On the motion of vertical and oblique sand jets in stagnant immiscible liquids

Abstract

Sand jets and particle clouds in water and viscous fluids have been a frequent subject of intense research and are pertinent to many environmental, industrial, and engineering processes. Mixing and dispersion of sand jets and particle clouds in water have been studied to design and optimize wastewater dredging disposal and marine bed capping. Motion of dispersed particles in viscous fluids is of great interest in design and operation of oil-sand tailing ponds and modeling magma flows. The motion of vertical and oblique sand jets passing through an immiscible layer is controlled by the properties of background fluids, the physical characteristics of sand particles, and the initial release conditions. Predicting the fate of the instantaneously released sediments in stratified oil-water system requires knowledge of how various physical factors contribute to the formation process of sediment clouds. Laboratory experiments were conducted to study the behaviour of particle clouds passing through two immiscible fluids (i.e., oil and water), formed by instantaneous release of dry sand particles from different angles and various heights above the oil layer, and to understand the effects of controlling parameters on the formation of particle clusters. Different air release heights h, release angle θ, nozzle diameters do, and sand masses m were tested. Nozzle size and mass of sand particles were grouped to form a non-dimensional parameter as L/do where L is the length of pipe filled up with sand particles. Wide ranges of aspect ratios (1≤L/do≤19.6 for vertical and 1.5≤L/do≤24.5 for oblique sand jets) were considered. Air release height was normalized to form non-dimensional air release height as η. Effects of the characteristics of sand jets in air such as mass flow rate, sand impact velocity, and jet diameter on the evolution of oily sand jets were investigated. It was found that the diameter of sand jet in air linearly correlated with the nozzle diameter. Evolution of oily sand jets with time was investigated using image processing and boundary visualization techniques. Different shapes of the frontal head and various evolution patterns were observed based on the initial parameters. The frontal width and velocity of oily sand were measured for different evolution times. Dimensional analysis was performed, and empirical correlations were introduced to predict the frontal width and velocity of particle clouds passing through immiscible layer. The average shear stress in the immiscible layer and in the early stages of evolution was calculated from the measurements: the normalised shear stress between sand particles and the immiscible layer was found to linearly increase with the impact momentum. The average drag coefficient of sand jet front was calculated and results were compared with the classical drag models. The average drag coefficient of oily sand jets was found to be smaller than the drag coefficient of individual sand particles in a steady-state condition.