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-1 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-1 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.

A Modified k-ε Model for Computation of Flows with Large Streamline Curvature

“…e above equations (3)- (9), along with the turbulent kinetic energy ( ) represent a nonlinear expression for the Reynolds stress tensor in terms of available mean �ow and turbulent statistical variables. In order to develop an improved linear eddy-viscosity model, York et al [6] adopted the �rst (linear) term in (3) to develop a semi-implicit expression for the turbulent viscosity coefficient. e process is to linearize the anisotropy tensor with respect to the mean strain rate.…”

“…All other details of the model, including model constants and two-layer near-wall treatment, are identical to those used in [6], and the reader is referred there for a complete description.…”

“…Alternatively, York et al [6] proposed a simple modi�ed form of the turbulent viscosity coefficient ( ) to incorporate rotation and curvature effects, and the resulting -model was validated by typical �ow cases such as rotating channel �ow, �-bend �ow, and internally cooled turbine airfoil con�ugate heat transfer. e model satis�es realizability and invariance principles and was presented as a simple "plug-in" for use with existing two-equation turbulence models.…”

“…e model satis�es realizability and invariance principles and was presented as a simple "plug-in" for use with existing two-equation turbulence models. e effect of curvature and rotation is included in the turbulent viscosity coefficient via the effective rotation rate magnitude term, which was approximated by York et al [6] based on the assumption that the local �ow conditions correspond to two-dimensional, simple shear �ow in a frame rotating with the �ow. For the test cases considered, the model was found to make a signi�cant improvement in two-dimensional �ow problems.…”

“…e new eddy-viscosity coefficient expression was implemented into a two-layer -model in the same manner as that in [6]. In the present study, the model was tested for two representative �ow problems.…”