STUDY OF A VORTICAL FLOW

Abstract

An experimental investigation is made of an unconfined vortex formed on a fixed plane boundary, in particular by a fixed horizontal disk whose axis of symmetry is coaxial with the axis of rotation of the vortex. Through flow visualization, the vortex formed at the low Reynolds number (based on the tangential velocity at the disk edge and disk radius) range is seen to break down in forms similar to those previously documented for a confined flow, in spite of the vast differences between both sets of apparatus. Altogether, eight different types of breakdown are noted, including the commonly observed bubble and spiral breakdown as well as the double helix disruption. In addition, our unconfined flow also revealed the existence of a conical shaped breakdown which was only recently observed under confined swirling flows (Sarpkaya, T., Phys. Fluids, 7, 2301-2304, 1995). This conical breakdown is characterized by a conical shaped breakdown envelope and occurs at the high swirl regions. At the high Reynolds number range, the vortex structure erupts from the base into a large scale turbulent flow. Following this, the flow visualization results are presented on a chart using parameters related to the intrinsic flow properties of the vortical flow, namely; circulation, extent of vortex stretching and core size. Velocity profiles across the boundary layer and effusion core of the vortex were measured by means of a 4-beams, 2-components Laser Doppler Anemometer at Reynolds number, Re, ranging from 10000 to 25000. The results of the boundary layer measurements show that the boundary layer remains turbulent over most parts of the disk but tends to revert to its laminar state as the flow is convected radially inwards to the effusion core. The results also indicate that the point of laminar reversion occurs closer to the effusion core as the Reynolds number is increased. Thus, the zone of relaminarized fluid decreases with increasing Reynolds number. In addition, the stability of the boundary layer is found to be controlled by two main factors: an inflexional instability caused by the crossflow velocity profile and a stability factor caused by the favorable pressure gradient. At lower Reynolds number, the radial pressure gradient has a very strong stabilizing effect on the boundary layer and acts to revert it to its laminar state upstream of the effusing core. On the other hand, at higher Reynolds number the inflexional instability caused by the crossflow velocity dominates while the stabilizing influence of the favourable pressure gradient recedes. As such, laminar reversion at the higher Reynolds number range occurs closer to the effusion core. Finally, velocity measurements across the effusion core shows that the extent or radius of the effusion core (taken to be the radial position where departure from the potential flow occurred) is proportional to Re·½ for all the Reynolds number considered, with a constant of proportionality of 8. 77. This result is consistent with the base pressure measurements of a similar vortex (Khoo et al., Expt. Thermal and Fluid Sci., 7, 307-318, 1993}.