A two-layer model for buoyant inertial displacement flows in inclined pipes

作者：Etrati Ali^*; Frigaard A

来源：Physics of Fluids, 2018, 30(2): 022107.

DOI：10.1063/1.5019366

We investigate the inertial flows found in buoyant miscible displacements using a two-layer model. From displacement flow experiments in inclined pipes, it has been observed that for significant ranges of Fr and Re cos beta/Fr, a two-layer, stratified flow develops with the heavier fluid moving at the bottom of the pipe. Due to significant inertial effects, thin-film/lubrication models developed for laminar, viscous flows are not effective for predicting these flows. Here we develop a displacement model that addresses this shortcoming. The complete model for the displacement flow consists of mass and momentum equations for each fluid, resulting in a set of four non-linear equations. By integrating over each layer and eliminating the pressure gradient, we reduce the system to two equations for the area and mean velocity of the heavy fluid layer. The wall and interfacial stresses appear as source terms in the reduced system. The final system of equations is solved numerically using a robust, shock-capturing scheme. The equations are stabilized to remove non-physical instabilities. A linear stability analysis is able to predict the onset of instabilities at the interface and together with numerical solution, is used to study displacement effectiveness over different parametric regimes. Backflow and instability onset predictions are made for different viscosity ratios. Published by AIP Publishing.

• 出版日期2018-2