Hydrodynamic Behavior of Non-spherical Particles in Confined Vertical Flows: A Resolved CFD-DEM Study

This study employs resolved CFD-DEM simulations to demonstrate that non-spherical polymetallic nodules experience significantly enhanced drag and reduced terminal velocities compared to volume-equivalent spheres due to shape-induced wake asymmetry, while revealing how particle size and confinement govern distinct drag variance behaviors during vertical hydraulic transport.

The Gist

Imagine you are trying to move a pile of strange, lumpy rocks (called polymetallic nodules) from the bottom of the ocean up to a ship using a giant, vertical straw. This is how deep-sea mining works. The big question for engineers is: How do these weirdly shaped rocks behave when water rushes up the straw to carry them?

Most computer models used to design these systems treat every rock as if it were a perfect, smooth marble. But in reality, these rocks are bumpy, irregular, and look nothing like marbles. This paper asks: Does treating a lumpy rock like a smooth marble actually work, or does it give us the wrong answer?

To find out, the researchers built a super-detailed computer simulation (like a high-tech video game physics engine) that doesn't use shortcuts. Instead of guessing how water pushes on the rock, they calculated the water's push on every single bump and crevice of the rock.

Here is what they discovered, explained simply:

1. The "Lumpy Rock" vs. The "Smooth Marble"

When the researchers dropped these lumpy rocks into still water to see how fast they sink, the lumpy rocks fell about 28% slower than a smooth marble of the exact same weight and size.

• The Analogy: Imagine trying to swim through water. If you are a smooth, streamlined dolphin, you glide easily. If you are a lumpy, jagged piece of driftwood, you catch more water on your way down.
• Why it happens: The lumpy rocks have a larger "frontal area" (they catch more water) and they create a messy, asymmetrical wake behind them (like a chaotic trail of bubbles). This extra drag slows them down significantly.
• The Catch: Even though they fall slower, the total force pushing up on them (buoyancy) is the same as the marble. They just need to move slower to balance out that force.

2. The "Traffic Jam" in the Pipe

Next, they simulated water rushing up the pipe to carry these rocks. They looked at two sizes: "Small" rocks and "Large" rocks.

• The Smooth Marbles: When the water speed increased, the smooth marbles behaved predictably. At low speeds, they wobbled and settled. At high speeds, they zoomed up in a straight line, like cars merging onto a highway.
• The Lumpy Rocks: These were much more chaotic.
  • At low speeds: The small lumpy rocks didn't even make it up the pipe! They hovered near the bottom, spinning and wobbling in place, unable to overcome gravity. The smooth marbles, however, managed to move up.
  • At high speeds: Even when the water was fast enough to carry them, the lumpy rocks took longer to get to the top and moved in a much more erratic, spinning path. They were like a group of people trying to run up an escalator while spinning in circles, while the smooth marbles were just running straight up.

3. The "Spinning Top" Effect

The biggest difference was how the rocks rotated.

• Smooth Marbles: They mostly just went up. They didn't spin much.
• Lumpy Rocks: Because they are bumpy, the water hitting them made them spin wildly. This spinning (rotation) was tightly linked to their movement up and down.
• The Analogy: Think of a smooth marble as a bullet fired from a gun—it goes straight. Think of the lumpy rock as a boomerang or a spinning top thrown into a wind tunnel. It twists, turns, and changes direction constantly because of its shape. This spinning creates extra "friction" with the water, making it harder to transport.

4. The "Force Fluctuations" (The Bumpy Ride)

The researchers measured the "push" (drag force) the water gave the rocks.

• Small Rocks: Whether they were smooth or lumpy, the push was relatively steady.
• Large Rocks: Here is where it got wild.
  • Large Smooth Marbles: The push varied a bit as the water rushed past them, creating a predictable pattern of "bumps" in the force.
  • Large Lumpy Rocks: The push was wildly unpredictable. Because the rocks were spinning and changing shape relative to the water, the force would suddenly spike. It was like driving a car on a smooth road (smooth marbles) versus driving a car on a road where the bumps change every second depending on how the car is tilted (lumpy rocks).

The Bottom Line

The study concludes that while you can use a smooth marble model to get a rough idea of how these rocks will behave, it misses the details.

• If you use a smooth marble model, you might think the rocks will move up the pipe faster and more easily than they actually will.
• The lumpy rocks need more water speed to get moving, and once they are moving, they are less stable and harder to control because they spin and wobble.

In short: Nature is messy. You can't just pretend a jagged rock is a perfect sphere if you want to design a machine that actually works. The "lumpiness" adds a lot of extra drag and chaos that simple models ignore.

Technical Summary

Technical Summary: Hydrodynamic Behavior of Non-spherical Particles in Confined Vertical Flows

Problem Statement
The recovery of polymetallic nodules (PMNs) from deep-sea abyssal plains relies on hydraulic systems that transport coarse, irregular, and non-spherical particles through vertical risers. The efficiency of these systems depends on predicting particle entrainment, suspension stability, and transport behavior under strong gravitational forcing and geometric confinement. Current design practices often rely on unresolved Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) models that use empirical drag correlations calibrated for spherical particles or parameterized by scalar descriptors like sphericity. These approaches fail in confined flows (where particle-to-pipe diameter ratios $d/D \ge 0.2$) because they cannot capture orientation-dependent drag, asymmetric wall-deflected wakes, or the coupled rotational-translational motion inherent to non-spherical particles. Furthermore, it remains unclear whether substituting realistic PMN morphologies with volume-equivalent spheres preserves ensemble-level transport metrics or biases predictions of entrainment thresholds and pressure drops.

