1. PROJECT:
TO COMPARE DIFFERENT TURBULENCE MODELS FOR THE
SIMULATION OF THE FLOW OVER NACA0015 AIRFOIL
MME 9614
Applied Computational Fluid Mechanics and Heat Transfer
9th
December, 2015
Student Name: Kirtan R. Gohel Instructor Name: Professor C. Zhang

2. 1 | P a g e
1. Description:
While dealing with the simulation of an aerofoil sometimes it is confusing to determine which
turbulent model is most suitable for particular aerofoil. For that purpose, consider an aerofoil
of NACA0015 in a 2D plane. Profile of NACA0015 is symmetrical. Simulation of that
NACA0015 is done using ANSYS Fluent 16.0 and then it is determined which model is most
suitable for that aerofoil. Table 1.1 gives the parameters used for simulation.
Reynold's Number (Re) 3.20E+06
Density (𝜌) 1.225
Length of an aerofoil (L) 1 m
Dynamic viscosity (𝜇) 1.79E-05
Velocity (V) 46.74351 m/s
Table 1.1: Parameters for simulation
Below figure 1.1, represents the profile of NACA0015 in ICEM. That profile is taken from
aerofoil database [1]
.
Figure 1.1: Profile of NACA0015 aerofoil
2. Objective:
The main objective of that project is to determine which turbulent model is the most suitable
for the simulation of that NACA0015 aerofoil. In that project, firstly when the air is flowing
over an aerofoil then as per the angle of attack of air with the chord of an aerofoil, it exerts
some pressure on it. With different angle of attacks, its lift and drag co-efficient has to be
observed using different turbulence models and then to compare with the experimental data.
For comparison, turbulent models used are k-omega model, k- epsilon model and k-kl-omega
model.

3. 2 | P a g e
3. Numerical Model:
For that flow of air over an aerofoil, conservation equations for mass and momentum are
solved by solver. Following equations represents, conservation of mass and momentum as well
as continuity and momentum equations.
 Conservation of mass or continuity equation:
Equation for conservation of mass or continuity equation can be written as follows:
𝜕𝜌
𝜕𝑡
+ ∇. ( 𝜌𝑢⃗ ) = 𝑆 𝑚 Eq. (1)
Where, Sm = Mass added to the continuous phase from the dispersed second phase (For
example, due to vaporization of liquid droplets) and any user-defined sources.
Above eq. (1), represents the generalized form of mass conservation equation.
 Conservation of momentum equation:
Conservation of momentum in an inertial reference frame is described by following equation.
𝜕
𝜕𝑡
( 𝜌𝑢⃗ ) + ∇. ( 𝜌𝑢⃗ 𝑢⃗ ) = −∇𝑝 + ∇. ( 𝜏̿) + 𝜌𝑔 + 𝐹 Eq. (2)
Where, p = Static pressure
𝜏̿ = Stress tensor
𝜌𝑔 = Gravitational body force
𝐹 = External body force, which contains other model-dependent source terms such as
porous-media and user-defined sources
The stress tensor 𝜏̿ is given by,
𝜏̿ = μ [(∇𝑢⃗ + ∇𝑢⃗ 𝑇) −
2
3
] ∇. 𝑢⃗ 𝐼 Eq. (3)
Where, μ = Molecular viscosity
I = Unit tensor
 Continuity equation:
For 2-D, steady and incompressible flow the continuity equation is,
𝜕𝑢
𝜕𝑥
+
𝜕𝑣
𝜕𝑦
= 0 Eq. (4)
 Momentum equation:
Momentum Equation for the viscous flow in x and y directions are, respectively:
𝜌
𝐷𝑢
𝐷𝑡
= −
𝜕𝑝
𝜕𝑥
+
𝜕𝜏 𝑥𝑥
𝜕𝑥
+
𝜕𝜏 𝑦𝑥
𝜕𝑦
+ 𝜌𝑓𝑥 Eq. (5)
𝜌
𝐷𝑣
𝐷𝑡
= −
𝜕𝑝
𝜕𝑦
+
𝜕𝜏 𝑥𝑦
𝜕𝑥
+
𝜕𝜏 𝑦𝑦
𝜕𝑦
+ 𝜌𝑓𝑦 Eq. (6)

