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Comparison of Aerodynamic Performance of NACA 23012 and NACA 4412

Airfoil: A Numerical Approach

Conference Paper · December 2022

DOI: 10.5281/zenodo.7710580

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 International Conference on Mechanical, Industrial and Energy Engineering 2022
22-24 December, 2022, Khulna, BANGLADESH

ICMIEE22-170
Comparison of Aerodynamic Performance of NACA 23012 and NACA 4412 Airfoil: A Numerical
Approach
Manish Bhadra Arnab1,*, Mohammad Ilias Inam1
1
Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna-9203, BANGLADESH

ABSTRACT
Two of the most widely used airfoils worldwide are NACA 23012 and NACA 4412. The purpose of this study is to investigate
and compare the aerodynamic characteristics of these two airfoils for a constant Reynolds number of 5×10^6. These
simulations were conducted in 2D using Spalart-Allmaras as turbulence model by ANSYS Fluent. Numerical results
demonstrate that the lift coefficient increases with the angle of attack up to certain values, after that it decreases due to flow
separation. The drag coefficient also increases with the angle of attack for both airfoils. However, the rate of increment is
much higher after a certain angle of attack due to flow separation. Results also show that the lift coefficient is much higher
for NACA 4412 compared to NACA 23012 for each angle of attack. It also observed that the critical angle of attack for NACA
23012 is 18°, whereas flow is separated one degree earlier in NACA 4412. The whole set of simulated results can be
considered as a reference to validate computational fluid dynamics analyses of similar studies.

Keywords: CFD, NACA 23012, NACA 4412, Lift-to-drag ratio, Spalart-Allmaras.

1. Introduction sufficiently. The study is conducted by using Spalart-

An airfoil is the cross-sectional design of an item, Allmaras turbulence model.
such as a wing, sail, or the blades of a propeller, rotor, or
turbine, whose motion through fluid can provide 1.1 Background Study
significant lift compared to drag. Lift and drag forces are Two of the most important parameters for this study
generated and applied to the airfoil when a fluid flow are lift force and lift coefficient. If the fluid incorporates
passes over a body with an airfoil shaped design. The a circulatory flow around the body, like a spinning
normal force component acting on the airfoil is called lift cylinder, lift on the body will be generated. The
force and the force component parallel to the motion of perpendicular component to lift is drag which acts on the
the flow is called drag force. Different types of airfoils parallel direction to the flow. [4]
interact differently with flow passing over it and the
generated lift force varies significantly. NACA 23012
and NACA 4412 are two of the most widely used airfoils
throughout history. About one tenth of all conventional
aircrafts or rotorcrafts have used either of these two
airfoils [1]. Three alternative methods, including field
testing, analytical/semi-empirical models, and CFD
(Computational Fluid Dynamics) can be used in order to
study the flow characteristics over such airfoil bodies.
The first one, although being quite intricate and
expensive, produces exact results. The second one is less
reliable, while CFD is the most time and resource
efficient method for direct measurements.
Extensive studies have been conducted, both Fig.1 Forces acting on an airfoil [5].
experimentally and analytically on these airfoil shapes.
Numerical results vary slightly in comparison with Lift coefficient (CL) is a dimensionless unit that
experimental ones due to the nature of governing relates to the lift force to the area and dynamic pressure,
equations of the turbulence model which is use for the where dynamic pressure is determined using fluid mass
analysis. NASA’s Langley Research Center has well density and flow speed, shown in Eq (1). For three
documented works on these airfoils [2]. The data dimensional wings, the downwash generated near
provided by Langley Research Center [3] for Re of 1.52 the wing tips reduces the overall CL of the wing.
million, which is used to validate the computational
𝐹𝐿
method for 13.87ᴼ angle of attack for NACA 4412 airfoil 𝐶𝐿 = (1)
is used to validate the results of this study. 0.5𝜌𝑉 2 𝐴
In the case of an aircraft of relatively low speed
range and low altitude, Reynolds number around Re = Another parameter, drag coefficient (CD) is another
5×106 can capture the aerodynamic conditions dimensionless quantity that is used to measure the drag

* Corresponding author. Tel.: +88-01725497014

E-mail addresses: m.arnabhadra@gmail.com
or resistance of an object subjected to flow over its body,
shown in Eq (2).

𝐹𝐷
𝐶𝐷 = (2)
0.5𝜌𝑉 2 𝐴

Lift-to-drag ratio (L/D ratio) is essentially the ratio

between lift coefficient and drag coefficient which is
shown in Eq (3). An aircraft with a high L/D ratio
indicates that it produces a large amount of lift or a small
amount of drag. Large lift means more weight lifting
capacity and a small amount of drag means less thrust to
Fig.3 2D NACA 23012 airfoil profile.
drive the aircraft. So, it is critical to measure for the L/D
ratio of the airfoils under same conditions.

