0.018833 0
1 18 0.931759 0.020967 0
1 19 0.923666 0.023189 0
1 20 0.915157 0.025492 0
1 21 0.906239 0.02787 0
1 22 0.89692 0.030315 0
1 23 0.887208 0.03282 0
1 24 0.877113 0.035379 0
1 25 0.866643 0.037983 0
1 26 0.855808 0.040626 0
1 27 0.844618 0.043299 0
1 28 0.833083 0.045996 0
1 29 0.821214 0.048708 0
1 30 0.809023 0.051428 0
1 31 0.79652 0.054149 0
1 32 0.783717 0.056862 0
1 33 0.770626 0.059562 0
1 34 0.757261 0.062239 0
1 35 0.743633 0.064888 0
1 36 0.729755 0.067501 0
1 37 0.715642 0.07007 0
1 38 0.701306 0.07259 0
1 39 0.686761 0.075053 0
1 40 0.672022 0.077452 0
1 41 0.657103 0.079782 0
1 42 0.642018 0.082037 0
1 43 0.626783 0.084209 0
1 44 0.611412 0.086295 0
1 45 0.595921 0.088287 0
1 46 0.580325 0.090181 0

29
1 47 0.564639 0.091972 0
1 48 0.548881 0.093656 0
1 49 0.533064 0.095227 0
1 50 0.517206 0.096682 0
1 51 0.501323 0.098016 0
1 52 0.48543 0.099228 0
1 53 0.469545 0.100312 0
1 54 0.453682 0.101268 0
1 55 0.43786 0.102091 0
1 56 0.422094 0.102781 0
1 57 0.4064 0.103335 0
1 58 0.390631 0.103735 0
1 59 0.374849 0.103903 0
1 60 0.359189 0.103834 0
1 61 0.343666 0.10353 0
1 62 0.3283 0.102994 0
1 63 0.313108 0.102231 0
1 64 0.298107 0.101246 0
1 65 0.283315 0.100046 0
1 66 0.268749 0.098636 0
1 67 0.254425 0.097025 0
1 68 0.24036 0.09522 0
1 69 0.22657 0.093231 0
1 70 0.213071 0.091066 0
1 71 0.199878 0.088737 0
1 72 0.187006 0.086254 0
1 73 0.17447 0.083627 0
1 74 0.162283 0.080868 0
1 75 0.150458 0.077989 0
1 76 0.139009 0.075003 0
1 77 0.127947 0.071922 0
1 78 0.117285 0.068757 0
1 79 0.107033 0.065524 0
1 80 0.097202 0.062233 0
1 81 0.087802 0.058898 0
1 82 0.078841 0.055531 0
1 83 0.070329 0.052146 0
1 84 0.062274 0.048755 0
1 85 0.054682 0.045369 0
1 86 0.047561 0.042001 0
1 87 0.040916 0.038662 0
1 88 0.034754 0.035364 0
1 89 0.029079 0.032115 0
1 90 0.023895 0.028928 0
1 91 0.019207 0.02581 0
1 92 0.015017 0.02277 0
1 93 0.011328 0.019817 0
1 94 0.008143 0.016958 0
1 95 0.005462 0.014199 0
1 96 0.003287 0.011545 0
1 97 0.001618 0.009002 0
1 98 0.000456 0.006574 0
1 99 -0.0002 0.004262 0

