Modelling of pressure drop in periodic square-bar packed beds

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., $α= 30^\circ$, $\mathrm{Re}_\mathrm{p} = 100, 200$) 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 ($α\leq 10^\circ$) and lattice-like ($α\geq 15^\circ$), fundamentally altering the friction factor. Furthermore, the maximum friction factor obtained in the creeping regime occurred at $α= 25^\circ$, whereas in the inertial regime, this occurred at $α= 60^\circ$. 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.

Figures (17)

• Figure 1: (a) The laboratory-scale packed bed of christin2025. (b) The cross-section of the packed-bed geometry christin2025 formed from six modules, each rotated by 30° relative to the preceding one. (c) Schematic of the geometry of each module showing the circle enclosing the dodecagon defining the outer geometry of the slits. The streamwise direction is oriented perpendicular to the surface of the paper.
• Figure 2: Visualizations of the simulation domains (i.e., volumes occupied by the fluid) for each of the studied rotation angles, ranging from $5^\circ$ to $90^\circ$. The streamwise direction is oriented vertically, with the flow moving from bottom to top.
• Figure 3: Non-dimensional specific surface area $a_v B$ and bed-to-particle diameter ratio $D/d_{\mathrm{eq}}$ as a function of the rotation angle $\alpha$
• Figure 4: (a) Schematic representation of the simulation domain for the case with a module angle of $50°$. Part of the domain is clipped for clarity. The first zoomed-in view illustrates the orientation of the mesh, while the second highlights the mesh structure between adjacent layers. (b) Detailed view of the refined mesh at the same angle
• Figure 5: Computational mesh of the $60°$ simulation domain, representing periodically repeated module used for averaging