A simple and robust linear eddy‐viscosity formulation for curved and rotating flows

Abstract

Purpose

The purpose of this paper is to present a new eddy‐viscosity formulation designed to exhibit a correct response to streamline curvature and flow rotation. The formulation is implemented into a linear k‐ ε turbulence model with a two‐layer near‐wall treatment in a commercial computational fluid dynamics (CFD) solver.

Design/methodology/approach

A simple, robust formula is developed for the eddy‐viscosity that is curvature/rotation sensitive and also satisfies realizability and invariance principles. The new model is tested on several two‐ and three‐dimensional problems, including rotating channel flow, U‐bend flow and internally cooled turbine airfoil conjugate heat transfer. Predictions are compared to those with popular eddy‐viscosity models.

Findings

Converged solutions to a variety of turbulent flow problems are obtained with no additional computational expense over existing two‐equation models. In all cases, results with the new model are superior to two other popular k‐ ε model variants, especially for regions in which rapid rotation or strong streamline curvature exists.

Research limitations/implications

The approach adopted here for linear eddy‐viscosity models may be extended in a straightforward manner to non‐linear eddy‐viscosity or explicit algebraic stress models.

Practical implications

The new model is a simple “plug‐in” formula that contains important physics not included in most linear eddy‐viscosity models and is easy to implement in most flow solvers.

Originality/value

The present model for curved and rotating flows is developed without the need for second derivatives of velocity in the formulation, which are known to present difficulties with unstructured meshes.

Citation

York, W.D., Walters, D.K. and Leylek, J.H. (2009), "A simple and robust linear eddy‐viscosity formulation for curved and rotating flows", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19 No. 6, pp. 745-776. https://doi.org/10.1108/09615530910972995