Application of spectral/hp element methods to high-order simulation of industrial automotive geometries

Abstract

Flow predictions around cars is a challenge due to massively separated flow and complex flow structures generated. These flow features are usually poorly predicted by present industrial computational fluid dynamics (CFD) codes based on a low fidelity Reynolds averaged Navier Stokes (RANS) approach simulating the mean effects of turbulence. On the other hand, high fidelity approaches resolve turbulent scales but require many more degrees of freedom than classical techniques for an accurate solution. Previous applications have shown that the coupling of the spectral/hp element method and implicit large eddy simulation (iLES) turbulence treatment could be a potential candidate to perform high-fidelity simulations. This work aims at transferring the spectral/hp element technology to the automotive industry in which high Reynolds numbers and complex geometries are typical. Recent developments in stabilisation techniques such as the discontinuous Galerkin kernel spectral vanishing viscosity (SVV) and high-order meshing capabilities open the possibility of the application of the spectral/hp element method to complex cases. The technology is first implemented to an industrial case proposed by McLaren Automotive Limited (MLA) at a realistic Reynolds number of 2,3 million based on the front wheel diameter and is compared to a RANS numerical development tool. Differences in terms of vortical structures arrangement, principally due to the front wheel wake are highlighted. In parallel, a workflow is developed to systematically address similar complex cases. The interaction between h-refinement, related to the size of the elements of the mesh, and p-refinement, corresponding to the polynomial expansion order, is investigated on the SAE notchback body. Two different hp-refinement strategies with similar numbers of degrees of freedom are employed, the first one with a fine mesh and a third-order accurate polynomial expansion and the second one with a coarse mesh and a fifth-order accurate polynomial expansion. Results show that a minimum level of h-refinement is necessary to capture flow features and that p-refinement can subsequently be used to improve their resolution. The final part focuses on wheel rotation modelling. Scale-resolving techniques are intrinsically unsteady and therefore require sophisticated techniques to correctly model rotating wheels. A procedure, built upon an immersed boundary method (IBM) called the smoothed profile method (SPM), is developed to model complex three-dimensional rotating geometries, in particular rim spokes. It is finally applied to an isolated rotating wheel case and results are compared to the moving wall (MW) and the moving reference frame (MRF) modelling techniques. It is concluded that the SPM is in better qualitative agreement with experimental results present in the literature than the two other modelling strategies.