UW-Platteville Formula SAE External Aerodynamics

Kevin Mikulski

University of Wisconsin-PlattevilleME4560 Computational Fluid Dynamics

For Dr. John IselinDecember 20, 2013

ABSTRACTThe aerodynamics package for the University of Wisconsin-Platteville’s Formula SAE team is

simulated using CD-Adapco’s Star-CCM+. The many decisions made with meshing and physics

are discussed within this document. The outcome of the simulation performed for the FSAE car

is that it has a coefficient of drag of 0.545 and a negative coefficient of lift of 0.354.

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ContentsABSTRACT................................................................................................................................................1

INTRODUCTION.......................................................................................................................................3

BACKGROUND INFORMATION FOR CURRENT DESIGN.................................................................3

THE MODEL..............................................................................................................................................4

MESHING CONDITIONS..........................................................................................................................5

PHYSICS CONDITIONS...........................................................................................................................7

MONITORING AND RESULTS................................................................................................................9

THE USE OF SIMULATIONS.................................................................................................................10

APPENDIX...............................................................................................................................................11

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INTRODUCTION

Aerodynamics for a racecar can be the difference between a slow and fast car in a

competition. The University of Wisconsin-Platteville enters a vehicle every year into

International competition in Lincoln, NE for Formula SAE. This competition limits a mini

formula one style racecar to a 610cc motor with a 20mm restrictor causing limitations in engine

power. Due to engine restrictions, reduction in drag can help to increase the acceleration of the

vehicle. The proper use of downforce on the racecar helps the tires utilize their traction better in

sweeping corners.

The competition limits top speeds of the competition courses to around 65 mph, so

aerodynamics do not seem like they would be that much help. Many teams have shown that a

significant downforce generating system such as large wings and an undertray can decrease lap

times over a mile long course by up to 5 seconds. At competition, a majority of the top 10 teams

utilize some type of downforce generating device, and all look to reduce drag in any way that

they can.

The use of computational fluid dynamics (CFD), specifically CD-Adapco Star-CCM+, is

essential to helping improve the aerodynamics of the race car. The previous design use of CFD

will be discussed in regards to the Formula SAE car. Next, the solid model will be discussed.

After, the meshing and physics conditions set within CFD will be explained. Finally, the results

from the simulation will be discussed.

BACKGROUND INFORMATION FOR CURRENT DESIGN

Over the past two years, the Formula car’s aerodynamics package has changed

significantly due to the use of CFD. The undertray of the car, the area that encompasses under

the cockpit and the diffuser at the rear of the vehicle, had originally been developed using a flat

plane under most of the vehicle and then near the rear of the chassis (Figure 1), it bent at a 7.5

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degree angle to the edge of the chassis. This design created some downforce without much drag

penalty.

Through research of the elements that other teams use at competition, an elliptical or

parabolic shape was looked into (Figure 2). The first design used a quarter ellipse to the edge of

the chassis, which showed promise, but then a parabolic design was developed with a 7.5 degree

“take-off” angle from the origination of the parabola (Figure 3). This design showed an increase

of downforce of 1.5-2 times the original design.

One other design concept that was investigated was to increase the length of the

undertray past the end of the chassis in two “tunnels” on either side of the main chassis (Figure

4). The center section of the undertray still ends at the chassis because of the necessity of a quick

jack bar on the rear of the chassis. It was determined that this gives the car the greatest

downforce for a fairly simple design if the tunnel runs to the farthest extent of the region

aerodynamics devices are allowed by the rules.

The nosecone (Figure 5) was also developed to reduce drag and increase the downforce.

Since the undertray acts similar to a venturi tube with air being compressed down to a throat and

then progressively diffused to create a low pressure area under the vehicle. The best designs

utilized large fillets on all the corners that can affect airflow over the car. Also, an angle closer to

parallel with the ground produced less drag on the vehicle. The nosecone design is restricted by

the chassis and impact attenuator, as well as overall weight. These design obstacles are followed

as closely as possible to reduce weight, while still helping to improve aerodynamics of the

formula car.

THE MODEL

The model of the formula car is a simplified model of the vehicle that is produced to try

and reduce the time that is required to solve the simulation. All parts that are within the model

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are closed off so that the simulation is not computing in areas that low fluid flow would not

affect the aerodynamic effects of the bodywork. The only parts included within the model are a

nosecone, center cockpit section, a driver with helmet, firewall, simplified engine, undertray, and

wheels (Figure 6).

To reduce the size of the simulation further, only half of the car is meshed and simulated

because the flow should be symmetric across the center plane of the car (Figure 10). In real life,

due to manufacturing inaccuracies, this may not be necessarily true, but the inaccuracies are not

able to be modeled with the tools that we have at our disposal.

MESHING CONDITIONS

The model is imported as parts from a parasold file from SolidWorks. The model is

imported as parts so that it is easy to make changes to the geometry without having to remake the

entire model. A wind tunnel part is then created around the car to a recommended size of about 5

car lengths upstream, 5 car widths to the side and above the car, and 10 car lengths downstream

(Figure 7).

