This report is a simulation for a flow over an airfoil "NACA 0009" at Reynolds number equals 1 million for four angles of attack using three different turbulence models and of cause a grid independence solution. The goal of this study is to apply the knowledge obtained from studying in the university and self-learning in order to solve a specific task of finding the coefficient of drag and lift for the airfoil. A youtube video made by me explaining how to simulate a flow over an airfoil: https://goo.gl/9VYRFM Team members: Ahmed Kamal Shalaby Ahmed Gaber Ahmed Esraa Mahmoud Saleh

1. ALEXANDRIA UNIVERSITY
FACULTY OF ENGINEERING
Mechanical Engineering Department
Hydraulic Machines and Fluid Mechanics Branch.
‫جامعة‬‫ية‬‫ر‬‫اإلسكند‬
‫اهلندسة‬ ‫كلية‬
‫امليكانيكية‬ ‫اهلندسة‬ ‫قسم‬
‫شعبة‬‫اآلالت‬‫املوائع‬ ‫ميكانيكا‬ ‫و‬ ‫اهليدروليكية‬
FLUID MECHANICS II
Third Year
# Name
2 Alaa Refaay Garib
27 Ahmed Gaber Ahmed
53 Ahmed Abd El-Kader
63 Ahmed Kamal Shalaby
102 Esraa Mahmoud Saleh

2. Page | 1
Table of contents
List of figures...............................................................................................................................2
Abstract.......................................................................................................................................3
Introduction .................................................................................................................................4
Problem specification ...................................................................................................................4
Airfoil design...............................................................................................................................5
Grid generation ............................................................................................................................6
General set up ..............................................................................................................................8
Models selection...........................................................................................................................8
Wall treatment..............................................................................................................................9
Domain material.........................................................................................................................11
Boundary conditions...................................................................................................................11
Solution method .........................................................................................................................12
verification.................................................................................................................................13
validation...................................................................................................................................15
Post-processing ..........................................................................................................................17
Comments on results...................................................................................................................18
References .................................................................................................................................18
External links.............................................................................................................................18

3. Page | 2
List of figures
Figure 1 (Problem specification diagram) .................................................................................4
Figure 2 (Design diagram).........................................................................................................5
Figure 3 (Design modeler file)...................................................................................................5
Figure 4 (Trimetric view)...........................................................................................................6
Figure 5 (Named selections)......................................................................................................6
Figure 6 (Generated three grids)................................................................................................7
Figure 7 (Zoom in airfoil grid)...................................................................................................7
Figure 8 (Four regimes of turbulent flow) .................................................................................9
Figure 9 (Implementing a wall function formulation) ...............................................................9
Figure 10 (Y+
)..........................................................................................................................10
Figure 11 (Residuals)...............................................................................................................12
Figure 12 (Pressure verification 1) ..........................................................................................13
Figure 13 (Pressure verification 2) ..........................................................................................13
Figure 14 (Velocity verification 1) ..........................................................................................14
Figure 16 (CL vs angle of attack) ............................................................................................16
Figure 17 (CD vs angle of attack)............................................................................................16
Figure 18 (Pressure contour)....................................................................................................17
Figure 20 (Streamlines)............................................................................................................18

4. Page | 3
Abstract
The goal of this study is to apply the knowledge obtained from studying in the university and
self-learning in order to solve a specific task of finding the coefficient of drag and lift in an
airfoil for several angels of attack using three models.
The software used in this report is ANSYS – FLUENT.

5. Page | 4
Introduction
To accomplish the case perfectly, there are several steps that must be considered.
- Specifying the physical problem.
- A computational domain is chosen, and a grid is generated.
- Boundary conditions are specified.
- The type of fluid (water, air, gasoline, etc.) is specified
- Discretizing the governing equations to find the mathematical model.
- The initial guesses at the center of each cell.
- Once the solution has converged, flow field variables such as velocity and pressure
are plotted and analyzed graphically.
- Global properties of the flow field, such as pressure drop, and integral properties, such
as forces (lift and drag) and moments acting on a body are calculated from the
converged solution.
- Verification of the results
- Validation of the results
- Grid independence results
- Plotting the relation between 𝐶𝐿, 𝐶 𝐷 and angle of attack
Problem specification
• Simulating a flow over the air foil “NACA 0009” with Reynolds number equals 106
for 4 angles of attack (0°,5°,10° and 15°).
• Finding the coefficient of lift 𝐶𝐿 and the coefficient of drag 𝐶 𝐷 for each case.
• Plotting 𝐶𝐿 and 𝐶 𝐷 against the angle of attack.
• Comparing the results with the results of the internet for the same conditions.
• Comparing between different turbulence models.
• Finally, making a grid independence solution using three different grids.
Figure 1 (Problem specification diagram)

