The SquAd derivation: A Square Additive approach to the turbulent Prandtl number V3

Liquid metals have been chosen as primary coolant of innovative nuclear systems under current development. They present a very high thermal conductivity and hence a very low molecular Prandtl number. This feature challenges the modeling of turbulent thermal flows applying the Reynolds analogy. This paper addresses this challenge. A new formula for the turbulent Prandtl number is derived in terms of local variables available from two-equations turbulence models. The derivation is a direct consequence of the expected square additivity of the molecular and flow parameters defining the effective viscosity and the effective conductivity. The formula does not degenerate and leads to a Kays like formulation if approximated. While constrained by the quality of the turbulent viscosity modeling, it has the potential to improve the numerical simulation of turbulent thermal flows.

@Article{Mor23,
  author       = {Moreau, V.},
  title        = {The SquAd derivation: A Square Additive approach to the turbulent Prandtl number V3},
  journal      = {Open Research Europe},
  number       = {43},
  volume       = {3},
  month        = {september},
  year         = {2023},
  publisher    = {European Commission},
  note         = {Version 3 restarting review process},
  keywords     = {Kays, Turbulent Prandtl Number, low Prandtl number, Reynolds Analogy, PATRICIA},
  doi          = {10.12688/openreseurope.15367.3},
  url          = {https://publications.crs4.it/pubdocs/2023/Mor23},
}