Numerical Methods and Turbulence Modeling for LES of Piston Engines: Impact on Flow Motion and Combustion

Abstract

In this article, Large Eddy Simulations (LES) of Spark Ignition (SI) engines are performed to evaluate the impact of the numerical set-upon the predictedflow motion and combustion process. Due to the high complexity and computational cost of such simulations, the classical set-up commonly includes “low” order numerical schemes (typically first or second-order accurate in time and space) as well as simple turbulence models (such as the well known constant coefficient Smagorinsky model (Smagorinsky J. (1963) Mon. Weather Rev. <b>91<b/>, 99-164). The scope of this paper is to evaluate the feasibility and the potential benefits of using high precision methods for engine simulations, relying on higher order numerical methods and state-of-the-art Sub-Grid-Scale (SGS) models. For this purpose, two high order convection schemes from the Two-step Taylor Galerkin (TTG) family (Colin and Rudgyard (2000) J. Comput. Phys. <b>162<b/>, 338-371) and several SGS turbulence models, namely Dynamic Smagorinsky (Germano et al. (1991) Phys. Fluids <b>3<b/>, 1760-1765) and sigma (Baya Toda et al. (2010) Proc. Summer Program 2010, Stanford, Center for Turbulence Research, NASA Ames/Stanford Univ., pp. 193-202) are considered to improve the accuracy of the classically used Lax-Wendroff (LW) (Lax and Wendroff (1964) Commun. Pure Appl. Math. <b>17<b/>, 381-398) - Smagorinsky set-up. This evaluation is performed considering two different engine configurations from IFP Energies nouvelles. The first one is the naturally aspirated four-valve spark-ignited F7P engine which benefits from an exhaustive experimental and numerical characterization. The second one, called Ecosural, is a highly supercharged spark-ignited engine. Unique realizations of engine cycles have been simulated for each set-up starting from the same initial conditions and the comparison is made with experimental and previous numerical results for the F7P configuration. For the Ecosural engine, experimental results are not available yet and only qualitative comparisons are performed to enforce the analysis and conclusions made on the F7P configuration. Regarding SGS models, only slight differences are found at the aerodynamic level even if sigma allows a better resolution of small structures of the velocity field. However, all results are in cycle-to-cycle variability envelopes from Granet (Granet et al. (2012) Combust. Flame <b>159<b/>, 1562-1575) and these single cycle computations don’t permit to distinguish clear improvements on macroscopic parameters such as resolved kinetic energy, heat release or mean in-cylinder pressure. Concerning numerical schemes, TTG schemes also allow a slighlty better resolution of small scale vortices but global quantities such as resolved kinetic energy and SGS viscosity are comparable. Nevertheless, clear differences appear between the different schemes in the combustion stroke. This is attributed to a better resolution of the flame-turbulence interaction process during the free flame propagation period, leading to an increase of the resolved part of heat release. It is also shown in this paper that an adjustment of the efficiency constant in the Thickened Flame (TF) model is compulsory to account for the over dissipation of the smallest resolved structures if LW is used. In the light of these conclusions an hybrid setup, called ES O<sub>2<sub/> (Engine Stroke Optimal Order), which consists in using TTGC during combustion and LW elsewhere is proposed and applied to the two engines configurations. Results are in good agreement with the ones obtained in the case of a full TTGC simulation, while the CPU (Central Processing Unit) cost increase is only about 10% compared to LW. The accuracy of LW seems therefore to be sufficient for pure aerodynamic phases, while the use of TTGC only during combustion permits an improvement in the LES quality. The hybrid ES O<sub>2<sub/> method thus appears as an attractive approach to improve further calculations accuracy without being greatly penalized by additional CPU costs in multi-cycle simulations.