A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

TLDR

The study compares its new model against the standard k‑ε eddy viscosity model. The paper proposes a new k‑ε eddy viscosity model with a revised dissipation‑rate equation and realizable eddy‑viscosity formulation. The model introduces a dissipation‑rate equation derived from the mean‑square vorticity fluctuation dynamics and a realizable eddy‑viscosity formulation, and is validated on a range of high‑Reynolds‑number flows against experimental data. The unified‑coefficient model accurately predicts diverse turbulent flows and outperforms the standard k‑ε model.

Abstract

A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.