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Where, due to characteristics of the 2-D flow in continuity equation the term 𝜕𝑤 𝜕𝑧⁄ and in
momentum equation, 𝜕𝜏 𝑧𝑥 𝜕𝑧⁄ and 𝜕𝜏 𝑧𝑦 𝜕𝑧⁄ drop out.
4. Turbulence Models:
For the purpose of analysis, three different turbulent models are considered.
4.1 The SST k-omega turbulence model:
The k-omega SST turbulence model includes transport of the turbulence shear stress in the
definition of the turbulent viscosity. These features make this model more accurate and reliable
for a wider class of flows (for example, adverse pressure gradient flows, aerofoils and transonic
shock waves) than the standard and the BSL - models. So, that is the main reason behind
choosing k-omega SST turbulence model over standard and BSL model. K-omega SST
turbulence model is governed by,
𝐷𝜌𝑘
𝐷𝑡
= 𝜏𝑖𝑗
𝜕𝑢 𝑖
𝜕𝑥 𝑗
+ 𝛽∗
𝜌𝜔𝑘 +
𝜕
𝜕𝑥 𝑗
[( 𝜇 + 𝜎𝑘 𝜇 𝑡)
𝜕𝑘
𝜕𝑥 𝑗
] Eq. (7)
𝐷𝜌𝜔
𝐷𝑡
=
𝛾
𝑣 𝑡
𝜏𝑖𝑗
𝜕𝑢 𝑖
𝜕𝑥 𝑗
− 𝛽𝜌𝜔2
+
𝜕
𝜕𝑥 𝑗
[( 𝜇 + 𝜎 𝜔 𝜇 𝑡)
𝜕𝜔
𝜕𝑥 𝑗
] + 2𝜌(1 − 𝐹1)𝜎 𝜔
1
𝜔
𝜕𝑘
𝜕𝑥 𝑗
𝜕𝜔
𝜕𝑥 𝑗
Eq. (8)
Where, 𝛽∗
= 𝜀 𝑘𝜔⁄ and the turbulence stress tensor is
𝜏𝑖𝑗 = −𝜌𝑢𝑖
′ 𝑢𝑗
′̅̅̅̅̅̅̅ = 𝜇 𝑡 (
𝜕𝑢 𝑖
𝜕𝑥 𝑗
+
𝜕𝑢 𝑗
𝜕𝑥 𝑖
−
2
3
𝜕𝑢 𝑘
𝜕𝑥 𝑘
𝛿𝑖𝑗) −
2
3
𝜌𝑘𝛿𝑖𝑗 Eq. (9)
The turbulence viscosity can be estimated by 𝑣𝑡 = 𝑎1 𝑘/max(𝑎1 𝜔, 𝛺𝐹2), where 𝛺 is the
absolute value of the vorticity, 𝑎1 = 0.31 and the function 𝐹2 is given by,
𝐹2 = 𝑡𝑎𝑛ℎ {[𝑚𝑎𝑥 (
2√𝑘
0.09𝜔𝑦
,
500𝑣
𝑦2 𝜔
)]}
2
Eq. (10)
Where, y is the distance to the nearest surface.
The coefficients β, 𝛾, 𝜎𝑘 and 𝜎 𝜔 are defined as functions of the coefficients of the k-𝜔 and k-𝜀
turbulence models and they are listed as follows:
𝛽 = 𝐹1 𝛽1 + (1 − 𝐹1) 𝛽2 , 𝛾 = 𝐹1 𝛾1 + (1 − 𝐹1) 𝛾2 &
𝜎𝑘 = 𝐹1 𝜎𝑘1 + (1 − 𝐹1) 𝜎𝑘2 , 𝜎 𝜔 = 𝐹1 𝜎 𝜔1 + (1 − 𝐹1) 𝜎 𝜔2 Eq. (11)
Where, the function F1 is
𝐹1 = 𝑡𝑎𝑛ℎ {[𝑚𝑖𝑛 [𝑚𝑎𝑥 (
√𝑘
0.09𝜔𝑦
,
500𝑣
𝑦2 𝜔
) ,
4𝜌𝜎 𝜔2 𝑘
𝐶𝐷 𝑘𝜔 𝑦2
]]
4
} Eq. (12)
And the coefficient C𝐷 𝑘𝜔 is
𝐶𝐷 𝑘𝜔 = 𝑚𝑎𝑥 (2𝜌𝜎 𝜔2
1
𝜔
𝜕𝑘
𝜕𝑥 𝑗
𝜕𝜔
𝜕𝑥 𝑗
, 10−20
) Eq. (13)

