An experimental and numerical study on the wall lubrication force in dispersed liquid-liquid flow

Abstract

Many analytical, experimental and numerical works have been devoted to the accurate prediction of volumetric fraction distribution in the wall region, which is important for the numerical simulation of dispersed flow. Within the two-fluid-model framework, it depends upon the correct modeling of interfacial forces, and among them there is the wall lubrication force. In this prospective paper, we try to contribute with the discussion by studying the effect of wall lubrication forces in a dispersed liquid-liquid flow. Instead of bubbles, oil droplets dispersed in turbulent water flow are moved away from the wall. This phenomenon has been recently observed in a dispersed oil-water flow in a horizontal pipe and one of the findings is that it is related to drag reduction. One of the industries that have interest in this kind of problem is the energy industry. The pipe flow of oil-in-water dispersion is very common in the Brazilian offshore production scenario. An experimental campaign was carried out to measure the wall water thickness as a function of mixture velocity. The frictional pressure-drop was also measured to estimate the oil droplet average diameter. The Reynolds lubrication equation is solved using the finite element method to compute the lubrication force in the gap between a typical oil droplet and the pipe wall. Two methods were used to solve it, the Gauss-Seidel and Successive Overrelaxation. The ratio of lubrication to buoyancy forces is computed for the flow condition studied in this work, and the results suggest that the occurrence of wall lubrication force is a reasonable explanation for the observed concentration of dispersed oil droplets in the turbulent core of the pipe.