Modelling of pressure drop in periodic square-bar packed beds

TL;DR

This study numerically investigates pressure drops in square-bar packed beds with various geometries, revealing how rotation angles influence flow regimes and friction factors, and providing models for permeability prediction.

Contribution

It introduces a detailed numerical analysis of non-spherical packed beds with variable geometries, extending understanding beyond spherical packings.

Findings

Flow geometry classification as channel-like or lattice-like based on rotation angle.

Maximum friction factor occurs at different angles in creeping and inertial regimes.

Module-equivalent diameter effectively predicts permeability using Ergun correlation.

Abstract

Understanding fluid flow through porous media with complex geometries is essential for improving the design and operation of packed-bed reactors. Most existing studies focus on spherical packings, having as a consequence that accurate models for irregular interstitial geometries are scarce. In this study, we numerically investigated the flow through a set of packed-bed geometries consisting of square bars stacked on top of each other and arranged in disk-shaped modules. Rotation of each module allows the generation of a variety of geometrical configurations at Reynolds numbers of up to 200 (based on the bar size). Simulations were carried out using the open-source solver OpenFOAM. Selected cases (e.g., $\alpha = 30^\circ$, $\mathrm{Re}_\mathrm{p} = 100, 200$) were compared against Particle Image Velocimetry measurements. Results reveal that, based on the relative rotation angle, the realized geometries can be classified as channel-like ($\alpha \leq 10^\circ$) and lattice-like ($\alpha \geq 15^\circ$), fundamentally altering the friction factor. Furthermore, the maximum friction factor obtained in the creeping regime occurred at $\alpha = 25^\circ$, whereas in the inertial regime, this occurred at $\alpha = 60^\circ$. The module-equivalent diameter, based on the angle-dependent wetted surface area, collapses the friction factor onto the Ergun correlation and yields good permeability predictions for the lattice-like geometries.