An empirical model of the wetted wall fraction in separated flows of horizontal and inclined pipes

Abstract

This study reports an experiment to investigate the wetted wall fraction (WWF), which represents the shape of the continuous interface of the air–water stratified and wavy flow regimes, in horizontal and inclined pipes with an inner diameter of 40 mm. Using the experimental data, a semi-empirical model to predict the WWF was developed based on the energy balance for the liquid phase in separated flows. The model used a relationship between the WWF and the center of gravity of the liquid phase with a concave interface that can describe continuous changes to the flow regime from a stratified to an annular. The coefficients of the model were empirically determined based on a wide range of experimental data from the literature obtained in the air and various liquids covering a void fraction of greater than 0.79, a pipe with inner diameter in the range 24–150 mm, density differences varying from 812 to 1052 kg/m3, a range of liquid phase viscosity of 0.87–5.66 mPa s, surface tension ranging from 27.9 to 72.7 mN/m, a wide range of inclination angles from −27° for a downward flow to +3° for an upward flow, and gas and liquid Reynolds numbers based on a superficial velocity of up to 219,000 and 7500, respectively. This WWF model was tested using an extensive experimental database of the WWF and void fraction in the stratified and wavy flow regimes, and yielded the best agreement compared with existing models in the literature.