1. 1
A RANS CFD Study of an FSAE Three-
Element Front Wing Design
Joshua German, Kevin Cassel Ph.D.
Illinois Institute of Technology, Chicago, Illinois
This short paper serves to shed some light on the process of setting up a Reynolds-Averaged-
Navier-Stokes, RANS CFD simulation to predict the performance of an FSAE 3 element front wing
design. The downforce produced by the front wing helps provide more traction for race car tires during
cornering but will also produce some drag due to finite wing effects and trailing edge separation. The aim
of the simulation is to optimize the front wing design for production of maximum downforce to drag
ratio. This paper highlights some factors that affect this downforce to drag ratio like the wing element
angle of attack and spacing between wing elements. Results from the study show optimal downforce/drag
at an angle of attack,(AoA) of 5 degrees for the top two wing elements and a flat main wing. Future work
on this paper would focus on a parameterized shape optimization study of the wing elements.

2. 2
I. INTRODUCTION
The combination of the thin-airfoil and finite wing theory have been the backbone behind the
science of the lift force produced by a wing aligned to a freestream velocity. If a finite wing is
inverted and still aligned perpendicular to a freestream velocity, it produces a downforce if the
effective AoA of the wing is non-trivial or the wing is cambered as shown in the image below.
Figure 1: Image of Inverted airfoil and pressure variation description
This property of inverted wings is used in different applications especially in the automobile
or car racing industry. There is a tendency for cars to lift off the ground or skid when negotiating
a curved bank because of centripetal forces involved. Inverted wings are frequently used in the
front and rear of the car to produce additional downforce on the car to enable the tires gain more
traction so as to negotiate these turns at high speed. The formula one racing industry and its
subsidiary organizations like Formula Society of Automotive Engineers, FSAE have
competitions where a huge number of the racing cars use this inverted wings to give the race cars
an aerodynamic edge of going through tight
bends without slowing down, hence decreasing
individual lap time. Advanced engineering tools
are allocated to the development of efficient
wings because the added downforce production
comes with a drag penalty due to finite wing
effects.
Figure 2: Image of a multi-element wing used in the design of a front wing assembly.

3. 3
The major duty of the front wing is to provide downforce but it also performs the duty of
diverting air away from the tires and setting up the airflow for the rest of the chassis skin of the
car. Hence, it is very important to take into consideration a lot of parameters such as drag penalty
and separated flow when designing the front wing. The body of this paper goes into detail of
analyzing the front wing designs with respect to downforce/drag and basic airflow
considerations.
II. METHODS
The front wing assembly analyzed in this paper was design on Autodesk INVENTOR with
the aid of sketch and extrude commands. The airfoil profile chosen to create the wing was the
Selig 1223, because of its favorable characteristics at low Reynolds numbers flows of 300,000-
500,000. A 3D model was constructed on INVENTOR with a main wing panel and two extra
wing elements above the main plate. End plates were put on the side to prevent spillage of high
pressure airflow from the top to the low pressure/high velocity region at the bottom. This is
formally known as the finite wing effect that induces drag and vortices trailing the wing edges.
The baseline model of the wing is shown below without any design alterations.
Figure 3: Perspective and side view of the baseline design of the front wing
The table below describes the geometrical design of the baseline front wing configuration.
Main Wing/Plate
End Plates
2nd
wingelement
3rd
wingelement

4. 4
Component Airfoil Chord (m) Angle (Degrees) Span(m)
Main Wing Selig 1223 0.3048 0 1.524
2nd wing element Selig 1223 0.1524 20 0.378
3rd wing element Selig 1223 0.1524 45 0.378
Table 1: Geometric specifications of front wing assembly
Mesh:
The geometry shown in Fig. 3 was then exported as a parametric solid into a
Computational Fluid Dynamic (CFD) software code produced by CD-Adapco called STAR-
CCM+. The geometry is inherently unclean for direct simulation so an in-house tool is used to
surface wrap the geometry to overcome any face/edge related errors. Only half of the wing is
cleaned up and used for the set up since both halves are identical, we can save computational
resources by just analyzing one half section. To make a fluid domain where the aerodynamic
interactions can be captured, a wind tunnel box is made around the wing, whose volume is then
subtracted from the wind tunnel domain. A base mesh element volume size is chosen and
different areas of the fluid region are refined to capture sharp gradients in quantities. The walls
of the wings surfaces are considered no slip regions so we have to refine the mesh around these
areas to capture boundary layer interactions properly; the refinement of the boundary layer will
affect the skin friction and separation prediction immensely.
Figure 4: Wind tunnel/ fluid domain around the half wing
FlowInlet
Half Wing
Ground surface
Outlet

5. 5
Figure 5: Refined region around wing surface and thing prism layers for boundary layer
The number of cells required to give a relatively mesh independent solution was found to be
about 4 million. Every subsequent model used in the study had an approximate mesh size of 4
million cells with an average of 5-10 mins meshing time.

