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Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
NUMERICAL ANALYSIS OF MODIFIED NACA 4412 AIRFOIL FOR IMPLEMENTATION
OF LOW REYNOLDS NUMBER VAWTs
Fazlar Rahman1,2*, Syed Wasim Ul Huda3, Sadia Tarannum Sneha3, Jubayer Hossain1,4, Mohammad Rejaul Haque1
1Faculty, Department of Mechanical and Production Engineering (MPE)
Ahsanullah University of Science and Technology (AUST), Dhaka, Bangladesh
2Department of Mechanical Engineering
Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh
3Graduate, Department of Mechanical and Production Engineering
Ahsanullah University of Science and Technology (AUST), Dhaka, Bangladesh.
4George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology, Georgia, USA
*Corresponding Author Email: fazlar.rahman.mpe@aust.edu
Abstract: The section parameters of the NACA 4412 airfoil are modified for the best lift/drag ratio at a low Reynolds
number (1.22 × 105) to implement in Vertical Axis Wind Turbines (VAWTs). The lift and drag characteristics are
evaluated numerically within the range of angle of attack (AoA) 100 to 150 using the opensource tools Xflr5 and
Qblade. The highest ratio of the coefficient of lift to drag (Cl/Cd) and coefficient of power (Cp) are investigated for
modification of each section parameter by repeated iterations. The Cp value is evaluated by Qblade’s Double Multiple
Stream tube (DMS) algorithms for solidity ratios (SR) of 0.33 and 0.17, respectively, over a range of tipspeed ratios
(TSR). The numerical analysis results are validated by comparing with the baseline NACA 4412 airfoil’s experimental
results. The highest Cp values are found to be 0.387 (at TSR 2.4) and 0.365 (at TSR 2.6) for the SR of 0.33 and 0.17,
respectively, which complies with the Betz limit (Cp = 0.59) and higher than the baseline airfoil NACA 4412 airfoil.
This study will facilitate the implementation of the modified NACA 4412 airfoil in VAWTs for use on the rooftops of
urban and suburban households at a low airspeed.
Keywords: NACA 4412 airfoil; VAWT; Xflr5; QBlade; Betz’s law; Low Reynolds Number.
INTRODUCTION
Due to global warming and the greenhouse effect,
the energy obtained from renewable sources such as
solar, wind, hydro, tidal, geothermal, and biomass gets
priority worldwide [1]. However, wind energy has
become one of the most exciting topics among
researchers because of its green nature, plenty and
readily available, costfree [24], and the recent global
energy crisis. It is a sustainable and promising
renewable energy resource, continuously gaining
attention and popularity [56]. Researchers are trying to
develop mechanical systems to extract energy from the
wind, even at low air speeds. Vertical Axis Wind
Turbines (VAWT) and Horizontal Axis Wind Turbines
(HAWT) are used to develop mechanical energy from
the wind [78]. VAWT and HAWT rotate in a direction
parallel and perpendicular to the airflow, respectively [7,
9]. HAWT is the most common and suitable for large
scale application in offshore, coastal, level terrain, open
landscape, and rural areas [9, 10] with stable and steady
wind conditions. Despite higher efficiency [711],
HAWT has some drawbacks, such as operation depends
on wind direction, requires a yaw controlling system,
ample space, higher and stronger tower, high
maintenance cost, and harmful to ecology [7, 11, 12]. In
addition, it has a higher installation cost since it
comprises a yaw controlling system and nacelle, which
contains a gearbox, generator, and rotor mounted at the
top of the tower [12]. However, VAWT can receive air
from any direction, even in the crossflow directions,
requires small space and compact auxiliaries, and is easy
to design, maintain, and install [7, 8, 10]. It operates
effectively with turbulent and highly fluctuating wind
from any direction without a yaw system, making it
suitable to install over the rooftops of buildings in urban
and suburban areas where the wind is unstable and gusty
[7, 10, 13]. For smallscale and residential applications,
VAWT performs better than HAWT [10, 13]. Compared
to HAWT, the deficiency of VAWT can be
compensated, even overcompensated, by placing
multiples close together since it requires less installation
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
space [11]. It will continue to play a vital role in wind
energy [8, 11], especially for sustainable and
decentralized energy [14] at the microscale for rural
homes [6]. This study investigates the drag and lift
characteristics of the modified NACA 4412 airfoil to be
implemented in VAWTs at low airspeed.
