A three-dimensional numerical study of laminar buoyancy-driven columnar vortices

Abstract

This study deals with the development of a low momentum whirling laminar plume that results from the interaction between a plume and a circulating flow imposed by a cylindrical rotating screen. Numerical simulations were performed by direct simulation of the fully three-dimensional flow governed by the compressible Navier-Stokes and energy equations. The rotating thermal plume forms a columnar vortex governed by the Grashof (GR) and nondimensional rotation velocity (Reynolds number (ReR)), based on the cylindrical domain’s radius and the angular frequency of rotation of the permeable lateral surface. Numerical solutions were obtained in the range 102<Gr<106 and 10<ReR<150. The vortex generated bifurcates into a pair of steady co-rotating vortices within the range 104<Gr<2×105 and 30<ReR<100. The steady state configuration of the flow is described and analysed, showing the evolution of the vorticity contours in cross-sections that start out as circlets, gradually turn into an ellipse and end up bifurcating into a pair of co-rotating vortices. The role of the boundary layer is also described, showing an increase in the distance between the co-rotating vortex pair for a given Gr and ReR numbers but in the absence of a boundary layer. At last, the temporal evolution of the vortex splitting process is compared to measurements of merging of two co-rotating vortices available in the literature, uncovering that the two phenomena take similar timescales to occur.