This is the research paper that was published in the AIP Conference Proceedings this year. This paper contains the new modification design in NACA 2412 airfoil and different aerodynamics characteristics were determined and compared with the basic airfoil and multiple conclusion were made for the results. This was actually my B.Tech. min project work back on 2016 Nov end.

1. AIP Conference Proceedings 2204, 030009 (2020); https://doi.org/10.1063/1.5141572 2204, 030009
© 2020 Author(s).
Study on effect of semi-circular dimple on
aerodynamic characteristics of NACA 2412
airfoil
Cite as: AIP Conference Proceedings 2204, 030009 (2020); https://doi.org/10.1063/1.5141572
Published Online: 10 January 2020
Y. Sowmyashree, D. I. P. Aishwarya, S. Spurthy, Roshan Sah, B. V. Pratik, H. V. Srikanth, and R. Suthan

2. Study on Effect of Semi-circular Dimple on Aerodynamic
Characteristics of NACA 2412 Airfoil
Y. Sowmyashree 1 a)
, D. I. P. Aishwarya 1 b)
, S. Spurthy 1 c)
, Roshan Sah 2 d)
B. V. Pratik 1 e)
, H. V. Srikanth 1 f)
, R. Suthan 1 g)
1
Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, India
2
Department of Aerospace Engineering, IIT Kharagpur, India
a)
shreeyj@gmail.com, b)
aishu.pug@gmail.com, c)
spurthyccc@gmail.com d)
sahroshan11@gmail.com
e)
prathikbv1997@gmail.com f)
holalusrikanth@gmail.com g)
aero.suthan@gmail.com
Abstract The present work is an attempt to enhance the aerodynamic efficiency of NACA 2412 airfoil through surface
modifications, for various angles of attack. The surface of NACA 2412 airfoil is modified by providing semi-circular
outward and inward dimples on the lower surface. The lift and drag coefficients were determined at the different angle of
attack ranging from 00
to 120
using computational fluid dynamics (CFD) analysis. During the study the NACA2412 airfoil
was modeled in ANSYS Workbench, the structured mesh was generated in ICEM-CFD, and the flows were analyzed using
ANSYS Fluent solver at a Reynolds number of 2 x105
. The CFD analysis showed decreased pressure drag and increased lift
since the flow separation was delayed due to the turbulence created by the semicircular dimples. The effects of surface
modifications on aerodynamic efficiencies of airfoil were compared for the different angle of attack, and the inward dimple
was proved to be more beneficial.
NOMENCLATURE: L= Lift, D=Drag, CL= Coefficient of Lift, CD= Coefficient of Drag, CL/CD = Aerodynamic
Efficiency.
1. INTRODUCTION
From the moment a new aircraft is thought of, investments are made to increase the aerodynamic efficiency. The
primary objective of any aviation expert or engineer is to make aircrafts more pilot friendly and monumental efforts
are being made to reduce the drag. One of the biggest hurdles in enhancement of lift is flow separation and this
phenomenon is encountered even in low speed regimes however, at low subsonic speed, flow again reattaches as a
turbulent boundary layer [1, 2]. Mueller et al., [3] reported the importance of Reynolds number and boundary layer
effects on airfoil in designing the small aerial vehicles. An abrupt decrease in lift and sudden shoot in drag was
found at low Reynolds number due to non-reattachment of laminar separation to the airfoil surface in time.
Zhang[4] highlights the geometrical effects on the airfoil flow separation and transition. The results of DNS of
incompressible flow over NACA-4412 and NACA-0012-64 showed a stronger adverse pressure gradient field in the
leading edge region of the NACA 0012-64 airfoil due to the rapidly varying surface curvature. The above literatures
reported that the poor aerodynamic efficiency of airfoils at high angle of attack in a low Reynolds number flow is
because of flow separation. Numerous researches have been carried out on surface modifications of airfoils to
enhance the aerodynamic efficiency of airfoil by delaying the flow separation. Several researchers have proposed
various methods to delay the flow separation, amongst which usage of vortex generators to delay the boundary layer
separation by creating turbulence is proliferating [5].
Siauw et al.,[6] investigated the impulsively activated pneumatic vortex generators on the conventional NACA0015
airfoil. The study reported the flow regime and separation phenomenon at 100
AOA for a Reynolds number of 1 x
106
and established a statistical relationship between pressure and velocity signals during flow attached and
separations. The dynamic stall and its effects on lift and pitching moment for NACA0012 airfoil was analyzed by
Niu et al., [7]. The study reported the variable droop leading-edge technique to reduce the dynamic stall also to
improve the aerodynamic characteristics. However the conventional slats, droops and flaps for altering the camber
are equally helpful in delaying the flow separation; improvements in the aerodynamic performance of NACA0012
airfoil namely an increase in lift coefficient was observed on introduction of highly cambered flap [8]. James et
al.,[9] proposed the technique of controlling flow separation by secondary blowing which resulted in increased lift
with delayed stalling angles.
