A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation

Authors: Grigoriev, I.G., Wallin, S.W., Brethouwer, G.B., Johansson, A.V.J.
Document Type: Article
Pubstate: Published
Journal: Physics of Fluids
Volume: 25   105112
Year: 2013


The explicit algebraic Reynolds stress model of Wallin and Johansson [J. Fluid Mech.403, 89 (2000)] is extended to compressible and variable-density turbulent flows. This is achieved by correctly taking into account the influence of the mean dilatation on the rapid pressure-strain correlation. The resulting model is formally identical to the original model in the limit of constant density. For two-dimensional mean flows the model is analyzed and the physical root of the resulting quartic equation is identified. Using a fixed-point analysis of homogeneously sheared and strained compressible flows, we show that the new model is realizable, unlike the previous model. Application of the model together with a K ? ? model to quasi one-dimensional plane nozzle flow, transcending from subsonic to supersonic regime, also demonstrates realizability. Negative “dilatational” production of turbulence kinetic energy competes with positive “incompressible” production, eventually making the total production negative during the spatial evolution of the nozzle flow. Finally, an approach to include the baroclinic effect into the dissipation equation is proposed and an algebraic model for density-velocity correlations is outlined to estimate the corrections associated with density fluctuations. All in all, the new model can become a significant tool for CFD (computational fluid dynamics) of compressible flows.