Data-driven uncertainty quantification for Formula 1: Diffuser, wing tip and front wing variations

Abstract

This work introduces a new uncertainty quantification method to better deal with scarce data and long simulation run times in Formula 1 design. Race cars are produced in low quantities and for maximum performance. Thus, their designing process is characterised by manufacturing data shortage and complex Computational Fluid Dynamics simulations with long run times. Their car aerodynamics is subject to many random variables that introduce uncertainty into the down-force and drag performance, such as variations in ride height, front wing direction and pitch angle. To accurately predict the car performance during a race, it is important to study the effect of these random variables. This assessment cannot be performed with the standard deterministic Computational Fluid Dynamics approaches used in Formula 1. Even with regard to stochastic approaches, no efficient method has so far been suggested that addresses the problem of data scarcity. The reason for this is that most efficient uncertainty quantification methods fit probability distributions to the scarce data. It is shown in this work that probability distribution fitting can create a significant error using a simple two-dimensional diffuser example. Subsequently, the use of a new data-driven Polynomial Chaos method and its sparse multi-dimensional extension is suggested and demonstrated for Formula 1 to reduce such errors. This method allows to avoid distribution fitting because it is based on pure data. SAMBA’s general formulation also makes it easier to combine any possible inputs within a sparse description for problems with many variables. SAMBA is applied to two realistic car three-dimensional Computational Fluid Dynamics simulations: a NACA 0012 tip wing and the front part of a Formula 1 car. The probabilistic variations of the lift and drag of these two configurations are calculated using SAMBA and shown to be significant.

Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems

“…In such high-dimensional cases, correlations may exist between the uncertain parameters. These issues are dealt with in the gPC literature with the use of sparse grids, data-driven techniques, or variational approaches, [1,3,32].…”

“…However, in real-life applications, the system behavior is significantly affected by parametric uncertainties. As an example, geometric uncertainties in the shape of the front wing, diffuser, and the tip of a Formula (1) can affect its performance [1]. A small selection of other examples can be found in References [2][3][4][5].…”

Computational Investigation of the Aerodynamics of a Wheel Installed on a Race Car with a Multi-Element Front Wing

“…The CFD model setup was crucial for correctly comparing different racing scenarios [37] or for investigating the effect of the wake on the following car [38]. Moreover, car aerodynamics are subject to a number of random variables that introduce uncertainty into the downforce performance; the effects of the random variations in these parameters are important to accurately predict a car's performance during the race [39,40]. The authors carried out a fluid dynamics analysis of a multielement front wing with a Gurney flap on a Formula 1 car [41] and an extensive aerodynamics analysis on the profile of the ground effect with the Gurney flap to investigate the vortex-shedding phenomena that can occur in certain conditions [42].…”

Study of the Effect of Vertical Airfoil Endplates on Diffusers in Vehicle Aerodynamics

“…The progress of vehicle aerodynamics, as a combination of the test process in wind tunnels and computational fluid dynamics (CFD), has significantly evolved in recent years in both road and motorsports cars [10]. CFD deserves special attention for its rapid advance in terms of simulation capability, accuracy, predictability, and software availability, and has allowed researchers around the world that cannot afford wind tunnel facilitates to contribute towards field predicting, for instance, the uncertainty of the car set-up [11,12].…”