Spectral/hp large eddy simulation of vortex-dominated automotive flows around bluff bodies with diffuser and complex front wing geometries

Abstract

In this research project, it is demonstrated the use of spectral/hp element method for simulations of fully 3D complex geometries. Such solutions at high Reynolds numbers and with higher order polynomials were previously intractable due to numerical stability issues affecting the convergence of the scheme. For this approach, we have employed the latest development of continuous Galerkin spectral vanishing viscosity (CG-SVV) with a discontinuous Galerkin (DG) mimicking kernel. Together with dealiasing techniques, the numerical stability and convergence characteristics of the spectral/hp element method have been greatly improved. These advances in numerical methods are also supported by novel meshing strategies, taking advantage of the additional flexibility in changing the uniform polynomial orders of the mesh and the solution. As a result, efficient simulations can be formulated with consistent and highly accurate solutions obtainable.

Specific for this work, the focus is on complex geometries often found in automotive engineering. To reduce the computational demands, this research explored the use of symmetry boundary conditions for large eddy simulations (LES) using a half model. It is found that if only the average flow properties near the body are of interest, such an approach can provide more than 50% reduction in simulation time while maintaining the solution quality. In terms of improving the solution resolution, as one might expect from a p-type method we have observed that increasing the polynomial order can be a more effective approach in comparison to conventional mesh refinement. In the three test cases, we have successfully exploited the use of polynomial accuracy of 4th, 5th and 6th order. This is the first comprehensive study using polynomials of such high orders, and the corresponding solutions are obtained for fully 3D geometries using spectral/hp element method.

Three test cases have been considered, the first being the simulations of the original Ahmed Body serves as a validation study for 3D simulations of the spectral/hp element method. The Ahmed Body is one of the most widely studied bluff bodies used for automotive conceptual studies and computational fluid dynamics (CFD) software validation. For this validation study, the differences in results obtained using various polynomial orders for the mesh as well as for the solution interpolation have been examined in detail. With the proposed approach, we were able to obtain fairly good correlations with the aerodynamic quantities for polynomial orders of 5 and above. Regarding the flow features around the body, solutions from the 6th order polynomial showed clear advantage in the slant vortex intensity. With the computational facilities, further increase of solution polynomial order is not feasible; however, the required solution resolution can also be obtained via the use of local mesh refinement. We determine that this level of solution accuracy, after comparing with various studies in the literature, cannot be obtainable using steady-state simulations such as the very popular Reynolds averaged Navier-Stokes (RANS) method.

Based on the validation result, the second test case involved the simulations of Ahmed Body geometries with a simplified diffuser using the proposed method. This case serves as an independent study examining the suitability of the method for design analysis. Using the same 6th order polynomial and Refined mesh, the solution successfully identified the flow features consistent with to past literature on underbody diffusers. Additionally, we have found that the geometry of the reference body imposes a quite significant influence on the performance of the diffuser, as well as identified some strong interplay between the lower-side vortex and the diffuser flow. The toolchain has clearly demonstrated its capability in assisting integrated design analysis for a simplified road vehicle equipped with a diffuser.

In the final test case, a new benchmark study case for aerodynamic design of high-performance vehicles and racing cars, the Imperial front wing is proposed. This study consists of a multi-element front-wing based on a Formula One front wing design. It generates complex flow features including ground effects, and multiple vortex system development and interaction. We used this test case as a challenging examination of our proposed method and simulation strategy using the spectral/hp element method. The simulations were also supported by an independent experimental study and results obtained for comparison achieved a high level of agreement. Using a polynomial order of 4th and above have successfully correlated the flow velocity fields at various planes downstream, while increasing the polynomial order to 5th will further result in a good matching of flow visualisation details.

From all three test cases, the spectral/hp element method when applied to suitable meshes at reasonably polynomial orders has been able to accurately and consistently yield reliable solutions in good agreement with experiment. The benefits of using high order polynomials for mesh generation of complex geometries, and for solution interpolation of higher accuracy have enabled the use of much coarser meshes than would typically be applied in commercial CFD codes. The progress made in this research is a solid step forward for the adaptation of the spectral/hp element for industrial level applications.