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Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Published online by Cambridge University Press:  18 December 2023

F. Rein Open the ORCID record for F. Rein [Opens in a new window] ,
L. Carénini Open the ORCID record for L. Carénini [Opens in a new window] ,
F. Fichot ,
B. Favier Open the ORCID record for B. Favier [Opens in a new window]  and
M. Le Bars Open the ORCID record for M. Le Bars [Opens in a new window]
F. Rein*
Affiliation:
Aix Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France IRSN, St Paul lez Durance, France
L. Carénini
Affiliation:
IRSN, St Paul lez Durance, France
F. Fichot
Affiliation:
IRSN, St Paul lez Durance, France
B. Favier
Affiliation:
Aix Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France
M. Le Bars
Affiliation:
Aix Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France
*
†Email address for correspondence: florian.rein@protonmail.com
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Abstract

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.

JFM classification

Convection: Convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 977 , 25 December 2023 , A26
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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