New dimensionless number for gas-liquid flow in pipes

Two-phase flow modeling is a general problem in science and engineering. Two-phase flow phenomenon is inherently complicated and characterized by a large number of flow variables. It is historically known that the lack of proper dimensionless numbers in two-phase flow is one of the major shortcomings as compared to single-phase flow. A new dimensionless number (Slippage Number) for gas-liquid flow in pipes is proposed in this paper. The number is defined as the ratio of the difference in the gravitational forces between slip and no-slip conditions to the inertial force of the gas. It is found to be a function of Froude number based on the mixture velocity especially in the elongated bubble, slug, churn, bubble, and high film thickness wavy annular flow patterns. The liquid holdup data for a wide range of fluid and flow conditions (different viscosities, densities, pipe diameters, inclination angles, gas and liquid flow rates) can be correlated with a single curve using the Slippage Number. The value of the number varies from highest to lowest for bubble, elongated bubble, slug, churn, stratified and annular flow patterns, respectively. It is close to zero for homogeneous flow patterns like mist and dispersed bubble flows. We also show that this number may be used as a flow pattern identifier.