Modeling the Onset of Gas Entrainment in a Single Downward Discharge From a Stratified Gas-Liquid Region With Liquid Crossflow

The critical height at the onset of gas entrainment, in a single downward oriented discharge from a stratified gas-liquid region with liquid crossflow, was modeled. The assumptions made in the development of the model reduced the problem to that of a potential flow. The discharge was modeled as a point-sink while the crossflow was said to be uniform at the main pipe inlet. The potential function was determined from a superposition of known solutions for a point-sink and uniform flow. The resulting system of three equations demonstrated that the flow field was dominated by the discharge and crossflow Froude numbers. The system was solved numerically and provided a relationship between the geometry, flow conditions, dip location, and critical height. The model predicted that the critical height increased with the discharge Froude number and decreased with the crossflow Froude number. With no imposed crossflow, the model prediction demonstrated agreement with transient and quasisteady experimental data to within ±30%. Existing experimental correlations showed inconsistent crossflow effects on the critical height and disagreed with the model predictions at high discharge Froude numbers.