A family of explicit algebraic models for Reynolds stresses and passive scalar fluxes

A family of explicit algebraic models for Reynolds stresses and passive scalar fluxes is proposed and a few variants are discussed, according to the selected set of model constants. Validation is attempted against direct numerical simulation in a steady closed-channel flow for two values of the Reynolds number, indicating the ability of the model to reasonably predict the anisotropy tensor and the scalar flux components when considering wall functions to account for near-wall effects. The production of turbulent kinetic energy is well predicted, while the neutral turbulent Prandtl number has values in agreement with the literature. The proposed model is then compared with an experiment on a heated cylinder with slight temperature variations, with satisfactory results. The proposed model can be applied to various 2D simply-sheared flows involving a passive scalar, i.e. if stratification effects are negligible.