Wind turbines are operated based on the drag and
lift forces developed at the airfoil due to the
aerodynamic effect. There are three types of VAWTs
used to generate energy from the wind. The drag and lift
based VAWTs are known as Savonius and Darrieus
type [9, 11] and a new emerging type known as Mixed
Vertical Axis Wind Turbine (MVAWT) [9, 15]. NACA
4412 airfoil is used in lightweight, and lowaltitude
flying aircraft [16]. Large birds, unmanned aerial
vehicles (UAV), and radiocontrolled aircraft are also
operated at low altitudes in an incompressible flow field
at 105<Re<106, where viscous forces dominate the
inertial forces [17, 18]. Besides, the maximum liftto
drag ratio decreases extensively for the Reynolds
number 104 to 105 [19]. The Reynolds number within the
range 105<Re<106 refers to the low Reynolds number
[18]. Since wind turbines operate at low altitudes and
low airspeed, the NACA 4412 airfoil is chosen in this
study. The lift and drag characteristics are investigated
at a low Reynolds number of 1.22 × 105 by varying the
section parameters of the airfoil for implementation in
the VAWT. The opensource numerical tools Xflr5 and
QBlade are used to simulate the lift and drag
characteristics of the modified NACA 4412 airfoil. This
study will facilitate the design of VAWT for use on the
rooftops of commercial and residential buildings in
urban and suburban areas.
Numbers of praiseworthy studies reported
modifying and optimizing the NACA baseline airfoil for
use in the VAWT. Carrigan et al. [9] optimized the
NACA 0015 airfoil to implement it in VAWTs using the
numerical tool Ansys Fluent and increased efficiency by
6% from the baseline airfoil. Whittlesey [11]
investigated Selig S1210 and DU 06W200 airfoils to
eliminate selfstart problems in VAWTs for the wind
farm. Moreover, Ma et al. [4] optimized the NACA 0018
airfoil for moderate tip speed ratios to improve the
performance of VAWT. Ramadan et al. [2] investigated
the shape optimization of the Sshape blade for the
Savonius turbine using the numerical analysis tool
Ansys Fluent. Baghdadi et al. [10] worked on the
dynamic shape optimization of VAWT using the blade
morphing technique of the NACA 0021 airfoil. Nguyen
and Metzger [13] optimized NACA 0012, 0015, and
0018 airfoils by changing the height and diameter of the
VAWT for use in urban and suburban areas. Nakhchi et
al. [3] worked on the numerical simulation of the
aerodynamic performance of the NACA 4412 airfoil
over a wide range of Reynolds numbers. Chen and Kuo
[7] studied the impact effect of the pitch angle of
NACA0012, 2412, and 4412 airfoils for small Darrieus
VAWT. Shukla and Kaviti [8] studied the impact of
profile modification of NACA 0012, 0015, 0018, and
002 airfoils of straightbladed VAWT. Ockfen and
Matveev [20], Haque et al. [21], and Chaitanyaa et al.
[22] also investigated the aerodynamic characteristics of
the NACA 4412 airfoil. However, to our knowledge, no
study has been reported on modifying section
parameters of the NACA 4412 airfoil to implement it in
VAWTs. This study aims to evaluate the lift and drag
characteristics of the NACA 4412 airfoil by varying
foursection parameters, such as maximum camber,
maximum thickness, leadingedge (LE) ratio, and
trailingedge (TE) ratio, through repeated iterations for
use in VAWTs.
METHODOLOGY
The foursection parameters, such as leadingedge
(LE) radius, trailingedge (TE) thickness, maximum
camber, and maximum thickness of the NACA 4412
airfoil, are varied for the best possible lift and drag. The
lift and drag characteristics are simulated using open
source numerical analysis tools Xflr5, Xfoil, and
Qblade, which are widely used to analyze airfoil
sections for low Reynolds numbers. The ratio of the
coefficient of lift and drag (Cl/Cd) is evaluated for
Reynolds number 1.22 × 105 for changing the four
section parameters within the range of Angle of Attack
(AoA) 100 to 150. The coefficient of power (Cp) is also
determined for changing each section parameter with
respect to tipspeed ratios (TSR) to justify the
implementation of the modified airfoil in VAWTs for
low airspeed. The lift and drag characteristics and Cp
value are evaluated by repeated iterations over a range
of angles of attack (AoA) and TSRs. The typically
accepted solidity ratio (SR) for VAWT is 0.09 to 0.36
[23] and TSR 2.0 to 6.0 [24]. The Cp value is
investigated for each modification for SR 0.33 and 0.17
over a range of TSRs. The simulated characteristics are
compared with the baseline NACA 4412 airfoil. The
accuracy of the numerical analysis tools is verified by
comparing the coefficient of lift (Cl) and coefficient of
drag (Cd) of the numerical analysis with that of the
experimental data of Miley [25]. The section parameters
are varied to evaluate lift and drag characteristics shown
in Fig.1 and Table1.
