A Modified Model for Diffusion in Second-Moment Turbulence Closures

A study has been carried out to determine the relative roles of the three diffusion sub-processes contained in the Lumley (1978) diffusion model. The three sub-processes are described as being the production of turbulent transport, the third-order pressure-velocity process, which regulates the relative magnitudes of the turbulent transport components, and the pressure-diffusion. The present work describes a unique method for calibrating the model based on an analysis of zero-mean-shear turbulence. On the basis of the analysis, and using recent direct numerical simulation and experimental data, the coefficients in the Lumley (1978) model are modified such that the model gives the correct behavior in the diffusive limit. The modified model was then validated by carrying out CFD predictions for three benchmark flows of engineering interest. The modified Lumley (1978) diffusion model has two clear advantages over the more commonly used Daly and Harlow (1970) model. First, unlike the Daly and Harlow (1970) model, the modified Lumley (1978) model is mathematically correct and second, it was shown in the present validation that the modified Lumley (1978) model gives the most consistently reasonable predictions.