Project 1 Flow past Airfoil

School of Engineering Taylor’s University

MEC4513 COMPUTATIONAL FLUID DYNAMICS (CFD) Individual Project 1 Flow Past a NACA Airfoil Test

NAME : CHIN JITVE ID NO : 1002B71539 YEAR/SEM : YEAR 4 / SEMESTER 7

School of Engineering Taylor’s University Malaysia 14th October 2012

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Table of Contents ABSTRACT ………………………………………………………………………………...3 1.0 Introduction………………………………………………………………………..3 Project Objective ………………………………………………………………....4 Problem Statement ………………………………………………………………..4 2.0

Literature Review …………………………………………………………………5 NACA Airfoil …………………………………………………………………….5 Bernoulli’s Principle ……………………………………………………….……..6 Lift and Drag ……………………………………………………………...……...6

3.0

Research Methodology …………………………………………………………...7 Physical Model ……………………………………………………………………7 Computational Domain …………………………………………………………...8 Solution Setup …………………………………………………………………….9 Turbulence Model ……………………………………………………………….11

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Results and Discussions …………………………………………………………15 Coefficient of Pressure ……………………………………………….………….15 Coefficient of Lift and Drag on Increasing AoA—Inviscid …………….…...…17 Coefficient of Lift and Drag on Increasing AoA—Spallart-Allmaras ……..…..18 Bernoulli’s Principle Concept ………………………………………….………..22

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Recommendation ………………………………………………………………..24 Drag Coefficient ………………………………………………………………...24 Settings for Fluent ……………………………………………………………....24 Suggestion for Further work …………………………………………………….25

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Conclusion ………………………………………………………………………25

References …………………………………………………………………………………26 Appendix ………………………………………………………………………………….29

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ABSTRACT The complex commercial computational fluid dynamics (CFD) software, FLUENT offers a convenient way to model a fluid dynamic problem. This study involves a subsonic fluid flow past a two dimensional NACA airfoil 0012. The procedure is done following a reliable tutorial from Cornell University. The geometry and meshes used are the same for every test or model. However, computational set up such as inlet, outlet, boundary condition and turbulence model are varied to see if there is any improvement as close as the experimental data. Lift and drag coefficients, pressure and velocity component are determined using two types of turbulence models, inviscid and Spallart-Allmaras. Theories of aircraft are explained and comparison showed excellent agreement among the results.

1.0

Introduction

Advances in computing technology and software have revolutionized the design process of engineering vehicles such as aircraft and automobiles. In the area of fluid dynamics, there are many commercial computational fluid dynamics (CFD) packages available for modeling flow in or around objects [1]. There are three main components to the implementation of CFD methodology: pre-processing, solving and post processing. Pre-processing includes the creation of geometry, mesh generation, physics and fluid properties and boundary conditions. There are many ways to solve the pre-processing problem, ranging from transport equations, physical models and solver settings. Lastly, we can interpret and view the results in form of XY plots, velocity vectors, contour and so on. Figure 1 bellows shows the flow chart of the overall analysis.

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Figure 1: Flowchart of The Three Main Elements of a CFD Analysis [2] Project Objective The foremost objective of this project is to reproduce published or experimental data for NACA 0012 in the subsonic flow regimes in order to become familiar with the software interface and functions. This project is to expand ones understanding about the concept of the software by creating a situation or environment of a real life problem, and also to find a suitable method to get the desired results by varying inputs supported by solid evidence.

Problem Statement Lift and drag coefficient is the most fundamental parameters in flight of an aircraft. It is to determine whether if the wing would generate lift instead of induced drag, moving through the high rate mass flow with other parameters involved such as angle of attack (AoA) and shape and sizes of airfoil. The motivation of this study is to know how to obtain the lift and drag coefficient using CFD software, FLUENT because it convenient as the user can do many setting. The data gained in this FLEUNT can provide answers to problems. The problem addressed are as follows: 1. For inviscid model, does the pressure coefficient at AoA of 6 degrees coincide with the benchmark value? 2. For inviscid model, does the lift and drag coefficient at AoA of 6 degrees coincide with the benchmark value? 4


3. How does the lift and drag coefficient change on increasing AoA? 4. Validate the principle behind Bernoulli’s principle

2.0

Literature Review

This section contains brief literature review of basic knowledge of what is needed for the project. NACA Airfoil It is important to know the fundamentals of an airfoil or wings of an aircraft. This can specifically determine what is needed to be analyzed by varying the components of the airfoil. Figure 2 below shows the nomenclature of airfoil of an aircraft in the aviation field.