6. Page | 5
Airfoil design
- Downloading the airfoil (NACA 0009) coordinates from the internet and edit it on
Excel to be readable for ANSYS design modeler by saving it as text (.txt file)
- Importing the coordinates to the modeler and draw the fluid domain
- Subtract the airfoil from the domain
- Divide the domain to 6 regions
- Naming the boundary condition faces
Next figure shows the final look at the file before generating the grid,
Figure 2 (Design diagram)
Figure 3 (Design modeler file)

7. Page | 6
Grid generation
The grid is very important to accomplish accurate results, so the case and the results must be
grid independent.
For that the case is solved at one angle, one model and three grids and if the results are the
same we will continue the report with only the fine grid.
P.S: The results of the grid independence are in the results section.
The following table shows the characteristics of the three grids,
Course Medium Fine
No. of elements 75000 236250 600000
Skewness 0.40048 0.43971 0.39993
Aspect ratio 62.317 63.482 63.992
Figure 4 (Trimetric view)
Figure 5 (Named selections)

8. Page | 7
P.S: The meshing also depends on anther parameter which is 𝑦+
, but that will be explained
later in the set-up section.
Figure 6 (Generated three grids)
Figure 7 (Zoom in airfoil grid)

9. Page | 8
General set up
- The free stream velocity is not even close to sonic speed, so the type of solver is
pressure-based.
- The velocity is absolute and the case will be solved as steady.
- The gravity effect on the airfoil is neglectable.
P.S: At first the case is solved with the fine grid, with one model for all the angles of attack,
then solved with 2 other solvers.
Models selection
The solving method is based on Reynolds-Averaged Navier-Stokes(RANS)
- Variables decomposed in a mean part and a fluctuating part, u = 𝑢̅ + 𝑢̀
- Navier-Stokes equations averaged over time
- Turbulence models are necessary
First model is Realizable k–ε which has some benefits:
- Accurately predicts the spreading rate of both planar and round jets.
- Also, likely to provide superior performance for flows involving rotation, boundary
layers under strong adverse pressure gradients, separation, and recirculation.
Second model is RNG k–ε which has a modified dissipation rate equation.
Third model is Shear Stress Transport k–ω (SST) which is the best of them
The SST model is a combination of the k-ε model in the free stream and the k-ω model near
the walls.
- The SST k–ω model uses a blending function to gradually transition from the standard
k–ω model near the wall to a high-Reynolds-number version of the k–ε model in the
outer portion of the boundary layer.
- Contains a modified turbulent viscosity formulation to account for the transport
effects of the principal turbulent shear stress.
- SST model generally gives accurate prediction of the onset and the size of separation
under adverse pressure gradient.
So, the three models are Realizable k–ε, RNG k–ε and SST k–ω.
P.S: The energy equation is deactivated as it has a neglectable effect on the results.

10. Page | 9
Wall treatment
The turbulent flow near a wall can be divided into four regions. At the wall, the fluid velocity
is zero, and in a thin layer above this, the flow velocity is linear with distance from the wall.
This region is called the viscous sublayer, or laminar sublayer. Further away from the wall is
a region called the buffer layer. In the buffer region, turbulence stresses begin to dominate
over viscous stresses and it eventually connects to a region where the flow is fully turbulent
and the average flow velocity is related to the log of the distance to the wall. This is known as
the log-law region. Even further away from the wall, the flow transitions to the free-stream
region. The viscous and buffer layers are very thin and if the distance to the end of the buffer
layer is 𝛿 , then the log-law region will extend about 100𝛿 away from the wall.
Since the thickness of the buffer layer is so small, it can be advantageous to use an
approximation in this region. Wall functions ignore the flow field in the buffer region and
analytically compute a nonzero fluid velocity at the wall. By using a wall function
formulation, you assume an analytic solution for the flow in the viscous layer and the
resultant models will have significantly lower computational requirements. This is a very
useful approach for many practical engineering applications.
Figure 8 (Four regimes of turbulent flow)
Figure 9 (Implementing a wall function formulation)

11. Page | 10
The equilibrium assumption is used to set boundary conditions for turbulent kinetic energy
(k), dissipation rate (ε) or specific dissipation rate (ω), that was one of the main reasons for
choosing those three models.
Wall functions allow the use of a relatively coarse mesh in the near-wall region thereby
reduce the computational cost and helps with the grid independence.
The chosen wall function is the Scalable Wall Function.
- For k–ε models, the scalable wall functions method assumes that the wall surface
coincides with the edge of the viscous sublayer (y* = 11.26). Hence fluid cells are
always above the viscous sublayer, and inconsistency of predictions due to near-wall
mesh refinement is avoided.
- In the SST model, near-wall treatment is handled automatically by the solver; scalable
wall functions are not available.
P.S: 𝑌+
range should be 30> 𝑌+
> 500
So, after solving the case the 𝑌+
is checked and it was 92.43 (O.K)
Figure 10 (Y+)

