Vorticity transport in laminar steady rotating plumes

Abstract

A steady laminar rotating thermal plume was investigated by the numerical solution of the 3D momentum and energy equations. The flow originated from a low momentum hot jet (Richardson number Ri = 173 and Grashof number Gr = 5000) issued from a small inlet in the bottom wall of a cylindrical domain with a permeable lateral surface that is rotating (Ekman number Ek = 12). Second order accurate calculations of the structure and dynamics of the buoyant vortex were investigated, with specific emphasis on the evolution of the vorticity distributions and their effects on the ensuing vortex. Budgets of the vorticity transport equations were investigated to analyze the genesis of the developed axial vorticity, explaining how the whirling flow was generated. Nonslip and slip bottom boundary conditions allowed the investigation of the impact of the boundary layer on the axial vorticity generation. The results showed that there is a conversion of radial vorticity into axial vorticity. The radial vorticity was found to be generated not only in the boundary layer but also by tilting of the tangential vorticity, which results from buoyancy. Additionally, the boundary layer was found to have a strong impact on the generation of axial vorticity, but not to be necessary to generate the whirl. In fact, a stronger whirl was originated without the effect of the boundary layer, since the axial vorticity was generated closer to the inlet, where additional stretching is provided by the acceleration of the flow.