Comprehensive Study of 3D Liquid Flow Fields in Additive Manufactured Structures for SMART Reactors Using Large-Scale Vertical Magnetic Resonance Imaging and Computational Fluid Dynamics

TL;DR

This work addresses the lack of experimental flow data in TPMS-based reactor internals by delivering fully 3D velocity fields via MRI velocimetry in a large-bore vertical MRI for three additively manufactured TPMS geometries ($G$, $G_{45}$, $SD$) at $50 \le Re_S \le 300$ and porosity $\epsilon=70\%$. A detailed CFD workflow in OpenFOAM is established to cross-validate the MRI measurements, using a CAD-based domain, grid-convergence analysis, and axial- slice averaging to enable direct comparison. Key findings show pronounced geometry-driven flow features: strong axial channelling in Gyroid, pronounced merge-split mixing in Schwarz-Diamond, and reduced channelling with Gyroid rotation, all corroborated by fair-to-good pixel-wise agreement between CFD and MRI (typical $\text{rRMSE}$ around $40$–$75\%$ depending on $Re_S$). The integrated MRI-CFD framework provides a robust basis for investigating heat and mass transfer and reactive flow in TPMS reactor internals, informing design strategies for SMART Reactors and enabling scalable, non-invasive validation of complex porous media flows.

Abstract

Triply Periodic Minimal Surface (TPMS) structures have emerged as a new class of porous materials with variable geometries and favourable transport properties, making them promising for reactor internals in chemical engineering. However, experimental data on internal TPMS flow behaviour are still limited. To address this gap, the flow behaviour in additively manufactured TPMS structures is analysed using three-dimensional Magnetic Resonance Imaging (MRI) velocimetry in a large-bore vertical 3 T MRI system, in cylindrical columns of 38 mm diameter and Reynolds numbers between 50 and 300. Three different TPMS geometries are investigated, and consistency between Computational Fluid Dynamics (CFD) simulations and experimentally measured MRI velocity fields is established through cross-validation. The MRI system provides fully three-dimensional velocity fields with a divergence deviation below 6 %. MRI revealed distinct flow features: the Gyroid TPnS exhibited pronounced channelling, while the Schwarz-Diamond TPSf showed merge-split behaviour, achieving a 46 % increase in lateral mixing compared to the Gyroid TPnS structures. Numerical simulations reproduce the flow features and show agreement with the MRI data. The combined methodology demonstrates the suitability of MRI velocimetry for the experimental validation of CFD simulations and establishes a robust foundation for future studies of heat and mass transfer, as well as reactive flow, in structured reactor systems.

Figures (15)

• Figure 1: Unit cells employed in this study: (a) Gyroid TPnS $(\alpha = 0^\circ)$ (G), (b) Gyroid TPnS $(\alpha = 45^\circ)$ (G45), and (c) Schwarz-Diamond TPSf (SD). All structures exhibit a porosity of $\epsilon = 70\%$ and a unit cell size of $10 \times 10 \times 10~\text{mm}^3$.
• Figure 2: Generation process of the structures, exemplified by the Gyroid TPnS $(\alpha = 0^\circ)$. (a) Unit cell design. (b) Assembly of the structure as a rectangular block and subsequent mapping into a cylindrical geometry. (c) Integration of the surrounding wall and clamping connectors into the cylindrical design. The red section indicates the FOV for the MRI measurements, covering a length of 20 mm with 20 slices of 1 mm thickness. For clarity, the figure shows a reduced number of slices.
• Figure 3: Left: Schematic flow diagram of the experimental setup showing the gear pump (1), the Coriolis MFM (2) for monitoring the mass flow rate, the degassing vessel (3) with the vacuum pump (4), the inlet acrylic pipe (5), the TPMS modules (6), and the MRI system (7). The main flow direction through the TPMS modules is oriented opposite to the gravitational acceleration $g$. Right: Close-up of the analysed area is illustrated, including the custom-built RF receive coil with single-channel (8) and the FOV within the module (9).
• Figure 4: Full-scale CFD configuration with an established flow profile, highlighting the analysed FOV (red), shown for the Gyroid TPnS $(\alpha = 0^\circ)$ structure.
• Figure 5: Normalised signal intensity plotted against frequency for each slice, exemplarily shown for the Gyroid TPnS $(\alpha = 0^\circ)$ at $Re_\text{S} = 156$ and $z=0~\text{mm}$ (see Tab. \ref{['tab:operating_cond']}). The histogram of the signal intensity for a single slice shows two main peaks, with the local minimum used to filter and retain only the flow signal.