Square Additive Approach to Turbulent Prandtl Number

Low Prandtl number liquid metals serve as primary coolant for MYRRHA and ALFRED, two Gen-IV reactors under development. The low Prandtl number induces discrepancies in the modeling of the turbulent heat transfer when directly treated according to the Reynolds analogy with a constant turbulent Prandtl number. In a former paper, we showed that the Kays correlations can be simply derived on a basic assumption with regards to the non-linear combination of stochastic effects and the variants then come from different approximations of a mother formula. In this paper, we proceed further with the constructive hypothesis to refine the formula, extending the principle of square additivity not only to the thermal conductivity but also to the viscosity. The derived formula has the merit to be simple and to not degenerate any more at vanishing turbulence.

@TechReport{Mor22,
  author       = {Moreau, V.},
  title        = {Square Additive Approach to Turbulent Prandtl Number},
  institution  = {CRS4},
  month        = {february},
  year         = {2022},
  address      = {Loc. Piscina Manna},
  keywords     = {Liquid Metal, Fast Reactors, Prandtl Number, Reynolds Analogy},
  url          = {https://publications.crs4.it/pubdocs/2022/Mor22},
}