Air Bubble Entrainment in Hydraulic Jumps: Similitude and Scale Effects

A hydraulic jump is the sudden transition from a high-velocity, supercritical open channel flow into a slow-moving, sub-critical flow. It is characterised by a sudden rise of the free-surface, with strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interactions between air bubble diffusion and momentum transfer are not completely understood. In the present study, new air-water flow measurements were performed in hydraulic jumps with partially-developed flow conditions. The experiments were performed in relatively large-size facilities with phase-detection probes. Experiments were performed with identical Froude numbers, but different Reynolds numbers or different relative channel widths. In hydraulic jumps with partially-developed inflow, void fraction distributions showed the presence of an advection/diffusion shear layer in which void fraction distributions followed an analytical solution of the diffusion equation for air bubbles. This advective diffusion layer was observed only for Re1 > 2.5 E+4. For smaller inflow Reynolds numbers, the air entrainment rate was too weak and air detrainment tended to dominate the air-water flow pattern. In the developing shear region, bubble chord time distributions showed a broad range of chord times. The distributions were skewed with a preponderance of bubble chord times smaller than the mean. A cluster analysis of bubble grouping was performed. Little bubble clustering was observed. An interparticle arrival time analysis suggested however that bubble clustering may occur preferentially for small bubbles with chord times less than 3 msec. Similar experiments with identical inflow Froude numbers and relative channel widths were repeated with a true geometric scaling ratio of Lr = 2 (i.e. 2:1 scale). The results showed drastic scale effects at small Reynolds numbers in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers leading to a lesser overall aeration of the jump roller, while dimensionless bubble count rates were drastically lower especially in the mixing layer. Bubble chord times were not scaled according to a Froude similitude. Experimental results suggested also that the relative channel width had little effect on the air-water flow properties for identical inflow Froude and Reynolds numbers within 8 < W/d1 < 22 for 0.25 < W < 0.50 m. Transverse air-water length scales were deduced from signal correlation analyses between two probes separated by a known transverse distance. In the bubbly flow region, the resulting length scale was related to the inflow depth. The dimensionless transverse length scale Z/d1 was typically between 0.25 and 0.4 irrespective of the inflow Froude and Reynolds numbers. It is a measure of transverse length scale of vortical structures advecting air bubbles in the developing shear layer.