30
1 100 -0.000352 0.002071 0
1 101 0 0 0
1 102 0.000845 -0.001923 0
1 103 0.002174 -0.003671 0
1 104 0.003982 -0.005246 0
1 105 0.006267 -0.006648 0
1 106 0.009025 -0.00788 0
1 107 0.012251 -0.008944 0
1 108 0.015941 -0.009842 0
1 109 0.020089 -0.010577 0
1 110 0.024689 -0.011154 0
1 111 0.029736 -0.011576 0
1 112 0.035224 -0.011847 0
1 113 0.041144 -0.011973 0
1 114 0.047491 -0.011958 0
1 115 0.054256 -0.011809 0
1 116 0.061433 -0.011531 0
1 117 0.069011 -0.01113 0
1 118 0.076984 -0.010614 0
1 119 0.085343 -0.009988 0
1 120 0.094078 -0.009262 0
1 121 0.103181 -0.008442 0
1 122 0.112643 -0.007536 0
1 123 0.122453 -0.006552 0
1 124 0.132604 -0.005499 0
1 125 0.143084 -0.004385 0
1 126 0.153884 -0.00322 0
1 127 0.164995 -0.002012 0
1 128 0.176405 -0.000769 0
1 129 0.188106 0.000497 0
1 130 0.200086 0.001779 0
1 131 0.212336 0.003067 0
1 132 0.224845 0.004351 0
1 133 0.237603 0.005623 0
1 134 0.250599 0.006873 0
1 135 0.263821 0.008091 0
1 136 0.277261 0.009268 0
1 137 0.290906 0.010396 0
1 138 0.304745 0.011466 0
1 139 0.318767 0.012469 0
1 140 0.332962 0.013397 0
1 141 0.347317 0.014242 0
1 142 0.36182 0.014996 0
1 143 0.376461 0.015652 0
1 144 0.391226 0.016204 0
1 145 0.406218 0.016652 0
1 146 0.421472 0.017061 0
1 147 0.436807 0.017444 0
1 148 0.452209 0.017798 0
1 149 0.467665 0.018119 0
1 150 0.483159 0.018404 0
1 151 0.498677 0.01865 0
1 152 0.514205 0.018856 0

31
1 153 0.529726 0.019018 0
1 154 0.545228 0.019136 0
1 155 0.560694 0.019208 0
1 156 0.57611 0.019232 0
1 157 0.591461 0.019208 0
1 158 0.606731 0.019135 0
1 159 0.621907 0.019014 0
1 160 0.636973 0.018844 0
1 161 0.651914 0.018626 0
1 162 0.666716 0.018361 0
1 163 0.681364 0.01805 0
1 164 0.695842 0.017695 0
1 165 0.710138 0.017296 0
1 166 0.724235 0.016857 0
1 167 0.738121 0.016379 0
1 168 0.751781 0.015866 0
1 169 0.7652 0.015318 0
1 170 0.778367 0.01474 0
1 171 0.791266 0.014134 0
1 172 0.803884 0.013504 0
1 173 0.81621 0.012852 0
1 174 0.828229 0.012183 0
1 175 0.839929 0.011499 0
1 176 0.851299 0.010804 0
1 177 0.862326 0.010101 0
1 178 0.872998 0.009395 0
1 179 0.883305 0.008688 0
1 180 0.893235 0.007984 0
1 181 0.902778 0.007287 0
1 182 0.911923 0.0066 0
1 183 0.920662 0.005926 0
1 184 0.928983 0.005269 0
1 185 0.93688 0.004631 0
1 186 0.944342 0.004016 0
1 187 0.951361 0.003426 0
1 188 0.957931 0.002865 0
1 189 0.964044 0.002334 0
1 190 0.969693 0.001837 0
1 191 0.974872 0.001375 0
1 192 0.979576 0.000951 0
1 193 0.983798 0.000566 0
1 194 0.987535 0.000222 0
1 195 0.990782 -0.000078 0
1 196 0.993535 -0.000335 0
1 197 0.995793 -0.000547 0
1 198 0.997551 -0.000712 0
1 199 0.998808 -0.000831 0
1 200 0.999563 -0.000903 0
1 201 0.999815 -0.000927 0
1 0 1.000185 0.000927 0

