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

Abstract

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.

Effects of an Axial Magnetic Field on Vortex Breakdown and Fluid Layer

“…( 9) -( 11). The details of the GITT approach are given as follows, as an extension to hybrid solutions already detailed in reference (Quaresma et al 2020 andMatt et al2017). Hence, the eigenfunctions, eigenvalues, norms, and orthogonality properties for each potential in this problem determined, as follows:…”

“…Axi-symmetric boundary condition is specified along the axis (r=0), see Table 1. A streamfunction formulation is employed to implement the GITT approach (Lima et al 2013;Matt et al 2017;Quaresma et al 2020). Before starting with the integral transformation of Eqs.…”

Buoyancy force and magnetic field effects on laminar vortex breakdown and fluid layers

“…There are several studies in the literature examining vortex breakdown and fluid layers [3][4][5]. Some study is interested in the effect of thermal gradient which is the origin of the increase or decrease of stratification [6][7][8] and a decrease in the number of Nusselt [9,10].…”

Stability of an Electrically Conducting Fluid Flow between Coaxial Cylinders under Magnetic field

“…The thermal gradient direction may be the cause of the increase or decrease of a layering flow (Omi and Iwatsu 2005; Mahfoud and Bessaїh 2012a) and a reduction in the Nusselt number (Turan et al 2018;Quaresma et al 2020). One of the implemented methods by researchers to control or suppress the breakdown is the use of magnetohydrodynamics.…”