An Improved ‘Flywheel’ Model for Convective Turbulence in Liquid Metals

Abstract

We present and discuss some results on the effect of the Prandtl (Pr) number in the heat transfer properties of a Rayleigh—Bénard flow. Generally the Nusselt number Nu (the non-dimensional heat transfer) depends on geometrical parameters (shape of the cell and boundary conditions) and upon the Rayleigh (Ra) and Prandtl numbers. If one is only concerned with the flow changes induced by the last two parameters, however, all the other factors have to be ruled out. This consideration induced us to perform all the simulations in a fixed cell geometry (a cylindrical cell of aspect ratio 1 as in [1] and [2]). The effect of Ra and Pr has been then analyzed using different series of numerical simulations in which these factors were changed separately. In particular, two series of simulations were performed at “low” and “high” Prandtl, Pr = 0.022 and Pr = 0.7 respectively, with Ra varied in such a way to obtain a sufficiently long power law range of the Nu vs Ra relation. In the third series, in contrast, Ra was fixed at ≃ 6 × 10⁵, while Pr covered the range 2.2 × 10^-3 ≤ Pr ≤ 15. The analysis of the velocity and temperature fields, have shown that the fluid structures are different for low-Pr (≤ 0.3) and high-Pr flows. In the first case, the velocity and temperature fields are dominated by a large-scale flow filling the whole domain (see [3]). For high-Pr flow, on the contrary, the recirculating cell becomes much weaker and the temperature field is characterized by the appearance of plumes.