5. 4 | P a g e
The empirical constants of the k-𝜔 SST model are:
β*
= 0.09, β1 = 0.075, β2 = 0.0828, 𝛾1= 0.5532, 𝛾2 = 0.4404, 𝜎𝑘1 = 0.85, 𝜎𝑘2 = 1.0, 𝜎 𝜔1 = 0.5
and 𝜎 𝜔2 = 0.856.
4.2 The standard k-𝜺 turbulence model:
The turbulence kinetic energy “k”, and its rate of dissipation "𝜀", are obtained from the
following transport equations:
𝜕
𝜕𝑡
( 𝜌𝑘) +
𝜕
𝜕𝑥 𝑖
( 𝜌𝑘𝑢𝑖) =
𝜕
𝜕𝑥 𝑗
[(𝜇 +
𝜇 𝑡
𝜎 𝑘
)
𝜕𝑘
𝜕𝑥 𝑗
] + 𝐺 𝑘 + 𝐺 𝑏 − 𝜌𝜀 − 𝑌𝑀 + 𝑆 𝑘 Eq. (14)
𝜕
𝜕𝑡
( 𝜌𝜀) +
𝜕
𝜕𝑥 𝑖
( 𝜌𝜀𝑢𝑖) =
𝜕
𝜕𝑥 𝑗
[(𝜇 +
𝜇 𝑡
𝜎 𝜀
)
𝜕𝜀
𝜕𝑥 𝑗
] + 𝐶1𝜀
𝜀
𝑘
( 𝐺 𝑘 + 𝐶3𝜀 𝐺 𝑏) − 𝐶2𝜀 𝜌
𝜀2
𝑘
+ 𝑆𝜀 Eq. (15)
Where, 𝐺 𝑘 = Turbulence kinetic energy generated due to the mean velocity gradients
Gb = Turbulence kinetic energy generated due to buoyancy
YM = contribution of the fluctuating dilatation in compressible turbulence to the
overall dissipation rate
𝐶1𝜀 = Constant
𝐶2𝜀 = Constant
𝐶3𝜀 = Constant
𝜎𝑘 , 𝜎𝜀 = Turbulent Prandtl numbers for k and 𝜀
𝑆 𝑘 , 𝑆 𝑘 = User-defined source terms
Turbulent viscosity is computed by combining k and 𝜀 as follows:
𝜇 𝑡 = 𝜌𝐶𝜇
𝑘2
𝜀
Eq. (16)
Where, 𝐶𝜇 = Constant
Model constants 𝐶1𝜀 , 𝐶2𝜀 𝐶𝜇 , 𝜎𝑘 and 𝜎𝜀 have the following default values,
𝐶1𝜀=1.44, 𝐶2𝜀 = 1.92, 𝐶𝜇 = 0.09, 𝜎𝑘 = 1.0, 𝜎𝜀=1.3
4.3 The k-kl-𝝎 Model:
The k-kl-𝜔 model is considered to be a three-equation eddy-viscosity type, which includes
transport equations for turbulent kinetic energy (𝑘 𝑇), laminar kinetic energy (𝑘 𝐿), and the
inverse turbulent time scale (𝜔),
Eq. (17)
Eq. (18)

6. 5 | P a g e
Eq. (19)
The inclusion of the turbulent and laminar fluctuations on the mean flow and energy equations
via the eddy viscosity and total thermal diffusivity is as follows:
Eq. (20)
Eq. (21)
The effective length is defined as,
Eq. (22)
Where, λT is the turbulent length scale and is defined by
Eq. (23)
And the small scale energy is defined by
Eq. (24)
Eq. (25)
Eq. (26)
The large scale energy is given by
Eq. (27)
Here, the sum of small scale and large scale energy yields the turbulent kinetic energy kT.
The turbulence production term generated by turbulent fluctuations is given by
Eq. (28)
Where, the small-scale turbulent viscosity is 𝑣 𝑇,𝑠
Eq. (29)
And
Eq. (30)
Eq. (31)
A damping function defining the turbulent production due to intermittency is given by
Eq. (32)

