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

This study utilizes large-scale 3T vertical Magnetic Resonance Imaging (MRI) and Computational Fluid Dynamics (CFD) to characterize and validate 3D liquid flow fields within additively manufactured TPMS structures, revealing that Schwarz-Diamond geometries significantly enhance lateral mixing compared to Gyroid structures.

The Gist

The "Labyrinth in a Bottle" Study: Making Better Chemical Reactors

Imagine you are trying to clean a very dirty sponge. If you just pour water over the top, the water might find one easy path through the middle, zip straight to the bottom, and leave most of the sponge dry and dirty. This is a huge problem in chemical engineering. When scientists build "reactors" (giant containers where chemicals mix to make things like medicine or fuel), they want the liquid to touch every single nook and cranny of the container to ensure the reaction happens perfectly.

This paper describes a high-tech way to peek inside these complex "sponges" to see exactly how liquids move through them.

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1. The "Super-Sponges" (TPMS Structures)

Instead of using random pebbles or simple tubes, the researchers used something called TPMS structures.

The Analogy: Think of a standard sponge as a messy pile of tangled yarn. Now, imagine a sponge designed by a master architect using mathematical equations—it has smooth, flowing, interconnected tunnels that look like a piece of modern art. These are the TPMS structures. They are incredibly efficient because they have massive surface areas but no sharp corners to get stuck in.

The researchers tested three specific "architectural styles":

• The Gyroid: A series of winding, helical tunnels.
• The Rotated Gyroid: The same tunnels, but tilted at a 45-degree angle.
• The Schwarz-Diamond: A structure that looks like a series of diamond-shaped rooms that constantly merge and split.

2. The "X-Ray Vision" (MRI Velocimetry)

The problem is that these structures are solid and opaque. You can't just stick a camera inside a metal or plastic block to see the liquid moving.

The Analogy: Imagine trying to figure out how people are moving through a crowded, winding maze inside a dark building. You can't see them, but you have a "magic sensor" that can detect the movement of every single person through the walls.

That "magic sensor" is a 3-Tesla MRI machine (the same kind used in hospitals). By adding a special salt to the water, the researchers turned the liquid into something the MRI could "see." They didn't just see where the water was; they saw exactly how fast it was moving in 3D.

3. The "Digital Twin" (CFD Simulations)

To make sure their MRI "magic sensor" wasn't lying to them, they used Computational Fluid Dynamics (CFD).

The Analogy: This is like building a perfect video game version of the maze on a computer. They ran a simulation to see how they thought the water should move, and then they compared the "video game" results to the "real-life" MRI results. If the video game and the real life matched, they knew their math was solid.

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4. What did they find? (The Results)

The study revealed that the "architecture" of the sponge changes everything:

• The Gyroid (The "Highway" Problem): The standard Gyroid was a bit too efficient at being a highway. The liquid found "express lanes" and zipped through the center, leaving the sides relatively untouched. This is bad for a reactor because the "sides" don't get to do their job.
• The Rotated Gyroid (The "Speed Bump" Solution): By simply tilting the structure by 45 degrees, they broke up those express lanes. It forced the liquid to wander more, making the flow more even.
• The Schwarz-Diamond (The "Dance Partner"): This was the superstar. Because its channels constantly merge and split, the liquid is forced to swirl and mix aggressively.
  • The Analogy: If the Gyroid is a straight hallway, the Schwarz-Diamond is a crowded dance floor where people are constantly bumping into each other and changing direction. This "merging and splitting" increased mixing by 46% compared to the Gyroid.

Why does this matter?

By understanding these tiny, invisible "dances" of liquid, engineers can design much smaller, faster, and more efficient reactors. This could lead to cleaner energy production, more effective medicines, and less waste in chemical manufacturing. They’ve essentially created a "blueprint" for building the perfect, high-performance microscopic labyrinths of the future.

Technical Summary

Technical Summary: Comprehensive Study of 3D Liquid Flow Fields in Additively Manufactured TPMS Structures

1. Problem Statement

In chemical engineering, structured reactor internals (like Triply Periodic Minimal Surfaces, or TPMS) are preferred over traditional packed beds because they offer higher surface-to-volume ratios, better heat/mass transfer, and lower pressure drops. However, characterizing the internal fluid dynamics of these complex, porous, and tortuous geometries is extremely difficult.

