Uncertainty quantification and race car aerodynamics

Car aerodynamics are subjected to a number of random variables which introduce uncertainty into the downforce performance. These can include, but are not limited to, pitch variations and ride height variations. Studying the effect of the random variations in these parameters is important to predict accurately the car performance during the race. Despite their importance the assessment of these variations is difficult and it cannot be performed with a deterministic approach. In the open literature, there have been no studies dealing with this uncertainty in car racing aerodynamics modelling the complete car and assessing the probability of a competitive advantage introduced by a new geometry. A stochastic method is used in this work in order to predict the car downforce under stochastic variations and the probability of obtaining a better performance with a new diffuser geometry. A probabilistic collocation method is applied to an innovative diffuser design to prove its performance with stochastic geometrical variations. The analysis is conducted using a complete three-dimensional computational fluid dynamics simulation with a k-ω turbulence closure, allowing the performance of the physical diffuser to be more accurately represented in a stochastic real environment. The random variables included in the analysis are the pitch variations and the ride height variations in different speed conditions. The mean value and the standard deviation of the car downforce are evaluated. © IMechE 2014

Efficient Uncertainty Quantification of Turbulent Flows through Supersonic ORC Nozzle Blades

This work aims at assessing different Uncertainty Quantification (UQ) methodologies for the stochastic analysis and robust design of Organic Rankine Cycle (ORC) turbines under multiple uncertainties. Precisely, we investigate the capability of several state-of-the art UQ methods to efficiently and accurately compute the average and standard deviation of the aerodynamic performance of supersonic ORC turbine expanders, whose geometry is preliminarily designed by means of a generalized Method Of Characteristics (MOC). Stochastic solutions provided by the adaptive Simplex Stochastic Collocation method, a Kriging-based response surface method, and a second-order accurate Method of Moments are compared to a reference solution obtained by running a full-factorial Probabilistic Collocation Method (PCM). The computational cost required to estimate the average adiabatic efficiency, Mach number and pressure coefficient, as well as their standard deviations, to within a given tolerance level is compared, and conclusions are drawn about the more suitable method for the robust design of ORC turbines

Subcell resolution in simplex stochastic collocation for spatial discontinuities

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC–SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers’ equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC–SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples