INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES-IJET

Hacı Sogukpinar, Vol.4, No.4, 2018

Low Speed Numerical Aerodynamic Analysis
of New Designed 3D Transport Aircraft
Hacı Sogukpinar
Department of Electric and Energy, Vocational School,
University of Adiyaman, Adiyaman 02040, Turkey(hsogukpinar@adiyaman.edu.tr)‡

Corresponding Author; Hacı Sogukpinar, Department of Electric and Energy,
Vocational School, University of Adiyaman, Adiyaman 02040,
Turkey, Tel: +90 (416) 223 38 00,
Fax: + 90 416 223 21 29, hsogukpinar@adiyaman.edu.tr

Received: 27.02.2018 Accepted: 13.01.2019

Abstract - In this study, a new airfoil was designed by using aerodynamic features of the NACA (National
Advisory Committee for Aeronautics) 0012 airfoil and numerical calculation was conducted by using Spalart–
Allmaras Turbulence Model. Lift and drag coefficients were calculated and compared with experimental result tocorrelate numerical calculation accuracy of CFD (Computational Fluid Dynamics) model. Then, according to the
new airfoil data, a 3D aircraft fuselage, wings and tail section were modeled by using modified NACA 0012 airfoil.
Finally, 3D model aircraft were simulated for cruise flight, climb and descending at the angle of attack +10° and 10° respectively. The simulation results were interpreted in terms of fluid dynamics. Study indicates that during
the ascending and descending of the aircraft, very large vortices were formed by the low pressure effect occurringat the rear upper or lower part of the fuselage. Vortices originating from the rear body were caused with the wing
tip vortices but the vortex due to the back of the fuselage was found to be very large compared to the wingtip.
Furthermore, for each simulation, formation of the wingtip vortices were investigated and presented. Study showsthat during ascending the vortex formation was formed in roll up but it was roll down in the phase of descending.
Key words: 3D simulation, Aircraft, vortex, airfoil, Aerodynamic Analysis, lift, drag1. Introduction
After the first flight of the Wright brothers,
new sectors has emerged and research in the wholeaviation continued rapidly. As a result of great
efforts, dream of the larger airplane and longer
distance flights has become real. The high cost offuel and global warming effects made the need formore efficient airplanes in terms of aerodynamics,
and the work has progressed in this direction.
Especially at airports, vortices formed during
landing and takeoff which affect other flightnegatively. For the last 30 years, winglets have beendeveloped and used to reduce wingtip vortex.
Aerodynamic flow as a whole for an aircraft has notbeen investigated but usually only the flow over thewing, the fuselage, the tail and winglet were
investigated. But within the framework of anagreement between NASA (National Aeronautics
and Space Administration) and Boeing, Boeing 747
passengers’ aircraft were analyzed numerically as awhole and presented [1]. The document provides
aerodynamic features of lift, drag, pitching moment,rolling and yawing moment, and side force
coefficients and also contains information aboutcharacteristics of the high lift and propulsion system
and landing gear. However, the presented data
handles in the form of numeric data and graphs but
there is no 2D or 3D direct stream graphics. Flowover generic military airplane was simulated as awhole by using SST turbulence model and comparedwith experiment [2]. Velocity distribution and eddy
viscosity on the surface of the aircraft were given
visually and comparatively with the experiment andthere was a good agreement between numericalcalculation and observation. The main purpose ofthat work was only to summarize the role of theconcepts behind the SST model in current and future
CFD simulations of engineering flows. The Boeing
747-200 jumbo jet was numerically investigated andthe pressure distribution over the entire surface of theaircraft presented [3]. But the velocity distribution of153

