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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.

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.

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.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

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).

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference r_o-r_i. Moreover, several Darcy numbers have been considered.

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.