6. 6
Physics:
In defining the physic in the fluid domain several models were enabled to accurately
capture the physics of the flow regime. From practice and prior literature, the best models and
algorithms to predict a subsonic, external, separation prone viscous flow are as follows:
Regime / Algorithm Model
Wall Treatment Low y+ wall treatment
Turbulence Model Reynolds-Averaged Navier Stokes
K-Omega Turbulence
SST (Menter) K-Omega
Time Steady
Equation of State Constant Density
Fluid Gas-Air
Flow Solver Segregated flow solver
Table 2: Selected models for flow domain physics
The low y+ wall treatment was chosen because the mesh was fully refined on the wall surfaces to
capture the boundary layer. This was settled upon after various test runs to tweak and get the
mesh to a suitable refinement as we expect separated flow in some areas of the fluid domain. As
observed in Fig 4 the boundaries of the fluid domain were specified as follows:
Boundaries Boundary condition
Inlet Velocity Inlet- 50mph
Turbulent viscosity ratio- 0.1
Outlet Pressure Outlet- Atmospheric
Turbulent viscosity ratio- 10
Walls of wing surface No-slip, zero velocity condition
Symmetry wall Symmetry plane
Ground Slip wall
Table 3: Boundary conditions for fluid domain boundaries
After the boundary conditions were defined and test cases were ran, the simulation was found to
have converged after 1200 iterations by monitoring residuals that reduced by 3 to 4 orders of

7. 7
magnitude and downforce & drag monitors that converged on a value after these iteration. The
angle of attack on the baseline model was then varied to obtain different designs and each of
these cases were re-meshed and ran to produce downforce/drag predictions. The effect of the
spacing distance between wing elements was also studied by varying the height of each wing
from the bottom element.
Design Main wing AoA 2nd element AoA 3rd element AoA
Baseline 0 20 45
Design1 0 0 0
Design2 0 5 5
Design3 0 10 10
Design4 0 20 20
Design5 0 25 25
Design6 0 25 35
Table 4: Geometric variation of baseline design
III. RESULTS AND DISCUSSION
Flow field Velocity and Pressure:
The flow field was analyzed by looking at pressure plots, velocity vectors, streamlines
and any other representation to help understand the flow patterns. The baseline model was used
as a yardstick for comparison to the other seven designs.
Figure 6: Isometric and cut plane view of pressure distribution over the baseline model.

8. 8
Figure 7: Velocity distribution in a cut plane of the baseline design
Figure 8: Velocity distribution in a cut plane of design 1

9. 9
Figure 9: Velocity distribution in a cut plane of design 4
Figure 10: Streamlines along the free streamand aft of the wing

10. 10
From Fig 6, one would notice the high pressure build up on top of the wings, this is what
is translated to downforce to the front of the car. It is also noticeable that this high pressure zone
spills over the end plate which would cause the induced vortices observed in coming figures. A
quick look at the velocity distribution of a cut plane of the baseline design in fig.7 shows very
minimal separation on the wings but a recirculation zone behind the wing. In the next section we
would observe how this phenomenon resulted in a more severe drag penalty for this
configuration. The observation is quite different for the design 1 configuration as seen in Fig 8; a
separation bubble is quite distinct on all 3 elements of the wing. The benefit of the multi-element
wing to act as one giant wing is lost in this case because the wings are not aligned favorably for
the coander effect to be possible. This configuration will produce less drag but also produce a
relatively small lift compared to the baseline. Design 4 appears to perform somewhere in
between design 1 and baseline as seen in fig 9. We still get a separation bubble on element 3,
which means if that element was rotated some more independently, we could produce a better
multi-element wing. Fig 10 shows the behavior of the flow aft of the wing. The wing seems to
have this up-wash (Tracking the effective wing surface) vortex effect for particles that go
directly under the multi element section. It also seems to collect the lower sideslip freestream to
its core. This could be beneficial to feed the diffuser with high speed flow which would be
favorable for the car. The vortices are as a result of 3D wing effect.
Aerodynamic Forces:
Figure 11: Plot of Downforce as a function of 2nd and 3rd element AoA
0
50
100
150
200
250
300
350
400
450
500
0 5 10 15 20 25 30
DownForce(N)
Angle of Attack of 2nd and 3rd element Wing
Lift Vs Angle