12. Page | 11
Domain material
The domain is air and assuming that the temperature is 25°C we can get all needed properties
of the air using an online calculator “link in the external links section”
µ=1.8444*10−5
Kg/m.s, ρ=1.1845 Kg/𝑚3
Boundary conditions
Calculating the free stream velocity:
Re =
𝜌𝑉𝐿
µ
= 106
1.1845 ∗ 𝑉∞ ∗ 1
1.8444 ∗ 10−5
= 106
𝑉∞= 15.571 m/s
The inlet:
velocity-inlet and the specification method is “components”.
X = V cos 𝛼
Y = V sin 𝛼
Z = 0
Where α is the angle of attack.
For the turbulence part:
The turbulence intensity in the free stream is usually available from the tunnel characteristics.
In modern low-turbulence wind tunnels, the free-stream turbulence intensity may be as low as
0.05%, but unfortunately, we couldn’t find any experimental data for this case.
So, we used data from a similar case for NACA 0012 at Re equals 6 million from NASA
Langley Research Center. “link in the external links section”
Turbulence intensity=0.052%
Freestream turbulent viscosity=0.009
The previous data could be hand calculated as in sharcnet but there is no need for that.
The outlet:
Pressure-outlet and the gauge pressure is zero.
Turbulence intensity and freestream turbulent viscosity are the same like inlet.
Airfoil:
Airfoil boundary type is wall.

13. Page | 12
Solution method
• Scheme: coupled
At first the case is solved with first degree equations to have a better initial guess. then solved
as second degree for more accurate results.
• Residuals are set to 1 ∗ 10−6
• Reported files:
For 𝐶𝐿, x = - sin 𝛼 y = cos 𝛼
𝐶 𝐷, x = cos 𝛼, y = sin 𝛼
Figure 11 (Residuals)

14. Page | 13
verification
The verification is done after the initialization of the initial guesses on the boundary
conditions to be exactly as we set before.
Verification here is an example using the fine mesh at 0° angle of attack.
Next figure shows the pressure contour
Figure 12 (Pressure verification 1)
Figure 13 (Pressure verification 2)

15. Page | 14
Next figure shows the velocity contour,
As shown in the previous figures:
- At stagnation point, pressure is maximum and velocity equals zero
- At the inlet, the velocity is as we set before
- At the outlet, the pressure is atmospheric
- At the airfoil wall, velocity equals zero
Figure 14 (Velocity verification 1)
Figure 15 (Velocity verification 2)

16. Page | 15
validation
As we don’t have any experimental data, the validation in this report is using the data from
the internet that made using xfoil software. “link in the external links section”
There are 2 kinds of data at Re=106
: Ncrit=9 & Ncrit=5
We used Ncrit=9 as it refers to standard wind tunnels and commonly used.
The coefficient of lift using fine grid:
Internet K- ε realizable K- ε RNG K-ω SST
0° 0.0000 0.0000 0.0000 0.0000
5° 0.6245 0.54921 0.54530 0.50511
10° 1.0642 0.90976 0.93351 0.85761
15° 1.1258 0.71796 0.70016 0.72380
The coefficient of drag using fine grid:
Internet K- ε realizable K- ε RNG K-ω SST
0° 0.00422 0.00152 0.00153 0.00153
5° 0.00923 0.00632 0.00621 0.01664
10° 0.01621 0.04919 0.04842 0.05756
15° 0.06115 0.13511 0.13689 0.13773
Grid independence results using K- ε realizable at zero angle of attack:
Coefficient of lift results:
Course Medium Fine
No. of elements 75000 236250 600000
Internet 0.00000 0.00000 0.00000
ANSYS 0.00000 0.00000 0.00000
Coefficient of drag results
Course Medium Fine
No. of elements 75000 236250 600000
Internet 0.00422 0.00422 0.00422
ANSYS 0.00202 0.0 1730 0.00152

17. Page | 16
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16
CL vs α
Internet K- ε realizable K- ε RNG K-ω SST
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 2 4 6 8 10 12 14 16
CD vs α
Internet K- ε realizable K- ε RNG K-ω SST
Figure 15 (CL vs angle of attack)
Figure 16 (CD vs angle of attack)

18. Page | 17
Post-processing
The following figures are the results for 5° angle of attack using K- ε realizable
Figure 17 (Pressure contour)
Figure 19 (Velocity contour)

19. Page | 18
Comments on results
- Results are very close using small angles of attack and increasing the angle of attack
to 15° comes with decreasing the accuracy of the solution which makes sense because
the stall angle is around 12.75°
References
- Fluid Mechanics Fundamentals and Applications - Yunus A. Cengel.
- Computational Fluid Dynamics, Principles and Applications - J. Blazek.
External links
- http://airfoiltools.com/
- https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-
application/
- http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html
- https://www.sharcnet.ca/Software/Fluent6/html/ug/node217.htm
- https://turbmodels.larc.nasa.gov/
- https://confluence.cornell.edu/
End of the report
Figure 18 (Streamlines)