Fig.1: Typical Airfoil Nomenclature [22].
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Table1: Section parameters of NACA 4412 airfoil varied for the best Cd/Cl ratio
Parameter
Enlargement
Reduction
Trailing edge thickness
12% and 32%
60%
Leading edge radius
20%, 25% and 30%
20% and 30%
Maximum camber
5%, 6.4% and 10%
5% and 6.8%
Maximum thickness
12%
7.0%
GOVERNING EQUATIONS
The following governing equations are solved
numerically to evaluate the aerodynamic characteristics,
such as drag, lift, and power coefficient of the modified
NACA 4412 airfoil section [26, 27].
(1)
(2)
(3)
The equation (1), (2), and (3) are known as Von
Karman momentum integral equation, kinetic energy
shape parameter equation, and Laplace equation,
respectively, for an airfoil [26, 27]; where H, H*, H**,
Me, Cf, and CD are the regular shape parameter, kinetic
energy shape parameter, density shape parameter, Mach
number at the end of the boundary layer, skin friction
coefficient, and dissipation coefficient, respectively [26,
27]. The relationship between the regular shape
parameter (H), Mach number at the end of the boundary
layer (Me), and kinetic shape factor (Hk) is given by the
following equation [27].
(4)
Numerical Analysis:
The numerical analysis tools Xflr5, Xfoil, and
QBlade, are used to solve the governing equations (1) to
(4) and to simulate the lift and drag characteristics. Xfoil
is a popular and reliable CFD tool widely used in the
aircraft industry to design and analyze lowspeed
unmanned and micro aerial vehicles [27, 28]. It is
developed by MIT in 1986 [28]. In Xfoil, the governing
equations are solved using a higherorder 2D panel
method and a fully coupled viscous/inviscid iteration
method [28]. Xfoil codes perform better at subsonic
velocity Mach number less than 0.70 and a low
Reynolds number flow [27]. It can evaluate the lift and
drag characteristics of the airfoil with inverse design
capability. The Xflr5 is developed by André Deperrois
[29], which uses exact Xfoil code and userfriendly
graphical interfaces [27]. It solves governing equations
by the vortex lattice method, 3D panel method, and
lifting line theory. Xflr5 is also used to design and
analyze entire wing aircraft at low Reynolds numbers
[22, 27]. QBlade was developed in 2010 by Berlin
Technical University as opensource software for wind
turbine simulation, which is integrated seamlessly into
the Xfoil GUI interface [30, 31]. QBlade uses the Blade
Element Momentum (BEM) and Double Multiple
Stream tube (DMS) algorithms to solve the governing
equations [30, 31]. The BEM algorithm is used for
simulating HAWTs and DMS for VAWTs [32]. DMS
algorithm is an extended version of the BEM algorithm,
where VAWT is viewed as two HAWTs in a row. The
BEM algorithm is computationally efficient and cost
effective [30], and all correction factors, such as tip and
root loss, drag and 3D correction, and aspect ratio
effects, are already incorporated [30, 31]. Besides,
QBlade is used for blade design, optimization, rotor
simulation, and evaluation of the performance of wind
turbines [30, 32, 33].
In this study, Xfoil is used to evaluate the ratio of
the coefficient of lift (Cl) and drag (Cd) with respect to
AoA for the variations of section parameters, such as
maximum camber, maximum thickness, leadingedge
(LE) radius, and trailingedge (TE) ratio of the NACA
4412 airfoil. DMS algorithm is used to examine the
coefficient of power (Cp) of the VAWT with the
modified NACA 4412 airfoil.
Modification of section parameters:
The aerodynamic characteristics of the NACA 4412
airfoil, such as drag, lift, and power coefficient, are
studied by changing its foursection parameters
iteratively. The section parameters include trailingedge
(TE) thickness, leadingedge (LE) radius, maximum
chamber, and maximum thickness. The ratio of liftto
drag coefficient (Cl/Cd) over a range of angles of attack
(AoA) and the coefficient of power (Cp) over a range of
tipspeed ratio (TSR) are investigated for the variation
of each section parameter. The velocity and force
components of the VAWT are shown in Fig.2.
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Fig.2: Velocity and Force Components in VAWT [34,
35].
The angle of attack (AoA) is the angle between the
direction of the incoming air to the line connecting the
leading and trailing edge of the airfoil [8]. In Fig.2,
,
and
represent the freestream air velocity,
tangential velocity of the blade, and undistributed
airflow velocity, respectively. and are the drag and
lift force acting on the blade. The angle, α between
and
is the AoA and
=
+
. The lift and
drag force are given by the following equations.