the fluid sweeping the surface of the plane was not
calculated or given. Therefore, places where swirls
are not seen. Another investigation explains theapplication of optimization techniques for based oncontrol theory for complex aircraft configurations[4] and numerical calculation was conducted forbusiness jet by using Euler equations. This method
used Euler equations to reconstruct all
configurations of the aircraft by using new multiblock implementation. According to the calculation
result, pressure distribution on the entire surface ofthe plane was presented. With the development of
current computer technology CFD's practice
revolutionized the aerodynamic design process andit has joined the wind tunnel and flight test as themain means of trade. Boeing Commercial Airplanes
use CFD technology, developed by its academia andNASA, and has been used in new planedevelopment. More than 20,000 CFD cases werecompleted to design a new aircraft in Boeing
Company [5]. In other studies, 2D and 3D wing
sections were studied extensively [6-12], but it isquite rare to investigate the 3D shape of a plane foraerodynamic analysis. Especially, flow analysis was
rarely performed by sending fluid from different
angles to the aircraft surface.
In this study, a new airfoil with high lift
coefficient at angle of attack zero degree wasmodeled by using aerodynamic characteristics of
NACA 0012 airfoil. The NACA 0012-X airfoil wascompared both experimental and theoretical NACA
0012 data to check the simulation correctness of theComputational
Fluid
Dynamics(CFD)
approximation. The airplane fuselage and wings
were created using the NACA 0012-X airfoil andnumerical calculation conducted by using the SpaAlmrs turbulence model. The streamline velocity
distribution on the wing and fuselage were presented
and compared according to the simulation result.
2. Spalart–Allmaras Turbulence Model
The Spalart-Allmaras model is a oneequation model that solves a modeled transport
equation for the kinematic eddy turbulent viscosity.
The model solves only one transport equation for thequantity 𝑣, it is equivalent to the eddy viscosity awayfrom the walls [13]. This model was designed
specifically for aerospace applications that include
wall-bounded flows and has been shown to provide
good results for boundary layers exposed to negative
pressure gradients. This module includes thestandard version of the Spalart-Allmaras model
without trip term [14, 15]. One model equation for
undamped turbulent kinematics is given by equation
(1):
#$
#%

+ 𝐮. ∇𝑣 = 𝑐,- 𝑆𝑣 − 𝑐0- 𝑓0
678

$
23

4

-

+ ∇.
5

𝑣+

𝑣 ∇𝑣 +∇𝑣. ∇𝑣(1)
5
Reynold stresses were evaluated by using
Boussinesq eddy viscosity assumption [16] and are
expressed by (2):

6

-<678

:;

5

𝑐0- = 79
8 +

$

>?

$

>? <6;9 ?

, 𝜒 = , 𝑓0- =(2)

The turbulent viscosity was calculated by (3):𝜇 E = 𝜌𝑣𝑓$(3)To achieve faster decaying behavior of destructionin the outer boundary layer, a function 𝑓0 was used[17].Additional definitions were given in thefollowing equations (4-6) where g acts as a limiter
that prevents great values of 𝑓0 . Both r and 𝑓0 are
equal to 1 in the log-layer and decrease in the outerregion.
𝑓04 = 1 −L>-<>H;9, 𝑓0 = 𝑔𝑐04 (𝑟 − 𝑟)𝑟 = 𝑚𝑖𝑛$Q: 8 ; 2 8 3

J
-<63?

-

L

J
KJ <63?

,𝑔 = 𝑟 +(4), 10 , 𝑆 = 𝑚𝑎𝑥 Ω +$𝐶WX% min 0, 𝑆 − Ω + 8 8 𝑓$4 , 0.3Ω

(5)

𝑆=

(6)

