drag and downforce analysis of racecar rear diffuser
TRANSCRIPT
Drag and Downforce Analysis of Racecar Rear Diffuser
Brendan Welch
UNC Charlotte, Department of Mechanical Engineering, MEGR 3242
Applied Vehicle Aerodynamics
May 4, 2021
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Table of Contents
Table of Contents .......................................................................................................................... 2
Abstract .......................................................................................................................................... 3
Objectives....................................................................................................................................... 3
CAD Model .................................................................................................................................... 3
Baseline Simulation ....................................................................................................................... 6
Mesh............................................................................................................................................ 6
Physics ........................................................................................................................................ 8
Results ........................................................................................................................................ 9
Improvements .............................................................................................................................. 15
No Diffuser ................................................................................................................................... 17
With Diffuser ............................................................................................................................... 24
Conclusions .................................................................................................................................. 31
References .................................................................................................................................... 33
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Abstract
The purpose of this project was to analyze the effects on drag and downforce caused by adding a
rear diffuser to a race car. This was done by modelling a race car in SolidWorks and simulating
the model driving at 150mph with and without a rear underbody diffuser. Plots and reports of
drag and downforce coefficients were generated for each case and their convergence values were
compared. From this comparison, it was found that this rear diffuser increased the downforce of
the vehicle at the cost of slightly increasing drag. The increase in drag was surprising given that
the wake region behind the vehicle was shrunk down by the smoother velocity transition caused
by adding the diffuser. The amount of induced drag the diffuser got rid of was outweighed by the
increased skin friction caused by faster flow below the vehicle. It was then determined that this
rear diffuser would be beneficial for cars running tracks with more tight corners than long
straights because of the simultaneous increase in downforce and drag.
Objectives
This project was completed to test the effects of a rear diffuser on downforce and drag. This was
accomplished by generating a CAD model of a racing vehicle in SolidWorks and running three
CFD simulations in Star CCM. The three simulations were a baseline simulation to analyze the
volume mesh, one simulation on a model car without a diffuser, and one simulation on a model
car with a diffuser. The CAD model of the vehicle and CFD simulations had limits and
restrictions that are tabulated below (See Table 1).
Table 1: Dimensional and cell count restrictions.
CAD Model The first step to be completed for this project was designing a baseline car CAD model. This
model was given a set of prescribed dimensions for overall length, front overhang, rear
overhang, height, wheel diameter and width, etc. A CAD model was made in SolidWorks
adhering to all of these guidelines and is shown below (See Figure 1).
Overall Length
[mm]
Overall Width
[mm]
Overall Height
[mm]
Front Overhang
[mm]
4400 1900 1100 1250
Rear Overhang
[mm]
Wheel Diameter
[in.]
Wheel Width
[in.]
Cell Count
[millions]
1100 28 14 3 to 5
4
Figure 1: Drawing of car modelled in SolidWorks with prescribed dimensions.
Once this model was completed, another model with a rear diffuser on the back was generated.
The diffuser was roughly based on the reference image shown below (See Figure 2).
Figure 2: Underbody diffuser reference image1.
Images of the model car with an underbody diffuser are shown below (See Figures 3 and 4).
Some notable similarities between this diffuser and the one designed are the fins diverting air
slightly away from the center plane and the low area right behind the wheels. One major
difference is the length of the designed diffuser being much shorter than in the reference, as the
diffuser was not allowed to extend past the rear axle.
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Figure 3: Drawing of car modelled in SolidWorks with prescribed dimensions and rear diffuser.
Figure 4: Diffuser fin dimensions and underbody view.
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This CAD model adheres to all requirements outlined in the project specifications. Once both of
these models were completed, the assemblies were exported as Parasolid files to be tested in Star
CCM.
Baseline Simulation
Mesh
The model was prepared similarly to prior CFD projects in the course with a surface wrapper -
simulation volume - subtract operation - volume mesh workflow. The surface wrapper was
formed with a base size of 8mm and custom controls along the part’s curves limiting the wrapper
cell size to 0.4-2mm. An image of the completed surface wrapper can be seen below (See Figure
5).
Figure 5: Surface wrapper across front bumper of vehicle.
