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Proceedings of the Fluids Engineering Division Summer Meet
FEDSM 2017
July 30-August 2, 2017, Hilton Waikoloa Village, Waikoloa, HI, USA
FEDSM 2017– 69372
Computational Analysis of Benzing Airfoils for Optimization in a Wing Configuration for a
Formula SAE Car
Yuling Su
Wing Design Lead, Jayhawk Motorsports
Department of Mechanical Engineering,
University of Kansas
Lawrence, Kansas, USA
Akshay Basavaraj
Graduate Student,
Department of Aerospace Engineering,
University of Kansas
Lawrence, Kansas, USA
ABSTRACT
Wing selection plays a crucial role for race cars in terms of
downforce generation. This is essential to maintain traction
which leads to faster lap timings, and maintain efficiency in the
performance of the race car. In this paper, the numerical
simulation of a Formula SAE (FSAE) Car wing configuration
is performed. The main focus involves Benzing airfoils, which
are expected to show considerably better performance in terms
of downforce production in a race car than conventional
airfoils. The wing configuration utilized in this research paper
consists of a single main plane and two flaps. The freestream
velocity of the flow is in the range of 10-60mph (4-26m/s). The
122 series of Benzing airfoils is utilized for the main plane and
the 153 series of Benzing airfoils is utilized for the flaps for
manufacturing reasons. Nine different combinations of Benzing
airfoils are utilized for the aforementioned wing configuration.
It is noticed that an appropriate selection of the airfoils for the
main plane and flaps with a fixed angle of attack difference,
leads to a 12-15% increase in downforce amongst the Benzing
airfoil combinations. Similarly, it is also observed that certain
combinations show 12-15% decrease in drag in comparison too
poor performing Benzing airfoil combination. Data from an on-
track test is used in order to verify the approach utilized in this
paper for validation purposes. It is observed that the Benzing
airfoil does improve the average cornering speed of the car by
around 8% in comparison to the previous configuration of
S1223 airfoil as the main plane and the Goe 477 airfoil as the
flap.
INTRODUCTION
Airfoil selection for wings of racecars play an important role as
they affect the cornering, straight-line speed, slaloming and
overall performance of the vehicle [1-3]. In the case of a
Formula SAE car, it is essential to know that the restrictions
imposed by the rules constrain the length of the front and rear
wings. Therefore, it becomes necessary to select airfoils which
get the best out of the given wing configuration. The tradeoff
observed between the downforce generated and the induced
drag produced in a racecar must be checked for optimal
performance. This serves as the primary motivation for this
research paper. An analytic study conducted [2] shows that
high downforce generating airfoil is not ideal for optimum
performance due to the presence of induced drag. Experimental
track testing shows [3] that analytical prediction for the racecar
performance is not ideal since due to simplifications made
during the analytic study which does not account for the non-
uniform flow which exists in nature. Simplifications of the
aerodynamic models for CFD also has its limitations [4] since
it tends to predict the downforce accurately in comparison to
the drag force experienced by the body. High down force
generating airfoils [5] have been studied on the rear wings using
inverse airfoil design. Due to the flow constraints on the wake
developments of the front wings, they cannot be optimized for
high downforce [5]. This methodology proves to be slightly
faulty as increased down force on the rear end would lead to
over-steering of the vehicles during cornering. A Particle Image
Velocimetry (PIV) study [6] of a formula one car shows that it
is essential to control the wake of the front wheel since they
shed strong longitudinal vortices. Development of high lift
airfoils for race-cars with restrictions on the geometry is not
always beneficial since induced drag will be generated,
affecting the mileage of the car [7-8]. Lamination parameters
were investigated [9] in order to reduce the induced drag by
tailoring the rear wing, but new airfoils need to be tested in
order to verify this approach. Implementation of new
aerodynamic configurations were studied [10] with Benzing
airfoils in order to observe the impact of increase in the number
of elements. This paper deals with the impact of airfoil selection
for a simple wing configuration of an FSAE car and finding the
best combination of Benzing airfoils taking into account
manufacturability as well. A computational approach is used to
study the impact of camber and thickness on a fixed wing type
configuration. Track test data is used to verify if the approach
is suitable for future designs for wings of race cars.
