Froude Similitude and Scale Effects Affecting Air Entrainment in Hydraulic Jumps

A hydraulic jump is the rapid transition from a high-velocity to a low-velocity open channel flow. It is characterized by strong turbulence and air bubble entrainment. Detailed air-water flow properties were measured in hydraulic jumps with partially-developed inflow conditions. The present data set together with the earlier data of Chanson (2006) yielded similar experiments conducted with identical inflow Froude numbers but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction and bubble count rate distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10⁵, some viscous scale effects were observed in terms of the rate of entrained air and air-water interfacial area.