: ;2 32𝑆]^ 𝑆]^ Ω =2Ω]^ Ω]^Where, 𝑓0- is damping fuction, κ is von K𝑎rm𝑎n
constant, 𝑆 is modified vorticity, S is magnitude ofvorticity, 𝑙0 is distance to the closest wall, 𝑣, iskinematic viscosity, 𝑆]^ and Ω]^ are mean strain rate
and mean rotation rate tensors respectively andrepresented by:
𝑆]^ = 0.5 ∇𝑢 + ∇𝑢 E Ω]^ = 0.5 ∇𝑢 − ∇𝑢 E
(7)
𝑇he default value of model constants are:𝑐,- = 0.1355, 𝑐,4 = 0.622,𝑐$4 = 7.1𝜎 = 2 3
𝑐04 = 0.3, 𝑐0f = 2, 𝜅$ = 0.41, 𝐶WX% = 2.0
3. CFD Modeling method
NACA 0012 is one of the commonly usedairfoil due to its aerodynamic properties. Hundredsof experimental and theoretical investigations havebeen carried out for this wing section. Wind tunnel
experiment of NACA 0012 was conducted in theLangley Low-Turbulence Pressure Tunnel [18] toinvestigate
thelow-speed
aerodynamic
characteristics of the NACA 0012 airfoil, which
offers good opportunity to examine CFD simulation
technicque. For the numerical calculation
Commercial software COMSOL 5.3 was used. To
eliminate the effect of the domain size on the
numerical simulation, computational domain andboundary conditions extended at least 100c awayfrom airfoil. Computational domain is as shown in
Fig. 1. Inlet port was set to velocity inlet and output
port was set to output. Low number meshdistribution may produce computation with large
error but high number mesh increase computational
time. Therefore mesh number in acertain range wereused which is compatible with experiment. C typemesh with 86,800 mesh element were created andapplied to distribute flow field in the domain and freestream contiditon. High concentrated meshdistribution was applied closed to wall. Mesh
distribution around new designed airfoil NACA
0012-X is presented in Fig.2.

154

100c

200c

100c

aerodynamic characteristic close to NACA 0012 butwith a high lift coefficient was designed and named
as NACA 0012-X. The newly designed airfoil was
simulated by using the Spalart-Allmaras Turbulence
Model and compared with theoretical andexperimental data of NACA 0012 as presented in
Fig.4. According to the simulation results, high lift
coefficient were obtained in all angle of attack andlift coefficients were calculated at the angle of attack
at 0° and 3° as 0.16 and 0.49 respectively.

Fig. 1: Computational domain and boundary
condition.

(a)Fig. 2. Mesh distribution around airfoil NACA
0012-X
The model fuselage was designed according to
the NACA 0012-X profile, with a chord length of 1
m. Aircraft wing was designed from NACA 0012-X
airfoil with 1.1 m wing span. Wing incidence was set
to 3°. The leading edge sweep was depicted as 8.5°.
Zero twist and dihedral angle were applied to themodel. Basic tail configuration with NACA 0012
airfoil was adopted. For the 3D calculation, separatemesh distribution for the model aircraft and theexternal environment were applied and freetetrahedral mesh type with extra fine mesh was
adopted for both side. 3D body of model with meshdistribution is presenten in Fig. 3.

Fig. 3. Mesh distribution around aircraft modeledfrom NACA 0012-X(b)Fig. 4. Comparison of Lift and Drag coefficientversus angle of attack.
Drag coefficient for newly designed airfoil was
calculated lower than both experiment andtheoretical data of NACA 0012 airfoil at the angle ofattack until 11°. Lift to drag ratio for NACA 0012-X
airfoil were calculated and presented comparatively
with NACA 0012 airfoil in Fig. 5. Maximum lift todrag ratio was calculated at the angle of attack
around 3° therefore streamline velocity is alsopresented in Fig.5(b).

4. Results and discussions
Numerical calculation was conducted for
NACA 0012 airfoil and lift and drag coefficientswere calculated with Spalart–Allmaras turbulencemodel with the angle of attack from -4° to +18° andpresented in Fig. 4, and obtained data were comparedwith experimental observation [18]. It is observedthat theoretical results are in a good agreement withthe experimental results. An airfoil with an

155

(a)

(b)
Fig. 5. Lift to drag ratio (a) and streamline velocity
field (b) of NACA0012-X
The stream line velocity field of the NACA 0012-X
airfoil is given in Fig.6 at the angle of attack 12° and
14° and almost laminar flows are calculated in bothFig. 6(a) and Fig. 6(b) but the flows separation starts
on the upper rear side of airfoil. The low pressure
region (reddish) in both images shifted to the front
side of the airfoil, which increase the drag as
expected to do. Since the low pressure is on leadingedge side of airfoil so low pressure pulls wing to thatside therefore this automatically increases dragcoefficient. The lift coefficients were calculated as
1.41 and 1.57, and the drag coefficients were 0.015
and 0.022, at the angle of attack 3°for the NACA
0012 and NACA 0012-X.

