Flow instabilities driven by Prandtl number effect and rotation-depth coupling effect in the cylinder with a top disk

Abstract

We employed linear stability analysis to investigate the Prandtl number (Pr) effect and rotation-depth coupling effect on the complex flow instability in a cylinder with a top disk. The dependence of the critical Rayleigh number on the Pr number, as well as the relationship between the critical disk rotation rate and the aspect ratio at Pr = 6.7, were obtained. Results reveal that the flow stability increases with increasing Pr number, and the convection instability stems from the inertial mechanism for 0.011 ≤ Pr ≤ 0.0258 and thermal buoyancy mechanism for 1.4 ≤ Pr ≤ 28.01. Regarding the rotation-depth coupling effect for the melt with Pr = 6.7, a decreasing melt level leads to a general increase in the critical disk rotation rate. Furthermore, within the interval of aspect ratio (ratio of depth to cylinder radius) 0.7 ≤ Γ ≤ 1.62, multiple transitions of the flow state from stable to unstable and then back to stable were observed with increasing disk rotation rate before finally becoming unstable. Energy analysis reveals that multiple transitions in the flow state are attributed to the competition between thermal buoyancy and inertial mechanisms.