11. 11
Figure 12: Plot of Drag as a function of 2nd and 3rd element AoA
Figure 13: Plot of Downforce/Drag as a function of 2nd and 3rd element AoA
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
Drag(N)
Angle of attack of 2nd and 3rd element wing (Degrees)
Drag curve
0
2
4
6
8
10
12
0 5 10 15 20 25 30
DownForce/Drag
Angle of attack of 2nd and 3rd element Wing(Degrees)
DownForceto Drag ratio Curve

12. 12
Figure 14: Design comparisons with respect to downforce and Drag
The designs were basically constructed as a function of the AoA of the last two wing
elements, hence Fig 11-13 show the variation of aerodynamic forces, downforce and drag with
AoA. As expected downforce and drag will increase as AoA increases but Fig 13 shows that
after 5 degrees, drag is increasing faster than downforce hence the negative slope. So the angle
that optimizes the downforce to drag ratio is roughly around 5 degrees. Figure 14 presents a good
comparison of other designs to the baseline design with a low downforce/drag of 4.6. No design
is necessarily bad but can be adapted for different race regimes. For a straight track, a race car
would need to accelerate fast so a configuration like design 1 (low drag) would be optimal while
a configuration like the baseline or design 7 will be optimal for a meandering circuit event (high
downforce needed). The latter case has a higher drag penalty so more power is required to go just
as fast.
Design 1
Design 2
Design 3
Design 4
Design 5
Design 6
Design 7
Base Design
0
100
200
300
400
500
600
0 20 40 60 80 100 120
DownForce(N)
Drag (N)
Design Comparisons

13. 13
Figure 15: Plot of Downforce as a function of wing element spacing
Figure 16: Plot of Downforce/Drag as a function of wing element spacing
340
360
380
400
420
440
460
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
DownForce
Spacinginbetween wingelements minus offset spacing(m)
DownForceas a function of element spacing Design 4
6.1
6.2
6.3
6.4
6.5
6.6
6.7
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
DownForce/Drag
Wingelement spacingminus minimumoffset spacing(m)
Momentum bleeding

14. 14
Figure 17: Velocity distribution of design 4 with just minimum offset spacing
Figure 18: Velocity distribution of design 4 with 0.015m spacing

15. 15
Figure 19: Velocity distribution of design 4 with 0.07m spacing
Figures 15-19 present visual aids to observing the effect of the distance between wing elements.
Downforce actually increases considerably as the spacing is increased from its offset spacing of
0.0047m to 0.07m. The design 4 is used as the underlying configuration since it has the midrange
performance; the spacing in-between the wing elements was varied to produce Figures 15-19.
The separation bubbles that appear in fig 17 is as a result of the fact that there is not enough
space in between elements to bleed excess air; the blockage is what probably causes the
boundary layer to disengage itself from the upper surface. A quick look at Figures 17-19 shows
how the spacing affects the increase in downforce. The spacing in between the wing elements
allows air with momentum from a preceding element to interact with the boundary layer of the
next element. The added momentum allows for a faster flow on the underside of the wing that
increases the pressure difference and produces more downforce. The difference in flow speeds in
the undersides of the elements is clearly observable when Fig 17 and 19 are compared.

16. 16
Flow field Vorticity:
Figure 20: Vorticity rendering of design 1
Figure 21: Vorticity rendering of the baseline design
Separatedflow
Vortices

17. 17
Figure 20 and 21 are visual aids to validate the theory that as we increase the AoA attack and
downforce production the vorticity and vortex intensity increases. This materialized as an
increase in aerodynamic drag experienced as AoA is increased. We can observe a thicker vortex
filament in the baseline design compared to design 1 that possesses zero angle of attack and
reduced induced drag as observed from the earlier sections.
IV. CONCLUSION
In conclusion, we can theorize from the results that significant spacing is required in-between
wing elements for them to function optimally. It was also observed that different designs would
be optimal for different race configurations but an AoA of 5 degrees provided the highest
downforce to drag ratio. Future consideration will expand the scope of the project into running a
shape optimizer to morph the main wing or wing elements to have varying cross-sectional chords
or AoA to see how a parametrized design would increase performance.
V. REFERENCES
[1]. C. Penny “FSAE Technical Resource Guide”,STAR-CCM Knowledge Base