Magnetic Particle Tracking (MPT) is a relatively new non-invasive measurement technique which is often used to study dense granular flow. Its basic principle relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength at a suitable distance from the tracer. By assumption of a magnetic dipole and the use of minimization techniques, both location and orientation of the tracer can be determined. MPT is therefore uniquely suited for the study of non-spherical particles. The performance of the localization is largely dependent on the signal-to-noise ratio and very often relies on nonlinear optimization techniques, as the definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. In this paper, we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach is in the speed and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques.

The hydrodynamics of the Expanded Bed Adsorption process is studied through simulations combining Computational Fluid Dynamics and the Discrete Element Method. A representative base case is defined, based on process design parameters commonly encountered in literature. Then, 19 other cases are defined, each representing a singular adjustment to the column design, material properties, or operating conditions. The parameters that are varied are the expansion factor, liquid viscosity, bed aspect ratio, mean particle density, width of the particle density distribution, width of the particle size distribution, column taper angle, and column alignment angle. The impact of each adjustment on the bed behaviour is discussed, using the local particle size distribution and solids dispersion coefficient as main indicators of bed stability. Optimal performance was found for an expansion factor of two to three, and the combination of particle size distribution and particle density distribution was found to greatly improve bed stability. The mixing process of the liquid and solid phases is concluded to be of highly complex nature, and cannot simply be predicted from the liquid flow velocity.

Lubrication forces play a major role in the behaviour of fluid–solid systems, where they affect the collisions between particles. Current implementations of lubrication forces in unresolved simulations often suffer from shortcomings, such as neglecting parts of the physics or relying on arbitrarily defined parameters. In this short communication, we propose a novel implementation, rigorously defined based on physical and numerical factors. Both particle roughness and deformation are considered, and the model accuracy is demonstrated through comparison with experimental results.

Magnetic particle tracking (MPT) was employed to study a rotating drum filled with cork particles, using both air and water as interstitial medium. This noninvasive monitoring technique allows for the tracking of both particle translation and rotation in dry granular and liquid–solid systems. Measurements on the dry and floating bed rotating drum were compared and detailed analysis of the bed shape and velocity profiles was performed. It was found that the change of particle–wall and particle–particle interaction caused by the presence of water significantly affects the bed behavior. The decreased friction leads to slipping of the particles with respect to the wall, rendering the circulation rate largely insensitive to increased drum speed. It was also found that the liquid–particle interaction is determining for the behavior of the flowing layer. The well-defined experiments and in-depth characterization performed in this study provide an excellent validation case for multiphase flow models.

In this work, large-scale simulations of the blast furnace hearth are presented, conducted using a model combining Computational Fluid Dynamics, the Volume of Fluid method, and the Discrete Element Method. Using a 5 m diameter, full-3D geometry, the influence of burden weight, bi-disperse packing, and blocked tuyeres on the liquid and solids flow within the hearth are investigated. Horizontal and vertical porosity profiles are presented, and the influence of the dynamic liquid level on the state of the deadman is evaluated. The liquid iron flow during tapping is visualised, and the influence of a coke-free space on the flow pattern is analysed. The magnitude of the circumferential flow through the corner of the hearth is analysed, and found to decrease with increasing burden weight pressure and coke diameter in the bed centre. A significant influence of the dynamic deadman on the liquid flow pattern is found, especially in case of a floating deadman. In addition to the liquid flow, the solid coke flow towards the raceways is analysed. Two pathways for coke particles towards the raceway are uncovered, one path through the actively flowing layer above the deadman, and a second path moving through the deadman and entering the raceways from below. The balance between these two mechanisms was found to change during the tapping cycle. Lastly, implementations for heat and dissolved carbon mass transfer are presented, and demonstrated using a full-scale 10 m hearth simulation. Additional closures for heat and mass transfer rates are required, but the current model is found in good shape for future work.

The blast furnace hearth plays an important role in the operational stability and lifetime of the reactor. The quasi-stagnant bed of coke particles termed the deadman undergoes complex interaction with the flowing hot metal, and remains largely ill-understood. In this work, a cold model blast furnace hearth is presented, and studied using both numerical and experimental techniques. Magnetic Particle Tracking (MPT) is used to investigate the individual particle behaviour within the cylindrical, opaque bed. At high liquid holdup, the particle bed was found to alternate between floating and sitting states, following the liquid level during the tapping and filling cycle. This bed motion was found to induce a migration of particles, thereby slowly renewing the deadman. The rate of horizontal migration increases with the vertical bed amplitude, and the renewal of particles is concentrated around the opening of the tap hole. No direct influence of the coke-free space on the tapping rate was found in these experiments. Instead, the disturbance of the packing in front of the tap hole was observed to lead to a higher tapping rate. Additionally, a coupled numerical framework is presented, in which Computational Fluid Dynamics (CFD), the Volume of Fluid (VOF) method and the Discrete Element Method (DEM) are combined. A simulation set-up is presented which closely replicates the experimental conditions. The position and movement of the floating bed are found to be well-predicted by the VOF/CFD-DEM model. Particle trajectories are presented, and migration of particles within the deadman is observed. Alongside the particle motion, the liquid flow pattern during draining of the vessel is visualised. It is concluded that a coke-free space underneath the deadman significantly impacts the shape of the liquid flow pattern, which affects the erosion processes within the blast furnace hearth.

Liquid-solid systems are frequently encountered in industrial processes and it is broadly recognised that numerical simulations are a useful tool for gaining insight in these processes. In this study, the unresolved CFD-DEM approach is extended with a complete momentum coupling for liquid-solid flows. Established correlations are used for the drag and lift forces, while new implementations are introduced for the unsteady interaction forces. A virtual mass force model based on the work of Felderhof (Felderhof 1991) is introduced, which accounts for the local particle volume fraction and the liquid-solid density ratio. The Basset history force, which is usually neglected due to computational difficulties related to its implementation, is evaluated according to the approach proposed by Parmar et al. A liquid fluidised bed is used as a demonstration case for the extended model. In this work, it is shown that with appropriate stabilisation measures, the Basset history force is approximated accurately (within 5%), while computational efficiency is maintained ( < 30% increase in computational time). Furthermore, the relevance of the complete momentum coupling is demonstrated by analysis of the solids mixing in the liquid fluidised bed. It is shown that when accounting for the complete interaction force, solids mixing is up to 20% slower compared to simulations with the drag-only approach.

The solubility and diffusivity of CO₂ in a series of 1-alkyl-3methylimidazolium tricyanomethanide ionic liquids ([C_nmim][TCM] with n = 2, 4, 6, 7, 8; ILs) was studied using a magnetic suspension balance at temperatures ranging from 298 to 353 K and pressures up to 2 MPa. The effects of temperature, pressure, and alkyl chain length on CO₂ solubility and diffusivity were examined. The electrolyte PC-SAFT (ePC-SAFT) equation of state was used to describe the solubility of CO₂ in the ILs. The Henry's law constant and the excess properties of solvation (Gibbs free energy, enthalpy, and entropy) were calculated. A series of equations derived from Fick's second law were evaluated, and a Fourier expansion of Fick's second law of diffusion was found to be the most suitable model for deriving diffusivities from gravimetric data. The diffusivities range from 10^-10 to 10^-9 m²·s^-1 in the temperature and pressure ranges applied. The activation energies for CO₂ diffusion (12-16 kJ·mol^-1) were found to be in the range of traditional solvents. (Graph Presented).