2
NOMENCLATURE
α Angle of Attack in Degrees
μ Coefficient of Viscosity in Ns/m2
ρ Density in kg/m3
aL Lateral G-force
c Chord Length in inches
l Characteristic length in meters
r Radius of the turn in meters
CL Coefficient of Downforce
CD Coefficient of Drag
D Drag force in Newton
L Downforce in Newton
m Mass of the car in Kg
S Surface area of the wing in in.2
V Velocity in mph
Vc Cornering velocity in mph
W Weight of the car in N
METHODOLOGY
Computational Methodology
In order to evaluate the flow around the airfoils, the κ-ω Shear
Stress Transport model is used. The governing equations of the
κ-ω SST involve the formulation of the turbulent kinetic energy
and the specific dissipation rate [11].
Star CCM+ provides a discretized platform for the
aforementioned equation. The CAD models for the airfoils and
the preliminary model for the race car were carried out and the
conditions for the computational analysis is carried out between
0-60 mph which correspond to 0-27 m/s. One of the other major
advantages of using the κ-ω SST models for prediction is its
accuracy in predicting forced convection similar to the DNS
models [12].
The governing equations of the Mentor’s κ-ω SST [11- 12] are
given by
ρ(
+
+
) = Pκ – β1ρκω +
[ (μ + σκμturb)
] +
[ (μ + σκμturb)
] +
[ (μ + σκμturb)
] (1)
ρ(
+
+
) = Pκ – β2ρκω2 +
[ (μ + σκμturb)
] +
[ (μ + σκμturb)
] +
[ (μ + σκμturb)
]+ 2(1- F1)(
+
+
) (2)
Where κ is the turbulent kinetic energy term and ω is the
specific dissipation rate and Pκ is the production term.
The turbulent viscosity is given by
μturb =
(3)
Airfoil Selection
Benzing airfoils are used and compared with a previously tested
airfoil configuration in order to check if they would improve the
downforce component on the race car. Benzing airfoils have a
different manner of nomenclature in comparison to NACA 6
Digit airfoils. The first two digits indicate the thickness of the
airfoil in % of chord length. The third digit indicates the
position of maximum thickness in terms of tenths of the airfoil
chord length. The fourth and fifth number indicates the
maximum camber of the airfoils and similar to thickness, the 6th
digit indicates the position of maximum thickness in terms of
the tenths of chord length(c).
The 122 series of Benzing airfoils are used for main planes due
to feasibility in manufacturing. The high camber observed in
the 122 series airfoils, makes it difficult to manufacture using
conventional carbon fiber manufacturing process. The thin
nature of the 122 series also reduces the life-span of the airfoils
in racing if it were to be used as flaps. Given the brittle nature
of carbon fiber upon high levels of aerodynamic load acting
upon it, thin flaps would provide more maintenance issues in
spite of improved aerodynamic performances.
Table.1. Configurations of different Benzing airfoils in the wing
configuration
Main Plane
Flaps
Be 122-125
Be 153-105
Be 153-055
Be 153-175
Be 122-155
Be 153-105
Be 153-055
Be 153-175
Be 122-185
Be 153-105
Be 153-055
Be 153-175
Selig 1223
Goe 477
Wing Analysis
A preliminary analysis of the wing is carried out for the given
configuration in order to select a suitable airfoil. The chosen
configuration involves a main plane with two flaps. The main
plane is kept at an angle of attack of 80. The first flap is kept at
an angle of attack of 350 and the second flap is kept at an angle
of attack of 600. Reynolds number range affects the accuracy
of simulations [13] since at low values, the readings obtained
can show deviation in comparison to coast down tests.
Re =
(4)
The Reynolds number range for the simulations vary from 5.5
x 104 to 1.46 x 106. At lower velocities, the readings for the
computational simulations may not be as accurate compared to
a track test [13]. The domain of the flowfield is made large
enough in order to account for the external flow. Table 2 and 3
provide details on the geometry of the wing configuration used
and the configuration used in Star CCM+.