Once this was completed, a simulation volume was generated as a block part. The size of the
simulation volume kept in line with the recommended dimensions of 3 times the length of the
vehicle in front, 13 times the length of the vehicle behind, 8 times the height of the vehicle tall,
and 6 times the width of the vehicle wide2. The full simulation volume was divided into smaller
block regions for volume mesh refinements. The coordinates for the overall simulation volume
and each volume region are tabulated below (See Table 2).
Table 2: Corner coordinates of volume controls for baseline mesh.
x y z x y z
Sim. Vol. -13 -0.95 0.004 57 6.65 8.8
Level 2 3.5 -0.95 0 9 1.5 3
Near -2 -0.95 0 7 1.2 2
Underbody -0.25 -0.95 0 4.9 0.3 0.1
Block TitleCorner 1 [m] Corner 2 [m]
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A subtract operation was then conducted, subtracting the surface wrapper around the vehicle
from the “Sim. Vol.” block. An image of the resulting wind tunnel is shown below (See Figure
6).
Figure 6: Interior view of simulation volume.
An automated, trimmed mesh was then generated with the parameters tabulated below (See
Table 3).
Table 3: Automated mesh base parameters.
The number of prism layers and near wall thickness were determined by (1), (2), and (3) where
‘I’ is the turbulence intensity (1%), ‘V’ is the velocity (150mph), ‘y1’ is the near wall thickness,
‘y+’ is a non-dimensional constant (3 for this case), ‘Cµ’ is a constant equal to 0.09, ‘ρ’ is the
density of air, ‘n’ is the number of prism layers, ‘PLTT’ is the prism layer total thickness, and ‘r’
is the stretch factor (r = 1.15 in this case).
𝐾 =3
2𝐼2𝑉2 (1)3
𝑦1 =𝑦+µ
𝐶µ1/4
𝜌𝐾 (2)3
𝑛 =ln(1−
𝑃𝐿𝑇𝑇
𝑦1(1−𝑟))
ln(𝑟) (3)
The top prism layer thickness of 1.361mm has a rather large volume ratio in relation to the
surrounding mesh, which has a size of approximately 12mm.
Custom controls were implemented into the automated mesh to better optimize the flow
development. First, the prism layers were disabled for the walls of the wind tunnels and the
Base Size
[mm]
# Prism
Layers
PLTT
[% Base]
Near Wall
Thickness [mm]
Top Layer
Thickness [mm]
24 18 40 0.125 1.361
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coarseness of the cells along the walls were set to a range of 200% - 2000% base size. Next, the
block regions were given custom cell sizes. These values are tabulated below (See Table 4).
Table 4: Cell size in terms of percent base for baseline mesh.
Once this setup was completed, the automated mesh was executed. A side view of the mesh with
the refined block regions labelled is shown below (See Figure 7).
Figure 7: Volume mesh scene with labelled refined regions.
Physics
A new physics continua was generated to simulate this car driving straight at 150mph. Tabulated
values for the initial conditions are shown below (See Table 5).
Table 5: Initial velocity and pressure conditions for physics setup.
This properly defines the flow of air and moving ground around the vehicle. In order to properly
simulate wheel rotation, the wheels were given a local rotation rate of 1800rpm, found by
converting the tangential velocity in mph to angular velocity of a 28in. tire in rpm. The axis and
rotation data was tabulated and is shown below (See Table 6).
Table 6: Wheel rotation properties.
Region: Level 2 NearUnder-
body
[% Base] : 200 100 50
Initial Velocity
[mph]
Inlet Velocity
[mph]
Outlet Pressure
[psi]
Ground Tangential
Velocity [mph]
<150 0 0> 150 0 <150 0 0>
Wheel Axis Origin [m]Diameter
[mm]
Rotation
Rate [rpm]
Front <0, -1, 0 > (1.25, -0.1778, 0.3556) 711.2 1800
Rear <0, -1, 0 > (3.30, -0.1778, 0.3556) 711.2 1800
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After this was completed, reports for downforce and drag coefficients were generated. The
downforce coefficient report analyzed forces in the negative ‘z’ direction with a reference
velocity of 150mph. The drag coefficient report analyzed forces in the positive ‘x’ direction with
the same reference velocity of 150mph. The frontal areas, densities, and viscosities were left
unchanged for comparison’s sake. A plot was generated for both of these reports as well as the
residuals, completing the physics setup.
This physics setup remained constant for all simulations conducted.
