A rational model for the turbulent scalar fluxes

Abstract

The paper reports on an alternative approach to modelling the turbulent scalar fluxes that arise from time averaging the transport equation for a scalar. In this approach, a functional relationship between these fluxes and various tensor quantities is constructed with guidance from the exact equations governing the transport of fluxes. Results from tensor representation theory are then used to obtain an explicit relationship between the fluxes and the terms in the assumed functional relationship. Where turbulence length– and time–scales are implied, these are determined from two scalar quantities: the turbulence kinetic energy and its rate of dissipation by viscous action. The general representation is then reduced by certain justifiable assumptions to yield a practical model for the turbulent scalar fluxes that is explicit and algebraic in these quantities and one that correctly reflects their dependence on the gradients of mean velocity and on the details of the turbulence. Examination of alternative algebraic models shows most to be subsets of the present proposal. The new model is calibrated using results from large–eddy simulations (LESs) of homogeneous turbulence with passive scalars and then assessed by reference to benchmark data from heated turbulent shear flows. The results obtained show the model to correctly predict the anisotropy of the turbulent diffusivity tensor. The asymmetric nature of this tensor is also recovered, but only qualitatively, there being significant quantitative differences between the model predictions and the LES results. Finally, comparisons with data from benchmark two–dimensional free shear flows show the new model to yield distinct improvements over other algebraic scalar–flux closures.

Thermal Transport and Entropy Production Mechanisms in a Turbulent Round Jet at Supercritical Thermodynamic Conditions

“…Moreover, it can be seen that with increasing axial distance, the heat fluxes are returning slightly to the isotropic state, but do not reach a fully-isotropic behavior. This suggests, that extended heat flux models might be appropriate in the context of RANS, as proposed in [42][43][44] and others from investigations in subcritical applications.…”

Measurements of turbulent diffusion in uniformly sheared flow

“…Corrsin (1974) suggested that the asymptotic values of the turbulent diffusivities could be estimated from Eulerian properties, as surrogates for their Lagrangian counterparts, for example as D 22 ≈ u ′2 2 T 11 . Additional theoretical arguments have been made by Tavoularis & Corrsin (1985), Rogers et al (1989) and Younis et al (2005) to derive asymptotic expressions for the turbulent diffusivity tensor components in shear flows. These theories will be revisited in a later section.…”

Prediction of momentum and scalar transport in turbulent swirling flows with an objective Reynolds-stress transport closure

“…Recently developed algebraic scalar-flux models (e.g. [19,20]) are capable of obtaining anisotropic turbulent diffusivities and thus have the potential of obtaining predictions that are comparable to those of the scalar-transport closure. …”