32
#group #point #x cord #y cord #z cord
1 1 1 0 0
1 2 0.999758 0.000068 0
1 3 0.999032 0.000274 0
1 4 0.997823 0.000615 0
1 5 0.996132 0.001091 0
1 6 0.993961 0.0017 0
1 7 0.99131 0.002441 0
1 8 0.988183 0.003311 0
1 9 0.984583 0.004308 0
1 10 0.980511 0.005429 0
1 11 0.975972 0.006669 0
1 12 0.970971 0.008026 0
1 13 0.96551 0.009496 0
1 14 0.959595 0.011073 0
1 15 0.953231 0.012753 0
1 16 0.946424 0.014531 0
1 17 0.93918 0.016403 0
1 18 0.931504 0.018362 0
1 19 0.923405 0.020403 0
1 20 0.91489 0.022521 0
1 21 0.905965 0.024709 0
1 22 0.896639 0.02696 0
1 23 0.886921 0.02927 0
1 24 0.876819 0.031632 0
1 25 0.866343 0.034038 0
1 26 0.855503 0.036484 0
1 27 0.844308 0.038961 0
1 28 0.832768 0.041465 0
1 29 0.820896 0.043988 0
1 30 0.808701 0.046523 0
1 31 0.796195 0.049065 0
1 32 0.783391 0.051606 0
1 33 0.770299 0.054141 0
1 34 0.756934 0.056663 0
1 35 0.743307 0.059165 0
1 36 0.729431 0.061641 0
1 37 0.715321 0.064086 0
1 38 0.700989 0.066492 0
1 39 0.68645 0.068855 0
1 40 0.671717 0.071167 0
1 41 0.656806 0.073424 0
1 42 0.64173 0.075619 0
1 43 0.626506 0.077748 0
1 44 0.611147 0.079803 0
1 45 0.595668 0.081781 0
1 46 0.580087 0.083676 0
1 47 0.564417 0.085483 0
1 48 0.548675 0.087197 0
1 49 0.532877 0.088814 0
1 50 0.517038 0.090329 0
1 51 0.501174 0.091737 0
1 52 0.485303 0.093036 0

33
1 53 0.469439 0.09422 0
1 54 0.4536 0.095287 0
1 55 0.437801 0.096233 0
1 56 0.422059 0.097055 0
1 57 0.40639 0.09775 0
1 58 0.390664 0.098305 0
1 59 0.374939 0.098666 0
1 60 0.359335 0.098828 0
1 61 0.343869 0.098792 0
1 62 0.328558 0.098558 0
1 63 0.31342 0.098128 0
1 64 0.298472 0.097504 0
1 65 0.283731 0.09669 0
1 66 0.269213 0.095689 0
1 67 0.254934 0.094505 0
1 68 0.240912 0.093143 0
1 69 0.227162 0.091608 0
1 70 0.213699 0.089906 0
1 71 0.200539 0.088044 0
1 72 0.187695 0.086029 0
1 73 0.175183 0.083867 0
1 74 0.163016 0.081568 0
1 75 0.151208 0.079139 0
1 76 0.13977 0.076589 0
1 77 0.128717 0.073926 0
1 78 0.118058 0.071161 0
1 79 0.107805 0.068302 0
1 80 0.097969 0.06536 0
1 81 0.08856 0.062343 0
1 82 0.079587 0.059261 0
1 83 0.071059 0.056125 0
1 84 0.062983 0.052944 0
1 85 0.055369 0.049728 0
1 86 0.048221 0.046485 0
1 87 0.041547 0.043226 0
1 88 0.035352 0.039959 0
1 89 0.029642 0.036692 0
1 90 0.024421 0.033434 0
1 91 0.019693 0.030193 0
1 92 0.015462 0.026976 0
1 93 0.011729 0.023789 0
1 94 0.008498 0.020639 0
1 95 0.00577 0.017531 0
1 96 0.003547 0.014471 0
1 97 0.001828 0.011461 0
1 98 0.000615 0.008507 0
1 99 -0.000093 0.005611 0
1 100 -0.000298 0.002775 0
1 101 0 0 0
1 102 0.000791 -0.002676 0
1 103 0.002067 -0.005217 0
1 104 0.003823 -0.007622 0
1 105 0.006057 -0.009892 0

