Selective Withdrawal of Two-Layer Stratified Flows with a Point Sink

Abstract

The selective withdrawal of two-layer stratified flows with a point sink was investigated, considering the effect of the boundary. An analytical expression was developed for predicting the incipient Froude number as a function of the distance from the sink to the boundary (scaled by the distance from the sink and the interface). The effect of the boundary becomes significant when the relative distance is less than 2. The incipient Froude number reduces to 1.27 from 2.54 as the point sink approaches to the reservoir bottom. An analytical expression for computing the discharge ratio when both the layers withdraw was formulated and the velocity within each layer can be predicted. The analytical results were compared with the computational fluid dynamics (CFD) results. The CFD solver can successfully model velocities and the interface position in a selective withdrawal scenario for two-layer stratified flows.