Two-dimensional bubble clustering in hydraulic jumps

Abstract

Hydraulic jumps are characterised by turbulent flow structures and air entrainment. As a result of the turbulence–bubble interaction, non-random bubble distributions are observed in the bubble transport processes, forming bubble clusters. This paper presents a physical investigation of bubble/droplet clustering events in hydraulic jumps based upon a two-dimensional near-wake clustering criterion. Clusters were identified with consideration of bubble–bubble interplay in both longitudinal and transverse directions. In the highly-aerated flow region of the roller, more than 50% of bubbles were advected in two-dimensional clusters. Though the largest percentage of clusters was formed by two bubbles, over 10% of clusters were large two-dimensional cluster structures consisting of six bubbles or more. Clustering properties such as cluster production rate, average cluster size and clustered particle size distributions were analysed and their spatial distributions were presented for an inflow Froude number 7.5 with various Reynolds numbers from 3.4×104 to 1.4×105. All clustering properties decreased in the longitudinal direction as the turbulence dissipated and flow de-aerated. Comparison between the one-dimensional and two-dimensional clustering criteria was discussed along with their limitations. The quantification of the clustering properties provided a valuable measure of the correlation between air entrainment and turbulence development in such complex air–water flows.