MECH 3305 Numerical Project #1-B
Connor Keay B00831266
Lucas Pereira B00838161
Submitted for Dr. Groulx
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Table of Contents
Introduction............................................................................................................................................. 4
Theory..................................................................................................................................................... 5
Numerical Model..................................................................................................................................... 6
Results and Discussion ............................................................................................................................ 8
Wheel studies without winglet ............................................................................................................. 8
Wheel studies without winglet and rolling wheel ............................................................................... 12
Wheel studies with winglet h=0.56m ................................................................................................. 15
Wheel studies with winglet h=0.6m ................................................................................................... 19
Wheel studies with winglet h=0.65m ................................................................................................. 22
Conclusion ............................................................................................................................................ 26
References............................................................................................................................................. 27
Table of Figures
Figure 1 Front wheel winglet new F1 cars ................................................................................................ 4
Figure 2 Geometry and location for winglet above wheel ........................................................................ 6
Figure 3 velocity field streamlines over non spinning wheel 150km/h ...................................................... 8
Figure 4 Velocity y-component over non spinning wheel no winglet 150km/h @ cut line 2.6 m. ............. 9
Figure 5 Velocity Field for a wheel not spinning and no winglet V=250km/h ............................................ 9
Figure 6 Velocity y-component over non spinning wheel no winglet 250km/h @ cut line 2.6 m. ........... 10
Figure 7 Velocity Field for a wheel not spinning and no winglet V=350km/h .......................................... 10
Figure 8 Velocity y-component over non spinning wheel no winglet 350km/h @ cut line 2.6 m. ........... 11
Figure 9 Velocity Field for a wheel spinning and no winglet V=350km/h ................................................ 12
Figure 10 Velocity y-component over spinning wheel no winglet 150km/h @ cut line 2.6 m. ................ 12
Figure 11 Velocity Field for a wheel spinning and no winglet V=250km/h .............................................. 13
Figure 12 Velocity y-component over spinning wheel no winglet 250km/h @ cut line 2.6 m. ................ 13
Figure 13 Velocity Field for a wheel spinning and no winglet V=350km/h .............................................. 14
Figure 14 Velocity y-component over spinning wheel no winglet 350km/h @ cut line 2.6 m. ............... 14
Figure 15 Velocity Field for a wheel with winglet h=0.56 V=150km/h .................................................... 15
Figure 16 Velocity y-component over spinning wheel h=0.56 m 150km/h @ cut line 2.6 m. .................. 16
Figure 17 Velocity Field for a wheel with winglet h=0.56 V=250km/h .................................................... 16
Figure 18 Velocity y-component over spinning wheel h=0.56 m 250km/h @ cut line 2.6 m.. ................. 17
Figure 19 Velocity Field for a wheel with winglet h=0.56 V=350km/h .................................................... 17
Figure Velocity y-component over spinning wheel h=0.56 m 150km/h @ cut line 2.6 m.20 ................... 18
Figure 21 Velocity Field for a wheel with winglet h=0.6 V=150km/h ...................................................... 19
Figure 22 Velocity y-component over spinning wheel h=0.6 m 150km/h @ cut line 2.6......................... 19
Figure 23 Velocity Field for a wheel with winglet h=0.6 V=250km/h ...................................................... 20
Figure 24 Velocity y-component over spinning wheel h=0.6 m 250km/h @ cut line 2.6......................... 20
Figure 25 Velocity Field for a wheel with winglet h=0.6 V=350km/h...................................................... 21
Figure 26 Velocity y-component over spinning wheel h=0.6 m 350km/h @ cut line 2.6......................... 21
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Figure 27 Velocity Field for a wheel with winglet h=0.65 V=150km/h .................................................... 22
Figure 28 Velocity y-component over spinning wheel h=0.65 m 150km/h @ cut line 2.6 ....................... 23
Figure 29 Velocity Field for a wheel with winglet h=0.65 V=250km/h ................................................... 23
Figure 30 Velocity y-component over spinning wheel h=0.65 m 250km/h @ cut line 2.6 ....................... 24
Figure 31 Velocity Field for a wheel with winglet h=0.65 V=350km/h ................................................... 24
Figure 32 Velocity y-component over spinning wheel h=0.65 m 350km/h @ cut line 2.6 ....................... 25
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Introduction
The 2022 F1 season saw the introduction of a huge body and aero changes for teams. This
was largely due to landslide victories and dynasties of the past and the FIA wanting to improve
the ’raceability’ of the cars. One of these aero changes was a small winglet over the front wheels,
in theory they clean up the wake created by the spinning wheels and direct air flow away from the
rear whing which creates lots of the turbulent or ‘dirty’ air behind the cars. This gives the cars
behind a better chance of catching up as their downforce and cornering will not be as affected by
the car in front.
