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

Abstract

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.