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Low-order models for predicting radiative transfer effects on Rayleigh–Bénard convection in a cubic cell at different Rayleigh numbers

Published online by Cambridge University Press:  21 April 2021

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:
LISN, 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: laurent.soucasse@centralesupelec.fr
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Abstract

This paper presents low-order models of Rayleigh–Bénard convection of a radiating gas in a cubic cell, in the Rayleigh number range $Ra \in [ 10^6\text {--}10^8 ]$. Numerical simulations are carried out for an air–$\textrm {H}_2\textrm {O}$–$\textrm {CO}_2$ mixture assumed to be radiating (coupled case) or transparent (uncoupled case). When coupling with radiation, it is shown that the kinetic energy of the flow and the thermal energy increase. At $Ra=10^6$, planar flow states are observed when radiation is taken into account, while diagonal flow states prevail in the uncoupled case. From $Ra\ge 3\times 10^7$, quasi-stable diagonal flows are observed in both coupled and uncoupled simulations, with occasional brief reorientations. The reorientation frequency seems to decrease with the Rayleigh number and seems to increase with radiation. A proper orthogonal decomposition (POD) analysis reveals that 11 of the first 12 POD eigenfunctions are preserved over the Rayleigh number range, whatever the coupling conditions. However, POD eigenvalues are higher with radiation. POD-based low-order models are derived at different Rayleigh numbers, for both coupled and uncoupled cases. Radiative transfer effects are added in the model in an a priori fashion, from uncoupled simulation data. Coupled POD models predict the energy increase with radiation and the loss of stability of the diagonal rolls at $Ra=10^6$. Uncoupled and coupled models correctly reproduce reorientation frequencies over the Rayleigh number range. Finally, a generalised model is derived, solely based on uncoupled simulation data at $Ra=10^7$ and energy scaling laws. This generalised model captures the change in dynamics associated with radiation effects and variations in Rayleigh number, except at $Ra=10^6$.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models

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JFM Papers
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Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A5
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© The Author(s), 2021. Published by Cambridge University Press

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