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International audience; 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 air/H2O/CO2 mixture at room temperature and at a Rayleigh number of 107 . 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 π/2of 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.

International audience; We show that, in the case of turbulent Rayleigh–Bénard convection, shadowgraphcan be used to gain quantitative results on the plume statistics and velocity. For thispurpose, we compare the experimental shadowgraph of a Rayleigh–Bénard cell withthe synthetic shadowgraph obtained by calculating the integrated two-dimensionalLaplacian of the temperature field from a numerical simulation very similar to theexperiment. We use image processing tools to enhance the quality of the shadowgraphimage, and obtain quantitative statistics for the thermal plumes, such as plume densityand plume velocity distribution. To highlight the efficiency of this new process ofplume counting, we use, both in the experiment and in the numerical simulation,a turbulent Rayleigh–Bénard convection cell with a rough bottom surface and asmooth top surface, where the statistics of the plumes can be influenced (or not)by the roughness. In addition, the distribution of velocity obtained from processingthe synthetic shadowgraph images of the direct numerical simulations (DNS) or theexperimental shadowgraph images, are compared to the velocity fluid at mid-plane ofthe DNS or particle image velocimetry measurement in the experiment, respectively.It will be shown that the mean velocity profile measured using the advection of theplumes is different from the average Eulerian velocity profile.

International audience; abstract

International audience; We present direct numerical simulations of turbulent buoyant convection over a rough heated plateplaced in a Rayleigh Bénard cell. The roughness is introduced by a set of cubic obstacles regularlyspaced, modelled by using an immersed boundary method. This study aims at clarifying interactionsbetween the large scale circulation filling the box, plume emission and the enhancement of the heattransfer. The simulations are performed in a box-shaped cell at fixed Prandtl number (Pr = 4.38)with the Rayleigh number Ra ranging from 5 à 10 5 to 5 à 10 9 .As expected, results show an enhancement of heat transfer measured by the Nusselt number Nu,depending on the relative sizes of the mean boundary-layer thicknesses and the obstacle height inagreement with previous experimental and numerical studies from the literature (for example [1,2, 3]). By varying Ra, we investigate the successive regimes of the turbulent heat transport, frominactive roughness to a regime where the heat transfer relative increase is larger than the relativesurface increase induced by roughness addition (figure 1). Plume fluctuation dynamics and boundarylayer structure near obstacles will be reported.