(5)
(6)
where Cd and Cl are the coefficient of drag and
coefficient of lift, respectively, ρ is the air density, and
A is the blade area. The value of Cd and Cl varies with
the AoA and characteristics of the airfoil.
The tipspeed ratio (TSR) is an essential parameter
for examining the airfoil section for the wind turbine and
its efficiency. It is the ratio of the tipspeed of the blade
to the free stream air velocity [32]. The tipspeed ratio
(TSR) of the turbine is expressed by the following
equation.
Fig.3: Schematic diagram of VAWT [4].
(7)
where ω = rotor angular velocity, r = radius of the rotor,
and
= free stream velocity of air, as shown in Fig.3.
The coefficient of power (Cp) is the ratio of power
developed by the wind turbine to the total wind power
flowing to the turbines at a specific speed [8]. It depends
on the wind speed, angle of attack (AoA), turbine
rotational speed, and other factors. Also, it is a measure
of the turbine’s overall efficiency [8]. The equation of
power coefficient (Cp) is given by the following Eq. (8)
and Eq. (9), respectively.
(8)
(9)
where T = torque, ρ = air density, D = rotor diameter, h
= blade span, V∞ = free stream velocity, c = blade chord
length, = kinematic viscosity of air, and = Tipspeed
ratio.
VAWT Rotor blade design
The threebladed rotor is the most suitable for
VAWT [14]. This study investigates a threebladed H
type straight blade (SB) rotor of 0.90 m and 1.8 m
diameters by specifying blade height, chord length, and
twist angle, as shown in Table2. In Htype, the blades
are straight and parallel to the axis of rotation [14]. The
wind speed of 7 m/s is considered for the Reynolds
number of 1.22 × 105. The design of the Htype blade is
shown in Fig.4. Solidity ratio for a VAWT ranges from
0.09 to 0.36 [23]. It is the ratio of the blade overall area
to the turbine's swept area, defined as
,
where n, c, and d are the number of blades, blade chord
length, and rotor diameter, respectively [23]. This study
evaluated the coefficient of performance (Cp) for a high
solidity ratio of 0.33 and a moderate solidity of 0.17. The
blade speed is higher at the tip compared to its root.
Therefore, it is required to twist the blade to a certain
degree to maintain constant AoA throughout the blade
and achieve higher efficiency. Besides, it influences the
ability to selfstart the three straightbladed VAWT [14].
In this study, the blade elements are twisted by 5 degrees
to prevent stalling, and achieve selfstart ability and
higher efficiency.
Fig.4: Htype Straight Blade VAWT designed by
QBlade.
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Table2: Blade geometry and solidity ratio (SR)
Blade
Configurations
Blade
elements
Rotor
height ‘h’
(m)
Chord
length ‘c’
(m)
Rotor
dia. ‘d’
(m)
Twist
angle
(deg.)
Blade
No.‘n’
Solidity ratio
(
Htype straight
blade
1
0
0.10
0.90
5
3
0.33
2
0.375
0.10
0.90
5
3
0.375
0.10
0.90
5
Htype straight
blade
1
0
0.10
1.80
5
3
0.17
2
0.375
0.10
1.80
5
3
0.375
0.10
1.80
5
Table3: Critical AoA, highest Cp and corresponding TSR ( of modified NACA 4412 airfoil
Section
parameters
Modifications
Critical
AoA
SR 0.33
SR 0.17
Highest Cp
Highest Cp
TE thickness
Reduced 60%
7°
0.37
2.4
0.25
2.4
Increased 60%
7°
0.254
2.4
0.20
3.0
LE radius
Reduced 20%
7°
0.248
3.0
0.188
3.0
Increased 20%
7°
0.366
2.6
0.31
3.0
Max. camber
Reduced 6.8%
8°
0.387
2.4
0.321
3.2
Increased 6.4%
6°
0.367
2.4
0.30
3.2
Max. thickness
Reduced 7%
7°
0.311
3.2
0.304
3.2
Increased 12%
5°
0.378
2.6
0.365
2.6
Baseline airfoil

7°
0.073
2.0
0.05
2.4
RESULTS AND DISCUSSION
The numerical analysis tool Xfoil is used to
investigate the lift and drag characteristics of the NACA
4412 airfoil for variation of the TE thickness, LE radius,
maximum camber, and maximum thickness. The ratio of
coefficient lift to drag (Cl/Cd) is evaluated for modified
section parameters over a range of AoA. The coefficient
of power (Cp) for the modified airfoil is also evaluated
over a range of tipspeed ratios (TSR, ) by using the
numerical analysis tool Qblade for the solidity ratio (SR)
of 0.33 and 0.17, respectively. The critical angle of
attack (AoA), maximum Cp value, and corresponding
TSR for the modified and baseline airfoils are
summarized in Table3. The lift and drag characteristics
over a range of AoA; and the Cp value over a range of
are described in the following subsequent paragraphs.
