Multidimensional Predictions of In-Cylinder Turbulent Flows: Contribution to the Assessment of k-ε Turbulence Model Variants for Bowl-in-Piston Engines

Multidimensional computational fluid dynamics (CFD) codes with reliable turbulence models are useful investigation and design tools for internal combustion engines, in-cylinder flow phenomena being critical to the combustion process and related emission sources. Although a variety of turbulence models has long been proposed, the assessment of even the most widely used $k-ε$ model is still lacking, especially for bowl-in-piston engines. This paper provides a survey of $k-ε$ turbulence model variants and their numerical implementation for in-cylinder flow analysis. Mean motion and turbulence quantities were simulated in the axisymmetric combustion chamber of a motored model engine featuring one centrally located valve and each of a flat-piston and cylindrical bowl-in-piston arrangements. A noncommercial CFD code developed by the authors was applied for calculation, using a finite-volume conservative implicit method and applying various order-of-accuracy numerical schemes. Simulation results are presented at the engine speed of 200 rpm throughout the whole engine cycle. These were obtained using three $k-ε$ turbulence model versions, standard, renormalization group (RNG) and two scale, each of which focuses on one main engine flow feature, i.e., compressibility, anisotropy, and high unsteadiness, respectively. Modified boundary conditions with respect to conventional logarithmic wall functions were applied. Effects of equation-differencing scheme and computational-grid spacing effects on flow predictions were tested. The numerical results were compared to those of laser Doppler velocimetry measurements and the influence of the $k-ε$ model variants on the flow-field features was examined during the induction stroke and around compression top dead center. For the flat-piston case, a comparison between the homemade and commercial STAR-CD® code results was also made.