Figure 1 Front wheel winglet new F1 cars
https://www.motorsport.com/f1/news/2022-f1-season-drivers-cars-tracks/6868238/
The purpose of this lab was to investigate the impact of the winglet on air flow around the
wheel and compare those results to the wheel flow of previous seasons (sans winglet). These results
were to be assessed over a range of three speeds; 150km/h, 250km/h, and 350km/h and over 3
winglet positions to capture the varying effects of the winglet in different set ups. This analysis
was done using COMSOL Multiphysics 6.0 to carry out a FEA (Finite Element Analysis) and
derive all of the below plots.
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Theory
The main responsibility for the wheel winglets in the scope of the new FIA regulations is
to reduces the vortices generated by the wheels and direct air flow away from the rear wing.
Vortices are created from high pressure air spilling over the wheel into the low-pressure zone
behind the wheel. This increases the pressure drag on the wheel and moreover the energy required
to produce a vorticity comes at the direct expense of the speed of the car.
The theory used for this report falls under chapter 7 of Fluids Mechanics (White 2011) flow pasted
immersed bodies and the use of our K-e turbulence model. This model has been found to accurately
predict the flow in the vicinity of rotating disks (Launder, 1974) and was developed for improved
performance in separated flows.
To run this model the assumption had to be made that flow over the wheel would be in 2D and
that all flow coming into the system would be ‘undisturbed’. It was also assumed that there was
no heat transfer between entities.
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Numerical Model
To capture the benefits generated by the addition of a winglet, five different geometries
were simulated: a rolling tire sans winglet, a static tire slipping through the asphalt, and a rolling
tire with three different winglet heights. Given that only the F1 teams have access to the
dimensions of the winglets, the geometries employed in this study were built with the aid of
pictures from operational winglets like the one shown in Figure 1. The main features identified by
the group are its curvy aerofoil like shape at the leading edge, and a thin long body which were
built in SolidWorks 2022 which is displayed in Figure 2. With the same information constraint,
the group chose to use the respective winglet heights for the study: 0.56 m, 0.6 m and 0.65 m.
Figure 2 Geometry and location for winglet above wheel
To model the flow over the tire, given the high velocities that an F1 car can achieve it was chosen
to use the k-ε turbulence model which is a very popular model used in industrial applications. This
model works by solving for two variables: k the turbulence kinetic energy, and ε the rate of
dissipation of turbulence kinetic energy (Frei 2017). This model excels at describing external
flows and therefore is suitable for the application in this study, and given below are the equations
that COMSOL solves for each simulation:
Equation 1
𝜌
𝜕𝑘
µ𝑇
+ 𝜌𝒖 ∙ ∇𝑘 = ∇ ∙ ((µ + ) ∇𝑘) + 𝑃𝑘 − 𝜌ε
𝜕𝑡
𝜎𝑘
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Equation 2
𝜌
𝜕ε
µ𝑇
ε
ε2
+ 𝜌(𝒖 ∙ ∇)ε = ∇ ∙ [(µ + ) ∇𝑘] + 𝐶ε1 𝑃𝑘 − 𝐶ε2 𝜌 , ε = ep
𝜕𝑡
𝜎ε
𝑘
𝑘
Equation 3
𝜌
𝜕𝒖
+ 𝜌(𝒖 ∙ ∇)𝒖 = ∇ ∙ [−𝑝𝒍 + 𝑲] + 𝑭
𝜕𝑡
Equation 4
𝜌∇ ∙ 𝒖 = 0
Equation 5
𝑃𝑘 = µ𝑡 [∇𝒖: (∇𝒖 + (∇𝒖)𝑇 )]
A control volume in the form of a box with 5m width and 1.64m height was used to carry out the
study. The boundary conditions applied on this problem are: a sliding wall that ramps its speed up
to one of the three maximum prescribed velocities, a fixed wall at the winglet since it is at the same
inertial frame as the car, a rotating wall at the tire that also ramps up to one of the prescribed
velocities, an inlet condition at the front of the wheel where the flow speed ramps up to the car’s
velocity, an outlet behind the car at a reference pressure of P=0, and finally an open boundary on
top of the car so that the flow can exit upwards of the control volume. Only one material was
applied in the simulation, and that was the air option in the COMSOL liquids and gases library.