Over the past decade, the experimental and numerical investigations have been carried out on various airfoils to
study the aerodynamic performance at various boundary conditions. However, the use of analysis software has
become much more popular due to its compatibility with the user in analyzing flow characteristics [10,11]. Matsson
Proceedings of the 2nd International Conference on Emerging Research in Civil, Aeronautical and Mechanical Engineering (ERCAM)-2019
AIP Conf. Proc. 2204, 030009-1–030009-7; https://doi.org/10.1063/1.5141572
Published by AIP Publishing. 978-0-7354-1955-1/$30.00
030009-1

3. et al., [12] analyzed the aerodynamic performance at low Reynolds number of NACA 2412 having a chord length of
230mm. The experimental and CFD simulations revealed that the stall angle lies between 14 and 16°. Sarkar et al.,
[13] carried out steady state simulation at low subsonic flow of 50 m/s and concluded that 5º AoA is optimum for
the NACA 2412 airfoil model. The numerical study was carried out on NACA 2412 airfoil for Reynolds number of
3x106
compared the accuracy of Spalart Allmaras, k-ω SST, DES (Detached-Eddy Simulation) and k-ω SST
turbulence models. The results declare that DES k-ω SST is most accurate in simulating the flow over NACA 2412
airfoil [14]. Islam et al., [15] attempted to modify the NACA 2412 airfoil to increase of lift coefficient for low
Reynolds number flow. Results indicated that sinusoidal leading edge as well as an outward dimpled upper surface
gives a better performance with an increase of turbulence. Dutta et al., [16] reported an enhanced lift coefficients
using flap for different AoA for NACA 2412 airfoil. However, at higher values of AoA, lift coefficient was found
to be decreased due to decrease in stall angle. Over past few decades the surface modification using dimples have
proven to be very efficient. Since the dimples impart the required kinetic energy for reattachment of flow at low
Reynolds number flow at higher angles of attack. Davies et al., [17] tested the effect of dimples on golf ball and
proved that balls with shallower dimples obtain long drives, their drag is reduced with considerate increase in the
lift. Beves et al., [18] later incorporated array of dimples in airfoil and showed that the velocity deficit was
minimised in the wake. Livya et al., [19] studied the effects of various shaped dimples namely semi-sphere,
hexagon, cylinder and square on NACA 0018 airfoil at velocities of 30m/s and 60m/s for AoA varying from 50
to
250
. The inward dimple configuration gave best results with improved aerodynamic efficiency. Srivastav et al., [20]
analysed the effect of inward and outward dimples on symmetric airfoil NACA 0018 and demonstrated that dimples
prove to be fruitful. Prasath et al., [21] carried out CFD simulation for low subsonic velocity of 18 m/s for
NACA0018 airfoil with dimples. The experimental and CFD were in good agreement that the dimples results in
delayed flow separation which reduces the drag. Rajasai et al., [22] analysed the effects of circular dimples on
NACA 2412 airfoil and concluded that the presence of a dimple increases the stall angle of the aircraft. Devi et al.,
[23] analysed triangular and square cavity on symmetric NACA 0012 airfoil. Square cavity improved lift coefficient
by 29.05%. Saraf et al., [24] analysed NACA0012 airfoil by varying the location of outer dimples and concluded
that dimples at 75% of the chord length has a 7% increase in lift coefficient. Narayana et al.,[25] analyzed the flow
parent for NACA 4415 airfoil the results yielded that inward dimple at 0.8C with 0.2 aspect ratio of the dimple had
maximum efficiency.
From the literature, it was found that several attempts have been made on the enhancement of lift of airfoil by
delaying flow separation. However, no significant studies have been reported on CFD analysis of NACA 2412
airfoil with dimples as a surface modification over wings. The current study focuses on studying the effects of
surface modification over NACA2412 airfoil on aerodynamic performance through CFD analysis.
2. METHODOLOGY
2.1 Modeling of NACA 2412 airfoil
The NACA 2412 airfoil coordinates were imported to Ansys workbench. The coordinates of NACA 2412 used to
draw airfoil is as shown in table 1. The model of NACA 2412 airfoil is as shown in fig 1(a) and fig 1(b).