7. 6 | P a g e
Eq. (33)
In Eq. (18), 𝑃𝑘 𝐿
is the production of laminar kinetic energy by large scale turbulent fluctuations,
such that
Eq. (34)
The large-scale turbulent viscosity 𝑣 𝑇,1 is modelled as
Eq. (35)
Where,
Eq. (36)
The limit in Eq. (35) binds the realizability such that it is not violated in the two-dimensional
developing boundary layer. The time-scale-based damping function 𝑓𝜏,1 is,
Eq. (37)
Where, 𝛽 𝑇𝑆 from Eq. (36) is,
Eq. (38)
Near-wall dissipation is given by,
Eq. (39)
Eq. (40)
In Equations (17-19), R represents the averaged effect of the breakdown of stream wise
fluctuations into turbulence during bypass transition:
Eq. (41)
𝛽 𝐵𝑃, which is the threshold function controls the bypass transition process:
Eq. (42)
Eq. (43)
The breakdown to turbulence due to instabilities is considered to be a natural transition
production term, given by
Eq. (44)
Eq. (45)

8. 7 | P a g e
Eq. (46)
From Eq. (19), the following damping is defined as,
Eq. (47)
The total eddy viscosity and eddy diffusivity are given by,
Eq. (48)
Eq. (49)
The turbulent scalar diffusivity is defined as,
Eq. (50)
Eq. (51)
Model Constants for that k-kl-𝜔 transition model are listed below:
5. Meshing:
For achieving more accurate solution, first step in CFD analysis is the generation of proper grid.
For this problem of 2D domain, grid generation was done by using commercial software package
named ANSYS ICEM 16.0. The mesh topology generated for this domain is quad mesh. In total,
there are three types of mesh generated. (1) Coarse, (2) Medium and (3) Fine.
Generally, for the meshing of aerofoil, 4 types of meshing can be done.
(1) “H” Grid
(2) “O” Grid
(3) “C” Grid
(4) “Y” Grid
For that project I have selected “H” grid for the formation of mesh.
Figure 5.1, 5.2 and 5.3 represents the coarse, medium and fine mesh respectively.

9. 8 | P a g e
Fig. 5.1: Coarse Mesh
Fig. 5.2: Medium Mesh
Fig. 5.3: Fine Mesh

10. 9 | P a g e
Table 5.1 shows the mesh details for these three different meshes.
Description Parameter Coarse Medium Fine
Domain
Extents
x-
coordinate
min (m) =
-1.000000e+01
min (m) =
-1.000000e+01
min (m) =
-1.000000e+01
max (m) =
2.000000e+01
max (m) =
2.000000e+01
max (m) =
2.000000e+01
y-
coordinate
min (m) =
-1.000000e+01
min (m) =
-1.000000e+01
min (m) =
-1.000000e+01
max (m) =
1.000000e+01
max (m) =
1.000000e+01
max (m) =
1.000000e+01
Volume
Statistics
Minimum
volume
(m3
)
4.10E-10 2.40E-10 2.33E-10
Maximum
volume
(m3
)
1.86E+00 3.41E-01 6.82E-02
Total
volume
(m3
)
6.00E+02 6.00E+02 6.00E+02
Face area
statistics
Minimum
face area
(m2
)
3.06E-06 3.62E-06 3.18E-06
Maximum
face area
(m2
)
1.99E+00 9.78E-01 3.02E-01
Mesh
Quality
Minimum
Orthogonal
Quality
8.09E-02 2.35E-01 2.42E-01
Maximum
Ortho
Skew
9.19E-01 7.65E-01 7.58E-01
Maximum
Aspect
Ratio
9.79E+02 4.51E+02 4.30E+02
Mesh
Size
Level 0 0 0
Cells 143216 233036 363996
Faces 288602 468542 730762
Nodes 145386 235506 366766
Partitions 4 4 4
Cell zone 1 1 1
Face zones 6 6 6
Table 5.1: Mesh Details

