Natural convection in a horizontal cylinder with axial rotation

Abstract

We study the problem of thermal convection in a laterally heated horizontal cylinder rotating about its axis. A cylinder of aspect ratio Γ=H/2R=2 containing a small Prandtl number fluid (σ=0.01) representative of molten metals and molten semiconductors at high temperature is considered. We focus on a slow rotation regime (Ω<8), where the effects of rotation and buoyancy forces are comparable. The Navier-Stokes and energy equations with the Boussinesq approximation are solved numerically to calculate the basic states, analyze their linear stability, and compute several secondary flows originated from the instabilities. Due to the confined cylindrical geometry-the presence of lateral walls and lids-all the flows are completely three dimensional, even the basic steady states. Results characterizing the basic states as the rotation rate increases are presented. As it occurred in the nonrotating case for higher values of the Prandtl number, two curves of steady states with the same symmetric character coexist for moderate values of the Rayleigh number. In the range of Ω considered, rotation has a stabilizing effect only for very small values. As the value of the rotation rate approaches Ω=3.5 and Ω=4.5, the scenario of bifurcations becomes more complex due to the existence in both cases of very close bifurcations of codimension 2, which in the latter case involve both curves of symmetric solutions.