Predication of wall shear stress of vertical upward co-current adiabatic air-water annular flow in pipes

Annular flow has been widely applied to industrials such as oil extraction, refrigerators, nuclear reactors and so on. Wall shear stress is one of the most important parameters for studying two-phase annular flow. When calculating wall shear stress from interfacial shear stress, the relationship between the wall shear stress and the interfacial shear stress is complicated and needs some parameters such as film thickness which requires high-precision measurement technique to acquire accurately. Besides, some wall shear stress correlations developed for annular flow are applicable to flow conditions at atmospheric pressure only. Because of these reasons, four databases for vertical upward co-current adiabatic air-water two-phase annular flow have been collected with wide range of flow conditions and different pressure conditions. Using these data, a simplified model between wall shear stress and interfacial shear stress is proposed. The new model is derived from the force balance analysis of the liquid film and gas core. As void fraction of annular flow is close to 1, the relationship between wall shear stress and interfacial shear stress can be simplified to be linearly. Based on this model and existing interfacial shear stress correlations, the wall shear stress can be calculated directly from flow conditions and fluid properties that can be readily obtained from experiments. Also, a new wall shear stress correlation calculated from wave velocities has been suggested. It is developed from frictional pressure drop correlation. Correlations for two-phase multiplier and wave velocity as well as pure empirical correlations also have been compared with existing databases. From data comparison, the newly proposed correlations in this study agree well with experimental data and other correlations with good prediction accuracy have been pointed out.