Modification of Trailing Edge (TE) Thickness:
The effect of variation of the TE thickness on the
lift and drag coefficients is shown in Fig.5(a).
Reducing the TE thickness by 60%, the Cl/Cd ratio
increases over the baseline NACA 4412 airfoil. Within
the range of AoA from 2.0 to 10 degrees, the Cl/Cd ratio
is found to be relatively higher. It is reduced gradually
for an AoA greater than 10 degrees and the negative
AoA. The maximum value of Cl/Cd is found at 7 degrees
AoA for reducing TE thickness by 60%. However, by
enlarging TE thickness by 60%, the Cl/Cd ratio increases
slightly more than the baseline NACA 4412 airfoil, but
not significantly. It is also found to be maximum at AoA
7 degrees.
It is noted that a nonzero Cl/Cd value is found at zero
degree AoA in baseline and modified airfoils due to the
viscous flow, boundary layer formation, and also
cambered nature of the NACA 4412 airfoil. It indicates
that there will be potentialflowlike behavior at zero
degrees AoA, as well as signifies the accuracy of the
numerical analysis. The result of this study will help
design the liftbased VAWT by using the NACA 4412
airfoil with modified TE thickness.
Modification of Leading Edge (LE) Radius:
The impacts of variation of the LE radius on the
coefficient of lift and drag of the NACA 4412 airfoil are
shown in Fig.5(b). Increasing the LE radius by 20%,
the Cl/Cd ratio is found to be higher than the baseline
NACA 4412 airfoil within the range of AoA from 2.0 to
11 degrees. The maximum value of Cl/Cd is found at 7
degrees AoA. However, by reducing the TE thickness
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Fig.5: Lift and drag characteristics for modification of (a) TE Thickness, and (b) LE Radius.
Fig.6: Lift and drag characteristics for modification of (a) Maximum Camber, and (b) Maximum Thickness.
by 20%, the Cl/Cd ratio increases slightly over the
baseline NACA 4412 airfoil and is also found to be
maximum at 7 degrees AoA. This study revealed that by
enlarging the LE radius by 20%, a higher lift can be
obtained from the baseline NACA 4412 airfoil at low
airspeed and will help design the liftbased VAWT. The
positive lift at zero degrees AoA also verifies the
appropriateness of the numerical analysis.
Modification of Maximum Camber:
As shown in Fig.6(a), for increasing the maximum
camber by 6.4%, the coefficient of lift to drag ratio,
Cl/Cd, is found to be higher than the baseline NACA
4412 airfoil until 6.0 degrees AoA and then found to be
lower than the baseline airfoil with increasing AoA. For
reducing maximum camber by 6.8%, the ratio of Cl/Cd
is found to be less than the baseline airfoil until 7
degrees AoA; then, it becomes higher than the baseline
airfoil with increasing AoA. The peak of Cl/Cd for this
modification is found at 8.0 degrees AoA. The ratio of
Cl/Cd is found very close to the baseline airfoil for the
negative AoA in both cases. The nonzero lift at zero
degrees AoA confirmed the accuracy of this study. This
result revealed that lift characteristics of the NACA
4412 airfoil could be enhanced by changing its
maximum chamber, which will help design liftbased
VAWTs for low airspeed.
Modification of Maximum thickness:
The lift and drag characteristics of the NACA 4412
airfoil for modification of the maximum thickness are
shown in Fig.6(b). It is investigated for increasing the
maximum thickness by 12% and reducing it by 7%. In
both cases, there is no significant change in Cl/Cd ratio
from the baseline NACA 4412 airfoil for the negative
AoA. For increasing the maximum thickness by 12%,
the value of Cl/Cd is slightly higher than the baseline
airfoil within the range of zero to 7.0 degrees AoA. It is
then decreased gradually and found to be lower than the
baseline airfoil. The highest value of Cl/Cd is found at
6.0 degrees AoA for this modification. For reducing the
maximum thickness by 7%, the Cl/Cd value is lower than
the baseline airfoil until 8.0 degrees AoA. After that, it
is observed to be slightly higher than the baseline airfoil,
and the peak value of Cl/Cd is found at 7 degrees AoA.