TABLE1. NACA 2412 airfoil coordinates
Upper Surface Co-ordinates Lower Surface Co-ordinates
x-axis y- axis x-axis y-axis
0.975825 0.006231 0.999916 -0.001257
0.905287 0.019752 0.975232 -0.003035
0.795069 0.038260 0.903730 -0.008033
0.655665 0.057302 0.792716 -0.015499
0.500588 0.072381 0.653352 -0.024500
0.344680 0.079198 0.499412 -0.033493
0.203313 0.072947 0.346303 -0.039941
0.091996 0.054325 0.208902 -0.042346
0.022051 0.028152 0.098987 -0.037507
0.00000 0.00000 0.026892 -0.023408
FIGURE 1 Airfoil Geometry (a). Imported NACA 2412 airfoil coordinates (b). NACA 2412 airfoil geometry
a) b)
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4. 2.1.1 Modifications to NACA 2412 airfoil
Raymer [26] explain that the phenomenon of stalling in airfoil depends on its thickness. It was reported that the fat
airfoil (thickness> 14%) stalls from leading edge where as thin airfoils stall from trailing edge. NACA 2412 being
very thin airfoil stalls from trailing edge hence the surface modification in terms of inward and outward dimple outer
dimple of diameter 2.5 mm at a distance of 80 mm from the leading edge is provided. The specifications are given in
table 2. The modified NACA 2412 airfoil is as shown in fig .2
TABLE 2 Specifications of wing model
Particulars Specifications
Airfoil series 2412
Chord 100mm
Type of dimple Semi-circular
Dia. Of dimple 2.5 mm
Location of dimple 80 mm chord (lower surface)
FIGURE 2 Modification Details (a) Outward dimpled airfoil geometry (b) Inward dimpled airfoil geometry
FIGURE 3 Mesh
2.2 Computational domain
In order to analyze the flow a computational domain is required hence a 2D planar fluid domain was generated. The
domain was sufficiently large (10 times the chord) to simulate free stream flow. This large domain reduces the walls
effects. The domain constituted of inlet, walls, airfoil and outlet.
2.3 Meshing
Structured mesh with an elemental size of 0.01 mm along with the far field effects was generated in ICEM-CFD
using O grid. The quality of the mesh was maintained above 0.85, the aspect ratio was brought down below 100. In
order to capture boundary layers an exponentially varying mesh size was used. The meshed model of computational
flow domain is as shown in fig 3.
2.4 Grid Independence Study
To ensure the CFD simulations didn’t vary with the grid size, the grid independence test was carried out. In order to
fix the number of nodes and the grid size an iterative process was employed. For finalizing the number of nodes the
simulation output with literature[27] where as, the size was fixed after numerous simulations by reducing the grid
size to 30% of its initial size starting from 0.1mm till the simulation results for CL was almost constant. Finally the
grid was brought down to 0.0001mm near the surface of airfoil and was varied exponentially to have 0.01mm grid
a) b)
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5. size at far field. The fig 4 (a) and fig 4(b) shows CL with respect to grid size and CL with respect to various AoA for
different grid sizes respectively.
FIGURE 4 Grid Independence Study (a) Variation of CL with grid size (b) Validation with Theoretical Values
2.5 Boundary Conditions
The boundary conditions used for CFD analysis of airfoils with and without dimples at the various angle of attack
ranging from 00
to 12 0
are as shown in table 3 . The solver model used in the study is a combination of k-ω (eq.(1)
and eq (2)) and k- Ɛ (eq (3) and eq (4)) turbulence models, Where the k-ω turbulence model is used for the inner
region of the boundary layer, and it switches to k-Ɛ turbulence model in the free shear flow. The kinetic energy is the
first transported variable ‘k’, and it determines energy in the turbulence. The second transported variable is specific
dissipation ‘ω’, and it determines the scale of the turbulence.
Transport equations for k-ω model:
ρu. ▽k = ▽.[(ƞ + ƞTσk) ▽k] + ƞTP(u) – ρkω (1)
ρu. ▽ω = ▽.[(ƞ + ƞTσ ω) ▽ω] + aωƞTP(u)/k - ρω2 (2)
Where: P(u) = u: ( ▽u + (▽u)T), and ƞT = ρk/ω
=0.09, =0.075, a=0.55
Transport equations for k-ԑ model:
ρu. ▽k = ▽.[(ƞ + ƞT/σk) ▽k] + ƞTP(u) - ρԑ (3)
ρu. ▽ԑ = ▽.[(ƞ + ƞT/σԑ) ▽ԑ] + Cԑ1ԑ ƞTP(u)/k - Cԑ2ρԑ2/k (4)
Where: P(u) = u: ( ▽u + (▽u)T), and ƞT = ρCμk2/ԑ
Cԑ1=1.44, Cԑ2=1.92, Cμ=0.09, σk=1.0, σԑ=1.3
Table 3 Boundary conditions
Parameter Condition/ Value
Flow velocity 30 m/s
Solver used Pressure based
Fluid condition Ideal fluid
Flow type Steady state flow
Viscous model Standard k-ϵ model with Standard wall function
Ambient temperature 300 K
Outlet pressure 0 Pa
Atmospheric pressure 1.01 x 105
Nm-2
Wall condition Stationary wall
Shear condition No slip
Density 1.17 kg/m3
Cp 1.005KJ/KgK
3. RESULTS AND DISCUSSIONS
Computational fluid dynamics simulations for various angles of attack ranging from 0 to 120
were carried out, and
the results of simulations of NACA 2412 airfoils with and without surface modifications were compared. The
a) b)
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6. aerodynamic characteristics such as the coefficient of lift (CL), the coefficient of drag (Cd) and Aerodynamic
efficiency (CL/Cd) were determined and analyzed for maximum aerodynamic performance. The results obtained
from the CFD simulation are as given in table 5. The results are plotted as shown in fig 5 (a), 5(b) and 5(c).