Figure 2: Airfoil Nomenclature [3] The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The NACA airfoil shape and sizes is determined using series of code either from the commonly four-digit series to a more complex five-digit series or 8 digit series. Definition of four digit series are as follows [4]: Four digit series : 1 2 3 4 1—maximum camber as percentage of the chord 2—distance of maximum camber from the airfoil leading edge in tens of percent’s of the chord 34—maximum thickness of the airfoil as percent of the chord.

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In this project, NACA 0012 is used. It was chosen because it has been used for many applications such as the B-17 Flying Fortress and Cessna 152. The helocpter Sikorsky S-61 SH-3 Sea King as well as horizontal and vertical axis wind turbines [5]. NACA 0012 has a maximum camber of 0% located 0% from the leading leading edge with a maximum thickness of 12% of the chord, which makes it a symmetric airfoil.

Bernoulli’s Principle Bernoulli’s principle describes the behavior of a fluid moving along a streamline. It states that an idea fluid without viscosity of friction, running through along a closed pipeline, the total energy remains constant throughout its length. Basically what stated here is an increase in flow speed lead to a reduction of pressure, and conversely, if the flow speed is reduced the pressure increases. The Bernoulli’s equation is given by [6]:

Where P = pressure density V = velocity g = gravitational acceleration h = elevation

Assumptions: points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction

Lift and Drag Lift and drag depends on the density of air, square of velocity, the air’s viscosity and compressibility, the size and shape of the body and the body’s inclination to the flow [7,8]. All these parameters are complex. To overcome this problem, lift and drag (CL and CD) coefficient is used to characterize the dependence with a single variable. [7] [8]

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3.0

Research Methodology

This section explains specifically about the methodology of CFD analysis. Physical setup, computational domain, solution setup and choices of turbulence model are explained in order as procedure.

PROCEDURE The procedure of this project is done following a tutorial on ‘Flow over an Airfoil’ section from Cornell University [9]. 1. For this case, a symmetrical NACA 0012 airfoil is used the velocity entering is at six degree angle of attack, with total magnitude of 1. The gauge pressure at the inlet is to be 0. As for the outlet, gauge pressure is also assumed to be 0. The airfoil will be treated as a wall.

Physical Model 2. The geometry of NACA 0012 airfoil can be generated at NACA 4 Digits Series Profile Generator website as shown in Figure 3 [10]. These coordinates are then imported into Excel worksheet and saved as text file.

Figure 3: Airfoil Profile Generator 7


3. ANSYS Design Modeler configured to 2D analysis and opened in the project schematic window. Coordinate files are imported into the Design Modeler by using ‘Concept 3D Curve’. 4. After the outline of the airfoil is generated, a surface is needed to be created within the outline. This is done so by clicking ‘Concepts Surface from Edges’.

Computational Domain 5. Next, a control fluid volume is needed to specify boundary conditions. This is done by creating a plane at the tail end of the wing and using simple sketching tool to draw a semicircle and a rectangle around the airfoil. 6. The sketches drawn are made to a surface with ‘Concept Surface from sketches’. Operation is set to frozen as to prevent the geometry airfoil from combining with the geometry that is created after freeze. Also Boolean is created between the C-mesh domain surface and the airfoil. 7. The control fluid volume is sliced and divided into four parts. Slicing the fluid volume into smaller volumes allows for greater control over mesh sizing. Then, the divided lines created by sketches will be projected onto the surface of the fluid volume to create the four quadrants. 8. Next, mapped face meshing control is applied to the geometry. Edge sizing is done to help smooth the transition between the four separate fluid volumes and creates a refined mesh around the airfoil. For the wall of the control fluid, number of divisions are set to 50 and behavior is set to hard. The first bias or the second bias type for the upper section and lower section, and bias factor of 150 is set. As for the curve part of the control fluid, number of division is set to 100 and hard, but the edges are not biased. Mesh is then generated as shown in Figure 4 and Figure 5.