A surface wrapper is used in the model to negate the possibility of having surface issues

that would cause an inability to create a volume mesh. Since the surface wrapper is being used,

the surface remesher has to be utilized so that the mesh is suitable for use as a computational

mesh. If the remesher had not been used, there would be many irregular shaped cells with bad

aspect ratios and transition ratios between each cell.

For volume meshing, a trimmer mesher with prism layers is used. A trimmer mesher was

selected because the predominate flow direction of the fluid is known, so it will reduce the

computational expense of the simulation. The selected number of prism layers and prism layer

thicknesses were chosen based on recommendations from CD-Adapco that were received in a

training seminar in November of 2013.

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The goal of the meshing regime is to reduce the wall-y+ value to try and be in the low

wall-y+ area. To get the wall-y+ reduced, a smaller boundary layer of prism cells needs to be

used. After convergence, most of the cells have a wall-y+ under 30, which is within the transition

area of the turbulence model. Although a low wall-y+ condition was not achieved, the all-y+

wall treatment picked by default by Star-CCM+ can cope with the conditions. It may result in

some error within the results, but as long as the y+ is kept small, there will be only small

amounts of error. All essential aerodynamic devices resulted in a wall-y+ less than 10. The mesh

was not further developed due to the potential increase in cells in the model to reduce

computational expense.

The base size of the model was based upon the area directly surrounding the formula car.

A base size of 24.0 mm was used with a maximum cell size within the region of 3600% of base,

which is 864.0 mm. The number of prism layers for the model is set to 5 layers, but that is not

applied to any surfaces because each boundary either has no prism layers, or a specified number

of prism layers. The number of points per circle in the surface curvature folder was increased to

60 to help better represent curves on the imported surface. The surface growth rate was reduced

to 1.1 so that the cells do not grow too quickly around the model. The wrapper scale factor was

reduced from 100% to 67% to help the surface wrapper recognize more complex geometries for

the surface remesher to more accurately represent the shapes in a computational mesh.

Two volumetric controls were created for the model. The first control is a box around the

car that stretches about 2 meters in front of the formula car, 20 meters behind the formula car and

1 meter above and to the side of the extents of the car model. The trimmer mesher was given an

isotropic size of 400% of the base mesh size to reduce how quickly the cells grow from the car.

The second volumetric control encompasses the ground layer up to 0.15 meters from the ground,

and is completely around the wheels and ground. An anisotropic refinement of 50% of the base

size for the trimmer is chosen in the y direction (up from the ground to ceiling).

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All aerodynamic surfaces, such as the nosecone, center, undertray, firewall and tires use a

modified prism layer mesh having a thickness of 8 mm with 12 prism layers and a near wall

prism layer thickness of 0.05 mm. A near wall prism layer thickness specifies the height of the

first prism layer and the program calculates a stretching factor that distributes the rest of the

layers through the thickness specified. The undertray needed a custom surface size to capture the

geometry accurately without any anomalies within the mesh. The engine has a separate prism

layer specification of 1 layer that is 1.5 mm because the flow around the engine is not essential to

the flow characteristics of the entire model. The ground has the final different prism layer

specification of a thickness of 25mm with 12 layers and a near wall thickness of 2mm to

represent the boundary layer created by the moving floor.

A trimmer wake refinement is also implemented behind the vehicle to capture the

turbulence behind the car. The wake refinement stretches 0.5m behind all the elements of the car

with a base size 100% of the reference base size. The default growth rate was set to medium to

reduce how quickly the cells grow around the parts.

The far field boundaries were split off and set as symmetry planes because the flows very

far from the car is parallel to the plane. The inlet is a velocity inlet because the car velocity will

be set. The far end of the wind tunnel is set as a pressure outlet at zero gage pressure. All the far

field, floor, inlet, and outlet boundaries are set with a target surface size of 3600% while keeping

the stock minimum surface size so that all the geometry will be resolved near the car, but the

cells far away from the car will be large since they will not affect the flow field.

PHYSICS CONDITIONS

The formula car model is a three dimensional model that is steady state with a constant

density fluid. External aerodynamics can typically be represented as a steady state model for a

less expensive model. To represent some of the more intricate vortices that are developed with

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the aerodynamics, an unsteady simulation may be necessary. An unsteady simulation would be

very computationally expensive though due to the need for a very small time step to capture the

vortices and any separation of the flow, thus keeping the courant number at about 1.0. The

segregated flow solver and constant density fluid were chosen due to the low speeds that are

encountered with a Mach number well below 0.2, making it so that fluid compressibility is

negligible. The under-relaxation factor for the pressure term of the segregated solver was

reduced to 0.1 for model stability and to solve the simulation quicker under direction from CD-

Adapco. A K-Omega turbulence model is chosen because it is best suited for external

aerodynamic flows with separation bubbles. The realizability coefficient for the SST (Menter) K-

Omega model was changed to 1.2 due to recommendations from CD-Adapco. The realizability

coefficient affects the amount of turbulent energy dissipation that occurs near an object. Cell

quality remediation was also selected to make sure that the model does not ‘blow up’ due to a

few bad cells created through the surface wrapping and remeshing.