Results
A baseline simulation with the above mentioned mesh and physics setup was run for 1000
iterations. Images of the velocity scalar scene across the center plane are shown below (See
Figures 8, 9, 10 and 11).
Figure 8: Velocity magnitude along the center plane for baseline case.
Figure 9: Horizontal velocity in the positive 'x' direction along the center plane for baseline case.
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Figure 10: Lateral velocity in the positive 'y' direction along the center plane for baseline case.
Figure 11: Vertical velocity in the positive 'z' direction along the center plane for baseline case.
Figures 8 and 9 show the a region of low velocity along the back of the vehicle where flow
separation most likely occurs. In these scenes, it is clear that one of the coarser, less defined
regions of flow is at the end of the hood just before the windshield starts. Figure 10 shows little
to no lateral velocity on the model. Figure 11 shows updrafts above the stagnation point of the
model and in the wake region of the vehicle, and downdrafts steadily forming around the back of
the car.
Streamline velocity scalars over the vehicle were generated to visualize the flow’s path around
the car. Images of these streamlines are shown below (See Figures 12 and 13).
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Figure 12: Velocity streamlines around vehicle along the center plane for baseline case.
Figure 13: Velocity scalar streamlines across the underbody of the vehicle for baseline case.
Figure 12 shows some air acceleration as air crests the top of the vehicle, and Figure 13 shows
some extreme acceleration just as the air is sucked underneath the front bumper of the car. The
air in the underbody gradually decreases in speed and then is pulled up violently to form a large
wake region behind the car.
Images of the coefficient of pressure distribution for this simulation were also captured and are
displayed below (See Figures 14 and 15).
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Figure 14: Pressure coefficient along the center plane for baseline case.
Figure 15: Total pressure along the center plane for baseline case.
These scenes show the formation of a low pressure region just behind the vehicle that extends
back into the wake. The coefficient of pressure distribution was imposed onto the half model
itself and is shown below (See Figures 16 and 17).
Figure 16: pressure coefficient overlayed onto vehicle body for baseline case.
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Figure 17: Pressure coefficient overlayed onto underbody for baseline case.
The point of lowest pressure can be found near the front of the underbody. The pressure
gradually increases along the underbody and then the airflow escapes and forms a wake.
Additionally, a scalar of the Wall Y+ of the baseline case was captured and is shown below (See
Figure 18).
Figure 18: Wall Y+ across body for baseline case.
The prism layer mesh was calculated for using a ‘y+’ value of 3, thus the variation in the Wall
Y+ scalar from 0 to almost 20 is surprising.
The graphs for drag and downforce versus iterations were generated for this model and are
shown below (See Figures 19 and 20).
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Figure 19: Drag coefficient vs iterations for baseline case.
Figure 20: Downforce coefficient vs iterations for baseline case
The converged upon coefficients were selected by hovering the cursor over the plots and aligning
the vertical axis’ value with roughly the average value of the converged portions of the graph.
These converged values are tabulated below (See Table 7).
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Table 7: Converged coefficients of drag and downforce for baseline case.
Based on the coefficient of downforce given here, the shape of this vehicle generates net lift. The
residuals plot for the baseline case is shown below (See Figure 21).
Figure 21: Residuals plot for baseline case.
The converged values on the residuals plot were also selected in the same manner and are
tabulated below along with the overall cell count of the baseline case (See Table 8).
Table 8: Converged residual values for baseline case.
Improvements
To improve the volume mesh, the flow needed two additional volumetric controls. One was
placed over the hood and the other was placed at the rear of the vehicle near where the diffuser
would be located. The revised mesh’s volume control coordinates and cell sizes are shown below
(See Tables 9 and 10).
SimulationCoefficient of
Drag
Coefficient of
Downforce
Baseline 0.2544 -0.5295
Simulation Cell Count Continuity SDR TKEX
Momentum
Y
Momentum
Z
Momentum
Baseline 4857072 0.0034 1.80E-08 0.0097 0.0022 0.017 0.017
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Table 9: Corner coordinates for volume controls in improved mesh.
Table 10: Cell size in terms of percent base for improved mesh.
Because the baseline simulation had 4.85 million cells, the addition of these two new volumetric
controls put the overall number of cells above the 5 million cell limit. To mitigate this, the
“Near” and “Level 2” regions were each shrunk by at least 1m in the ‘x’ and ‘z’ directions.
