Effect of mixed convection on laminar vortex breakdown in a cylindrical enclosure with a rotating bottom plate

Abstract

© 2020 Elsevier Masson SAS Vortex breakdown plays a central role in the performance of countless rotating machinery applications, many of which contain thermal gradients either inadvertently or by design. The effect of thermal gradients on vortex breakdown and further flow development in a cylindrical domain with a rotating bottom plate is examined using the Generalized Integral Transformation Technique (GITT) with a streamfunction-only formulation. A thermal gradient is imposed in the axial direction, such that the buoyancy forces oppose the base flow driven by the rotation of the lower plate, i.e. the temperature difference acts to stabilize the flow. The hybrid numerical-analytical approach is shown to accurately capture vortex breakdown phenomena for a variety of conditions involving single, double and triple recirculation bubbles. The buoyancy forces – expressed in terms of the Richardson number (Ri) – act to suppress vortex breakdown in all cases examined and led to a series of flow transitions with increasing Ri, characterized by the appearance of a stratified structure with multiple fluid layers. These flow transitions have a significant impact on the overall performance of the system. The torque coefficient decreases with Ri, compared to the base (isothermal) case following an empirical power law relationship, which is independent of Reynolds number, aspect ratio or number of fluid layers present. Flow stratification suppresses the transport of angular momentum; azimuthal velocity is shown to decline exponentially in the regions where layering occurs, accompanied by a sharp reduction in the Nusselt number, as fluid layers act to insulate the upper plate