An alternative to gradient diffusion models for material transport in Reynolds-averaged methods

Reynolds-Averaged Navier-Stokes (RANS) models often utilize gradient diffusion approximations for terms representing the transport of various quantities by turbulent velocity fluctuations, and thus model material mixing as a diffusion process with some turbulent viscosity. While reasonable in many canonical flows, this approach cannot capture shrinking mixing layers that may be observed in more complex situations such as when a strongly Rayleigh-Taylor stable pressure gradient is introduced onto an already developed mixing layer. We extend the Besnard-Harlow- Rauenzahn (BHR) family of variable density turbulence model to track transport equations associated with the turbulent transport and fluctuations in species mass fraction for each material, and show that the inclusion of these terms improves its ability to model certain phenomena associated with stabilized mixing layers. Although additional equations are introduced, they do not require new empirically tuned coefficients or closure models because the added equations may be derived directly from existing closures in the model. The approach employed here should be straightforward to extend to other variable density RANS models, so long as they track an equation for the turbulent mass flux.