Nonlinear Versus Linear Stress-Strain Relations in Engine Turbulence Modeling Under Swirl and Squish Flow Conditions

A general form of the stress-strain constitutive relation was introduced for the application of two nonlinear $k-ε$ turbulence models, namely, the algebraic Reynolds stress model of Gatski and Speziale (1993, “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” J. Fluid Mech., 254, pp. 59–78) and the cubic model of Lien et al. (1996, “Low Reynolds Number Eddy-Viscosity Modeling Based on Non-Linear Stress-Strain/Vorticity Relations,” Proceedings of Third Symposium on Engineering Turbulence Modeling and Measurements, Crete, Greece), to the numerical analysis of flow fields in a test engine with flat-piston and bowl-in-piston arrangements, under swirling and no-swirling flow motored conditions. The model capabilities in capturing turbulent flow features were compared to those of the upgraded linear RNG $k-ε$ model, which was previously indicated as a good compromise between accuracy and computational cost. Evaluations were made on the basis of the predicted flow evolution throughout the whole engine cycle, as well as of the comparison between the numerical and experimental results. Furthermore, the effect of the stress-strain relationship on the predicted averaged turbulence quantities and anisotropy-invariant values were examined, in addition to the sensitivity of the nonlinear models to the mesh quality. Finally, prospects concerning possible improvements of turbulence eddy-viscosity models were presented. The predictions were made by a newly developed CFD code embedding various accuracy-order finite-volume discretization schemes. Modified wall boundary conditions with respect to the conventional logarithmic-function approach were used, so as to make the local equilibrium hypothesis virtually ineffective.