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Figure 4: Full Domain Mesh

Figure 5: Close-up Mesh around Airfoil Solution Setup 9. Setup is then opened. Density based solver is chosen and viscous model is chosen to be inviscid. Flow of fluid is assumed to have no viscosity (frictional force). Density of air is assumed to be 1 kg/m3 for simplified calculations. Material chosen is air and the density is set to be constant.

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10. Figure 6 shows that as for boundary condition, the inlet velocity is at six degree angle which means cos and sin for both X-velocity and Y-velocity component. In this case, velocity inlet for X-velocity is cos6=0.9945 m/s and for Y-velocity is sin6=0.1045 m/s.

Figure 6: Velocity Inlet at 6 Degree 11. The outlet boundary condition type is set to pressure-outlet as for the airfoil is wall. 12. After that, solution method is configured by setting second order upwind for flow spatial discretization. This is to make the results more accurate. 13. Before simulation can be started, setting of FLUENT will solve simulation is based on user’s desire method. Here, the absolute convergences criteria are changed to 1e-6 to give more refine results or data. The method is initialized and then calculated for a number of iterations until the solution converges as shown in Figure 7.

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Figure 7: Convergence of Residual Plots against Number of Iterations

Turbulence Model 14. The same procedure is repeated with different velocity and reynold’s number and also supposedly using different turbulence model such as shown in Table 1 to make better comparison against one another. But only inviscid and Spallart-Allmaras was considered in this project as there was benchmark for the purpose of this project as benchmark for other models is hard to find and more complex.

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Table 1: Comparison of RANS Turbulence Model [11]

Inviscid flow past an airfoil Inviscid flow is used to simplify a complex problem. It is the flow of an ideal fluid that assumes no viscosity. The assumption that viscous forces are negligible can be used to simplify the Navier-Stokes solution to the Euler equations. Navier-stokes equation :

[12] This type of flow involves a balance between pressure gradients and convective acceleration. Since the flow is steady, the local (unsteady) acceleration is zero. Since the fluid is inviscid ( =0), there are no viscous forces. Convective acceleration and pressure gradients:

Spallart-Allmaras turbulent model Another model chosen is Spallart-Allmaras turbulence model. It is a relatively simple oneequation model that solves a modelled transport equation for the kinematic eddy (turbulent) 12


viscosity. It has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is economical and accurate for attached wall-bounded flows and flows with mild separation and recirculation but weak for massively separated flows, free shear flows and decaying turbulence, in which in this case is not significant [5].

[5]

[5]

[5] Where ̅ = operating parameter v = molecular viscosity S = magnitude of vorticity d = distance to the closest wall dt = distrance from point in the flow field to the trip on the wall wt= wall corticity at the trip = difference between velocity at the field point and that at the trip, gt = min (0.1,

/ wt

= grid spacing along the wall at the trip Therefore, these two models were selected as there was a benchmark to compare.

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Table 2: Summary of Parameter Settings Inviscid

Spallart-Allmaras

Type of airfoil

NACA 0012

Analysis type

2D

Length of chord

1m

Dimension of fluid volume (C-Mesh domain)

Radius of semicircle (front)–12.5 m Horizontal length of rectangular block (back) –12.5 m

MESH (Mesh Statistics) Nodes

40400

Elements

40000

Edge Sizing (rectangular) Number of Divisions

100

Behavior

Hard

Bias Type

_____ ___ _ _ (first option)

Bias Factor

150

Edge Sizing 2 (rectangular) Number of Divisions

100

Behavior

Hard

Bias Type

_ _ ___ _____ (second option)

Bias Factor

150

Edge Sizing 3 (semicircle) Number of Divisions

100

Behavior

Hard

Bias Type

No Bias

SETUP

(double precision and series processor)

Solver

Density based

Convergence Absolute

1e-6

Criteria (all residual eq) Number of iterations

5000

BOUNDARY CONDITION

Gauge pressure at inlet and

0 14


outlet Velocity inlet Magnitude

1 m/s

43.82204082

Angle of attack (degree)

6 (benchmark testing), 0-20

0-20

X-velocity

0.9945

Varies

Y-velocity

0.1045

Varies

Density (kg/m3)

1

1.225

Viscosity

--

1.7894x10-5

Reynold’s number

--

3x106

4.0

Results and Discussions

This section answers the issues as stated in problem statement above. All necessary comparisons were made in conjunction with benchmark available.

