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

Vincent Moreau
Open Research Europe, Volume 3, Number 43 - march 2023
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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 turbulent 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.

BibTex references

  author       = {Moreau, V.},
  title        = {The SquAd derivation: A Square Additive approach to the turbulent Prandtl number},
  journal      = {Open Research Europe},
  number       = {43},
  volume       = {3},
  month        = {march},
  year         = {2023},
  publisher    = {European Commission},
  note         = {Starting review process},
  keywords     = {Kays, Turbulent Prandtl Number, low Prandtl number, Reynolds Analogy, PATRICIA},
  doi          = {10.12688/openreseurope.15367.1},
  url          = {},

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