Robust pore-resolved CFD through porous monoliths reconstructed by micro-computed tomography: From digitization to flow prediction

TL;DR

This work addresses predicting pore-scale flow in complex, digitized porous media by combining a sharp immersed boundary method with Radial Basis Function-encoded signed distance fields within a parallel finite element framework. The methodology enables pore-resolved CFD directly from μCT data, verified with manufactured solutions and validated against experimental pressure drops up to pore Reynolds numbers $Re\le 30$. Adaptive RBF encoding reduces memory and computation, delivering a robust workflow from digitization to velocity and pressure fields and bridging sub-millimeter flow details to macroscopic properties, i.e., a physics-based digital twin for porous media. The approach reveals that network topology and preferential channels dominate pressure evolution at the studied scale, offering new design and optimization opportunities for heat exchangers, membranes, micro-reactors, and other porous-media devices.

Abstract

Porous media are ubiquitous in energy storage and conversion, catalysis, biomechanics, hydrogeology, as well as many other fields. These materials possess high surface-to-volume ratios and their complex channels can restrict and guide the flow. However, optimizing design parameters for specific applications remains challenging due to the intricate structure of porous media. Pore-resolved CFD reveals the effects of their structure on flow characteristics, but is limited by the performance of mesh generation algorithms for such complex geometries. To alleviate this issue, we use a sharp immersed boundary method which enables usage of Cartesian, non-conformal grids, within a massively parallel finite element framework. This method preserves the order convergence of the scheme and allows for adaptive mesh refinement (AMR). We introduce a radial basis function-based representation of solids that allows to solve the flow through complex geometries with precision. We verify the method using the method of manufactured solutions. We validate it using pressure drop measurements through porous silicone monoliths digitized by X-ray computed microtomography, for pore Reynolds numbers up to 30. Simulations are conducted using grids of 200M cells distributed over 8k cores, which would require 16 times more cells without AMR. Results reveal that pore network structure is the principal factor describing pressure evolution and that preferential channels are dominant at this scale. In this work, we demonstrate a robust and efficient workflow for pore-resolved simulations of porous monoliths. This work bridges the gap between sub-millimetric flow and macroscopic properties, which will open the door to design and optimize processes through the usage of physics-based digital twins of complex porous media.

Figures (22)

• Figure 1: Process of synthetizing a monolith (\ref{['sec:porous_samples_synthesis']}), digitizing this monolith (Section \ref{['sec:section_tomo']}), constructing a RBF-network representation of its shape (Section \ref{['sec:rbf_network_training']}) and simulating the flow through its pores (Section \ref{['sec:sim_setup']}). The flow simulation results show the monolith colored by the normalized pressure field at the surface, with the streamlines following the velocity field.
• Figure 2: Steps used to place RBF-nodes around an object and associate compact basis functions to each node. (A) Around a given object, (B) a uniform grid is formed (C) then adaptively refined near the boundary. (D) Nodes are placed at the center of each cell, (E) then a basis function is associated to each node. (F) The grid is not needed anymore.
• Figure 3: Shapes used for the verification of the flow around superquadric and RBF-encoded shapes.
• Figure 4: $\mathcal{L}2$ norm of the error of the MMS for the velocity and pressure fields with Q$_1$Q$_1$ elements around A a sphere, B a convex superquadric (Conv.Sup.) and C a concave superquadric (Conv.Sup.), both for analytical (full lines) and for RBF representations (dotted lines). Diamond and square markers signify pressure and velocity errors, respectively. For RBF representations, markers are half-filled in varying orientations depending of the number of RBF-nodes. $n$ is the order of convergence for the last two grids.
• Figure 5: $\mathcal{L}2$ norm of the error of the MMS for the velocity and pressure fields with Q$_2$Q$_1$ elements around A a sphere, B a convex superquadric (Conv.Sup.) and C a concave superquadric (Conv.Sup.), both for analytical (full lines) and for RBF representations (dotted lines). Diamond and square markers signify pressure and velocity errors, respectively. For RBF representations, markers are half-filled in varying orientations depending of the number of RBF-nodes. $n$ is the order of convergence for the last two grids.