Voronoï analysis of bubbly flows via ultrafast X-ray tomographic imaging

Abstract

Although clustering of bubbles plays a significant role in bubble column reactors regarding the heat and mass transfer due to bubble–bubble and flow field interactions, it has yet to be fully understood. Contrary to flows in bubble columns, most literature studies on clustering report numerical and experimental results on dilute or micro-bubbly flows. In this paper, clustering of bubbles in a cylindrical bubble column of 100 mm diameter is experimentally investigated. Ultrafast X-ray tomographic imaging is used to obtain the bubble positions within a hybrid Eulerian framework. By means of Voronoi analysis, the clustering behavior of bubbles is investigated. Experiments are performed with different superficial gas velocities, where Voronoi diagrams are constructed at several column heights. From the PDFs of the Voronoi diagrams, it is shown that the bubble structuring in terms of Voronoi cell volumes develops slower than the bubble size distribution. The latter reaches a steady state earlier with increasing column height. The measured PDFs are compared with the PDF of randomly distributed points, which showed that the amount of bubbles as part of clusters (Voronoi cells < $$V/\overline{V}_\mathrm{{cluster}}$$ ) as well as bubbles as part of voids (Voronoi cells > $$V/\overline{V}_\mathrm{{void}}$$ ) increases with the superficial gas velocity. It is found that all experiments have an approximate cluster limit $$V/\overline{V}_\mathrm{{cluster}}$$ of 0.63, while the void limit $$V/\overline{V}_\mathrm{{void}}$$ varies between 1.5 and 3.0.