Prandtl number effects in convective turbulence

Abstract

The effect of Prandtl number on the dynamics of a convective turbulent flow is studied by numerical experiments. In particular, three series of experiments have been performed; in two of them the Rayleigh number spanned about two decades while the Prandtl number was set equal to 0.022 (mercury) and 0.7 (air). In the third series, in contrast, we fixed the Rayleigh number at 6×10⁵ and the Prandtl number was varied from 0.0022 up to 15. The results have shown that, depending on the Prandtl number, there are two distinct flow regimes; in the first (Pr[lsim ]0.35) the flow is dominated by the large-scale recirculation cell that is the most important ‘engine’ for heat transfer. In the second regime, on the other hand, the large-scale flow plays a negligible role in the heat transfer which is mainly transported by the thermal plumes.

For the low-Pr regime a model for the heat transfer is derived and the predictions are in qualitative and quantitative agreement with the results of the numerical simulations and of the experiments. All the hypotheses and the consequences of the model are directly checked and all the findings are consistent with the predictions and with experimental observations performed under similar conditions. Finally, in order to stress the effects of the large-scale flow some counter examples are shown in which the large-scale motion is artificially suppressed.