Table.2. Benzing airfoil configurations for 2D Analysis
Chord Length in
inches
Angle of attack α in
degrees
Main Plane
17.5
8
Flap 1
6.5
35
Flap 2
6.5
60
3
Fig.1. Velocity Contours of Be 122-125 Main plane with Be
153- 175 flap configurations
Fig.2. Mesh of the Benzing Wing Configuration
Table 3. Details of the Star CCM+ configuration for analysis
Initial Turbulence Intensity
0.01
Initial Turbulence velocity
1 m/s
Initial Turbulence viscosity
10
Cells
2,882,199
Faces
8,669,502
Vertices
3,127,046
Velocity range
10-60 mph (intervals of
10 mph)
Domain Length
20 m
Domain Height
40 m
Domain Breadth
10 m
Number of iterations
10,000
y+ treatment
Low y+ treatment
Track Testing
The Formula SAE event conducted at the Michigan
International Speedway between May 10 -13, 2017 was used to
validate if the decision to select Benzing airfoils over
conventional airfoils would provide any form of improvement
in the performance of the race car. The only reliable data
obtainable which could be compared with the previous year’s
(FSAE 2016, Michigan International Speedway, May 11-14)
competition were cornering velocity and the respective lateral
G-force acting on the car. Data from the endurance event of the
competition is used for comparison purposes. Given the weight
of the car, assuming constant radius and constant velocity [2],
the cornering velocity is given by
vc = (
)1/2 (5)
The relation between cornering velocity and the lateral g-force
which is centrifugal acceleration normalized to gravity under
constant radius is given by
aL =
(6)
The lateral G-force observed provides insight into the effect of
aerodynamics in terms of improving the vehicle’s performance
at turns in terms of overcoming centripetal forces. The
indication of how the car behaves on the same turns as the
previous year’s design will be used to validate this approach. It
is expected from equation 6 that at the regions of cornering,
increased values of lateral G-force would correspond to a higher
cornering velocity. Decreased lateral G-force at straight line
speeds would indicate smoothness in transition of the car
exiting out of the corner. Although, equation 6 is developed for
a turn with a constant radius r, it can still be used to gauge the
improvement in cornering velocity of the race car.
Results and Conclusion
Wing Analysis
Fig.3. Velocity streamlines for Be 122 125 main plane with Be
153 055 flaps
Preliminary Wing analysis show that there is close to a 12-15%
improvement in the Downforce generated by the usage of Be
122-185 airfoil as the main plane with the Be 153-105 as the
flaps in comparison to Be 122-185 airfoil as the main plane with
the Be 153-175 airfoil as the flap. The Benzing airfoils tend to
show a better performance in terms of Downforce generation in
comparison to the Selig 1223 airfoil as the main plane with the
Goe 477 airfoil as the flaps. The L/D ratio generated by the
Benzing airfoils however, show relatively poor performance
compared to the S1223 and Goe 477 configuration. The last 3
digits of each airfoil are used to describe the behavior of the
configurations in terms of coefficient of downforce generation
and drag generation in the figures below (Figures 4-6). The
coefficient of drag and downforce are given by
CL =
(7)
CD =
(8)
4
Fig.4. Downforce Generated by Different Airfoils
Fig.5. Drag Force Generated by Different Airfoils
Fig.6. L/D ratio generated by Benzing Airfoils
Fig.7. Velocity streamlines for Be 122 125 main plane with Be
153 105 flaps
Performance of Benzing Airfoils
Two types of vortex streamlines were observed at the ends of
the wing configuration during the simulation. The first can be
considered as a stable vortex streamline, the primary vortex
streamline which is stable and is observed in all cases. The
second type of vortex streamlines can be considered as unstable
vortex streamlines which is observed in most if not all wing
configurations without the Be 153-055 flaps. On Preliminary
Analysis, the secondary vortex streamlines which tend to
generate an unstable spiral vortex streamlines (Figure .7.) could
be regarded as the reason for poor performance of airfoils with
reduced camber. These unstable vortex streamlines are reduced
with the implementation of endplates. Increased surface area of
the endplates counteracts the induced drag generated by the
trailing edge vortices. However, structural effects must be taken
into account alongside the competition regulations.
a. Be 122-125 and Be 153-105
In this combination, the downforce generated from the
computational results show considerable increase in
comparison to the use of S1223 and Goe 477 combination. The
relatively low camber of the flaps, leads to a lower value of drag
generated as well compared to other combinations. There is an
average of 16.42% increase in downforce generation in
comparison to the S1223 combination with the Goe 477 airfoils
as the flaps.
