A Modified Dissipation Equation for Reynolds Stress Turbulent Mixing Models

Abstract

A simple modification of the dissipation equation is proposed for augmented Reynolds stress models (RSM) devoted to the prediction of buoyancy-driven turbulent mixing at interfaces. It is based on the partition of the kinetic energy into a “directed” large-scale part related to the turbulence mass flux and a “nondirected” small-scale part internal to the interpenetrating fluid structures. Such a partition is a cornerstone of some two-fluid models but does not appear naturally in the RSM framework. Conditional averaging on the concentration is used as a simple way to provide an equivalent decomposition with the variables available in the augmented RSM. Defining a dissipation equation mimicking the “nondirected” energy rather than the full kinetic energy does not introduce any new coefficient, preserves the properties of the original RSM, and improves its transient behavior in response to a sudden acceleration of the flow. Connections can finally be drawn between the resulting model and two-scale models.