Table 4. CL, Cd and CL/Cd for NACA 2412 airfoil with and without dimples
Angle of
attack(α)
CL Cd CL/Cd CL Cd CL/Cd CL Cd CL/Cd
NACA 2412 airfloil without
modifications
NACA 2412 airfoil with
outward dimple
NACA 2412 airfoil with
inward dimple
0 0.2183 0.018 12.125 0.2332 0.02649 8.803327 0.220934 0.0185 11.9424
2 0.4104 0.0226 18.15929 0.432685 0.0308 14.04821 0.423771 0.0246 17.22646
4 0.5895 0.03545 16.62906 0.683071 0.04155 16.43974 0.630765 0.0367 17.18706
6 0.8100 0.048 16.875 0.865485 0.0495 17.48455 0.8667 0.0518 16.73166
8 0.9873 0.0705 14.00426 1.04091 0.061158 17.02002 1.066284 0.0748 14.25513
10 1.1304 0.099 11.41818 1.141704 0.07894 14.46293 1.19212 0.118 10.10271
12 1.2751 0.11665 10.93116 1.362466 0.1085 12.55729 1.316561 0.13 10.1274
FIGURE 5 Analysis Plots (a) CL versus AOA. (b) CD versus AOA (c) Aerodynamic Efficiency versus AOA
At the free stream conditions, the molecules of air travel with the flow velocity and when the flow is interrupted by
the airfoil the molecules first strike the leading edge and their velocity reduce to zero. The lift is generated in the
airfoil due to the pressure differences on upper and lower surface so to enhance the lift; the pressure on the upper
surface should be low when compared to the lower surface. The same is evidently seen in pressure contours shown
in Fig 7, 8 and 9. It is very evident that at higher AOA the flow tends to separate from trailing edge. The presence of
dimple imparts the turbulent kinetic energy which helps in reattached of flow and hence flow adheres to the airfoil
surface.
FIGURE 6 Analysis Results for 00
AOA of Unmodified Airfoil (a) Pressure contour (b) Velocity contour (c) Pressure
Distribution along the length of the chord
FIGURE 7 Analysis Results for 120
AOA of Unmodified Airfoil (a) Pressure contour (b) Velocity contour (c) Pressure
Distribution along the length of the chord
a) b) c)
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7. FIGURE 8 Analysis Results for 120
AOA of Airfoil with Outward Dimple(a) Pressure Contour (b) Velocity contour (c) Pressure
Distribution along the length of the chord.
FIGURE 9 Analysis Results for 120
AOA of Airfoil with Inward Dimple (a) Pressure contour (b) Velocity contour c) pressure
distribution along the length of the chord.
4 CONCLUSIONS
The concept of surface modification through dimple is burgeoning, with the extreme benefit of making an aircraft
more maneuverable by changing flow characteristics. Implementation of dimple over NACA 2412 airfoil has proven
to be more effective in altering various aspects of the flow structure with varied lift and drag forces. The following
conclusions have been drawn from the work.
• Comparative study between surface modified and unmodified NACA2412 airfoils for constant inlet
velocity (i.e. constant Reynolds number) showed that surface modified airfoils have better aerodynamic-
performances compared to unmodified airfoil.
• Among the surface modifications provided, the inward dimple has better aerodynamic features. The inward
dimple has proved to be more suitable than the outward dimple because it gives high aerodynamic
efficiency as noted by the results of this study.
• The only drawback of outer dimple configuration is produced more drag as compared to unmodified airfoil.
Based on this result inward dimple is suggested over airfoil which will sense boundary layer separation and
dimple arrange in least drag and high lift configuration. Also it increases the aerodynamic efficiency and
therefore improving the performance of aircraft.
• The idea will also assist in shorter take-off at low speeds. In general, the present study was aimed to
improve the maneuverability and performance of an aircraft by flow variation over the airfoil.
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