34
1 106 0.008765 -0.012027 0
1 107 0.011942 -0.014028 0
1 108 0.015585 -0.015895 0
1 109 0.019688 -0.017629 0
1 110 0.024245 -0.019232 0
1 111 0.02925 -0.020704 0
1 112 0.034698 -0.022047 0
1 113 0.040581 -0.023264 0
1 114 0.046893 -0.024355 0
1 115 0.053626 -0.025324 0
1 116 0.060773 -0.026172 0
1 117 0.068325 -0.026902 0
1 118 0.076274 -0.027517 0
1 119 0.084613 -0.02802 0
1 120 0.093332 -0.028415 0
1 121 0.102423 -0.028706 0
1 122 0.111876 -0.028895 0
1 123 0.121682 -0.028988 0
1 124 0.131831 -0.028989 0
1 125 0.142315 -0.028902 0
1 126 0.153123 -0.028733 0
1 127 0.164245 -0.028487 0
1 128 0.175672 -0.028169 0
1 129 0.187393 -0.027785 0
1 130 0.199398 -0.02734 0
1 131 0.211676 -0.026841 0
1 132 0.224218 -0.026294 0
1 133 0.237011 -0.025705 0
1 134 0.250046 -0.025081 0
1 135 0.263312 -0.024428 0
1 136 0.276797 -0.023753 0
1 137 0.29049 -0.023062 0
1 138 0.30438 -0.022363 0
1 139 0.318455 -0.021661 0
1 140 0.332704 -0.020964 0
1 141 0.347114 -0.020277 0
1 142 0.361674 -0.019608 0
1 143 0.376371 -0.018962 0
1 144 0.391193 -0.018346 0
1 145 0.406228 -0.017759 0
1 146 0.421506 -0.01716 0
1 147 0.436866 -0.016543 0
1 148 0.452292 -0.01591 0
1 149 0.46777 -0.015266 0
1 150 0.483286 -0.014615 0
1 151 0.498826 -0.01396 0
1 152 0.514373 -0.013304 0
1 153 0.529914 -0.012651 0
1 154 0.545433 -0.012003 0
1 155 0.560916 -0.011363 0
1 156 0.576348 -0.010734 0
1 157 0.591713 -0.010118 0
1 158 0.606997 -0.009517 0

35
1 159 0.622184 -0.008932 0
1 160 0.637261 -0.008366 0
1 161 0.652211 -0.007818 0
1 162 0.667021 -0.007292 0
1 163 0.681675 -0.006786 0
1 164 0.696159 -0.006303 0
1 165 0.710459 -0.005841 0
1 166 0.724559 -0.005403 0
1 167 0.738447 -0.004987 0
1 168 0.752108 -0.004593 0
1 169 0.765528 -0.004221 0
1 170 0.778693 -0.003872 0
1 171 0.79159 -0.003543 0
1 172 0.804206 -0.003235 0
1 173 0.816528 -0.002948 0
1 174 0.828544 -0.002679 0
1 175 0.84024 -0.002429 0
1 176 0.851604 -0.002197 0
1 177 0.862625 -0.001982 0
1 178 0.873292 -0.001782 0
1 179 0.883592 -0.001598 0
1 180 0.893516 -0.001427 0
1 181 0.903052 -0.001271 0
1 182 0.912191 -0.001126 0
1 183 0.920923 -0.000994 0
1 184 0.929238 -0.000872 0
1 185 0.937127 -0.000761 0
1 186 0.944583 -0.000659 0
1 187 0.951596 -0.000566 0
1 188 0.95816 -0.000482 0
1 189 0.964267 -0.000406 0
1 190 0.96991 -0.000338 0
1 191 0.975084 -0.000277 0
1 192 0.979783 -0.000222 0
1 193 0.984001 -0.000174 0
1 194 0.987733 -0.000133 0
1 195 0.990977 -0.000097 0
1 196 0.993728 -0.000067 0
1 197 0.995982 -0.000043 0
1 198 0.997739 -0.000024 0
1 199 0.998994 -0.000011 0
#group #point #x_cord #y_cord #z_cord
1 1 1.000000 0.000000 0
1 2 0.999753 0.000036 0
1 3 0.999013 0.000143 0
1 4 0.997781 0.000322 0
1 5 0.996057 0.000572 0
1 6 0.993844 0.000891 0
1 7 0.991144 0.001280 0