𝐶𝐿
L/D ratio = (3)
𝐶𝐷

Another important parameter, angle of attack can be

defined as the angle between the chord line and
streamwise flow direction, shown in Fig. 1. Here the
chord length is the distance between the trailing edge and
the point where the chord intersects the leading edge. In
Fig. 2, the general airfoil design parameters of an airfoil
are shown.
Fig.4 2D NACA 4412 airfoil profile.

2.2 Computational Domain and Mesh Generation

A computational domain, shown in Fig.5 was used
for these simulations. Airfoil chord length was assumed
one meter. Domain size and different boundary
conditions used for this simulation is shown in figures.

Fig.2 Airfoil design parameters [6].

In flow analysis, the Reynolds number (Re) is a

dimensionless quantity which generally indicates
towards the relationship between inertia forces and
viscous forces under various fluid flow conditions. The
flow separates from an airfoil at the trailing edge. And
from those trailing edges, vortices may generate. The
flow velocity increases along with the Reynolds number
which increases the turbulence as well. So it is considered
to compare as the general aerodynamic conditions remain
constant under same Reynolds number. Reynolds
number can be written as:

𝜌𝑉𝐿
𝑅𝑒 = (4)
𝜇 Fig.5 Computation domain [9].

2. Methodology Mesh is important parameter for simulations. For

2.1 Airfoil improved convergence and wall function control, C-type
The following figures, Fig.3 shows NACA 23012 mesh was created, shown in Fig. 6. Fine mesh was
and Fig.4 shows NACA 4412 profile as 2D sketches created near to the wall, shown in Fig. 7.
respectively. The CSV coordinates of the airfoils were
taken from NACA airfoil database [7-8], then imported
to SOLIDWORKS to create the two-dimensional
sketches of the airfoils with 1m chord length for both
cases.

ICMIEE22-170- 2
 Fig.6 Mesh around the whole domain.

Fig.8 Variation of L/D ratio with number of elements.

It shows that after a certain number of elements are

reached, percentage change the lift to drag ratio becomes
very insignificant, under 1% which is acceptable and thus
the mesh with 80,600 elements is considered as ideal and
is used for all the numerical simulations of both airfoil
profiles.

2.4 Numerical Conditions

Fig.7 Zoomed in mesh around the airfoil. To compute and validate the solver scheme, both
airfoils were generated with 1m in chord length with a far
While still producing a satisfactory degree of field having 81164 nodes and 80600 elements. Biased
solution, the use of wall functions close to the wall region edge sizing was used in mesh to maintain a reasonable y+.
may significantly improve the overall results. Meshing Outlet condition was kept as pressure outlet type. Hybrid
was adequately biased to create the desired inflation layer. initialization with external aero-favorable settings was
The effective y plus value for solving the turbulence used for computation.
model in viscous sublayer region is y+<5. It is defined as:
Table 1 Boundary conditions
𝜏𝜔 No Input Value
√𝜌 1 Type of fluid Air
𝑦+ = 𝑦 × 2 Fluid density 1.225 [kg/m3]
𝜇 (5)
3 Flow velocity 73.037 [m/s]
4 Operating pressure 101325 Pa
5 Operating temperature 288.16 K
Here y is defined as the distance from the wall to the
6 Reynolds Number 5×106
centroid of the first fluid cell. For all simulations in this
7 Chord length 1M
study, 𝑦 + value was always kept bellow 1.
8 Model Spalart-Allmaras
9 Viscosity 1.7894×105 [kg/ms]
2.3 Mesh Independence Test
Mesh independence test is done in order to
2.5 Turbulence Model
determine the most optimized mesh for obtaining a
With only one equation, the Spalart-Allmaras
precise numerical result which will also be less resource
turbulence model is primarily intended for
consuming and time efficient in running the simulations.
straightforward external aerodynamic analysis. A
For this study a set of simulations were conducted by
transport equation for eddy viscosity is included in this
increasing the amount of mesh elements from 15,000 to
model. Here the distribution of the Reynolds stress is
144,000 to get the optimized mesh. This was achieved by
determined in order to create a closed system of the
altering the body edge sizing for each mesh.
central equation for the mean motion of a flow. In this
NACA 4412 airfoil was considered for this test using
analysis, strain/vorticity-based SA model is used with a
Spalart-Allmaras turbulence model. Fig.8 shows the lift
turbulent viscosity ratio of 1.
to drag ratio for a specific angle of attack of 13.87° in Re
The working variable 𝑣̂ transport equation is given
= 1.52 × 106 .
by,

