ALE-FE Method for Two-Phase Flows with Dynamic Boundaries

Abstract

Bubbles and drops dynamics through capillaries of variable cross-section still remain of considerable importance in two-phase flows through porous media. Experimental studies are found in the literature where the motion of immiscible bubbles in different fluids is investigated. Recovery of oil by chemical flooding, biological processes and crude oil transportation in through pipelines are examples of industry-related applications. We seek to study numerically the effects of the surface tension, bubble dynamics and channel geometry influence for two-phase flows in channels with variable cross-section using a moving mesh moving boundary domain scheme, which dramatically shortens the domain length. Such a scheme moves the computational boundary nodes according to the variable cross-section of a given problem dynamically. In this work, we present several physical problems where the crosssections change periodically or arbitrarily according to the geometry. Figure 1 is a schematic diagram of the axisymmetric sinusoidal channel showing the wave equation as function of the bubble's centroid position. Figure 2 shows a numerical simulation of axisymmetric two-phase flow found in capillaries with variable cross-section, where the top boundary is represented by a wave function. The rising bubble motion is due to gravity acting on the x-axis. The bubble, represented by the red colour, has its center of mass fixed in space, and the top boundary moves accordingly to the bubble's centroid velocity. The new methodology proposed to simulate two-phase flows in variable cross-sectioned channels shows interesting results, good accuracy to describe interfacial forces and bubble dynamics in different complex geometries with moving boundaries.