Inviscid—Coefficient of Pressure (Cp) at AoA = 6 degrees The pressure coefficient along the airfoil is compared for the experimental data and the CFD simulation [9].

Figure 8: Coefficient of Pressure of Experimental Data and FLUENT Simulation [9] 15


Figure 9: Coefficient of Pressure of Obtained As can be seen from Figures above, the CP obtained can be represent the red crosses in Figure 8, that is 40000 elements. The pattern of the graph of CP obtained is similar to the experimental data just that the y-axis is inverted. It also can be seen that the peak for the positive value of CP is 1 and the tail end of the graph at 1m is approximately 2.5. However, the peak value of negative CP is slightly different with the experimental data which may be due to meshing problems which involve accuracy, types and way of meshing, nodes and elements and so on.

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Inviscid—Coefficient of Lift (CL) and Drag (CD) at AoA = 6 degrees The lift and drag coefficient was determined at angle of attack of 6 degrees and also the velocity magnitude of air.

Table 3: Comparison of Coefficient of Drag and Lift of Obtained and Experimental Data Obtained Data

Experimental Data [9,13,14]

Lift Coefficient (CL)

0.68215323

0.6630

Drag Coefficient (CD)

0.0036004795

0.0090

Table 1 shows that at that particular velocity of air and angle of attack, the CL obtained, 068215323 is very close to the experimental data, 0.6630. Contrariwise, drag coefficient shows the opposite. The CD for obtained is 0.0036004795 which is far apart from the experimental value, 0.0090. The percentage error for CL is acceptable range whereas percentage error for CD is

= 2.89% which is in the = 60% which lies

outside the acceptable error margin. This may be due to inaccuracy and unsuitability of settings in the boundary conditions as FLUENT interface is complex. It is very hard to determine the accurate CD values in FLEUNT as other works is found to have 20% error in CD and 5-10% error in CL [15].

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Spallart-Allmaras (SA) --Performance of Lift and Drag Coefficient (CL & CD) of Airfoil on Increasing AoA Table 4: Lift Coefficient on Increasing AoA Angle of Attack(O) 0 5 10 15 20

Drag Coefficient 0.009981315 0.012809639 0.024619832 0.25374234 0.21935411

Lift Coefficient -7.20E-05 0.52885362 0.9959853 1.1405255 0.81872978

Lift Coefficient (CL) against the angle of attack (AoA) 1.40E+00 1.20E+00 1.00E+00 y = -0.0003x3 + 0.0023x2 + 0.1027x - 0.0017 R² = 0.9998

8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00 0

5

10

15

20

-2.00E-01

Figure 10: Data Obtained for Lift Coefficient Against Angle of Attack (AoA)

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Figure 11: Comparison between experimental data from Abbott et al and three different turbulent models simulation results of the lift coefficient curve for NACA 0012 airfoil [5] Table 4 and Figure 10 and Figure 11 show that lift coefficient increases when angle of attack increases. The dimensionless lift coefficient increased linearly with angle of attack. Flow was attached to the airfoil throughout this regime. At an angle of attack roughly 15 to 16o, the flow on the upper surface of the airfoil began to develop [16]. Stall is said to happen. Stall is an undesirable phenomenon in which the aircraft wings produce an increased air resistance and decreased lift. It usually occurs when critical angle attack of airfoil is exceeded. The critical angle is usually around 16o for light aircraft, without high-lift devices.