Finally, to determine the appropriate mesh size for the proposed simulation the group carried out
a mesh convergence study prior to all simulations, with a rolling tire at a speed of 350 km/h with
the winglet at height = 0.56 m. The parameter observed for convergence is the maximum speed
attained in a cutline located 2.6 m from the center of the wheel, Table 1 below displays these
results:
Table 1 Mesh Validation results and simulation times.
Mesh Size
Maximum Speed (m/s)
Simulation Time (s)
Extremely Coarse
100.78
242
Extra Coarse
105.48
161
Coarser
107.63
319
Coarse
106.87
1158
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As it can be seen, the velocities seem to converge at the coarser size and given that coarse has a
simulation time almost three times longer, it was concluded that using coarser would be suitable
for this study. Finally, this same cut line was used in the results for displaying the y components
of the velocity in the xy graphs.
Results and Discussion
Wheel studies without winglet
Figure 3 velocity field streamlines over non spinning wheel 150km/h
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Figure 4 Velocity y-component over non spinning wheel no winglet 150km/h @ cut line 2.6 m.
Figure 5 Velocity Field for a wheel not spinning and no winglet V=250km/h
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Figure 6 Velocity y-component over non spinning wheel no winglet 250km/h @ cut line 2.6 m.
Figure 7 Velocity Field for a wheel not spinning and no winglet V=350km/h
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Figure 8 Velocity y-component over non spinning wheel no winglet 350km/h @ cut line 2.6 m.
For a slipping wheel without winglets, it is can be seen that the size and shape of the resultant
vortices is highly dependent on the velocity of the flow. With lower velocities, it is very large but
then decreases at the moderate velocity and then increases again at the highest velocity. The
shape and size of the resultant vortices is important since it is tied with the total drag force
experience by the wheel.
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Wheel studies without winglet and rolling wheel
Figure 9 Velocity Field for a wheel spinning and no winglet V=350km/h
Figure 10 Velocity y-component over spinning wheel no winglet 150km/h @ cut line 2.6 m.
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Figure 11 Velocity Field for a wheel spinning and no winglet V=250km/h
Figure 12 Velocity y-component over spinning wheel no winglet 250km/h @ cut line 2.6 m.
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Figure 13 Velocity Field for a wheel spinning and no winglet V=350km/h
Figure 14 Velocity y-component over spinning wheel no winglet 350km/h @ cut line 2.6 m.
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Unlike the slipping wheel, the shape and size of the vortices created after interacting with the wheel
are completely independent of the car’s velocity. It can also be noted that there is a general slight
downwards trend in the y component of the velocity field, but the magnitudes of that are fairly
small compared to the overall velocity magnitude by less than 10%. Most of the fast-moving air is
directed above the wheels and towards the rear wing which matches the aerodynamic design of
previous F1 cars.
Wheel studies with winglet h=0.56m
Figure 15 Velocity Field for a wheel with winglet h=0.56 V=150km/h
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Figure 16 Velocity y-component over spinning wheel h=0.56 m 150km/h @ cut line 2.6 m.
Figure 17 Velocity Field for a wheel with winglet h=0.56 V=250km/h
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Figure 18 Velocity y-component over spinning wheel h=0.56 m 250km/h @ cut line 2.6 m..
Figure 19 Velocity Field for a wheel with winglet h=0.56 V=350km/h
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Figure Velocity y-component over spinning wheel h=0.56 m 150km/h @ cut line 2.6 m.20
At a height of 0.56m there is a slight improvement in the downward flow of the air away
from the rear wing. The velocity field plots are relatively similar to the spinning wheel with no
winglet at that height and the improvements are hard to see by only looking at them. However,
when looking at the xy graph showing the y components of velocity with height it is then possible
to observe the improved downflow with a peak at -10 m/s with no winglet at 350 km/h compared
to double that value at -20 m/s with the winglet at this position. The velocity does not seem to
change the flow field significantly in terms of streamlines and vortices, other than slightly
narrowing the vortex formed behind the wheel at higher speeds. It does however, affect the y
component of the gases after passing through the wheel therefore will send more air away from
the rear wing in a shorter length.
