Swirling Flows Characteristics in a Cylinder Under Effect of Buoyancy

Swirling flows have been investigated extensively aiming at providing further insight into the conditions that cause abrupt flow stagnation and associated breakdown. This latter complex feature may be evidenced, for instance, in the benchmark model flow driven by one end disk of an upright cylinder of given aspect ratio [1, 2]. Several prior studies provided means of controlling breakdown onset as it can be harmful / beneficial, depending upon the application considered. Hereafter, are presented selected investigations based on kinematic, geometric and thermal means of vortex flows control. Of note, Mullin et al. [3] demonstrated the effects of including a tapered center body and showed it to alter significantly breakdown onset and location. In particular, they argued that the inhibition / suppression of the vortex structure depended on the axial pressure gradient sign, induced by the conical axial rod, whose circular base is sealed to either the rotating or the stationary disk of the enclosure. Manungua et al. [4], through numerical simulations and dye visualizations, attributed the effective vortex control to the role of vorticity strength, modified upstream of the vortex by the differential rotation of a partial rotating disk flash mounted into the top lid. More recently, breakdown topology in an enclosure shrouded by a polygonal cross section sidewall was explored numerically and experimentally by Naumov et al. [5]. Despite the drastic change in the lateral geometry, the findings revealed that the core flow which displays breakdown remains axisymmetric and the 3D non axisymmetric behavior was remarked in the bulk flow adjacent to the sidewall. The topology and parameter dependence of breakdown was addressed by Jones et al. [6]. Their analysis led to the identification of the adequate parameters which allowed consistent comparison between bubble breakdown observed in a torsionally driven cylinder flow and the spiral type vortex occurring in flows through openended pipes. More recently, Shtern [7] highlighted the role of the swirl decay as a physical mechanism to control breakdown development. Thermal effects on confined vortex flows were addressed numerically by, for instance, Lugt et al. [8]. Their findings evidenced the sensitivity of breakdown to weak buoyancy caused by an unstable thermal stratification resulting from a slightly heated bottom disk. Under stable thermal stratification, significant effects on the swirling flow topology were reported by Omi et al. [9] who extended the investigation to account for co-/counter-rotating end disks. Compressibility effects were demonstrated by Herrada et al. [10, 11], in the case of a non-Boussinesq swirling flow driven by the bottom disk rotation of a cylinder with and without a central rod. A combination of buoyancy and rod differential rotation provided efficient means of vortex flows control: a forced axial temperature gradient was shown to enhance or eliminate the vortex features; depending on the sign of the temperature gradient. Flow stagnation and associated breakdown which occur in a swirling jet under effect of thermal buoyancy was addressed by Dina et al. [12] who performed PIV measurements and concluded that a temperature gradient between the jet core and its surrounding fluid causes the suppression/enhancement of the vortex pattern; depending on the sign of the gradient. Effects of a density variation on a confined isothermal swirling flow which exhibits on-axis vortex breakdown, driven by the top disk rotation of a cylinder, were recently addressed experimentally by Ismadi et al. [13] using axial injection of dye, denser or lighter than the ambient liquid. Flow visualizations indicated that heavy dye enhanced the formation of breakdown while very light dye injection (density variations of order 0.01%) caused the occurrence of offaxis ring type vortices and modified the threshold of breakdown onset. Concerns over the symmetry/asymmetry of onaxis breakdown in a cylinder were noted by several investigators: dye visualizations often provide images of vortices with asymmetric folds while 3D numerical counterparts, under well controlled conditions, predict axisymmetric patterns [6, 14, 15]. This discrepancy is often attributed to the inevitable imperfections of the set up and operating conditions such as a 0.01% misalignment of the cavity axis [14] or a slight tilt (≈2°) of one end disk [15]. Motivated by the above considerations, the current work explored numerically the sensitivity of a helical flow and associated vortex characteristics to a differential heating in a disk-cylinder system. Buoyancy was first implemented by a warm/cool axial fluid injection then by means of a differentially heated/cooled tiny rod.