(b)
Fig. 6. Streamline velocity fields for NACA 0012X
Model aircraft fuselage and wings were
designed using NACA 0012-X airfoil and tailsection was made from NACA 0012. Numericalcalculations were performed for model airplane
using Spalart-Allmaras Turbulence Model at theangle of attack zero but the maximum lift to dragratio was achieved at 3° therefore wing incidence
was set to 3 °. 3D streamline velocity field of modelwith top and bottom view is as shown in Fig. 7 andside view is shown in Fig. 8. The graph was plottedby sending fluids over the top and bottom of the wing
surface a sequence of layer on the x-y plane. As
shown in Fig. 7 and Fig. 8, air flows faster at the topof the plane (reddish color) and slower at the bottom(light color) and laminar flow formed on both sides
and fluid continues to sweep the surface of theaircraft front to back properly. Along the fuselage
surface, fluid is seen in light color because no slip
boundary condition was applied.

(a)

(a)

(b)

Fig. 7. 3D streamline velocity field of model withtop (a) and bottom (b) view.

156

Fig. 8. 3D streamline velocity field of model withside view.

Fig. 11. Top rear view of climbing aircraft at theangle of 10°.

The fluid was sent as a single layer on x-z plane
along the model aircraft and is shown in Fig. 9. It
should be emphasized that the fluid only moves overthe fuselage and there is no flow on the wing and tail.
As we compare the color distribution of the fluid, it
is observed that the fluid moves at equal speeds on
the top and bottom of the fuselage but fluid moves
more slowly behind the plane and along the fuselage
surface because of the shadow effect and the no-slip
condition respectively.

As it is shown in Fig. 11, the formation of the wingtip
vortex is clearly visible, but a much larger formationof vortex occurs at the rear of the body. When theplane ascending, it forms a low pressure region at theupper back of the fuselage. And this region leads tothe formation of wave peaks from bottom to top.
These apices move outward from the body and turninto gigantic vortex waves combining with wingtip
vortex at the back of the plane. When the image fromthe upper front of a flight ascending at the angle ofattack 10° is given in Fig. 12, it appears that thevortex formed at the rear of the body is larger than
the wingtip vortex.

Fig. 9. 3D streamline velocity field over fuselage
with side view.
The wingtip vortex was calculated by sending fluidon the x-z plane along the wing surface and is given
in Fig. 10. The wingtip vortex formation is enlarged
and shown in the same Fig. 10. Due to the pressure
difference at the top and bottom of the wing, air flowrolls up into large vortices near the wingtip as seenin Fig. 10. There is no angle of incidence of theplane, but only the wings have three degrees ofincidence. Therefore the wingtip vortex is seen to beless in the cruise flight.

Fig. 10. Wingtip vortex at 3° wing incidence at
cruise flight.
Numerical calculation was carried out by giving a
10° angle of attack to the model aircraft and top rear
view and top front view are shown in Fig.11 andFig.12 respectively.

Fig. 12. Top front view of climbing aircraft at theangle of 10°.
The lateral-top and bottom-front views of the planerising at an angle of 10 ° are given in Fig. 13 and Fig.
14, respectively. When Fig. 13 and Fig.14 are
examined, fluid rises to the low pressure region of
the back upper part of the body and forms wave
peaks. The vortex formed at the upper back of the
body is very large compared to the wingtip vortex asshown in Fig.13.

