A Mechanistic Model of Liquid Film Movements in Pipe Elbows for Annular Flow

Abstract

A mechanistic model of film movements is developed based on the treatments on the annular flow field. The initial conditions at the inlet are determined by adopting a validated film thickness correlation of fully developed upward annular flow in vertical pipes. The overall pressure gradient is assumed to be uniform all along the axial distance within the elbow and the static pressure is also uniform on every cross section. The axial velocities of the liquid film and the core region are both uniform on the cross-sectional plane. The droplets are assumed to travel in straight lines normal to the inlet plane until colliding on and absorbed by the liquid film surface. The liquid film motion is divided into the axial and radial directions. Energy conservation law and Newton's second law are, respectively, used in the two directions. The film motion calculation is executed by using a discrete method with an explicit solution. The average film thickness and the circumferential thickness distribution on an arbitrary cross section can be obtained for the given flow conditions. The mechanistic model is verified by comparing the predicted circumferential distribution of film thickness with three series of experimental data from the literature. Parametric studies are also conducted to investigate the parameter effects and the range of application. The present work proves that the variation and distribution of film thickness within the elbows can be efficiently described by the mechanistic model.