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

Abstract

Abstract

Rayleigh–Bénard convection in a cubic cell under the effects of gas radiation up to Ra=109

“…However, all symmetries could be recovered for sufficiently long integration time, because of low-frequency reorientations of this large-scale roll in the horizontal plane, that are rotations of π/2 around the vertical axis [19,15]. Reorientations of the large-scale roll in the horizontal plane have also been reported in the case of a radiating gas in the range 10 6 ≤ Ra ≤ 10 8 [40], radiation causing an increase of the reorientation frequency.…”

“…Direct Numerical Simulations (DNS) have been performed, considering the air/H 2 O/CO 2 mixture as radiating (radiation case) or transparent (noradiation case, X H 2 O = 0, X CO 2 = 0 and thus P rad = 0) for 12 Rayleigh number values in the range 10 3 ≤ Ra ≤ 10 9 . The coupled algorithm for solving flow equations (2)-(4) and radiative transfer equation ( 8) has been extensively used and described in previous works, for both differentially heated cavities [32,33] and Rayleigh-Bénard cavities [39,40]. We will briefly recall here the main features of this algorithm.…”

“…A preliminary investigation [38] of radiation effects on RB convection in a cubic cell was limited to Ra = 10 7 and, due to limitations in computational resources, the integration time was not sufficient to capture LSC reorientations. More recently, low order models based on Proper Orthogonal Decomposition (POD) have been developed to analyse these LSC reorientations with and without radiation [39,40] in the range 10 6 Ra 10 8 . Similar first eigenmodes were found with and without radiation but with higher energies (eigenvalues) when radiation was taken into account.…”

Large scale reorientation in cubic Rayleigh-Bénard convection using particle tracking velocimetry

“…The mechanism behind reorientation in 3D cubic cells is part of current research and several models have been developed to understand the phenomena. In (Ji and Brown, 2020) a low dimensional model is derived to describe and predict reorientation events, in (Soucasse et al, 2019(Soucasse et al, , 2021 the flow fields are decomposed using POD (proper orthogonal decomposition) and the modes are used to model the dynamics of the reorientation process, while in (Vishnu et al, 2020) an energy transfer mechanism during reorientation events is analysed. Most studies focusing on reorientation events rely on direct numerical simulations (DNS).…”

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…A grey ROM for multigroup TRT problems was developed using POD-based representations of frequency averaged opacities and other coefficients [85]. POD-based ROMs for radiating fluids have been constructed by applying a linearized estimation of radiative transfer effects based on POD data of non-radiating fluids [86,87].…”