A gas entrainment model for hydraulic jumps in near horizontal pipes

We develop a simplified physical model for gas entrainment in the hydraulic jump, where the subcritical flow fills the pipe diameter. The model is compared to experimental data obtained in a previous study where the entrained gas flux (air) is measured directly. Different pipe diameters and fluids were considered. Based on the structure of the hydraulic jump, we suggest that an important mechanism is entrainment by liquid that is expelled from the front and plunges into the incoming liquid ahead of the front, coupled with gas leakage out of the front. Turbulence generation and circulation behind the front are accounted for.The model performs well when the entrainment parameters are tuned to values reported elsewhere for “plunging” liquid jets. With a single set of entrainment constants, we obtain satisfactory results for the different inflow velocities and pipe diameters. The model is designed for highly turbulent flows, where the effect of fluid viscosity is minor or absent. The entrainment rate could not be linked in a simple way to the Froude number. The model constitutes an explicit algebraic relation between the entrainment rate and the flow parameters (average inflow velocity and height of the jump).

► We model gas entrainment in hydraulic jumps confined by a pipe.
► The experimental gas flow rates were measured directly.
► We find evidence for entrainment caused by liquid expelled at the front.
► Our approach provides an approximate, but physically consistent model.
► The entrainment cannot be linked in a simple way to the Froude number.