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6. Solver Description:
In that project of aerofoil, Fluent 16.0 is used for its simulation. Air is passing over an aerofoil
from leading edge to the trailing edge. Because of that, it exerts some force either Drag and/or
Lift on that aerofoil. Solver description for all three models is described below.
For that project, type of solver is pressure-based, steady, absolute velocity formulation and 2D
space planar used. Model selection is SST k- 𝜔, standard k-𝜀 and Transition k-kl-omega
respectively. For material selection, air is selected from FLUENT material library. Boundary
conditions for top, bottom and inlet are same. Turbulent intensity and viscosity are 5% and
10% respectively. Reference values are computed from the inlet.
Pressure-velocity coupling scheme selected for that mesh is “Coupled”. Coupled algorithm
enables full pressure-velocity coupling, hence it is referred to as the pressure-based coupled
algorithm. The coupled scheme obtains a robust and efficient single phase implementation for
steady-state flows, with superior performance compared to the segregated solution schemes.
Turbulence schemes used for that project are “First Order Upwind” because that problem may
suffer instabilities due to turbulence. Flow courant number for that is 50. In order to prevent
solver to stop at a given criterion, convergence criterion is selected none.
7. Grid Independent test:
Grid independent test was performed for all those three meshes. Percentage error with 8 degree
angle of attack and k-𝜔 model was calculated for Drag coefficient (CD) and Lift coefficient
(CL) which is presented in the following table 7.1.
Mesh Aspect Ratio CD % Error CD CL
% Error
CL
Coarse 9.79E+02 0.0156963 N/A 0.830216 N/A
Medium 4.51E+02 0.0135843 13.45540032 0.850368 2.369798
Fine 4.30E+02 0.0134583 0.927541353 0.852029 0.194946
Table 7.1: CD and CL for coarse, medium and fine mesh
As per table 6.1, it is clear that fine mesh has percentage error for both drag coefficient and lift
coefficient less than 1%.
So, fine mesh is the most appropriate mesh for our analysis.
Profile for CD and CL with iterations for 8 degree angle of attack and k-𝜔 model is represented
in fig. (6.1) & fig. (6.2).

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Fig. 7.1: Plot of Iterations vs. Drag Coefficient
Fig. 7.2: Plot of Iterations vs. Lift Coefficient
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000 1200 1400 1600
DRAGCOEFFICIENT
ITERATIONS
ITERATIONS VS. DRAG COEFFICIENT
Coarse
Medium
Fine
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
0 200 400 600 800 1000 1200 1400 1600
LIFTCOEFFICIENT
ITERATIONS
ITERATIONS VS. LIFT COEFFICIENT
Coarse
Medium
Fine

13. 12 | P a g e
8. Analysis and Discussion of Results:
Drag and Lift coefficients of aerofoil can be calculated by following equations:
𝐶𝑙 =
𝐿
0.5𝜌𝑉𝛾
2
𝑙
Eq. (52)
𝐶 𝑑 =
𝐷
0.5𝜌𝑉𝛾
2
𝑙
Eq. (53)
Where, 𝐶𝑙 = Lift Coefficient
𝐶 𝑑 = Drag Coefficient
Fig 8.1: Plot of Angle of attack vs. Lift Coefficient
Calculation results of lift and drag coefficient for different turbulence models and the
experimental data of NACA0015 aerofoil’s are shown if fig. 8.1 and 8.2 respectively. It could
be seen from the fig. 8.1 that, for lift coefficient curve, k-kl-omega model was closest with the
experimental data. Also, for drag coefficient curve, k-kl-omega model is closest with the
experimental data. Drag coefficient’s larger deviation may be caused by the drag coefficient’s
sensitivity to the surface roughness and other factors.
-4 0 8
k-omega model -0.434321 0.000760264 0.852029
k-epsilon model -0.443045 0.000884098 0.872701
k-kl-omega model -0.438123 0.00075301 0.84433
Experimental data -0.2939 0 0.595
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LiftCoefficient
Angle of attack
Angle of attack vs. Lift Coefficient
k-omega model
k-epsilon model
k-kl-omega model
Experimental data