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Figure 12: Stalled Airfoil [16]

Drag Coefficient (CD) against the Angle of Attack (AoA) 0.35 0.3 0.25

y = -5E-05x4 + 0.0017x3 - 0.0166x2 + 0.048x + 0.01 R² = 1

0.2 0.15 0.1 0.05 0 -0.05

0

5

10

15

20

Figure 13: Data Obtained for Drag Coefficient Against Angle of Attack (AoA)

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Figure 14: Comparison between experimental data for fully turbulent boundary layer from Johansen and three different turbulent models simulation results of the drag coefficient curve for NACA 0012 airfoil [5] As for drag coefficient, the obtained data and the experimental data is very different. The obtained graph shows that the drag coefficient value is almost ten times as much compared to the experimental value. Also, the pattern of the graph in Figure 13 and Figure 14 is obvious, that the obtained data for drag coefficient fluctuates and AoA increases whereas it should have been a Ushape parabolic curve. The errors are explained further Recommendation section.

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Show the concept of Bernoulli’s principle Inviscid flow at velocity magnitude of 1 m/s and angle of attack of 10 degrees.

Figure 15: Velocity Vector of Airfoil from Top Isometric and Side View

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Figure 16: Pressure Contour of Airfoil from Top Isometric and Bottom Isometric View Bernoulli’s principle can be explained by referring to Figure 15 and Figure 16. As stated before in Literature Review, Bernoulli’s principle is simply means that pressure is inversely proportional to the velocity. Because airfoil has a smoother surface at the upper surface, the air tends to travel faster on the upper surface compared to the lower surface as shown in Figure 15 by the green-ish to red-ish zone colour which indicates high velocity. The lower surface has lower velocity indicated by the blue-ish zone colour. When there is high velocity, there is low pressure and vice versa as shown in Figure 16 by the zone colours. Air in the region of high pressure will travel to the lower pressure, thus generating lift. Thus, this proves that simulation using FLUENT can provide clarity to explain certain characteristics through graphics and numerical problem solving method. 23


5.0

Recommendation

All errors and inaccuracy of data obtained and how to improve is explained in this section. Drag coefficient It is found that drag coefficient obtained using FLUENT are always higher or lower than the experimental data when using turbulent model. This prediction are expected as the front half of the airfoil has laminar flow. The turbulence models cannot calculate the transition point from laminar to turbulent and consider that the boundary layer is turbulent throughout its length. Johansen (1997) contained experimental data of CD for NACA 0012 airfoil and Re=3x106, where boundary layer formed around airfoil is fully turbulent. It is established that for accurate CD, the most accurate model was the k-w SST model, second came the Spallart-Allmaras and latest in precision was the Realizable k-e as shown in Figure 14[5]. Thus, the turbulent model k-w SST model should be used instead but there is not enough information and time to do the simulation.

Settings for FLUENT The results and data obtained is less accurate and far from the experimental due to several factors such as meshes, turbulence model, boundary conditions and so on. To overcome this problem, the meshes around the airfoil should be C-type grid topology with high enough number of elements in such a way that meshes around airfoil edge is smooth. The type of element used should be hybrid between quadrilateral, triangular and tetrahedral elements.

Figure 17: Flow Regions around the Airfoil [5] Other than that, computational domain could be split into two different domains as shown in Figure 17 to run on mixed laminar and turbulent flow. It is found that the maximum error gained 24


is about 3.6%(closest as of now) for comparison of split grid and experimental data from McCroskey for transitional boundary layer [5]. The only downside is that the transition point have to be calculated through trial and error using CD as a benchmark. A new grid have to be generated if the transition point had to change (Silisteanu-Botez, 2010) [5].

Suggestion for Further Work The investigation of vortex generation should be implemented for better understanding of airfoil drag and lift. 3D analysis should be done instead of 2D for accuracy. Other turbulence model such as

6.0

Conclusion

In brief, the flow of NACA airfoil can be simulated in every way possible depending on user input parameters using FLUENT. Multiple problems can be solved without the need of building a physical setup everytime for testing, thus cost effective. It also can provide better understanding and explanation through graphics and animation such as the Bernoulli’s principle as the airfoil travels in a fluid medium with varying angle of attack. For this case, as for inviscid flow, the results gained does coincide with the experimental value, like pressure and lift coefficient. However, more improvement is needed for calculating drag coefficient as it has high error percentage from the experimental data. Besides that, Spallart-Allmaras model is needed to be tested with more configuration to fully utilize the accuracy of this turbulent model.

