Feasibility study for physics-informed direct numerical simulation describing particle suspension in high-loaded compartments of air-segmented flow

TL;DR

This study addresses the challenge of capturing dense particle suspensions in the Archimedes Tube Crystallizer by developing a particle-resolved Direct Numerical Simulation (DNS) framework based on the Finite Element–Fictitious Boundary Method (FEM–FBM) with a frictional hard-contact model. The DNS achieves fully two-way fluid–particle coupling and validates against experimental ATC data, reproducing the flow-map-regime transitions (green, yellow, red/yellow, red) and resolving phenomena such as rear loading and loss of vertical symmetry. Three quantitative metrics—Axial distribution $\overline{\phi}(s)$, Radial Distribution Index $I_r$, and Vertical Asymmetry $A_y$—are introduced to classify suspension regimes and enable objective comparison with experiments, offering a practical diagnostic for design. The results demonstrate the method’s predictive capability for dense suspensions and establish a mechanistic foundation for ATC crystallizer design, with future work toward larger particle counts and integration with population-balance closures.

Abstract

The Archimedes Tube Crystallizer (ATC) employs air-segmented flow in coiled tubes to achieve narrow residence time distributions for continuous crystallization. Taylor and Dean vortices drive particle suspension in this system. However, one-way coupled models fail to capture the fluid-particle feedback that becomes critical at higher loadings. We present a particle-resolved Direct Numerical Simulation (DNS) framework based on a Finite Element-Fictitious Boundary Method with hard-contact modeling of particle interactions. Simulations of L-alanine suspensions across varying particle sizes, solid contents, and rotational speeds are validated against experimental side-view imaging. Three quantitative metrics-axial distribution, radial index, and vertical asymmetry-are introduced to classify suspension regimes. The DNS results reproduce the experimentally observed flow map zones (green, yellow, red/yellow, red) and resolve subtle transitions such as rear loading and loss of vertical symmetry. This feasibility study demonstrates that DNS can reliably predict dense suspension behavior and provides a mechanistic foundation for crystallizer design.

Figures (10)

• Figure 1: Cumulative particle size distributions $Q_3$ of the seed crystals obtained from the sieving fractions 200 - 250 µm (a) and 250 - 315 (b). Additionally the respective mode diameter $d_{\text{mode}}$ is given.
• Figure 2: Schematic depiction of the setup used for the validation experiments. Additionally, the dimensions of the ATC are given.
• Figure 3: Regime classification flow map for the ATC. Reprinted from Sonnenschein.2021. Copyright CC BY 4.0
• Figure 4: Comparison for cases C1, C2, C3, and C4. C1 and C2 reprinted from Sonnenschein.2021. Copyright CC BY 4.0
• Figure 5: Comparison for cases C5, C6, C7, and C8.