Simulating Rotating Wheel Aerodynamics for the Bridgestone World Solar Challenge

Every two years, competitors worldwide set out on a grueling race across the Australian outback: the Bridgestone World Solar Challenge. This challenge is inclined towards promoting research on solar cars as a step towards sustainable transportation.

Blue Point, the car that won the World Solar Challenge in 2019, was designed and engineered by a Belgium-based team Agoria. Team Agoria constitutes thesis students from Katholieke Universiteit (KU) Leuven, some of the brightest minds in the field of vehicle design and engineering. While designing solar-powered cars, drag reduction is essential for minimizing power consumption. So, to find an optimum design within the set rules of the challenge, team Agoria ran multiple simulations using Cadence Fidelity CFD. The team tested multiple design changes using the high-fidelity mesh generation and simulation platform for optimum vehicle performance.

How Does the Rotation of Wheels Affect Drag?

In some of the earlier aerodynamic simulations of the car, the wheels were not considered or were assumed to be static. But this study focuses on the wheels, and simulations of the solar car were performed using both rotating and stationary wheels to evaluate the impact of rotation on the car’s total drag.

As a starting point, results from the literature review, i.e., previous simulations of the car without wheels, were considered. To reduce the computational time, the rim and tire were simplified. For example, the tire grooves were not considered, the wheel arch was simplified, and the gap for the suspension was closed, neglecting the flow inside the car. In addition, only half of the car was simulated.

Simplified tire, rim, and wheel arch (left); the position of the wheel in the car (right).

Meshing and Simulation Set-Up

From a CAD file in Parasolid format, a full hexahedral mesh with around 11.5 million cells was generated using Fidelity Hexpress. Further, the different surfaces were grouped automatically, simplifying the simulation process. By segregating all the narrow fillet surfaces in a separate group,  refinements were executed easily, allowing accurate capture of the curvature while maintaining the minimum possible cell count. In this manner, the car's leading and trailing edges were also captured precisely through an appropriate refinement.

 Full hexahedral mesh at the leading edge of the car on a y-constant cut plane.

Results

The simulations were run on a 26-core, 160 GB RAM workstation at the Applied Fluid Mechanics and (Aero) Acoustics research group at KU Leuven, campus Groep T Leuven. At first, a steady simulation was performed in 52 hours, corresponding to 4.5 CPU.h/M points. For unsteady simulations, the stationary wheels took 440 hours to stabilize, while the rotating wheels took only 44 hours. This difference can be entirely attributed to the vortex shedding observed in the case of stationary wheels. Moreover, the amplitude and frequency of vortex shedding were significantly reduced due to the rotating wheels.

Bottom view of the velocity for stationary (left) and rotating (right) wheels.

Q-Invariant and surface streamlines (red) on a vertical cut plane downstream of the car (x=-1.8). Stationary wheels (left) show vortex shedding compared to the rotating wheels (right).

The impact of rotating wheels on skin friction drag was subtle, while the pressure drag was significant. The simulation results also establish that the front wheels had higher pressure drag than the back wheels. This is explained by the lower stagnation pressure in the back wheel. Moreover, the flow approached the back wheel from the vortex shedding caused by the front wheel. The pressure in the wake just downstream of the front wheel (on the left) was lower than the pressure in the wake of the back wheel (on the right).

Bottom view of static pressure on the horizontal cut.

It was noted that the rotation of the wheels reduces drag by approximately 40%. This significantly impacts the car design as the coefficient of aerodynamic drag, C_dA, reduces by 10%. The simulations provide a detailed insight into the flow field around the rotating wheels. A small recirculation zone is observed at the front of the wheel and around the wheel arch. Here, the flow from upstream, between the wheel and the wheel arch, joins into a single flow stream.

Streamlines colored by velocity around the front tire.

Conclusion

This work with Fidelity Hexpress and Fidelity Flow provides a deeper understanding of the flowfield around rotating wheels and its impact on pressure drag. Rotation of the wheels results in a 40% decrease in drag on the wheels and a 10% reduction in C_dA of the complete car. This case study increases our confidence in simulation solutions as the results are very close to experimental testing (both on-road and wind tunnel testing).

References

1. Borgions K., Holemans T., Aerodynamic simulation of rotating wheels in a solar car. KU Leuven, Faculty of Engineering Technology. Master thesis, 2019.
2. Vandervelpen E., Uten J., Testing of turbulence models for the aerodynamic simulations of a solar car, KU Leuven, Faculty of Engineering Technology. Master thesis, 2018.

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Authors: 

Thomas Holemans, Kristof Borgions, and Maarten Vanierschot, campus Groep T Leuven, KU Leuven.

Colinda Francke, Senior Product Engineering Manager, Cadence.

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