Additionally, the number of prism layers was decreased by 1 by increasing the stretch factor
from 1.15 to 1.175, still keeping below the recommended maximum of 1.22. A table with the
mesh’s base size and prism layer properties is shown below (See Table 11).
Table 11: Improved mesh base size and prism layer parameters.
An additional benefit to increasing the stretch factor is the slight reduction in volume ratio
because of an increase in the top layer thickness of the prism layer.
In summary, the mesh was improved by implementing two additional volume controls at points
on the flow that were underdefined in the baseline case, over the hood and through the diffuser
region. In order to account for these extra cells in the budgeted 5 million cells, the “Near” and
“Level 2” blocks were shrunk and the stretch factor was increased. Incidentally, increasing the
stretch factor also increased the thickness of the top of the prism layer, marginally improving the
volume ratio between the prism layer and the cells directly adjacent to them. Images of the newly
improved mesh are shown below (See Figures 22 and 23).
x y z x y z
Sim. Vol. -13 -0.95 0.004 57 6.65 8.8
Level 2 -2.75 -0.95 0 8.5 1.5 2.5
Near -1.25 -0.95 0 7 1 2
Over Hood 0 -0.95 0.35 1.7 0.1 0.85
Diffuser Region 3.25 -0.95 0 4.9 0.3 0.4
Underbody -0.25 -0.95 0 3.25 0.3 0.1
Block TitleCorner 1 [m] Corner 2 [m]
Region: Level 2 NearOver
Hood
Diffuser
Region
Under-
body
[% Base] : 200 100 50 50 50
Base Size
[mm]
# Prism
Layers
PLTT
[% Base]
Near Wall
Thickness [mm]
Top Layer
Thickness [mm]
24 17 40 0.125 1.536
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Figure 22: Improved mesh scene with labelled volume control regions.
Figure 23: Close view of underbody and diffuser region volume controls.
No Diffuser
The physics setup and improved mesh setup discussed in the sections above were run for 1000
iterations on the CAD model car with no rear diffuser. The velocity profiles across the center
plane were captured and are shown below (See Figures 24, 25, 26, and 27).
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Figure 24: Velocity magnitude along the center plane for no diffuser case.
Figure 25: Horizontal velocity in the 'x' direction along the center plane for no diffuser case.
Figure 26: Lateral velocity in the 'y' direction along the center plane for no diffuser case.
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Figure 27: Vertical velocity in the 'z' direction along the center plane for no diffuser case.
These velocity profiles show the benefits of the improved mesh, with a more defined flow along
the end of the hood and a more defined wake region behind the car. Similar to the baseline case,
Figures 24 and 25 show a low velocity wake region forming behind the vehicle, and a sharp
increase in velocity near the front of the vehicle’s underbody which will cause significant skin
friction drag.
Streamline velocity scalars were captured for this simulation and are shown below (See Figures
28 and 29).
Figure 28: Streamline velocity scalars along center plane for no diffuser case.
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Figure 29: Streamline velocity scalars around body of model for no diffuser case.
The underbody streamlines were isolated from Figure 29 and are shown below (See Figure 30).
Figure 30: Streamline velocity scalars along underbody of model for no diffuser case.
The streamlines in Figure 30 show the air accelerating just as it enters the underbody. From
there, the air slowly decelerates until joining the wake region behind the vehicle.
The pressure distribution along the center plane of the vehicle is shown below (See Figure 31).
Figure 31: Coefficient of pressure along the center plane for no diffuser case.
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Figure 32: Total pressure along the center plane for no diffuser case.
Both Figures show a sharp decrease in pressure at the front of the underbody with a gradual
pressure increase as the flow moves towards the back. The coefficient of pressure across the
entire vehicle and under the body was captured to visualize this further (See Figures 33 and 34).
Figure 33: Coefficient of pressure across body of the vehicle for no diffuser case.
Figure 34: Coefficient of pressure distribution across underbody of vehicle for no diffuser case (note: car rear on the
right).
Figure 34 illustrates the pressure across the underbody. In order to better see how the pressure
varies in the diffuser region (for comparison sake, since this model does not have one) the range
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on the color bars was refined and clipping was deactivated. Additionally, a constrained
streamlines were fixed to the underbody to better visualize the flow paths.