The positive lift at zero degrees AoA ensures the
accuracy of the numerical analysis.
Coefficient of Power (Cp):
The tipspeed ratio (TSR) and coefficient of power
(Cp) are the most critical factors in evaluating the
performance of VAWTs. This study assessed the Cp
value over TSR ( for solidity ratios (SR) of 0.33 and
0.17 using the opensource tool Qblade with DMS
algorithm. The graphs of Cp vs. TSR ( for
modification of the LE radius, TE thickness, maximum
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Fig.7: Cp vs TSR for TE thickness modification (a) SR = 0.33, and (b) SR = 0.17.
Fig.8: Cp vs TSR for LE radius modification (a) SR = 0.33 and (b) SR = 0.17.
camber, and maximum thickness are shown in Fig.7 to
Fig.10. The effects of such modifications on the Cp
value are discussed in the subsequent paragraphs.
Modification of Trailing Edge (TE) thickness:
The graphs of Cp vs. TSR ( for changing the TE
thickness are shown in Fig.7. For reducing TE
thickness by 60%, the maximum value of Cp is found to
be 0.37 and 0.25 at = 2.4 for the solidity ratio (SR)
0.33 and 0.17, respectively. For enlarging TE thickness
by 60%, the maximum value of Cp is found to be 0.254
(at =2.4) and 0.20 (at = 3.0) for the SR 0.33 and
0.17, respectively. Whereas, for the baseline airfoil, it is
found to be 0.073 (at = 2.0) and 0.05 (at = 2.4) for
the SR 0.33 and 0.17, respectively. By varying the TE
thickness of the baseline NACA 4412 airfoil, the Cp
value is increased significantly from = 2.0 to = 4.0.
In both modifications, the Cp values are found to be
much higher than the baseline airfoil and lower than
Betz’s limit (Cp = 0.59) [36].
Modification of Leading Edge (LE) radius:
The Cp vs. TSR( graphs for modification of the
LE radius are shown in Fig.8. For increasing the LE
radius by 20%, the highest Cp value is found to be 0.366
(at = 2.6) and 0.31 (at = 3.0) for solidity ratio (SR)
0.33 and 0.17, respectively. For reducing the LE radius
by 20%, the peak Cp value is found to be 0.248 and 0.188
(at = 3.0) for SR 0.33 and 0.17, respectively. In the
baseline airfoil, the maximum Cp value is found to be
0.073 (at = 2.0) and 0.05 (at = 2.4) for SR 0.33 and
0.17, respectively. By changing the LE radius of the
NACA 4412 airfoil, the Cp value is enhanced
significantly within the range of = 2.0 to 3.5. The Cp
values are found to be considerably higher than the
baseline NACA 4412 airfoil and less than Betz’s limit
within the range of = 2.0 to 4.0 in both modifications.
Fig. 9: Cp vs TSR for Maximum Camber modification (a) SR = 0.33 and (b) SR = 0.17.
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Fig.10: Cp vs TSR for Maximum Thickness modification (a) SR = 0.33 and (b) SR = 0.17.
Modification of Maximum Camber:
The effects of variation of the maximum camber over
power coefficient (Cp) are shown in Fig.9. For reducing
the maximum camber by 6.8%, the highest Cp value is
found to be 0.387 (at = 2.4) and 0.321 (at = 3.2) for
SR 0.33 and 0.17, respectively. By enhancing the
maximum camber by 6.4%, the peak Cp value is found
to be 0.367 (at = 2.4) and 0.30 (at = 3.2) for SR 0.33
and 0.17, respectively. For the baseline airfoil, the
maximum Cp value is found to be 0.073 (at = 2.0) and
0.05 (at = 2.4) for SR 0.33 and 0.17, respectively. In
both cases, the Cp value is found to be significantly
higher than the baseline NACA 4412 airfoil and less
than Betz’s limit within the range of = 2.0 to 4.0.
Modification of Maximum Thickness:
The consequences of variation in the maximum
thickness of the NACA 4412 airfoil on the power
coefficient (Cp) are shown in Fig.10. The Cp value is
studied for increasing and decreasing the maximum
thickness by 12% and 7%, respectively. In both cases,
the Cp value is much higher than the baseline NACA
4412 airfoil for SR 0.33 and 0.17. However, for the same
solidity ratio (SR), there is no remarkable difference in
Cp between increasing and decreasing the maximum
thickness. For solidity ratio (SR) 0.33, it is found to be
0.378 and 0.365 (at = 2.60) for increasing and
reducing the maximum thickness by 12% and 7%,
respectively, and found to be 0.311 and 0.304 (at =
3.2) for SR 0.17, as shown in Figs. 10(a) and 10(b),
respectively. The Cp value of the baseline airfoil is the
same as the previous modification. The Cp value of the
modified airfoil is much higher than the baseline NACA
4412 airfoil within the range = 2.0 to 4.0.
