Kirchner, Paul

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  • Aerodynamic Optimization of a Formula SAE Body Paul G. Kirchner and Dr. Gary Mead

    Department of Automotive Engineering Technology, Minnesota State University Mankato


    Cebeci, Tuncer, and J Cousteix. Modeling And Computation of Boundary-layer Flows: Laminar, Turbulent And Tran-sitional Boundary Layers In Incompressible And Compressible Flows. 2nd rev. and extended ed. Long Beach, Ca-lif.: Horizons Publishing , 2005.

    Cooper, K. R. Bertenyi, T. Dutil, G. Syms, J. Sovran, G. The Aerodynamic Performance of Automotive Underbody Diffusers, SAE 980030, 1998

    Katz, Joseph. Race Car Aerodynamics: Designing for Speed. Cambridge, MA, USA: R. Bentley, 1995.


    I would like to thank the Northstar STEM Alliance for their funding contribution.

    I would also like to proudly thank Dr. Bruce Jones, Dr. Gary Mead, Dr. Jeffrey Doom, Kevin Schull,

    and Winston Sealy for all their help and support throughout this project.


    To analyze fluid dynamics turbulence models accuracy in calculating qualitative and quan-

    titative data.

    To understand the significance sidepod size and geometry play in engine heat manage-


    To understand the significance diffuser angle, throat positioning, and length play in under-

    tray performance.

    To optimize the vehicles undertray and sidepod design to produce the highest obtainable


    Formula SAE is the largest collegiate engineering competition in the nation organized by the So-

    ciety of Automotive Engineers. The competition challenges engineering programs from around

    the world to design and manufacture a small Formula-style race-car. The design process in-

    cludes all components of the automotive industry, including research, development, marketing,

    and financial management. For the 2012 competition in an effort to increase cornering speeds

    and cooling system reliability, MSU-Mankatos body was aerodynamically analyzed using com-

    putational fluid dynamics. The sidepod which houses the vehicles radiator, was altered focusing

    mainly on the effects of inlet size, length and shroud geometry. An undertray, which mount to

    the vehicles underbody, was designed utilizing diffusers to increase downforce, the vertical

    load provided by aerodynamic forces, as opposed to mass. The diffuser sections were simulat-

    ed focusing on the effects of inlet area, ramp angle, and length.

    Figure 1. Final CAD model of MSUMankatos 2012 Formula SAE Car.


    Figure 2. Engineering Laboratory Design 402 Wind Tunnel Figure 3. Front half of 1/8 scale model for validation

    CD-Adapcos Star+CCM Computational Fluid Dynamic software, with internal mesh gen-


    Due to the complexity of a Formula SAE cars geometry, initial simulations were run using

    a simplified bluff body, and symmetry plane implemented along the vehicles centerline

    to minimize the computational fluid domain.

    All initial simulations were run with an inlet velocity set to 35 mph, the average speed of

    a Formula SAE vehicle during an endurance run.

    Wind tunnel validation using ELDs model 402 wind tunnel.

    Helium Bubble Generator for flow visualization validation.

    Sidepod A Sidepod B Sidepod C

    Inlet Size (in) 8.45 in x 11 in 8.45 in x 15.25 in 11.5 in 18.5 in

    Inlet Area (in^2) 93.6 in^2 120.3 in^2 170 in^2

    Inlet/Rad (%) 80% 100% 145%

    Flow Rate (kg/s) 0.5438 0.5817 0.644

    Drag Force (lbf) 4.74 5.22 6.6

    Lift Force (lbf) 0.165 0.14 0.498

    Each sidepod was initially analyzed alone to ensure a maximum cell count of 500,000 cells to keep

    the simulation within the computers computational limits.

    The sidepods inlet area was altered between 80% and 145% of the radiator core size to analyze

    the effects the turbulent air behind the wheel has on the quality of air the radiator is receiving.

    The pressure drop across the radiator was calculated using experimentally derived data, from

    which a 4th order polynomial as a function of velocity was derived. Using this data and coeffi-

    cients were calculated and set for a porous baffle interface Eq. 1


    A polynomial was fit for the fan using the manufacturer given flow rates and pres-

    sures, this fan curve was then set for a fan interface within the simulation. Eq. 2


    Figure 4. Streamlines with velocity profile provide simulated flow visualization.

    Figure 5. Pressure contour of undertray, showing center of pressure.


    Table 1. Size, flow rate, drag force, and lift force from 3 sidepod designs.

    Using previous research from several sources as

    a starting point, multiple undertrays were designed varying the diffuser angle from 10 to 16.

    The center of pressure was set at the vehicles center of gravity in the for-aft position. (Figure 5)

    After the initial undertray designs, it was evident that flow separation occurred near 15.

    (Figure 7)

    Several design changes followed after verifying the optimum angle, altering the inlet area 30%,

    adding vortex generators, and the final addition of a keel nearly doubling the downforce.

    The final undertray has a predicted gain of 49 lbs of downforce, and a decrease of 14 lbs drag.

    The final design has been rapid prototyped using fused deposition modeling. The 1/8 scale

    model will be used for wind tunnel validation, as well as flow visualization validation using a he-

    lium bubble generator.

    Figure 9. Final undertray v. no undertray downforce plot Figure 8. Streamline and pressure contour on final body.

    Figure 6. Downforce per diffuser angle. Figure 7. Drag force per diffuser angle