Bounds on Two-Phase Flow: Part II — Void Fraction in Circular Pipes

Theoretical and empirical models for the gas void fraction (α) are reviewed. Simple rules are developed for obtaining rational bounds for the void fraction in two-phase flow. The lower bound is based on the separate cylinders formulation for turbulent-turbulent flow that uses the Blasius equation to predict the Fanning friction factor. The upper bound is based on the Butterworth relationship that represents well the Lockhart-Martinelli correlation. These two bounds are reversed in the case of liquid fraction (1−α). The bounds models are verified using published experimental data of void fraction versus mass quality at constant mass flow rate. The published data include different working fluids such as R-12 and R-22 at different pipe diameters, different pressures, and different mass flow rates. It is shown that the published data can be well bounded for a wide range of mass qualities, pipe diameters, pressures and mass flow rates. Further comparisons are made using the published experimental data of void fraction (α) and liquid fraction (1−α) versus the Lockhart-Martinelli parameter (X), for different working fluids such as R-12, R-22 and air-water mixtures.