The car is simulated at an air speed of 50 mph to represent an average sweeping corner

speed that is seen on an autocross track. Initial velocity in the region is set to 50 mph because the

predominate flow direction is known in the region. The floor is also set to be moving at 50 mph

in the direction of motion to represent a moving road under the car. Wheels are then set to have a

tangential velocity specification of 88 rad/s, which represents the wheel rotation rate of a 20”

diameter tire moving at a ground speed of 50 mph.

The inlet turbulence conditions are set to a turbulence intensity of 0.01 because of the low

amount of turbulence that occurs in an ambient flow and a turbulent viscosity ratio of 200 is

selected. The turbulent viscosity ratio is often used in low turbulence models to show the

importance of turbulence to the flow. Turbulent viscosity ratio is the ratio of the viscosity of a

turbulent fluid to that of the typical molecular viscosity. The ratio of 200 is recommended by

CD-Adapco. A turbulence source option of Ambient within the region was also selected. Adding

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an ambient turbulence adds terms to the K-Omega turbulence model to counteract the turbulence

decay that typically happens in external aerodynamics simulations.

MONITORING AND RESULTS

To monitor the convergence of the simulation and the key designs within the simulation,

two coefficient of force coefficient reports are created. One report, C_DF, measures the

coefficient of downforce (negative coefficient of lift). The other report measures the coefficient

of drag, C_DR. Both of the reports are fed the frontal area of the car through a Frontal Area

report. Only the car parts were selected for the drag and downforce reports, meaning that the tires

were not selected because the tires create their own vortices and large amounts of drag and

downforce that are not steady state, thus making it harder to determine if aerodynamic changes

actually affected the forces on the car.

To visualize the flow field, two derived parts are created. A section plane is created that

can be moved to areas of interest of the flow and streamlines are created to better visualize the

flow around the car. These derived parts are used in a scalar (Figure 11) and vector scene to

analyze the flow characteristics. Most important is that the flow does not separate from the

aerodynamics parts creating lower downforce and higher drag. Separation can be most easily

seen in the vector scene that is created.

Stopping criteria are setup that are based on an asymptotic convergence of both the

coefficient of drag and coefficient of downforce. The criteria is a Max-Min of 0.005 over 150

iterations. In the simulation showing the current design, the coefficient of downforce did not

converge, but instead had a periodic movement (Figure 13). To more accurately determine the

coefficient of downforce, an unsteady simulation should be performed. Because of the limited

amount of time left to complete the project, an unsteady simulation is impractical and will not be

performed.

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The final results of the simulation yielded a coefficient of drag of 0.545 and a coefficient

of downforce of 0.354. These are respectable results given the low complexity of the

aerodynamics package used on the FSAE vehicle.

THE USE OF SIMULATIONS

Over the last two years, the solutions to the simulations were used as a percentage

improvement versus a true indicator of drag and downforce created by the car due to a lack of

equipment and methodology to validate the simulations. In the spring, the Formula team will

most likely be purchasing a mobile data acquisition system, so there is a possibility of validating

the simulations before competition in June of 2014. To test the coefficient of drag, two coast

down tests can be performed and many calculations can get a coefficient of rolling friction and a

coefficient of drag. To validate the downforce, a skid pad test can be performed with and without

the aerodynamic devices to calculate a lateral acceleration, and can then be further calculated to a

change in downforce for many different radius skid pad tests.

This model and paper will be used by my predecessors on the team to help further

improve our aerodynamics package and our knowledge toward the topics of computational fluid

dynamics.

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APPENDIX

Figure 1: First iteration of undertray with straight bend at 7.5 degrees

Figure 2: Second Iteration of undertray utilizing 1/4 elipse and tunnels

Figure 3: Current design utilizing a parabolic shape

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Figure 4: Top view of undertray diffuser section labeling where the chassis ends and what section is considered the "tunnel"

Figure 5: Nosecone design showing angle of front to ground

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Figure 6: Imported parasolid geometry from SolidWorks

Figure 7: Windtunnel geometry created within Star-CCM+ showing a much larger volume than that taken by the formula car

Figure 8: Volume mesh showing much smaller cells near the formula car

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Figure 9: Symmetry Plane volume mesh around formula car

Figure 10: Volume mesh showing surfaces of 1/2 of formula car

Figure 11: Scalar scene on symmetry plane showing velocity magnitude of air moving around car

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Figure 12: Simulation Residuals showing a general downward trend and then flattening out toward end of simulation

Figure 13: Coefficient of Drag and Downforce monitors versus iteration showing an unsteady coefficient of downforce possibly due to vortices

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