Direct numerical simulations of the turbulent convection and thermal radiation in a Rayleigh-Bénard cell

Abstract

We perform direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection coupled with surface-to-surface radiation in a rectangular enclosure filled with air to investigate whether this interaction influences the heat transfer, temperature distribution and the flow structures. To do so, horizontal solid plates with finite conductivity are employed for the considered Rayleigh-Bénard cell. Such boundary conditions allow local variations of the temperature at the hot and cold interfaces due to their interaction with the fluid and surface radiation. In order to investigate the maximum effect of those boundary conditions, both interfaces are treated as a blackbody ε=1 and the cell is filled with a radiatively non-participating fluid (Prandtl number Pr=0.7). The effects of radiation for highly conducting plates are shown and compared to the case where radiation is neglected. It is found that due to highly conducting plates the mean temperature at the interfaces changes only 0.04% from the one of the infinite conductive plates. Furthermore, we observe that due to surface-to-surface radiation coupled with highly conducting plates, the mean temperature at the interfaces changes 0.1% at the interfaces and 0.2% in the bulk. It is shown that the temperature at the hot interface tends to decrease due to the radiative heat loss while the temperature at the cold interface slightly increases. Apart from that, we observe small changes in the temperature distribution at the interfaces due to surface-to-surface radiation. We notice that the highest temperatures at the top interface appear in the middle and the values steadily decrease towards the edges. Additionally, we observe a small drop of the convective Nusselt number and little variations of the temperature distribution at the interfaces. Finally, it is shown that all mentioned variations caused by heat radiation between interfaces are too small to visibly change the large scale flow structures when highly conducting plates are employed. It is also shown that in the non-radiation case of poorly conducting plates the heat transfer and the temperature variations at the interfaces are influenced significantly.