b. Be 122-125 and Be 153-055
The low camber provided by the Be 153-055 on the flaps leads
to a drag reduction of 7.8% compared to the Be 122-125 and Be
153-105 airfoil combination. This combination leads to the
lowest drag generated and shows the highest value of L/D of
the airfoils utilized. As shown in Figure 3, the trailing edge
vortices on the Be 153-055 airfoil do not initiate the unstable
spiral vortex streamlines which leads to increase in drag.
c. Be 122-125 and Be 153-175
The high camber of the flaps provides increased downforce
generation Drag force generation is considerably high
compared to the first two combinations. The L/D ratio is below
2, therefore, this combination may not be appropriate to use in
a race car wing configuration.
-0.102
-0.097
-0.092
-0.087
-0.082
10 30 50
Coefficient of Downforce
Velocity in mph
125+105
125+055
125+175
155+105
155+055
155+175
185+105
185+055
185+175
s1223+goe477
0.031
0.033
0.035
0.037
0.039
0.041
0.043
0.045
0.047
10 30 50
Coefficient of Drag
Velocity in mph
125+105
125+055
125+175
155+105
155+055
155+175
185+105
185+055
185+175
s1223+goe477
1.95
2.05
2.15
2.25
2.35
10 20 30 40 50 60
L/D ratio
Velocity in mph
125+105 125+055 125+175
155+105 155+055 155+175
185+105 185+055 185+175
5
d. Be 122-155 and Be 153-105
The 20% increase in the camber on the main plane from the
previous configuration, does not lead to an increase in
downforce generated. As expected, the increase in the camber
of the main plane also leads to an increase in drag. The L/D
ratio value observed is approximately close to 2.
e. Be 122-155 and Be 153-055
Similar behavior is observed as before and this combination
proves to be much worse since it is not much of an improvement
from the combination involving Be 122-155 airfoil as the main
plane and the Be 153-055 airfoil as the flaps. Although the L/D
ratio observed is above the value of 2.2, the downforce
generation is greatly reduced.
f. Be 122-155 and Be 153-175
The 15% camber of the main plane combined with the 17%
camber of the flaps provides the least downforce generation.
This combination also generates the least amount of induced
drag. Due to this, it leads to the second lowest L/D value
amongst the airfoils tested.
g. Be 122-185 and Be 153-105
The 18% camber of the main plane combined with the 10%
camber of the flaps provides the highest downforce generated.
However, this also leads to the highest value of induced drag
generated. This can be attributed to the increased strength
observed in the primary trailing edge vortices. However, the
unstable spiral vortex streamline is not observed. The L/D value
corresponding to this combination is approximately closer to 2.
In comparison to the S1223 and Goe 477 airfoil configurations,
it provides close to 18.8% increase in downforce generation.
h. Be 122-185 and Be 153-055
Like in the previous combinations, the Be 153-055 airfoils
being used as the flap provides a considerable reduction in drag.
It can be said that the Be 153-055 airfoil acts best for flaps in
race-cars for varying main planes due to reduction observed in
the trailing edge vortices. The unstable spiral vortex structures
enhanced due to the increase in the camber of the flaps observed
for the Be 153-105 and Be 153-175 flaps are not observed.
i. Be 122-185 and Be 153-175
The Be 122-185 airfoils as the main plane with the Be 153-175
airfoils as the flaps show very poor performance in terms of
downforce generation and does generate a lot of drag. This
could be due to the increased camber observed in both the main
plane and the flaps. It can be seen that higher camber does not
necessarily lead to improvement in aerodynamic characteristics
for the given wing configuration.
Track Testing Results
Track testing data from the FSAE event at the Michigan
International Speedway in Brooklyn Michigan, is used to
further evaluate the performance of the Benzing Airfoils. The
configuration of Be 122-125 airfoil as the mainplane and Be
153-105 airfoils as the flap was used for the car due to time
constraints in terms of manufacturing for the competition due
to immediate availability of its aerodynamic characteristics.
Unavailability of the instruments to conduct coast down testing
within the time constraint for the competition, led to an
alternative method to check the validity of the approach used.
Data obtained from the competition in the form of lateral G
force and the velocity of the vehicle at both the cornering speed
and the straightline speed is used to validate the approach.
