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 3.4×10 4 to 1.4×10 5 . 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 airwater flows. Dimensionless coefficient for side-by-side particle clustering characterisation Superscript (l) Property of leading particle (t) Keywords

Bubble convection and bubbly flow turbulent time and length scales in two-dimensional plunging jets

“…Correspondingly, the proportion of larger clusters consisting of three, four and more bubbles was consistently smaller for a lower jet impact velocity and decreased with increasing longitudinal distance. The PDFs of cluster size were comparable to the results from a study of hydraulic jump where the turbulent structures also tended to group bubbles into clusters during the horizontal bubble advection (Wang et al 2015a). The vanishing large clusters (N clu > 5) along the turbulent shear flow could be an indicator of decoupling between the convected bubbles and turbulent structures.…”

Two-phase air-water flows in hydraulic jumps at low Froude number: Similarity, scale effects and the need for field observations

“…The near wake clustering method is considered to be robust and effective because it relies on a comparison between the local characteristic air-water flow time scales. It is important to stress that the present data analysis was focused on the longitudinal air-water structure and did not consider any bubble travelling side-by-side [61,68]. Fig.…”

Air-water interaction and characteristics in breaking bores

“…In the bubbly region, clustering is linked to the effects of inter-particle turbulent interactions as well as the effects of inertial forces leading to bubble trapping, hence clustering, in large-scale turbulent eddies. When a bubble is trapped in a vortical structure, the centrifugal pressure gradient moves the bubble inside the coherent structure core where bubble-bubble interactions may further take place (TOOBY et al 1977, SENE et al 1994 compared to other related air-water flows (CHANSON et al 2006, CHANSON 2007, SUN and CHANSON 2013, WANG et al 2015.…”

“…Importantly the present analysis was conducted along a streamline and did not consider bubbles travelling side by side, as being part of a cluster. For discussions on two-dimensional clustering, see CHANSON (2013) andWANG et al (2015). The cluster analysis was performed in terms of the air-water chord time data set.…”