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Fig 8.2: Plot of Angle of attack vs. Drag Coefficient
Fig. 8.3, 8.4 and 8.5 represents the effect on pressure coefficient for different angle of attacks
when k-kl-omega model was applied. It can be seen from those figures that the leading edge of
the aerofoil had a larger curvature. It can be seen from those figures that, for different angle of
attacks, distribution of pressure on the aerofoil’s surface varied largely.
Fig 8.3: Pressure coefficient for 0° angle of attack
When the angle of attack is zero, pressure coefficient of aerofoil’s upper and lower surface are
nearly equal. This is because of the symmetricity of an aerofoil NACA0015.
-4 0 8
k-omega model 0.010573 0.00968192 0.0134583
k-epsilone model 0.0115741 0.0105091 0.0150882
k-kl-omega model 0.0136337 0.010494 0.024154
Experimental data 0.0134 0.0079 0.0289
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
DragCoefficient
Angle of attack
Angle of attack vs. Drag Coefficient
k-omega model
k-epsilone model
k-kl-omega model
Experimental data

15. 14 | P a g e
Fig 8.4: Pressure coefficient for 8° angle of attack
When the angle of attack is more than zero, on the upper surface of aerofoil pressure coefficient
is negative and on the lower surface it is positive. So, at that time lift force of aerofoil is pointed
up.
Fig 8.5: Pressure coefficient for -4° angle of attack
And when the angle of attack is less than zero, pressure coefficient on upper surface of aerofoil
is positive and at lower side it is negative. Therefore, at that time lift force of airfoil is pointed
below.
Fig. 8.6 represents the contours of pressure coefficient for 0° angle of attack using k-kl-𝜔
model. It can be seen that for upper and lower side of that aerofoil pressure coefficient is almost
same.

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Fig 8.6: Contours of pressure coefficient for 0° using k-kl-𝝎 model
Fig. 8.7 represents the contours of pressure coefficient for 8° angle of attack. In that case,
pressure coefficient is higher at the lower surface and it is lower at the upper side of the surface.
Fig 8.7: Contours of pressure coefficient for 8° using k-kl-𝝎 model
Fig. 8.8 shows the contours of pressure coefficient for -4° angle of attack. For that angle of
attack, pressure coefficient is higher on the upper surface and lower at the lower surface of the
aerofoil.

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Fig 8.8: Contours of pressure coefficient for -4° using k-kl-𝝎 model
As we know that pressure and velocity are inversely proportional to each other. Based on that
fact it is clear that when the angle of attack is zero then the velocity magnitude will be same on
both sides of the aerofoil. But, when angle of attack is more than zero, then velocity near the
upper surface of the aerofoil will be higher and pressure coefficient will be less in that region.
At the same time, velocity below the aerofoil will be less because of high pressure. That high
pressure air always try to come towards the low pressure region. So, when the air moves from
high pressure (Lower surface) to the low pressure (Upper surface) then it will provide lift in
the upward direction. Same way, when the angle of attack is less than zero, pressure will be
high on the upper surface of aerofoil. So, high pressure and low velocity air will move towards
low pressure and high velocity region. Therefore, lift will be downwards.
Fig 8.9: Contours of velocity magnitude at 0° angle of attack using k-kl-𝝎 model

18. 17 | P a g e
Fig 8.10: Contours of velocity magnitude at 8° angle of attack using k-kl-𝝎 model
Fig 8.11: Contours of velocity magnitude at -4° angle of attack using k-kl-𝝎 model
Contours of velocity magnitude for different angle of attacks using k-kl-𝜔 model are shown in
fig 8.9, 8.10 and 8.11.

19. 18 | P a g e
Wall Y plus:
 For K-epsilon model:
Fig 8.12: Y plus for -4 degree angle of attack for k-e model
Fig 8.13: Y plus for 0 degree angle of attack for k-e model
From figure 8.12, 8.13 and 8.14 it is clearly seen that for k-epsilone model with enhanced wall
treatment value of Y-plus is between 0 and 1.

20. 19 | P a g e
Fig 8.14: Y plus for 8 degree angle of attack for k-e model
 For K-omega model:
Fig 8.15: Y plus for -4 degree k-omega model
Fig 8.16: Y plus for 0 degree k-omega model

21. 20 | P a g e
Fig 8.17: Y plus for 8 degree k-omega model
From fig 8.15, 8.16 and 8.17, it is clearly seen that Y plus for k-omega model is between 0 and
1.
 For K-Kl-Omega model:
Fig 8.18: Y plus for -4 degree k-omega model
Using k-kl-omega model, Y plus ranges between 0 and 1 for -4, 0 and 8 degree angle of attack
as seen in fig 8.18, 8.19 and 8.20 respectively.

