ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

Abstract

A numerical method is described to study two-phase flows for single and multiple bubbles with phase change. The fluid flow equations are based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a new two-phase method with an improved model for the liquid-gas interface in microchannels. A successful adaptive mesh update procedure is also described for effective management of the mesh at the two-phase interface to remove, add and repair surface elements, since the computational mesh nodes move according to the flow. The Lagrangian description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The methodology proposed for computing the curvature leads to accurate results with moderate programming effort and computational cost and it can also be applied to different configurations with an explicit description of the interface. Such a methodology can be employed to study accurately many problems such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modelling of biological systems and efficient cooling of electronics for computational purposes, being the latter the aim of this research. The obtained numerical results will be described, therefore proving the capability of the proposed new methodology.