Fig. 13. Lateral top view of climbing aircraft at theangle of 10°.

Fig. 14. Sub front view of climbing aircraft at theangle of 10°.

157

A close-up side view of the fluid passing through thewing surface is shown in Fig. 15. It is seen in Fig. 15that the fluid passing over the top of the wing
continues to travel smoothly, but the fluid passing
along the bottom surface curves upwards to form thewingtip vortex.

Fig. 17. Side view of descending aircraft at theangle of -10°

Fig. 15. A close-up side view of the fluid passing
through the wing surface.
Wingtip vortex formation (Fig. 16) of the model
plane ascending at the angle of attack 10° (the total
wing incidence is 13°) is enlarged and for both side
is given in Fig. 16. A circular pattern of rotating air
is clearly visible at both side of wing.

Fig. 16. Wingtip vortex formation of ascending
aircraft at the angle of attack 10°.
Descending model aircraft with the angle of attack 10° was numerically analyzed and side view, lower
back view, upper-front view, and Sub-front view arepresented in Fig. 17, Fig. 18, Fig. 19 and Fig. 20
respectively. When the plane is tilted downward, alow pressure region is formed at the bottom of thetail (back bottom of the fuselage) as seen from thevelocity distribution of the fluid (light color), and theshedding effect arises from the body, and ascending
to the top of the tail. The fluid flows over the x-yplane, bends in the low pressure region andcontinues to create large air waves as seen in Fig 1720. The resulting hill-shaped waves move outward
from the wings, and merges with the wingtip vortex
and turn into circular vortex flows behind theaircraft. It is seen that the height of the vortex (wavepeak) rises from the wings towards the tail. Wingtip
vortex formation of descending model plane at theangle of attack -10° (the total wing incidence is 13°) is enlarged and for both side is given in Fig.
21.The direction of the emerging wingtip vortex forthe descending mode is opposite to that of theascending aircraft as shown in Fig.16 and Fig.21.

Fig. 18. Lower back side view of descending
aircraft at the angle of -10°

Fig. 19. Upper-front view of descending aircraft at
the angle of -10°

Fig. 20. Sub-front view of descending aircraft at theangle of -10°.

Fig. 21. Wingtip vortex formation of descending
aircraft at the angle of attack -10°.

158

5. Conclusion
Today
implementation
of
CFD
has
revolutionized the aerodynamic process. In the last
40 years, CFD has been added as a reliable tool forwind tunnel and flight test as a critical tool.
Aerodynamic performance of 3D model passenger
aircraft was modeled from modified NACA 0012
airfoil and were investigated by using Spalart–
Allmaras Turbulence Model. First, 2D simulation
data were compared with those obtained from windtunnel experiment to correlate the simulation
correctness of the Computational Fluid Dynamics(CFD) approach. Lift and drag coefficient of NACA
0012 and modified NACA 0012-X were calculated
and compared with experiment and comparison
shows a good agreement. Then using the newly
designed airfoil, the passenger plane's wings andfuselage were created. Aerodynamic properties of
the aircraft were investigated by sending air fromdifferent angles to the aircraft's wings and its
fuselage. According to the result of the simulation, it
is seen that during ascending or descending, large
wave dips are seen on the rear side of the fuselage.
According to the flow analysis, these ripples are dueto the difference in pressure at the top and bottom of
the tail. Wingtip vortex was also numericallyanalyzed and it is observed that during theascending, wing vortex is curved upwards, andduring descending it is curved down from bottom. In
the flow analysis, the vortex formed at the back of
the fuselage is seen to be larger and stronger
compared to wingtip vortex. The vortex formed at
the wingtip and at rear back of the body combine toform stronger circular vortices.
Acknowledgment
Many thanks to Middle East Technical University
and Adiyaman University for technical support.
Funding
This work was supported by Adiyaman University
Scientific
Research
Project(Projectno:
TEBMYOMAP/2018-0001).

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