An experimental and numerical study of the circular hydraulic jump

Abstract

This paper describes experiments and numerical simulations on the normal impact of a round liquid jet onto a horizontal surface, such as when water from a tap hits the bottom of a kitchen sink. In this case the liquid impacting on the surface spreads as a fast-flowing thin film and, at some distance from the point of impact, the thickness of the flow abruptly increases and the speed of the flow is reduced. In the experiments studied here the flow is axisymmetric about the axis of the jet, and the abrupt change in depth occurs at a given radius and is known as a circular hydraulic jump (CHJ). We present new experiments in which we measure the thickness of the liquid film inside and beyond the jump and use these measurements to estimate the governing parameters, the Weber, Froude and Reynolds numbers that determine the influence of surface tension, gravity and viscosity, respectively. We also carry out numerical simulations of the flow that show excellent agreement with the experiments and provide independent estimates of these dimensionless parameters. We find that, on the scale of a kitchen sink, and for water at high Reynolds number and low Bond number, at the jump the Weber number is of order unity while the Froude number is large, implying that the jump is controlled by surface tension. We also define a critical dimensionless jet flow rate at which this control no longer holds and gravity plays a significant role.