Numerical Investigation of Sand-Bed Erosion by an Upward Water Jet

Abstract

A numerical model based on computational fluid dynamics and kinetic theory of granular material is used to investigate sand-bed erosion due to an upward water jet. After verifying the numerical model, the onset and mechanism of the sand-bed erosion are analyzed. As the the inlet water-jet velocity increases, a cavity around the jet orifice is first formed by the water jet, and the sand bed is eroded with a significant expansion. The numerical simulation shows that the increase in sand particle size and sand-bed height can significantly increase the inlet water velocity, causing sand-bed erosion. In addition, the critical velocity leading to sand-bed erosion is decreased as the sand friction angle decreases. Based on the observation and analysis of the numerical simulation, an analytical model using force equilibrium analysis and Ergun’s equation is proposed. The interaction between the mobilized and static zones in the sand bed is taken into account using granular theory. The critical inlet water velocity leading to the sand-bed erosion can be determined using this analytical model. This study provides a fundamental understanding of the mechanism of sand-bed erosion, and this numerical technique is shown to be an effective and promising way to investigate sand-bed behavior under an upward water jet.