22. 21 | P a g e
Fig 8.19: Y plus for 0 degree k-omega model
Fig 8.20: Y plus for 8 degree k-omega model
So, using all three different turbulence models, it is seen that the value of Y-plus is within its
range.

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9. Conclusion:
In that project, mesh of NACA0015 aerofoil was created using ICEM CFD 16.0. Then its
aerodynamic performance was simulated numerically using FLUENT 16.0 when the Reynolds
number was 3.2 X 106
. Angle of attacks considered for that simulation are 0°, 8° and -4°.
Following conclusions are made in that project:
 When the angle of attack changes from -4° to 8°, lift and drag coefficient curves of
these three turbulence models had consistent movement with the experimental curve. It
is seen that, lift coefficient curves for these three models were much closer with the
experimental curve. But, drag coefficient curves differed largely with experimental
data. That could be because of the surface roughness or other factors. Three equation
k-kl-𝜔 model had best result in those three turbulent models.
 Lift force of aerofoil mainly comes from the front edge. The reason behind that is the
difference in the pressure coefficient on aerofoil’s front edge was much larger.
 When the angle of attack changes from less than zero to more than zero, pressure
coefficient positive and negative symbols of aerofoil’s lower and upper surface would
be changed. When the angle of attack is zero, pressure coefficients of aerofoil’s upper
and lower edge are same.
10. References:
[1] http://m-selig.ae.illinois.edu/ads/coord_database.html
[2] Ji Yao et al. (2012), “Numerical simulation of aerodynamic performance for two
dimensional wind turbine airfoils”, Procedia Engineering 31 (2012) 80 – 86.
[3] Eleni et al. (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, March 2012.
[4] E. Jacobs et al. (1933), “The characteristics of 78 related airfoil sections from tests in the
variable-density wind tunnel”, National Advisory Committee For Aeronautics.
[5] ANSYS Fluent Theory Guide.

24. 23 | P a g e
11. List of Tables:
Table No. Table Name Page No.
Table 1.1 Parameters for simulation 1
Table 5.1 Mesh Details 9
Table 7.1 CD and CL for coarse, medium and fine mesh 10
12. List of Figures:
Figure
No.
Figure Name
Page
No.
Fig 1.1 Profile of NACA0015 aerofoil 1
Fig. 5.1 Coarse Mesh 8
Fig. 5.2 Medium Mesh 8
Fig. 5.3 Fine Mesh 8
Fig. 7.1 Plot of Iterations vs. Drag Coefficient 11
Fig. 7.2 Plot of Iterations vs. Lift Coefficient 11
Fig 8.1 Plot of Angle of attack vs. Lift Coefficient 12
Fig 8.2 Plot of Angle of attack vs. Drag Coefficient 13
Fig 8.3 Pressure coefficient for 0° angle of attack 13
Fig 8.4 Pressure coefficient for 8° angle of attack 14
Fig 8.5 Pressure coefficient for -4° angle of attack 14
Fig 8.6 Contours of pressure coefficient for 0° using k-kl-𝜔 model 15
Fig 8.7 Contours of pressure coefficient for 8° using k-kl- 𝜔 model 15
Fig 8.8 Contours of pressure coefficient for -4° using k-kl- 𝜔 model 16
Fig 8.9 Contours of velocity magnitude at 0° angle of attack using k-kl- 𝜔 model 16
Fig 8.10 Contours of velocity magnitude at 8° angle of attack using k-kl- 𝜔 model 17
Fig 8.11 Contours of velocity magnitude at -4° angle of attack using k-kl- 𝜔 model 17
Fig 8.12 Y plus for -4 degree angle of attack for k-e model 18
Fig 8.13 Y plus for 0 degree angle of attack for k-e model 18
Fig 8.14 Y plus for 8 degree angle of attack for k-e model 19
Fig 8.15 Y plus for -4 degree angle of attack for k- omega model 19
Fig 8.16 Y plus for 0 degree angle of attack for k-omega model 19
Fig 8.17 Y plus for 8 degree angle of attack for k- omega model 20
Fig 8.18 Y plus for -4 degree angle of attack for k-kl-omega model 20
Fig 8.19 Y plus for 0 degree angle of attack for k-kl-omega model 21
Fig 8.20 Y plus for 8 degree angle of attack for k-kl-omega model 21