Thermal convection in inclined cylindrical containers

Abstract

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle ${\it\beta}$, $0\leqslant {\it\beta}\leqslant {\rm\pi}/2$, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number $\mathit{Nu}$ and Reynolds number $\mathit{Re}$. The considered Rayleigh numbers $\mathit{Ra}$ range from $10^{6}$ to $10^{8}$, the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the $\mathit{Nu}\,({\it\beta})/\mathit{Nu}(0)$ dependence is not universal and is strongly influenced by a combination of $\mathit{Ra}$ and $\mathit{Pr}$. Thus, with a small inclination ${\it\beta}$ of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small $\mathit{Pr}$, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to ${\it\beta}={\rm\pi}/2$, $\mathit{Nu}$ and $\mathit{Re}$ decrease with increasing ${\it\beta}$ in all considered cases. Generally, the $\mathit{Nu}({\it\beta})/\mathit{Nu}(0)$ dependence is a complicated, non-monotonic function of ${\it\beta}$.