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Reduced-order modelling of radiative transfer effects on Rayleigh–Bénard convection in a cubic cell

Published online by Cambridge University Press:  24 June 2020

Laurent Soucasse Open the ORCID record for Laurent Soucasse [Opens in a new window] ,
Bérengère Podvin Open the ORCID record for Bérengère Podvin [Opens in a new window] ,
Philippe Rivière  and
Anouar Soufiani
Laurent Soucasse*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8-10 rue Joliot Curie,91192 Gif-sur-Yvette, France
Bérengère Podvin
Affiliation:
LIMSI, CNRS, Université Paris-Saclay, Bât 507, rue du Belvédère, Campus Universitaire,91405 Orsay, France
Philippe Rivière
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8-10 rue Joliot Curie,91192 Gif-sur-Yvette, France
Anouar Soufiani
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8-10 rue Joliot Curie,91192 Gif-sur-Yvette, France
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents a reduced-order modelling strategy for Rayleigh–Bénard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh–Bénard cell is performed for an $\text{air}/\text{H}_{2}\text{O}/\text{CO}_{2}$ mixture at room temperature and at a Rayleigh number of $10^{7}$. It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of $\unicode[STIX]{x03C0}/2$ of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an a priori model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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