kεα: a three‐equation eddy‐viscosity model of turbulence

Abstract

Purpose

To provide an eddy‐viscosity turbulence model that accounts for the non‐equilibrium shape of the energy spectrum and for the effect of velocity correlation on turbulent viscosity.

Design/methodology/approach

The turbulence model is built using the standard kε model as the starting point. It is suggested that the character of turbulence depends on the time elapsed since its generation. Therefore, a local variable named “age of turbulence” or α, is defined and its transport equation is derived. Two hypotheses are formulated. The first one is that the shape of the energy spectrum depends on α. The second one is that also the effect of velocity correlation on turbulent viscosity is a function of α, in analogy with the dispersion coefficient of a particle in a turbulent flow. Hence, expressions for the characteristic time scaleτ_T and the turbulent viscosity ν_T are proposed and they are integrated in the standard kε model, resulting in a three equation model named here kεα. The expressions of ν_T and τ_T reduce to those of the kε model in decaying turbulence, and deviate from them in recently produced turbulence. The empirical constants are calibrated and various benchmark experiments are simulated.

Findings

A comparison between computed results and experimental data show that the kεα model is generally more accurate than the standard kε model.

Originality/value

The “age of turbulence” has not been used previously to characterise turbulence. The work is especially relevant for combustion/reacting applications, where the expression of the characteristic turbulence time scale is crucial for the estimation of the reactant mixing rates.

Citation

Ghirelli, F. (2007), "kεα: a three‐equation eddy‐viscosity model of turbulence", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 2, pp. 140-164. https://doi.org/10.1108/09615530710723939