Turbulence Scales Adapted Formulation of the k-ε Model

Abstract

© 2019 by Ricardo Software, Ricardo UK. Published by the American Institute of Aeronautics and Astronautics, Inc. The paper describes a re-formulated version of the Yang and Shih [1] k − e model for near-wall turbulence. New features include enhanced production of the turbulent energy dissipation rate and adjustments to turbulence time and length scales. The enhanced dissipation rate production aims to replace effects of the mean velocities second order derivatives. The turbulence time scale has lower and upper bounds corresponding to the Kolmogorov and real-izability condition time scale, respectively. In order to limit the excessive levels of the turbulent length scale in the near wall regions (that plague the k − e model performances), two methods are formulated in addition to well known Yap’s correction term: namely, direct limiting via eddy-viscosity and indirect limiting using new formulation for the cross-diffusion term in the dissipation rate equation. The first method requires the wall distance field whereas the latter does not. The accuracy of the proposed model is assessed through comparisons of model variants predictions with experimental data for the flat plate boundary layer with zero–pressure gradient, flow over backward facing step and the axisymmetric impinging jet. The model performance for these type of wall bounded flows is found to be satisfactory. Overall, similar or better accuracy is achieved in comparison to other eddy-viscosity models employed for the tested flow benchmarks.