• Optical limitations: Traditional methods like Particle Image Velocimetry (PIV) require optical access, which is hindered by the complex, non-transparent, and refractive nature of TPMS structures.
• Resolution limitations: Other tomographic methods (X-ray, Ultrasound, Electrical Capacitance) often lack the sub-millimeter spatial resolution required to resolve individual fluid channels within these structures.
• Knowledge Gap: While some studies exist for specific geometries (like the Schwarz-Diamond), there is a lack of comprehensive 3D data for other common geometries (like the Gyroid) and a lack of studies exploring how unit cell orientation affects internal flow.

2. Methodology

The researchers employed a dual approach combining advanced experimental imaging with high-fidelity numerical simulations.

• Experimental: Large-Scale Vertical MRI Velocimetry

  • System: A unique large-bore (400 mm diameter) vertical 3 T MRI system was used. The vertical orientation allows for larger, more industrially representative columns (38 mm diameter) and facilitates the natural rising of gas bubbles.
  • Materials: Three TPMS geometries were fabricated via additive manufacturing: Gyroid TPnS ($\alpha=0^\circ$), Rotated Gyroid TPnS ($\alpha=45^\circ$), and Schwarz-Diamond TPSf.
  • Fluid: Deionised water with copper sulphate ($34 \text{ mmol L}^{-1}$) was used to enhance MRI signal via short relaxation times ($T_1$).
  • Measurement: Phase-contrast velocity encoding was used to acquire 3D velocity fields with a lateral spatial resolution of $250\ \mu\text{m}$.

• Computational: Computational Fluid Dynamics (CFD)

  • Software: OpenFOAM (simpleFoam solver) was used to simulate steady-state incompressible flow.
  • Validation: The CFD models used the exact CAD geometries used for manufacturing. A grid convergence study (using the Grid Convergence Index, GCI) ensured the results were mesh-independent.
  • Cross-Validation: To allow direct comparison, CFD data were volumetrically averaged to match the 1 mm slice thickness of the MRI data.

3. Key Contributions

• Scale Advancement: The study achieved a higher ratio of column diameter to hydraulic diameter (up to 10.4) compared to previous MRI studies, making the setup more industrially relevant.
• Geometric Exploration: It is the first study to use MRI to investigate the flow behavior of the Gyroid TPnS and specifically examines the effect of unit cell rotation on fluid dynamics.
• Methodological Framework: It establishes a robust "cross-validation" workflow where MRI validates CFD, and CFD provides high-resolution details in regions where MRI signal-to-noise ratios are low (e.g., near walls).

4. Key Results

• Flow Feature Identification:
  • Gyroid ($\alpha=0^\circ$): Exhibited pronounced channelling, where fluid follows continuous pathways, leading to highly heterogeneous flow.
  • Rotated Gyroid ($\alpha=45^\circ$): Rotating the unit cell misaligned the channels with the main flow, suppressing channelling and promoting more locally homogeneous flow.
  • Schwarz-Diamond: Showed a unique "merge-split" behavior. This geometry achieved a 46% increase in lateral mixing (measured via hydraulic tortuosity) compared to the Gyroid structures.
• Validation Metrics:
  • Structural Integrity: MRI-derived cross-sectional areas showed good agreement with CAD models.
  • Mass Conservation: MRI underestimated mass flow rate by only ~5.1% on average, and the velocity field divergence was below 6%, proving physical consistency.
  • CFD-MRI Agreement: Qualitative and quantitative comparisons showed strong agreement in the Darcy-Forchheimer (laminar) regime, with pixel-wise axial velocity deviations around 40% (which decreases to ~10-14% in specific profiles).

5. Significance

This research provides a foundational toolkit for the design of SMART Reactors. By proving that MRI can accurately map 3D flow in complex, large-scale additive manufactured structures, the authors have opened the door for future studies to map heat transfer, mass transfer, and chemical reaction rates in real-time. The finding that unit cell orientation (rotation) can be used as a design lever to control mixing and channelling is a significant contribution to the field of reactor engineering.