Hybrid aerodynamic shape optimization of an undertray by using a novel parametric exponential–sigmoid diffuser design and adjoint-based full car simulation

A proper undertray and diffuser design is critically important in racing car aerodynamics, since it can increase downforce with reduced drag by enhancing the ground effect. However, the range of possibilities is wide, but constrained by regulations and without clear design paths to follow. This work proposes a parametric diffuser shape design based on a parametric exponential–sigmoid equation, which is used for 2D parametric optimisation via Kriging surrogates plus nested Halton sequence refinements. For the full undertray design, up to eight design parameters are considered to control the geometry of the leading edge and diffuser. After integration into the 3D full car model, the optimal design is simulated and compared to the current baseline which was designed through a traditional iterative process. In a second stage, the adjoint optimisation method is then applied onto the parametric-based optimal design for further refinement of the shape by focusing on improving the lift-to-drag ratio of the complete vehicle, which involves the 3D simulation with rotating wheels and other parts of the aerodynamic package during the adjoint iterations. A deep discussion on the performance and flow physics involved is carried out. In conclusion, the final hybrid shape design outperforms the lift-to-drag ratio of the baseline design by a massive 7.98%. This demonstrates that the proposed optimisation path of the customised exponential–sigmoid parametric diffuser shape equation plus an smart iterative CFD-based Halton sequence refinement and adjoint approach can lead to very efficient undertray designs. The contributions of this work may potentially set a precedent for further systematic developments in undertray design.