##### A multi-scale approach

# modelling of complex porous materials.

Porous media are widely applicable in for example filtration, ventilation, heat transfer, bio-engineering, drainage, oil extraction and drying processes. Fluid flow through porous media is an interesting but also complex field of study. This kind of flow consists of an interpenetrating liquid or gas through a labyrinth of solid material, for example, a randomly packed bed of beads, rocks, sand or straws. It could also be one solid material with holes or canals (such as a sponge).

##### analysing flow through porous media

Often, porous media are components in larger fluid flow systems. To analyze such systems, macro-scale flow and micro-scale flow are distinguished, where macro-scale flow runs through pipes, chambers and machinery and micro-scale flow occurs at the complex structure of porous components. Accurately simulating the micro-scale flow is difficult and time consuming. Instead, the porous component can be modelled as a black box, in which the main characteristics of the micro-scale flow are represented. These characteristics are the pressure drop over the porous medium and corresponding flow rate or flow velocity. To determine these, an experimental or a numerical approach can be used.

๐ฒ๐
๐ฝ๐ฒ๐ฟ๐ถ๐บ๐ฒ๐ป๐๐ฎ๐น ๐ฎ๐ฝ๐ฝ๐ฟ๐ผ๐ฎ๐ฐ๐ต

If the material of the porous component to be analyzed is already produced and easily available, an experimental setup is a fast and realiable way to obtain flow characteristics. In several projects, we used the setup shown in the figure, to experimentally measure the pressure loss through a porous medium. From the experimental data, the relation between pressure drop, flow rate and material length can be extracted.

๐ป๐๐บ๐ฒ๐ฟ๐ถ๐ฐ๐ฎ๐น ๐ฎ๐ฝ๐ฝ๐ฟ๐ผ๐ฎ๐ฐ๐ต

If the porous material is not physically available or is still conceptual, a micro-scale simulation of the porous material can be used. To this end, some knowledge of the material structure is needed.

This figure shows the result of a particular micro-flow simulation. Here, the flow was modelled through only a small part of the total material, incorporating a suitable void fraction and grain or pore size. Again, the relation between pressure drop, flow rate and length of the material is derived and scaled to match the total porous component.

๐ฐ๐ผ๐บ๐ฝ๐ฎ๐ฟ๐ถ๐๐ผ๐ป ๐๐ผ ๐ฎ๐ป๐ฎ๐น๐๐๐ถ๐ฐ๐ฎ๐น ๐ฟ๐ฒ๐น๐ฎ๐๐ถ๐ผ๐ป๐

The next step in analyzing a porous medium, is to compare the obtained characteristics from either an experimental or numerical approach to analytical relations for porous flow, such as Darcyโs law or the Ergun equation. For the example in this figure, we were able to find a good match between the simulation and the Ergun equation, validating the performed simulation. Additionally, the micro-scale simulation results matched experimental data as well. Hence, we can conclude that a numerical approach works well in this case. Replacing the porous component by a โblack boxโ with the obtained flow characteristics, saves extensive simulation effort in the analysis of the larger system. This can be implemented both in a system analysis as well as in a macro-scale CFD simulation.

## Demcon multiphysics.

Demcon multiphysics is an engineering agency with high-end expertise in the area of heat transfer, fluid dynamics, structural mechanics, acoustics, electromagnetism and nuclear physics. We support clients from a wide variety of market sectors and help them achieve their goals in research and development with deep physical insights.

We combine fundamental physical knowledge from an analytical approach with Computer Aided Engineering (CAE) simulations tools from ANSYS, MATHWORKS, COMSOL, STAR-CCM+ and FLUKA to setup, execute, analyze and evaluate numerical simulations. The use of Computational Fluid Dynamics (CFD), Finite Element Analysis (FEM / FEA), Lumped Element Modelling (LEM), Computational Electromagnetics (CEM) and Monte Carlo simulations enables us to make a virtual prototype of your design. With these techniques we can simulate the fluid and gas flows, energy exchange, heat and mass transfer, stresses, strains and vibrations in structures and the interaction of electromagnetic fields with other physical aspects like heat generation. Simulation-driven product development increases the development efficiency and reduces the product development time. Our services can therefore fully support you in the designing phase, from idea up to prototype, from prototype to final design.