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References [1]

Yassin, A.A.A.A & Elbashir A.M.A, 2011, Report of Simulation of Aerofoil NACA 4412 , University of Khartoum, Scribd.com, [online] Accessed on 8th October 2011 from http://www.scribd.com/doc/60960153/Report-of-Fluent-Simulation-of-Aerofoil-NACA4412

[2]

Salim M.S., 2012, CFD Solution Procedure—Part A, Accessed on 8th October 2012

[3]

Sharma A., 2012, Evaluation of Flow Behavior Around An Airfoil Body, Department of Mechanical Engineering, Thapar University, India, [online] Accessed on 9th October 2012 from http://dspace.thapar.edu:8080/dspace/bitstream/10266/2043/1/aman+sharma+801081033. pdf

[4]

The NACA Airfoil Series, undated, [online] Accessed on 10th October 2012 from http://people.clarkson.edu/~pmarzocc/AE429/The%20NACA%20airfoil%20series.pdf

[5]

Eleni D.C., Athanasios T.i. and Dionissios M.P., 2012, Evaluation of the turbulence models for the simulation of the flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil, Journal of Mechanical Engineering Research, Vol 4 (3), pp. 100-111.

[6]

Bernoulli’s Equation, undated, [online] Accessed on 7th October 2012 from http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

[7]

Benson T., undated, The Lift Equation, National Aeronautics and Space Administration, NASA Glenn Research Center, Cleveland, OH, [online] Accessed on 10th October 2012 from http://exploration.grc.nasa.gov/education/rocket/lifteq.html

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[8]

Benson T., undated, The Drag Equation, National Aeronautics and Space Administration, NASA Glenn Research Center, Cleveland, OH, [online] Accessed on 10th October 2012 from http://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/drageq.html

[9]

Mullen B.J., 2011, FLUENT Learning Module: Flow over an Airfoil, Cornell University, [online] Accessed on 7th October 2012 from https://confluence.cornell.edu/display/SIMULATION/ANSYS+WB+-+Airfoil++All+Pages

[10]

Trapp J. and Zores R., undated, NACA 4 Digits Series Profile Generator, [online] Accessed on 7th October 2012 from http://www.ppart.de/aerodynamics/profiles/NACA4.html

[11]

Bakker A., 2002, Applied Computational Fluid Dynamics—Turbulence Models, Dartmouth College, [online] Accessed on 11th October from http://www.bakker.org.

[12]

Bakker A., 2002, Applied Computational Fluid Dynamics—Classification of Flows, Dartmouth College, [online] Accessed on 11th October from http://www.bakker.org.

[13]

Sheldahl, R. E. and Klimas, P. C., March 1981, Aerodynamic Characteristics of Seven Airfoil Sections Through 180 Degrees Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines, Sandia National Laboratories, Albuquerque, New Mexico, [ online] Accessed on 13th October 2012 from http://www.cyberiad.net/library/airfoils/foildata/n0012cd.htm

[14]

Sheldahl, R. E. and Klimas, P. C., March 1981, Aerodynamic Characteristics of Seven Airfoil Sections Through 180 Degrees Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines, Sandia National Laboratories, Albuquerque, New Mexico. [online] Accessed on 13th October 2012 from

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http://www.cyberiad.net/library/airfoils/foildata/n0012cl.htm [15]

Calculating Drag Coefficient from FLUENT, 2000, CFD Online, [online] Accessed on 14th October 2012 from www.cfd-online.com

[16]

Aerodynamics: Stall and Spin, undated, [online] Accessed on 12th October 2012 from http://adamone.rchomepage.com/index6.htm

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Appendix Inviscid || velocity=1m/s || angle of attack=10 degree

Figure 18 : Streamline of Airfoil

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Figure 19: Pressure Gradient of Airfoil

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Figure 20: Vortex Swirling Strength

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Figure 21: Overall Contours vectors of airfoil

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Project 1 Flow past Airfoil

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