ICMIEE22-170- 3
 𝜕𝑣̂ 𝜕𝑣̂ The constants are:
+ 𝑢𝑗 = 𝑐𝑏1 (1 − 𝑓𝑡2 )𝑆̂𝑣̂
𝜕𝑡 𝜕𝑥𝑗
2
𝑐𝑏1 𝑣̂ 2 𝑐𝑏1 = 0.1355 𝜎=
3
𝑐𝑏2 = 0.622 𝑘 = 0.41’
− [𝑐𝑤1 𝑓𝑤 − 2 𝑓𝑡2 ] ( )
𝑘 𝑑
1 𝜕 𝜕𝑣̂ 𝑐𝑤2 = 0.3 𝑐𝑤3 = 2 𝑐𝑣1 = 7.1
+ [ ((𝑣 + 𝑣̂) )
𝜎 𝜕𝑥𝑗 𝜕𝑥𝑗 𝑐𝑏1 1+𝑐𝑏2
𝑐𝑡3 = 1.2 𝑐𝑡4 = 0.5 𝑐𝑤1 = +
𝜕𝑣̂ 𝜕𝑣̂ 𝑘2 𝜎
+ 𝑐𝑏2 ]
𝜕𝑥𝑖 𝜕𝑥𝑖 (6) The Spalart-Allmaras model has production and
destruction source terms that are non-zero in the
and the turbulent eddy viscosity is computed from: freestream conditions, even when vorticity is zero. The
source terms are, however, very small: proportional to
𝜇𝑡 = 𝜌𝑣̂𝑓𝑣1 (7) 1/d2 [9].

here, 2.6 Validation of the process

Data provided by Langley Research Center [3] is
𝜒3 (8) used to validate the simulation method. The method
𝑓𝑣1 = 3 primarily ran the computations for NACA 4412 with
𝜒 3 + 𝑐𝑣1
13.87ᴼ angle of attack. Then the CP data is compared by
𝑣̂ (9) overlapping on the curve generated by the Langley
𝜒= Research Center pressure data. Fig. 9 shows the
𝑣
comparison. Here the plot shows comparison with the
Spalart-Allmaras results from an independent CFD code,
𝜇 CFL3D by NASA.
and ρ is the density, 𝑣 = is the molecular kinematic
𝜌
viscosity, and μ is the molecular dynamic viscosity.
Additional definitions are given by the following
equations:

𝑣̂
𝑆̂ = Ω + 𝑓 (10)
𝑘 2 𝑑 2 𝑣2

Here Ω = √2𝑊𝑖𝑗 𝑊𝑖𝑗 is the magnitude of the

vorticity, d is the distance from the field point to the
nearest wall, and
6
𝜒 1+𝑐𝑤3
𝑓𝑣2 = 1 − 𝑓𝑤 = 𝑔 [ 6 ]
1+𝜒𝑓𝑣1 𝑔6 +𝑐𝑤3
Position, x (m)
𝑣̂
𝑔 = 𝑟 + 𝑐𝑤2 (𝑟 6 − 𝑟) 𝑟 = min [ ̂ , 10]
𝑆𝑘 2𝑑2
Fig.9 Pressure coefficient on the airfoil surface at
2) 1 𝜕𝑢𝑖 𝜕𝑢𝑗 13.87° angle of attack.
𝑓𝑡2 = 𝑐𝑡3 (−𝑐𝑡4 𝜒 𝑊𝑖𝑗 = ( − )
2 𝜕𝑥𝑗 𝜕𝑥𝑖
3. Result and Discussion
The boundary conditions are: 3.1 Lift and drag coefficients
The following Fig.10 shows lift coefficient plotted
𝑣̂𝑤𝑎𝑙𝑙 = 0 against different values of α for NACA 23012 and NACA
4412 airfoil profiles. Similarly, Fig.11 shows the
𝑣̂𝑓𝑎𝑟𝑓𝑖𝑒𝑙𝑑 = 3𝑣∞ : 𝑡𝑜: 5𝑣∞ variation of drag coefficient and Fig.12 shows the
variation of L/D ratio for both airfoils computed under
These boundary conditions on the SA turbulence field same Reynolds number and boundary conditions.
variable correspond to turbulent kinematic viscosity The critical angle of attack or the stall angle of attack
values of: where maximum lift occurs is determined to be:

𝑣𝑡,𝑤𝑎𝑙𝑙 = 0 Table 2 Critical angle of attack at Re= 5×106

Airfoil Critical Angle of Attack
𝑣𝑡𝑓𝑎𝑟𝑓𝑖𝑒𝑙𝑑 = 0.210438𝑣∞ : 𝑡𝑜: 1.294234𝑣∞ NACA 23012 18°
NACA 4412 17°

ICMIEE22-170- 4
 Also, from Fig.12, for higher angles of attack, after 11°,
both airfoils perform similarly but for lower angles of
attack, NACA 4412 airfoil performs significantly better.