VALIDATION OF ANALYSIS
Lift and Drag Characteristics:
The lift and drag force features of the modified
NACA 4412 airfoil are evaluated over a range of AoA
using the opensource numerical analysis tool Xfoil.
Xfoil is validated in numerous studies and recognized as
a standard airfoil analysis tool [31]. The coefficient of
lift and drag ratio (Cl/Cd) is found to be much higher than
the baseline NACA 4412 airfoil. The Xfoil is explicitly
developed for designing and analyzing aircraft wings at
low airspeed [26]. The accuracy of the Xfoil is already
established among researchers for low Reynolds
numbers [26]. In this study, the lift and drag
characteristics of the baseline and modified NACA 4412
airfoil are evaluated over a range of AoA by Xfoil at
Reynolds number 1.22 × 105. Then, it is compared with
the experimental results of Miley [25], as shown in Fig.
11(a) and Fig.11 (b).
The graphs of Cl vs. AoA and Cd vs. AoA are
obtained by the Xfoil, which follows the same trend as
the experimental results of Miley [25]. The coefficients
of lift (Cl) and drag (Cd) are found to be very close to the
experimental results within the range of AoA zero to 10
degrees (Fig.11).
Fig.11: Experimental results of Miley [25] and Xflr5/Xfoil results (a) Cl vs. AoA, and (b) Cd vs. AoA.
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
Beyond this range, less than zero and higher than 10
degrees AoA, the Xfoil results vary slightly from the
experimental results. Due to the tolerances and errors in
solving the stiffness matrix by numerical tool, the minor
variations between the numerical and experimental
results are unavoidable. These variations are
insignificant and negligible. Therefore, it is concluded
that the lift and drag characteristics of the modified
NACA 4412 airfoil evaluated in this study are within the
acceptable limit. In addition, positive nonzero Cl/Cd
values are found at zero degrees AoA in baseline and
modified airfoils. It happened due to the viscous flow,
boundary layer formation, and the
cambered/unsymmetrical nature of the NACA 4412
airfoil. This fact also established the accuracy and
validity of this study.
Validation of Coefficient of power (Cp):
The coefficient of power (Cp) is evaluated over TSR
( for modification of each section parameter of the
NACA 4412 airfoil for solidity ratios 0.33 and 0.17, as
shown in Table3. For solidity ratio (SR) 0.33, the
highest value of Cp is found to be 0.387 (at = 2.4) for
reducing maximum camber by 6.8%, and the second
highest is 0.378 (at = 2.6) for increasing the maximum
thickness by 12%. For SR 0.17, the peak Cp value is
0.365 (at = 2.6) for increasing the maximum thickness
by 12%, and the second highest is 0.321 (at = 3.2) for
reducing the maximum camber by 6.8%. The Cp value
is found to be less than Betz’s limit (Cp = 0.59) for
modification of each section parameter of the NACA
4412 airfoil, which justified the accuracy and
appropriateness of the numerical analysis.
Doma et al. [24] experimentally studied the two
bladed conventional, 50% and 100% STS (Shifted
Troposkien Shape) VAWT of symmetrical and
unmodified NACA 0015 airfoil for solidity ratios 0.59,
0.50, and 0.46, respectively. For the conventional
VAWT of SR 0.59, the peak Cp value is 0.26 at = 3.75.
The Cp value depends on the TSR (, which also varies
with the number of blades, blade profile, wind speed,
and type of wind turbine [37]. For the threebladed
VAWT of modified and unsymmetrical NACA 4412
airfoil and SR 0.33, the Cp value will be higher than the
twobladed conventional VAWT. Therefore, this study's
highest Cp of 0.387 is logical and acceptable. Since the
aerodynamic efficiency of the threebladed wind turbine
is higher than the twobladed wind turbine [38].
