kappa epsilon alpha: a three-equation eddy-viscosity model of turbulence

Journal article, 2007

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 k epsilon 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 alpha, 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 a. The second one is that also the effect of velocity correlation on turbulent viscosity is a function of alpha, in analogy with the dispersion coefficient of a particle in a turbulent flow. Hence, expressions for the characteristic time scale tau(T) and the turbulent viscosity v(T) are proposed and they are integrated in the standard k epsilon model, resulting in a three equation model named here k epsilon alpha. The expressions of v(T) and tau(T) reduce to those of the k epsilon 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 k epsilon alpha model is generally more accurate than the standard k epsilon 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.