Figure 35: Refined coefficient of pressure distribution with oil flows for no diffuser case (note: car rear on the left).
Based on the image above, it seems that the pressure starts to increase as the flow approaches a
point where it will be pulled into a low velocity wake region. This is consistent with Bernoulli’s
principle as lower velocities generally correlate with higher pressures. The oil flow lines show
that the flow ends up being pulled to the rear wheel region and trapped in a small wake. Ideally,
the diffuser will help maximize downforce by slowing down the increase in pressure by
minimizing the wake thus minimizing the decrease in velocity. Accomplishing these things
would alleviate the high pressure region located in the lower left of Figure 35 and increase
downforce.
Additionally, a scalar of the Wall Y+ of the no diffuser case was captured and is shown below
(See Figure 36).
Figure 36: Wall Y+ scalar across body for no diffuser case.
The plots for the coefficients of drag and downforce are shown below as well as a table of the
converged values (See Figures 37, 38, and Table 12).
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Figure 37: Coefficient of drag versus iterations for no diffuser case.
Figure 38: Coefficient of downforce versus iterations for no diffuser case.
Table 12: Coefficients of drag and downforce for no diffuser case.
Both of these coefficients are extremely similar to the baseline case. The residuals plot and a
table of converged residual values are shown below (See Figure 39 and Table 13).
SimulationCoefficient of
Drag
Coefficient of
Downforce
No Diffuser 0.2456 -0.5135
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Figure 39: Residuals plot for no diffuser case.
Table 13: Converged residuals values for no diffuser case.
With Diffuser
The physics setup and improved mesh setup discussed in the prior sections were run for 1000
iterations on the CAD model car with a rear diffuser. The velocity profiles across the center
plane were captured and are shown below (See Figures 41, 41, 42, and 43).
Figure 40: Velocity magnitude along the center plane for diffuser case.
Simulation Cell Count Continuity SDR TKEX
Momentum
Y
Momentum
Z
Momentum
No Diffuser 4967561 0.0032 1.30E-07 0.0053 0.0015 0.0126 0.0131
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Figure 41: Horizontal velocity magnitude in the 'x' direction along the center plane for diffuser case.
Figure 42: Lateral velocity in the 'y' direction along the center plane for diffuser case.
Figure 43: Vertical velocity in the 'z' direction along the center plane for diffuser case.
The major differences between the diffuser case and no diffuser case lie within Figures 40 and
41. At the start of the diffuser there is a secondary area of acceleration. Then, the air steadily
decelerates until joining a smaller wake region. A streamline scalar across the center plane was
also generated for better visualization of where the flow accelerates (See Figure 44).
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Figure 44: Streamline velocity scalars along center plane for diffuser case.
Streamline scalars around the underbody of the vehicle were also generated and are shown below
(See Figures 45 and 46).
Figure 45: Underbody streamlines for diffuser case.
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Figure 46: Diffuser view of underbody streamlines.
The streamlines show that most of the flow that gets sucked into the rear wheel and underneath
the underbody section behind the rear wheel eventually gets pulled back into the diffuser before
being deposited into the wake region behind the car.
The pressure distributions along the center plane of the vehicle are shown below (See Figures 47
and 48).
Figure 47: Coefficient of pressure along the center plane for diffuser case.
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Figure 48: Total pressure distribution along center plane for diffuser case.
The images above show that the there is an additional low pressure region at the start of the
diffuser, aligning with the air acceleration in Figure 41 and Bernoulli’s principle. This should
work to increase downforce at the cost of some drag, although the smaller wake due to the
diffuser reducing flow separation could make up for this.
The coefficient of pressure along the body of the vehicle was also captured and is shown below
(See Figures 49 and 50).
Figure 49: Coefficient of pressure across the body for diffuser case.
Figure 50: Underbody coefficient of pressure distribution for diffuser case (note: car rear on left).
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To better visualize the pressure distribution across the diffuser, the color bar range was refined
and clipping was deactivated. Flow lines were also added to the underbody to aid in
visualization. This edited image is shown below (See Figure 51).
Figure 51: Underbody coefficient of pressure with oil flows for diffuser case (note: car rear on left).
