Present Status of Second-Order Closure Turbulence Models. I: Overview

An overview of the second-order closure turbulence models is presented in this paper. Models studied include the k-ε-eddy viscosity model, k-ε-nonlinear Reynolds stress model, differential Reynolds stress model, k-ε algebraic stress model, near-wall second-order closure model, low-Reynolds number model, two-layer model, and multiscale model, which cover the efforts of scientists and engineers over the past 50 years. However, at the present time, there exists no unified turbulence model. Each model applies successfully to some turbulent flows, while it predicts unsatisfactory results for other flows, especially for flows that are very different from those for which the models were calibrated. To improve the prediction accuracy and the applicability of the existing turbulence models, modifying, or even remodeling, the ε equation, the dissipation rate of turbulent kinetic energy, and pressure-strain terms of the Reynolds stress, uiuj¯, equations is necessary.