Mean and Turbulent Bubble Velocities in Free Hydraulic Jumps for Small to Intermediate Froude Numbers: Fid-Bau Portal

Mean and Turbulent Bubble Velocities in Free Hydraulic Jumps for Small to Intermediate Froude Numbers

Zhang, Wenming / Liu, Minnan / Zhu, David Z. / Rajaratnam, Nallamuthu

Bubble characteristics in free hydraulic jumps for inflow Froude numbers ranging from 2.0 to 6.7 were measured using a single-tip optical probe, with a focus on mean and turbulent bubble velocities. It was found that the mean bubble velocity $u_{b}$ , to a large extent, is able to reflect the water-phase flow structure in a jump. In the boundary layer of the channel bed, $u_{b}$ follows the $1 / 7$ th power law in the vertical direction, and it follows a Gaussian distribution beyond that up to the water surface. Dimensionless maximum bubble velocity was found to be smaller than that for the classical wall jet up to a characteristic distance in the longitudinal direction; beyond that, however, they agree well with each other. Turbulence intensity of bubble velocity was found to first increase and then decrease with the vertical distance from the bed. The maximum value of turbulence intensity is 33% of the inflow velocity, which is comparable to that of the water-phase. Exponential relations are proposed to describe the variation of the maximum bubble velocity and maximum turbulence intensity of bubbles, in the longitudinal direction.