Numerical Study of Circular Hydraulic Jump Using Volume-of-Fluid Method

Abstract

When a vertical liquid jet impacts on a solid and horizontal surface, the liquid starts spreading radially on the surface, until a sudden increase in the fluid height occurs and a circular hydraulic jump (CHJ), easily seen in the kitchen sink, is formed. In this study, the formation of CHJ is numerically simulated by solving the flow governing equations, continuity and momentum equations, along with an equation to track the free surface advection using the volume-of-fluid (VOF) method and Youngs’ algorithm. The numerical model is found to be capable of simulating the jump formation and its different types. Extensive comparisons are performed between the model results and those of the available experiments and modified Watson’s theory. The model is shown to accurately predict the jump location and its behavior. Also a parametric study for the effects of different parameters including volumetric flow rate, downstream height, viscosity and gravity on the jump radius, and its characteristics is carried out. Compared with previous works on CHJ available in the literature, employing the VOF method considering the surface tension effects and performing a full parametric study and a complete comparison with experiments and theory are new in this paper. The simulations are performed for two different liquids, water and ethylene glycol, where it is found that the jump is more stable and its location is less sensitive to the downstream height for the more viscous liquid (ethylene glycol). When the downstream height is increased, the radius of the circular hydraulic jump reduces up to a certain limit after which there would be no stable jump. If the gravity is decreased, the radius of the jump and the length of the transition zone will both increase. The radius of the jump in microgravity conditions is less sensitive to the downstream height than it is in normal gravity.