Computational analysis of transport in three-dimensional heterogeneous materials

TL;DR

This paper presents an integrated, open-source computational framework for analyzing transport phenomena in complex 3D heterogeneous porous materials, including new algorithms for generating random packings and efficient upscaling techniques.

Contribution

It introduces a novel algorithm for generating random packings of ellipsoids and extends existing simulation tools into a comprehensive pipeline for studying transport in porous structures.

Findings

Convergence properties of transport in periodic sphere arrangements analyzed.

Heat transfer in layered and anisotropic materials demonstrated.

Upscaling methods validated with diverse 3D applications.

Abstract

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection-diffusion-reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.