This figure shows that the high pressure region on the bottom of the vehicle has shrunk
significantly with the addition of the rear diffuser, limiting it to only the underbody segment
directly behind the rear wheel. When following the flow lines, it looks like a little over half of
the flow was pulled towards the center fin and rode along the side of it before exiting into the
wake region. The other half of the flow made its way around the wheel, onto the underbody, and
then into the diffuser before exiting to the wake region. This image implies an expected increase
in downforce.
The plots of drag and downforce coefficients along with a table of converged values for the
diffuser case are shown below (See Figures 52, 53, and Table 14).
Figure 52: Drag coefficient versus iterations for diffuser case.
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Figure 53: Downforce coefficient versus iterations for diffuser case.
Table 14: Converged coefficients of drag and downforce for diffuser case.
Figure 53 was generated with a reference velocity of 0mph instead of 150mph. This was a
mistake, and after correcting the reference velocity the plot would not update. However,
correcting the reference velocity the report updated and the converged value was able to be
found by reading through the report. This is how the coefficient of downforce value was found.
The residuals plot and a table of converged residual values are shown below (See Figures 54 and
Table 15).
Figure 54: Residuals plot versus iterations for diffuser case.
SimulationCoefficient of
Drag
Coefficient of
Downforce
Diffuser 0.3081 -0.4489
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Table 15: Converged residual values for diffuser case.
Let it be noted that the additional 18,000 cells were due to the inclusion of the diffuser an the
cascading effects it had on the surface wrapper and automated mesh formation, not because of
any volume control or mesh parameter changes.
Conclusions
Below is a table with the converged coefficients for drag and downforce from each of the three
conducted simulations (See Table 16).
Table 16: Converged coefficients of drag and downforce from each simulation.
The table above shows that adding a rear underbody diffuser to a vehicle does increase the
downforce of the vehicle but causes an increase in drag. Because the vehicle being tested is a
streamlined body, the vast majority of drag that the body experiences is from skin friction, not
from pressure drag or vortices. Thus, the faster flow velocity beneath the vehicle at certain points
(highlighted on Figure 55 below) contribute to more drag than the decreased wake region
alleviates.
Figure 55: Horizontal velocity of no diffuser case (top) and diffuser case (bottom) with high velocity and wake
regions labelled.
Simulation Cell Count Continuity SDR TKEX
Momentum
Y
Momentum
Z
Momentum
With Diffuser 5185860 0.0084 1.49E-07 0.0099 0.0016 0.0211 0.0218
SimulationCoefficient of
Drag
Coefficient of
Downforce
Baseline 0.2544 -0.5295
No Diffuser 0.2456 -0.5135
With Diffuser 0.3081 -0.4489
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This explains the increase in the drag coefficient, but not the increase in downforce. The
underbody coefficient of pressure distributions for the no diffuser case and diffuser case are
placed side by side for comparison below (See Figure 56).
Figure 56: Underbody coefficient of pressure distribution with oil flow for no diffuser case (left) and diffuser case
(right). Pressure coefficient scalar ranging from -800 (blue) to 800 (red).
Figure 56 shows a drastic reduction in high pressure with the addition of the underbody diffuser,
and a more defined diversion of flow away from the wheel region. The lower pressure along the
back of the underbody allows for more rear downforce, which provides a significant performance
increase for racing vehicles.
Implementing a rear diffuser of this design results in an increase in fluid velocity below the car,
increasing drag despite a tighter wake region, and decreases pressure below the car, increasing
downforce. This tradeoff could be an asset to teams racing on tracks requiring lots of tight
cornering and fewer long straightaways.
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References
1. Formula 1 Dictionary. “Ferrari Underbody Diffuser.”. Accessed April 22, 2021.
http://www.formula1-dictionary.net/diffuser.html
2. The UNC Charlotte William States Lee College of Engineering Department of
Mechanical Engineering and Engineering Science. 2020. “MEGR 3242 Applied Vehicle
Aerodynamics, Instruction for Students, “Common Errors”. Last modified Spring 2021.
/courses/146421/files/folder/02%20Handouts?preview=12242559
3. The UNC Charlotte William States Lee College of Engineering Department of
Mechanical Engineering and Engineering Science. 2020. “MEGR 3242 Applied Vehicle
Aerodynamics, Instruction for Students, “Lecture Notes”. Last modified Spring 2021.
/courses/146421/files/folder/03%20Annotated%20Lecture%20Slides?preview=11797578