Methodology
This study employs a fully resolved CFD-DEM framework to investigate the hydrodynamics of non-spherical PMNs in vertical pipes representative of deep-sea mining risers.

• Numerical Framework: The approach couples the incompressible Navier-Stokes equations (solved via OpenFOAM) with Newton's equations of motion for discrete particles (solved via LIGGGHTS).
• Fluid-Solid Coupling: An Immersed Boundary (IB) method is used to resolve fluid-solid interactions directly at the interface without empirical drag laws. The no-slip condition is enforced via a direct forcing approach, and hydrodynamic forces are computed by integrating the fluid stress tensor over the particle surface.
• Particle Representation: Complex PMN geometries, reconstructed from X-ray computed tomography (CT) scans, are modeled using a multisphere approximation (rigid assemblies of overlapping spherical sub-particles). This allows for high-fidelity representation of irregular surfaces while maintaining computational tractability.
• Verification: The framework was verified against experimental data for single-sphere settling (Ten Cate et al., 2002) and the drafting-kissing-tumbling (DKT) benchmark for multiple spheres (Glowinski et al., 2001; Sharma and Patankar, 2005). Additionally, a multisphere approximation of a sphere was validated against a smooth sphere to confirm the accuracy of the geometric representation.
• Simulation Setup: Simulations were conducted for PMNs and their volume-equivalent spheres with effective diameters of 20 mm and 54 mm (volume-equivalent diameters of 16.4 mm and 44 mm) in a pipe of diameter $D=200$ mm. The study covered particle Reynolds numbers ($Re_p$) from 98 to 2904 and confinement ratios ($d/D$) of 0.082 and 0.22. Transport behavior was analyzed across fluid velocities ranging from $1.0u_t$ to $3.0u_t$ (where $u_t$ is the terminal settling velocity).

Key Results

1. Sedimentation and Drag Enhancement:

   • Non-spherical PMNs settle 27–29% slower than volume-equivalent spheres despite having identical mass and buoyancy.
   • This reduction in terminal velocity corresponds to a drag coefficient enhancement of 1.8 to 2.0 times that of spheres.
   • The increased drag arises from two factors: (1) a larger instantaneous frontal area (up to 1.5 times the volume-equivalent area due to the circumscribed sphere ratio) and (2) morphology-induced effects, including asymmetric wake structures and rotational-translational coupling.
   • Crucially, the terminal drag force remains equal to the submerged weight for both shapes; the lower velocity of PMNs is a result of generating the required hydrodynamic resistance at lower slip velocities.

2. Residence Time and Transport Regimes:

   • Transport behavior exhibits a velocity-driven transition from intermittent, settling-dominated motion to stable, convection-dominated entrainment.
   • At low velocities ($u_f = 1.0u_t$), small PMNs remain in a state of marginal suspension near the inlet, exhibiting oscillatory motion without net upward transport, whereas spheres show vertical dispersion.
   • As velocity increases, residence time distributions narrow for all particles. However, PMNs consistently exhibit larger mean residence times and higher variances compared to spheres, attributed to higher drag and stronger rotational-translational coupling.
   • At high velocities ($u_f = 3.0u_t$), all particles achieve spatially homogeneous distributions, though PMNs maintain enhanced rotational motion (angular velocities up to 80 rad/s) and helical trajectories.

3. Drag Force Statistics and Fluctuations:

   • The mean normalized drag force ($\hat{f}$) remains near unity across all conditions, confirming a steady-state balance between drag and submerged weight.
   • Small Particles ($d/D = 0.082$): Both spheres and PMNs exhibit narrow drag force distributions. For small PMNs, rapid reorientation effectively averages out orientation-dependent projected area fluctuations, making their behavior quantitatively similar to spheres.
   • Large Particles ($d/D = 0.22$):
     • Large spheres show a monotonic broadening of the drag distribution with increasing velocity, driven by wake unsteadiness and confinement effects.
     • Large PMNs exhibit significantly broader and skewed distributions with extended high-drag tails. This is driven by the superposition of wake-history effects and orientation-dependent forcing. Unlike small particles, the rotational time scales of large PMNs are comparable to wake evolution time scales, preventing the averaging of projected area variations.

Significance and Conclusions
The study elucidates the mechanisms by which particle shape influences drag, wake dynamics, and rotational-translational coupling in confined vertical flows. The primary contribution is establishing the quantitative bounds of applying volume-equivalent spherical models to non-spherical PMN transport.

• Qualitative Similarity: The underlying transport physics (progression from settling to convection-dominated regimes) is qualitatively similar for both PMNs and spheres. This suggests that first-order transport behaviors can be captured using spherical models with calibrated drag laws.
• Quantitative Divergence: Significant quantitative differences exist. PMNs exhibit 40–90% longer residence times and drag coefficients 1.8–2.0 times higher than spheres. These differences are critical for predicting minimum suspension velocities and pressure drops in deep-sea mining risers.
• Modeling Implications: While spherical approximations may suffice for reduced-order modeling of ensemble behavior, they fail to capture the specific intermittency and force fluctuations associated with large, non-spherical particles in high-confinement ratios. The resolved CFD-DEM approach presented here provides a necessary baseline for developing shape-specific corrections for such models.

The authors note that these findings apply to dilute ensembles and serve as calibration inputs; extrapolation to dense slurries involving hindered settling or plug flow remains outside the scope of this work.