Two-phase explicit CBS procedure for compressible viscous flow transport in porous materials

• Published in: International journal of numerical methods for heat & fluid flow Vol. 28; no. 2; pp. 336 - 360
• Main Authors: Cortellessa, Gino, Arpino, Fausto, Di Fraia, Simona, Scungio, Mauro
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 05.02.2018; Emerald Group Publishing Limited
• Subjects: Algorithms; Coefficients; Compressibility; Computational fluid dynamics; Computational physics; Computer simulation; Conduction heating; Conductive heat transfer; Conservation laws; Differential equations; Diffusion coefficient; Diffusion coefficients; Dye dispersion; Finite element method; Fluids; Forces (mechanics); Heat; Heat conduction; Heat exchange; Heat transfer; Interactions; Interfaces; Investigations; Liquid phases; Mass transfer; Mathematical models; Matrix methods; Mechanical engineering; Methods; Modelling; Numerical analysis; Permeability; Phase change; Phase transitions; Porous materials; Porous media; Resolution; Simulation; Theoretical analysis; Transport; Transport phenomena; Transport processes; Turbulence models; Vapors; Velocity; Viscosity; Viscous flow; Italy; Porous media; Local thermal non-equilibrium; Finite elements; Multiphase mixture model; Heat transfer
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-02-2017-0080

Purpose In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations. Design/methodology/approach Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix. Findings The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature. Social implications The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media. Originality/value For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).