The SquAd derivation: A Square Additive approach to the turbulent Prandtl number [version 3; peer review: 1 approved, 3 approved with reservations, 1 not approved]

Autor: Vincent Moreau
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Open Research Europe, Vol 3 (2023)
Druh dokumentu: article
ISSN: 2732-5121
DOI: 10.12688/openreseurope.15367.3
Popis: 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.
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