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Wheel studies with winglet h=0.6m
Figure 21 Velocity Field for a wheel with winglet h=0.6 V=150km/h
Figure 22 Velocity y-component over spinning wheel h=0.6 m 150km/h @ cut line 2.6
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Figure 23 Velocity Field for a wheel with winglet h=0.6 V=250km/h
Figure 24 Velocity y-component over spinning wheel h=0.6 m 250km/h @ cut line 2.6
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Figure 25 Velocity Field for a wheel with winglet h=0.6 V=350km/h
Figure 26 Velocity y-component over spinning wheel h=0.6 m 350km/h @ cut line 2.6
Shifting the winglet up to a height of 0.6m from the ground shows a much better
enhancement of downward flow away from the rear wings. Looking at the velocity field plots it is
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possible to observe the low velocity zone right after the wheel is shortened by a lot. Furthermore,
the xy graph displays an improvement in the downward y component of the velocity across all
tested velocities when compared to the winglet at height = 0.56m. The vortex created by the
immersed bodies is also reduced in size, which is an aerodynamic improvement given that it will
reduce overall drag. Similar to the winglet at the previous height, the velocity of the car does not
influence the shape of the vortex at all, and is only influencing the magnitude of the air flow.
Wheel studies with winglet h=0.65m
Figure 27 Velocity Field for a wheel with winglet h=0.65 V=150km/h
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Figure 28 Velocity y-component over spinning wheel h=0.65 m 150km/h @ cut line 2.6
Figure 29 Velocity Field for a wheel with winglet h=0.65 V=250km/h
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Figure 30 Velocity y-component over spinning wheel h=0.65 m 250km/h @ cut line 2.6
Figure 31 Velocity Field for a wheel with winglet h=0.65 V=350km/h
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Figure 32 Velocity y-component over spinning wheel h=0.65 m 350km/h @ cut line 2.6
Finally, the winglet at height = 0.65 m showed the best results in terms of directing the
flow downward, out of all winglet positions. Looking at the xy graphs showing the y component
of the flow’s velocity, this winglet position had a higher max downward velocity across all
velocities when compared o the other winglets, roughly exceeding the winglet at position h = 0.56
m by 60%, and being three times better than a spinning wheel with no winglet. Compared to the
winglet at position h = 0.6m there is only a rough 14% increase in the overall downward force,
however, this comes with a trade-off by creating a longer vortex behind the wheel, as seen by the
velocity field plots, which in turn will cause more overall drag. Finally, the shape and size of this
vortex is independent of the magnitude of the car’s velocity.
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Conclusion
This report investigated the effect of the new F1 winglets on the wheel by comparing the
velocity flow over three winglet positions and comparing it to a flow over a static and rolling
wingless tires. From the discussion above, it was concluded that the addition of a winglet
introduces a larger downward component to the velocity field after interacting with the tire when
compared to a rolling wheel without the winglet, exceeding it by a maximum of 300% in the tallest
configuration. The winglets also give the aerodynamic advantage of creating smaller turbulent
wakes which as a consequence will diminish the total drag. For the tested winglet positions, the
group discovered the taller winglets are better at directing the flow downward with the
disadvantage of creating longer vortices after a certain critical height. Furthermore, it was found
that for spinning wheels with winglets and without winglets the shape and size of the formed
vortices is independent of the velocity, whereas that is not true for a non spinning wheel.
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References
B.E. Launder, B.I. Sharma. Application of the energy-dissipation model of turbulence to the calculation
of flow low near a spinning disc, Letters in Heat and Mass Transfer,Volume 1, Issue 2, 1974,Pages 131137, ISSN 0094-4548,
White, Frank M. Fluid Mechanics. 7th ed. New York, N.Y: McGraw Hill, 2011. Print.
Walter Frei, Which Turbulence Model Should I Choose for My CFD Application?” COMSOL,
https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application/.
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