

Article
Capturing turbulent density flux effects in variable density flow by an explicit algebraic model
AbstractThe explicit algebraic Reynolds stress model of Grigoriev et al. [“A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation,” Phys. Fluids 25, 105112 (2013)] is extended to account for the turbulent density flux in variable density flows. The influence of the mean dilatation and the variation of mean density on the rapid pressurestrain correlation are properly accounted for introducing terms balancing a socalled “baroclinic” production in the Reynolds stress tensor equation. Applying the weakequilibrium assumption leads to a selfconsistent formulation of the model. The model together with a K ? ? model is applied to a quasionedimensional plane nozzle flow transcending from subsonic to supersonic regimes. The model remains realizable with constraints put on the model parameters. When density fluxes are taken into account, the model is less likely to become unrealizable. The density variance coupled with a “local mean acceleration” also can influence the model acting to increase anisotropy. The general trends of the behaviour of the anisotropy and production components under the variation of model parameters are assessed. We show how the explicit model can be applied to two and threedimensional mean flows without previous knowledge of a tensor basis to obtain the general solution. Approaches are proposed in order to achieve an approximate solution to the consistency equation in cases when analytic solution is missing. In summary, the proposed model has the potential to significantly improve simulations of variabledensity flows.

