Free Surface, Bubbly flow and Turbulence Measurements in Hydraulic Jumps

The hydraulic jump is the rapid transition from a high-velocity (supercritical regime) to a low-velocity (subcritical regime) open channel flow. It is characterized by the interaction of some strong turbulence with a free surface leading to air entrainment (bubbles, droplets, splashes) with macro-scale vortices, kinetic energy dissipation and a bubbly two-phase flow structure. The aim of this report is to present new free surface and air-water flow measurements in hydraulic jumps with partially-developed inflow conditions for a wide range of inflow Froude numbers (Fr = 3.1 to 8.5, Re= 24,000 to 62,000). New experiments were conducted in a large-size facility using ultrasonic displacement meters to describe the free surface features and a double-tip conductivity probe to study the two-phase flow properties. The mean and turbulent profiles of the air-water interface were documented. The data were processed in terms of some spectral analysis of the free surface fluctuations and compared with the frequencies of the horizontal oscillations of the toe. The free-surface measurements highlighted large fluctuations in the roller. A peak in free-surface fluctuation intensity was found in the first half of the roller reflecting the dynamic unsteady structure of the free surface in this flow region. This was followed by a gradual decrease in turbulent intensity. The normalized maximum free-surface fluctuation was found to be proportional to the inflow Froude number (Fr). Spectral analyses of the free-surface fluctuations showed dominant frequencies ranging from 0.5 to 4 Hz with decreasing frequencies when increasing Froude number. While the dominant frequencies were nearly constant in the roller, lower values were observed downstream of the roller implying that faster vortical structures developed in the roller itself. The air-water flow properties were investigated in terms of the distributions of void fraction, bubble count rate, bubble diameter, interfacial velocities, turbulent velocity fluctuations and turbulence time scales. The void fraction measurements (C) showed the presence of an advective diffusion shear layer where the air concentration vertical distributions were successfully compared with an analytical solution of the advective diffusion equation for air bubbles and compared well with earlier studies. The vertical distributions of bubble count rate (F) showed a marked peak (Fmax), with increased count rates with increasing Froude number. In the air-water shear layer, the maximum bubble count rate (Fmax) decayed with increasing distance from the jump toe as previously reported. Detailed results were presented concerning the mean bubble chord length, interfacial velocity and turbulent intensity. The vertical distributions of interfacial velocity followed closely a wall jet flow pattern. The turbulence intensity distributions exhibited large values in the jump roller with amplitude up to 400% for the largest Froude number. However the turbulence levels decreased with increasing distance from the jump toe. The probability density functions of bubble chord time exhibited a wide spectrum with a predominance of small bubble chord time for largest Froude numbers. The turbulence time scale data showed an increase with the relative elevation above the bed, as well as some decrease with increasing distance from the toe. Far downstream, nearly homogeneous profiles of turbulent time scales were observed with the smallest time scales. Simultaneous measurements of free surface and bubbly flow properties suggested some possible correlation between free surface and bubble fluctuations in terms of frequency. Some cross-correlation analysis showed large fluctuations with negative and positive correlations. Some spectral analysis of the cross-correlation function indicated predominant frequencies between 1.2 to 2.3 Hz depending on the distance to the toe. These were in agreement with free-surface fluctuations. A comparative analysis of Froude similar experiments was conducted with Reynolds numbers ranging from 25,000 to 98,000, and inflow depths of 0.012, 0.018 and 0.024 m. The results implied that the experimental data obtained with inflow Reynolds numbers up to 98,000 cannot be extrapolated to large-size prototype structures without significant scale effects in terms of void fraction, bubble count rate and bubble chord time distributions. Te result has important implications in terms of civil, environmental and sanitary engineering structures where the prototype Reynolds numbers range typically from 1E+6 to over 1E+8.