Furthermore, Roy et al. [35] also investigated the three
bladed VAWT of symmetrical and unmodified NACA
0015, where the highest Cp value is 0.37 at = 3.8 and
Reynolds number 105. In this study, the peak Cp values
are 0.387 (at = 2.4) and 0.378 (at =2.6) for SR 0.33
and 0.17, respectively, where a threebladed VAWT of
unsymmetrical and modified NACA 4412 airfoil
investigated at a relatively higher Reynolds number 1.22
× 105 than Roy et al. [35] study. In addition, in this study,
the blades are twisted from 5 to 7 degrees to achieve
higher efficiency and prevent stalling. Therefore, the
relatively higher Cp values of 0.387 and 3.78 obtained at
lower TSRs in contrast to Roy et al. [35], are logical and
justified. The highest Cp value found in this study is only
4.6% higher than the Roy et al. study. Furthermore, field
test data from Sandia laboratory shows that the Cp value
of the twobladed VAWT of NACA 0015 airfoil is 0.35
for SR 0.15 and Reynolds number 3.3 × 105, as shown
in Fig.12. It also supports the suitability and accuracy
of this study at SR 0.17.
Fig.12: Sandia lab field test data of Cp value for a 2
bladed NACA 0015 VAWT [36, 39].
In this study, the coefficient of power (Cp) of the
modified NACA 4412 airfoil is found to be much higher
than the baseline airfoil within the range of = 2.0 to
4.5. The highest value of Cp is found between = 2.4
and =2.6. The tipspeed ratio (TSR) for the VAWT
typically varies from 2 to 6 [24], which also supports the
appropriateness of this study. The turbine blades rotate
faster at higher TSR, which results in increased stress,
wear, fatigue, and vibration [37]. Since the peak Cp
values are found at moderate TSRs, this study will help
design VAWT with the modified NACA 4412 airfoil to
reduce vibration and erosion of the blade tips.
CONCLUSIONS:
This study revealed that the lifttodrag ratio (Cl/Cd)
of the NACA 4412 airfoil and coefficient of power (Cp)
of the NACA 4412 airfoilbased VAWT are enhanced
remarkably for modification of its section/shape
parameters, such as trailingedge thickness, leading
edge radius, maximum camber, and maximum
thickness. The authors made the following conclusions
from the results of this study:
(i) The lift of the baseline NACA 4412 airfoil increases
remarkably when reducing the TE thickness by
60%, increasing the LE radius by 20%, and
increasing the maximum camber by 6.4%.
However, the critical AoA remains the same as the
Numerical analysis of modified NACA 4412 airfoil for implementation of low Reynolds number VAWTs
Journal of Mechanical Engineering, Vol. ME X7, No. 1, XXXXX 2022
Transaction of the Mechanical Engineering Division, The Institution of Engineers, Bangladesh
baseline airfoil, as shown in Table 3. Also, no
significant lift improvement is observed for
changing the maximum thickness and negative
AoAs.
(ii) The Cp value of the modified airfoil is much higher
than the baseline airfoil within TSR ( 2.0 to 4.5.
The highest values of Cp are 0.387 (at 2.4) and
0.365 (at 2.6) for reducing the maximum
camber by 6.8% and increasing the maximum
thickness by 12%, respectively, as shown in Table
3. The TSR of VAWTs typically varies from 2.0 to
6.0. At higher TSR, turbine blades rotate faster,
which results in higher stress, fatigue, and vibration.
This study found the highest Cp values at moderate
TSRs, which will help design VAWTs with the
modified NACA 4412 airfoil at low airspeed. In
addition, it will save cost and time in the
preliminary design and feasibility study.
(iii) Positive and nonzero lift are observed at zero
degrees AoA in baseline and modified airfoils
because of the cambered/unsymmetric nature of the
NACA 4412 airfoil, viscous flow, and boundary
layer formation over the blade. In addition, the
highest Cp values found in this study are 0.387 and
0.365 for SR 0.33 and 0.17, respectively, and within
Betz’s limit (Cp = 0.59). It justifies the
appropriateness of this study.
(iv) This study will facilitate the implementation of the
modified NACA 4412 airfoil in VAWTs for use on
urban and suburban building rooftops at low
airspeed, which will help meet global green energy
demand.
ACKNOWLEDGEMENT
The authors would like to acknowledge the
Ahsanullah University of Science and Technology
(AUST), Dhaka for providing the required
computational facilities.
NOMENCLATURES
θ Boundary layer momentum thickness
ϕ Velocity potential function
ξ Vorticity
ue Velocity in Xdirection at the edge of boundary
layer
H Regular shape parameter
H* Boundary layer kinetic energy shape parameter
H** Boundary layer density shape parameter
Hk Boundary layer kinematic shape parameter
Me Mach number at the end of the boundary layer
Cf Skin friction coefficient
CD Dissipation coefficient
Cd Coefficient of discharge
Cl Coefficient of lift
c Blade chord length
D Rotor diameter
Tipspeed ratio (TSR)
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