3.2 Static Pressure Contour

From fig.13, it can be observed that as angle of attack
increases, pressure difference between top and bottom
surface also increases for both airfoils.

NACA 23012 NACA 4412

α=0° α=0°
Fig.10 Variation of CL for different angles of attack of
NACA 23012 and NACA 4412

α=5° α=5°

α=11° α=11°

Fig.11 Variation of CD for different angles of attack of α=16° α=16°

NACA 23012 and NACA 4412

α=20° α=20°

α=25° α=25°

Fig.13 Static Pressure Contours at different angles of

Fig.12 Variation of L/D ratio for different angles of attack of NACA 23012 and NACA 4412.
attack of NACA 23012 and NACA 4412
3.3 Velocity Contour
The drastic differences in lift and drag coefficients
Velocity contours of the two airfoils, NACA 23012
between the two airfoils after flow separation occurs,
and NACA 4412 for different angles of attack can be seen
shown in fig.10 and fig.11, is due the notable difference
by in Fig.14 below. It is observed that as angle of attack
is geometry, specially at the rear end of the two airfoils. increases, trailing edge separation occurs earlier for both.

ICMIEE22-170- 5
 NACA 23012 NACA 4412 4. Conclusion
In this study, the aerodynamic behaviors of NACA
23012 and NACA 4412 profiles were observed and
compared using Spalart-Allmaras turbulence model at
Re= 5×106. It is observed that NACA 4412 airfoil
generates more lift force than NACA 23012 airfoil. But
α=0° α=0° for higher angles of attack, both airfoils demonstrate
almost similar performance. Also, the trailing edge flow
separation occurs a degree later for NACA 23012 airfoil.

5. References

[1] https://m-selig.ae.illinois.edu/ads/aircraft.html
α=5° α=5° (Accessed: 13-Nov-2022).
[2] https://turbmodels.larc.nasa.gov/naca4412sep_val.
html (Accessed: 13-Nov-2022).
[3] https://turbmodels.larc.nasa.gov/naca4412sep_val_
sa.html (Accessed: 13-Nov-2022).
[4] Burton, T., Jenkins, N, Sharpe, D. and Bossanyi, E.
α=11° α=11° Wind Energy Handbook. Chichester, UK: John
Wiley & Sons, 2011; 65-67
[5] Panigrahi, D.C., Mishra D.P., CFD Simulations for
the Selection of an Appropriate Blade Profile for
Improving Energy Efficiency in Axial Flow Mine
Ventilation Fans, Journal of Sustainable Mining,
2014; Volume 13, Issue 1, Pages 15-21, ISSN 2300-
α=16° α=16° 3960.
[6] Yılmaz M., Koten H., Çetinkaya, E, Coşar, Z., A
comparative CFD analysis of NACA0012 and
NACA4412 airfoils. Journal of Energy Systems
2018; 2(4): 145- 159, DOI: 10.30521/jes.454193.
[7] http://airfoiltools.com/airfoil/details?airfoil=naca4
α=20° α=20° 412-il (Accessed: 13-Nov-2022).
[8] http://airfoiltools.com/airfoil/details?airfoil=naca2
3012-il (Accessed: 13-Nov-2022).
[9] Pranto, M.R.I. and Inam, M.I., 2020. Numerical
Analysis of the Aerodynamic Characteristics of
NACA4312 Airfoil. Journal of Engineering
α=25° α=25° Advancements, 1(02), pp.29-36.
[10] Spalart, P.R., Allmaras S.R., A one-equation
turbulence model for aerodynamic flows, AIAA
30th aerospace sciences meeting and exibit, 6-9 Jan
1993.
Fig.14 Velocity Contours at different angles of attack of
NACA 23012 and NACA 4412. NOMENCLATURE
V : velocity, m/s
3.4 Variation of Pressure Coefficient ρ : density, Kg/m3
υ : kinematic viscosity, m2-s
μ : dynamic viscosity, Pa-s
Cp : coefficient of pressure
CL : coefficient of lift
CD : coefficient of drag
Re : Reynolds number
c/L : chord length, m
Position, x (m) Position, x (m) α : angle of attack, degree
α=5° α=16° x : x axial position in the airfoil, m
i,j,k : cartesian unit vector
Fig. 15 Variation of CP along the surfaces of NACA
23012 and NACA 4412 airfoil.

ICMIEE22-170- 6

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