36
1 8 0.987958 0.001737 0
1 9 0.984292 0.002260 0
1 10 0.980147 0.002849 0
1 11 0.975528 0.003501 0
1 12 0.970440 0.004216 0
1 13 0.964888 0.004990 0
1 14 0.958877 0.005822 0
1 15 0.952414 0.006710 0
1 16 0.945503 0.007651 0
1 17 0.938153 0.008643 0
1 18 0.930371 0.009684 0
1 19 0.922164 0.010770 0
1 20 0.913540 0.011900 0
1 21 0.904508 0.013071 0
1 22 0.895078 0.014280 0
1 23 0.885257 0.015523 0
1 24 0.875056 0.016800 0
1 25 0.864484 0.018106 0
1 26 0.853553 0.019438 0
1 27 0.842274 0.020795 0
1 28 0.830656 0.022173 0
1 29 0.818712 0.023569 0
1 30 0.806454 0.024981 0
1 31 0.793893 0.026405 0
1 32 0.781042 0.027838 0
1 33 0.767913 0.029279 0
1 34 0.754521 0.030723 0
1 35 0.740877 0.032168 0
1 36 0.726995 0.033610 0
1 37 0.712890 0.035048 0
1 38 0.698574 0.036478 0
1 39 0.684062 0.037896 0
1 40 0.669369 0.039300 0
1 41 0.654508 0.040686 0
1 42 0.639496 0.042052 0
1 43 0.624345 0.043394 0
1 44 0.609072 0.044708 0
1 45 0.593691 0.045992 0
1 46 0.578217 0.047242 0
1 47 0.562667 0.048455 0
1 48 0.547054 0.049626 0
1 49 0.531395 0.050754 0
1 50 0.515705 0.051833 0
1 51 0.500000 0.052862 0
1 52 0.484295 0.053835 0
1 53 0.468605 0.054749 0
1 54 0.452946 0.055602 0
1 55 0.437333 0.056390 0
1 56 0.421783 0.057108 0
1 57 0.406309 0.057755 0
1 58 0.390928 0.058326 0
1 59 0.375655 0.058819 0
1 60 0.360504 0.059230 0

37
1 61 0.345492 0.059557 0
1 62 0.330631 0.059797 0
1 63 0.315938 0.059947 0
1 64 0.301426 0.060006 0
1 65 0.287110 0.059971 0
1 66 0.273005 0.059841 0
1 67 0.259123 0.059614 0
1 68 0.245479 0.059288 0
1 69 0.232087 0.058863 0
1 70 0.218958 0.058338 0
1 71 0.206107 0.057712 0
1 72 0.193546 0.056986 0
1 73 0.181288 0.056159 0
1 74 0.169344 0.055232 0
1 75 0.157726 0.054206 0
1 76 0.146447 0.053083 0
1 77 0.135516 0.051862 0
1 78 0.124944 0.050546 0
1 79 0.114743 0.049138 0
1 80 0.104922 0.047638 0
1 81 0.095492 0.046049 0
1 82 0.086460 0.044374 0
1 83 0.077836 0.042615 0
1 84 0.069629 0.040776 0
1 85 0.061847 0.038859 0
1 86 0.054497 0.036867 0
1 87 0.047586 0.034803 0
1 88 0.041123 0.032671 0
1 89 0.035112 0.030473 0
1 90 0.029560 0.028213 0
1 91 0.024472 0.025893 0
1 92 0.019853 0.023517 0
1 93 0.015708 0.021088 0
1 94 0.012042 0.018607 0
1 95 0.008856 0.016078 0
1 96 0.006156 0.013503 0
1 97 0.003943 0.010884 0
1 98 0.002219 0.008223 0
1 99 0.000987 0.005521 0
1 100 0.000247 0.002779 0
1 101 0.000000 0.000000 0
1 102 0.000247 -0.002779 0
1 103 0.000987 -0.005521 0
1 104 0.002219 -0.008223 0
1 105 0.003943 -0.010884 0
1 106 0.006156 -0.013503 0
1 107 0.008856 -0.016078 0
1 108 0.012042 -0.018607 0
1 109 0.015708 -0.021088 0
1 110 0.019853 -0.023517 0
1 111 0.024472 -0.025893 0
1 112 0.029560 -0.028213 0
1 113 0.035112 -0.030473 0

