State-of-the-art turbulent heat flux modelling for low-Prandtl flows

Turbulent heat transfer is a complex phenomenon, which has become the focus of turbulence modelling research in recent years. The closure of turbulent heat flux has conventionally been approached by the so-called eddy diffusivity approach in its most trivial version, the Reynolds analogy. While this approach provides a simple and efficient closure, it lacks accuracy when the similarity hypothesis between thermal and momentum fields is less justified, i.e. in presence of low Prandtl number fluids, such as liquid metals, for which the high molecular diffusivity compared to the kinematic viscosity leads to larger thermal turbulent structures compared to the momentum ones. The thermal turbulence modelling of this kind of fluids is further challenged by the scarcity of reference data. The present paper discusses the recent advancements in the heat flux modelling approaches, including closures for local turbulent Prandtl number, algebraic models and other higher-order models with special attention to low-Prandtl cases. Although these recently developed models provide a better alternative to the conventional approach, they also suffer from limitations of their own, and their validation is still ongoing. The present paper provides a thorough review of these shortcomings, including the need for calibration, the need for a priori knowledge of flow and heat transfer regimes, isotropic nature, lack of wall-modelling, together with their applicability to in-dustrial cases. Another major criteria to rank such models is their applicability to complex flow configurations where multiple flow regimes exist in a single flow domain. Global efforts are under way order to develop and validate a universal turbulent heat flux modelling approach. A brief account of such efforts in the in-ternational community is also presented herein. Rigorous testing and validation of such modelling approaches is required, preferably in an integral flow case over complex reactor-scale geometries, before they can be widely used by the nuclear design and development community.