Given the high sampling rate of the accelerometers, the
sampling rate is reduced to 50 Hz and is observed over a short
time period. Careful selection of data is necessary in order to
make a proper analysis. Although the data sets for figures 8 and
9 have been taken over the same time period, noise generated
from the accelerometer tends to overpopulate at straight line
speeds in the data obtained from the 2016 FSAE event and at
cornering speeds at the data obtained from the 2017 FSAE
event.
Fig.8. Behavior of the lateral G-force in at high velocities for
one instance of time
Upon the implementation of Benzing airfoils, the average
cornering velocity of the car did show improvement by around
8% and the time taken to reach maximum velocity was reduced.
The previous race car with the Selig 1223 airfoil with the Goe
477 flaps averaged a cornering velocity of 31.4 mph, in
comparison the race car with the Benzing airfoils averaged
around 34.1 mph. This can be partially attributed to the increase
in Downforce generated by the car upon the implementation of
Benzing airfoils.
Fig.9. Behavior of the lateral G-force after cornering
The above figure shows the increase in lateral G-force on the
race car after coming out of a corner, indicating higher corner
velocity. The track data also shows that increased downforce
provides smoother transition onto the race track while exiting a
corner. It could be argued that due to the increased downforce,
the car is able to recover quicker after a turn and overcome
centripetal force. The reduction in lateral G-force at straight line
velocity shows some positive insight into the implementation
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
40 50 60 70
Lateral G-force
Velocity in mph
S1223+ Goe 477 Benzing airfoils
-0.4
0.1
0.6
1.1
1.6
32 37 42 47 52
Lateral G-force
Velocity in mph
s1223+goe477 Benzing airfoils
6
of the Benzing airfoils with regards to race car performance. It
is advised however, not to extrapolate the downforce
characteristics from the track test data using equation 4 due to
the assumptions made which may not hold true in real life track
tests. However, the track test data does show that with the
increase in the Downforce generated, the cornering velocity can
be increased alongside providing smoother transition heading
out of a corner.
CONCLUSION
Due to limitations put forth by the extent to which
Computational Analysis can be carried out with accuracy, it is
observed that there exists an optimum configuration amongst
the airfoils wherein the Downforce generated can be
maximized. It is quite difficult to carry out the simulation of the
entire car to observe the effect of the Benzing airfoils due to the
increased computational load.
One of the major drawbacks of the Benzing airfoils observed
during computational analysis, lies in the fact that the region of
highest camber is situated at the center of the chord length. If
the maximum camber of an airfoil is to be positioned at the mid-
point of the chord length of the airfoils, minimal camber in such
instances provide optimal performance if it were configured as
a flap. This leads to minimization of unstable spiral vortex
streamlines which can be attributed to the increase in drag in
the wing configurations. It can be concluded that increase in
camber amongst the flaps in wings of a race car lead to poorer
performance, when the angle of attack in a given wing
configuration is fixed.
However, within the results obtained from the simulations, the
configuration of Be 122-125 airfoil as the main plane with the
Be 153-055 airfoil show the best performance. The
configuration of Be 122-155 airfoil with the Be 153-175 airfoil
proves to be poor as it is neither generating high down force nor
does it provide a high L/D value. The Be 153-055 airfoil acts as
an excellent flap configuration since the reduced camber at the
midpoint of the airfoil leads to decrease in the unstable spiral
vortices at the leading edge. Further research must be conducted
alongside experimental data to validate the optimum angle of
attack for the wing configurations of an FSAE car.
Track testing provides a more insightful view on the cornering
velocity of the vehicle as a function of downforce generated.
There is approximately 8% increase in the average cornering
velocity with the implementation of Benzing airfols. At straight
line speeds, Benzing airfoils show reduction in the lateral g-
force generated during the exiting of a corner in comparison to
the car with the S1223 and Goe 477 airfoils. From the
computational analysis and the track testing data, it can be seen
that the lift to drag ratio may not provide a clear picture of the
implementation of airfoils on the actual performance of a race
car.
ACKNOWLEDGEMENT
The authors would like to thank the entire Jayhawk Motorsports
team, University of Kansas for their support and information
provided for the completion of this paper. The authors would
like to thank Tyler Simpson, Junior, Mechanical Engineering,
University of Kansas for processing the track tested data for this
paper.
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