38
1 114 0.041123 -0.032671 0
1 115 0.047586 -0.034803 0
1 116 0.054497 -0.036867 0
1 117 0.061847 -0.038859 0
1 118 0.069629 -0.040776 0
1 119 0.077836 -0.042615 0
1 120 0.086460 -0.044374 0
1 121 0.095492 -0.046049 0
1 122 0.104922 -0.047638 0
1 123 0.114743 -0.049138 0
1 124 0.124944 -0.050546 0
1 125 0.135516 -0.051862 0
1 126 0.146447 -0.053083 0
1 127 0.157726 -0.054206 0
1 128 0.169344 -0.055232 0
1 129 0.181288 -0.056159 0
1 130 0.193546 -0.056986 0
1 131 0.206107 -0.057712 0
1 132 0.218958 -0.058338 0
1 133 0.232087 -0.058863 0
1 134 0.245479 -0.059288 0
1 135 0.259123 -0.059614 0
1 136 0.273005 -0.059841 0
1 137 0.287110 -0.059971 0
1 138 0.301426 -0.060006 0
1 139 0.315938 -0.059947 0
1 140 0.330631 -0.059797 0
1 141 0.345492 -0.059557 0
1 142 0.360504 -0.059230 0
1 143 0.375655 -0.058819 0
1 144 0.390928 -0.058326 0
1 145 0.406309 -0.057755 0
1 146 0.421783 -0.057108 0
1 147 0.437333 -0.056390 0
1 148 0.452946 -0.055602 0
1 149 0.468605 -0.054749 0
1 150 0.484295 -0.053835 0
1 151 0.500000 -0.052862 0
1 152 0.515705 -0.051833 0
1 153 0.531395 -0.050754 0
1 154 0.547054 -0.049626 0
1 155 0.562667 -0.048455 0
1 156 0.578217 -0.047242 0
1 157 0.593691 -0.045992 0
1 158 0.609072 -0.044708 0
1 159 0.624345 -0.043394 0
1 160 0.639496 -0.042052 0
1 161 0.654508 -0.040686 0
1 162 0.669369 -0.039300 0
1 163 0.684062 -0.037896 0
1 164 0.698574 -0.036478 0
1 165 0.712890 -0.035048 0
1 166 0.726995 -0.033610 0

39
1 167 0.740877 -0.032168 0
1 168 0.754521 -0.030723 0
1 169 0.767913 -0.029279 0
1 170 0.781042 -0.027838 0
1 171 0.793893 -0.026405 0
1 172 0.806454 -0.024981 0
1 173 0.818712 -0.023569 0
1 174 0.830656 -0.022173 0
1 175 0.842274 -0.020795 0
1 176 0.853553 -0.019438 0
1 177 0.864484 -0.018106 0
1 178 0.875056 -0.016800 0
1 179 0.885257 -0.015523 0
1 180 0.895078 -0.014280 0
1 181 0.904508 -0.013071 0
1 182 0.913540 -0.011900 0
1 183 0.922164 -0.010770 0
1 184 0.930371 -0.009684 0
1 185 0.938153 -0.008643 0
1 186 0.945503 -0.007651 0
1 187 0.952414 -0.006710 0
1 188 0.958877 -0.005822 0
1 189 0.964888 -0.004990 0
1 190 0.970440 -0.004216 0
1 191 0.975528 -0.003501 0
1 192 0.980147 -0.002849 0
1 193 0.984292 -0.002260 0
1 194 0.987958 -0.001737 0
1 195 0.991144 -0.001280 0
1 196 0.993844 -0.000891 0
1 197 0.996057 -0.000572 0
1 198 0.997781 -0.000322 0
1 199 0.999013 -0.000143 0
1 200 0.999753 -0.000036 0
1 0 1.000000 0.000000 0
NACA AIRFOIL PROFILES

40
NACA-6409
NACA-4412
NACA-0012

Flow analysis

More Related Content

What's hot (20)

Similar to Flow analysis (20)

More from Amiya Kumar Samal (8)

Recently uploaded (20)

Flow analysis