Topology of vortex breakdown in closed polygonal containers

Abstract

The topology of vortex breakdown in the confined flow generated by a rotating lid in a closed container with a polygonal cross-section geometry has been analysed experimentally and numerically for different height/radius aspect ratios $h$ from 0.5 to 3.0. The locations of stagnation points of the breakdown bubble emergence and corresponding Reynolds numbers were determined experimentally and numerically by STAR-CCM+ computational fluid dynamics software for square, pentagonal, hexagonal and octagonal cross-section configurations. The flow pattern and velocity were observed and measured by combining seeding particle visualization and laser Doppler anemometry. The vortex breakdown size and position on the container axis were identified for Reynolds numbers ranging from 500 to 2800 in steady flow conditions. The obtained results were compared with the flow structure in the closed cylindrical container. The results allowed revealing regularities of formation of the vortex breakdown bubble depending on $Re$ and $h$ and the cross-section geometry of the confined container. It was found in a diagram of $Re$ versus $h$ that reducing the number of cross-section angles from eight to four shifts the breakdown bubble location to higher Reynolds numbers and a smaller aspect ratio. The vortex breakdown bubble area for octagonal cross-section was detected to correspond to the one for the cylindrical container but these areas for square and cylindrical containers do not overlap in the entire range of aspect ratio.