The Dynamics of Two-Dimensional Buoyancy Driven Convection in a Horizontal Rotating Cylinder

The present study involves a numerical investigation of buoyancy induced two-dimensional fluid motion in a horizontal, circular, steadily rotating cylinder whose wall is subjected to a periodic distribution of temperature. The axis of rotation is perpendicular to gravity. The governing equations of mass, momentum and energy, for a frame rotating with the enclosure, subject to Boussinesq approximation, have been solved using the Finite Difference Method on a Cartesian colocated grid utilizing a semi-implicit pressure correction approach. The problem is characterized by four dimensionless parameters: (1) Gravitational Rayleigh number $Rag;$ (2) Rotational Rayleigh number $RaΩ;$ (3) Taylor number Ta; and (4) Prandtl number Pr. The investigations have been carried out for a fixed Pr=0.71 and a fixed $Rag=105$ while $RaΩ$ is varied from $102$ to $107.$ From the practical point of view, $RaΩ$ and Ta are not independent for a given fluid and size of the enclosure. Thus they are varied simultaneously. Further, an observer attached to the rotating cylinder, is stationary while the “g” vector rotates resulting in profound changes in the flow structure and even the flow direction at low enough flow rates $RaΩ<105$ with phase $“ϕg”$ of the “g” vector. For $RaΩ⩾105,$ the global spatial structure of the flow is characterized by two counter-rotating rolls in the rotating frame while the flow structure does not alter significantly with the phase of the rotating “g” vector. The frequency of oscillation of Nusselt number over the heated portion of the cylinder wall is found to be very close to the rotation frequency of the cylinder for $RaΩ⩽105$ whereas multiple frequencies are found to exist for $RaΩ>105.$ The time mean Nusselt number for the heated portion of the wall undergoes a nonmonotonic variation with $RaΩ,$ depending upon the relative magnitudes of the different body forces involved.