1. Introduction

Magnetically fluidized beds (MFBs) represent an advanced approach to enhance the performance of conventional fluidized beds, offering better control and more operational flexibility¹. By incorporating a magnetic field, more stable fluidization can be achieved at lower gas velocities, thereby reducing energy consumption, while improving process efficiency. This intensification is particularly valuable for handling large and/or dense particles, commonly used in industries applying powder processing, chemical reactions, selective oxidation and reduction processes², and gas-solid separations.

The ability to dynamically adjust particle behaviour using magnetic fields allows for more precise control over mixing, segregation, and stabilization in particle beds. This control is essential for optimizing key industrial applications where particle distribution and interaction critically influence reaction outcomes and overall efficiency. In this study, phase diagrams are developed using a comprehensive set of computational fluid dynamics-discrete element method (CFD-DEM) simulations, covering a wide range of MFB operating conditions. These diagrams offer the necessary insight into different operating regimes of MFBs, each having its advantages. The versatility and possible dynamic operation of MFBs under varying magnetic field intensities provide significant operational advantages, making them appropriate for diverse industrial processes that require precise control over fluidization behaviour.

2. Background

Magnetically susceptible particles interact with the applied magnetic field, thus improving the fluidization behaviour in an MFB. In MFBs magnetization can occur in two distinct operational modes: magnetic-first and magnetic-last mode. In the magnetic-first mode the magnetic field is applied before the gas flow is introduced, whereas in magnetic-last mode the gas flow is initiated prior to the application of the magnetic field. In an MFB each particle experiences a combination of forces including drag force, buoyant force, gravitational force and magnetic force. While buoyant and drag forces act upward, gravity pulls particles downward. The direction of the magnetic force depends on the orientation of the magnetic field, which can thus exert additional forces that are attractive or repulsive depending on the magnetic dipole moments of the magnetic particles ³. The non-magnetic particles in an MFB are subject to all interparticle forces except the magnetic forces.

3. Methodology

This study leverages a coupled CFD-DEM simulation framework to achieve a comprehensive analysis of particle-level hydrodynamics and gas-solid interactions, and as such probe the effectiveness of magnetic fields in enhancing fluidized bed performance. This coupled approach combines the advantages of both CFD and DEM methods, allowing for the simulation and visualization of gas flow and particle dynamics in a fluidized bed system.

3.1. Simulation Framework

The CFD component of the CFD-DEM framework models the gas phase using a continuum approach, solving the Navier-Stokes equations to describe the gas flow through the fluidized bed. The DEM component tracks the motion and interaction of individual particles, incorporating collision mechanics, contact forces, and magnetic forces. A soft-sphere DEM model is applied for studying the motion of the particles. The equations of this model are based on Newton's second law of motion. Two-way coupling ensures that the forces and velocities between the gas and solid phases are continuously exchanged throughout the simulation. The CFD component is implemented via OpenFOAM, while DEM is implemented via LIGGGHTS. Both are coupled by CFDEM coupling codes.

3.2. Magnetic Field Implementation

To simulate the effect of the magnetic field on the fluidized bed, a magnetic force term is added to the magnetic particles in the DEM. This force is proportional to the magnetic field strength and the magnetic susceptibility of the particles, which are here assumed to be ferromagnetic. The magnetic field is applied uniformly across the bed of magnetic particles, while its strength is varied during different simulation runs to evaluate its impact on bed dynamics. In addition to the externally imposed magnetic forces, interparticle magnetic forces are also implemented to study the aggregation and segregation characteristics in the MFB³.

3.3. Initial and Boundary Conditions

The presented study models Geldart D particles with a diameter of 1200 microns and a density of 1430 kg/m³, while the gas phase is air. A pseudo 2D bed (44*120*10) mm³ experimental setup filled with 4620 magnetic and 4620 non-magnetic particles is simulated. Additional boundary and operating conditions are applied as described as Wang et al⁴. To ensure uniformity, all the simulations are initiated as admixture packed beds meaning both magnetic and non-magnetic particles are equally well mixed in this state.

3.4. Fluidization Regimes and Phase Diagram Construction

A series of simulations is conducted to examine the effects of magnetic field gradients (0-0.35 T/m for magnetic-first and 0-0.6 T/m for magnetic-last mode) and gas velocities (0.0 to 1.2 m/s) on bed behaviour. From the simulations, minimum fluidization velocities, minimum bubbling velocities, segregation velocities, and magnetic gradients are calculated for magnetic-first and magnetic-last mode respectively, with the net magnetic force on magnetic particles acting upward and downward in an MFB. Minimum bubbling velocity is identified as the velocity at which bubbles first appear, marking the transition from a stabilized bed to a bubbling bed.

Segregation velocities are obtained by plotting the segregation index (S) as function of gas velocities for magnetic-first mode and as a function of magnetic gradients in magnetic-last mode. In the magnetic-first mode, only the segregation velocity at S=0.9 is needed to construct the operational phase diagram, while in the magnetic-last mode both the segregation magnetic gradients at S=0.1 and S=0.9 are needed. With these simulation results, i.e. magnetic field gradients and operating velocities, a phase diagram is composed, categorizing the fluidization regimes under various magnetic and gas flow operating conditions.

4. Results and Discussion

4.1. Pressure drop studies in MFB

Pressure drop studies involving fluidization and de-fluidization curves allow to determine the distribution of particles when the net magnetic force is acting upwards and downwards. When the magnetic gradient is applied upwards, the pressure drop decreases with an increase in magnetic force, while it increases when the magnetic force is applied downwards. From these pressure drop curves, minimum fluidization velocities, determining the onset of particle movement in a fluidized bed, are obtained.

4.2. Minimum bubbling velocity and segregation curves

The minimum bubbling velocities for all simulations are found by the use of the DEM as the onset of bubble formation is clearly observed. The gas velocity at the DEM timestep at which the first bubble appears, is evaluated as the minimum bubbling velocity. When the magnetic field force is applied upwards, both the minimum fluidization and bubbling velocities decrease with increasing magnetic field strength. Conversely, when the magnetic force is directed downwards, these velocities increase with rising magnetic field intensity. The segregation curves have different dynamics in magnetic-first and magnetic-last mode as the movement and characteristics of the magnetic particles in an MFB are a function of operating magnetic gradients and operating velocities.

4.3. Phase Diagram for Magnetic Fluidization

Gas velocities corresponding to various magnetic field intensities are plotted for magnetic-first mode, with the magnetic field gradient applied upwards or downwards, resulting in phase diagrams. Key parameters such as minimum fluidization velocity, minimum bubbling velocity, and segregation velocity at S=0.9 are used for their construction. In these phase diagrams fluidization regimes are categorized, including packed bed, magnetically stabilized bed, partially segregated bed, and fully segregated bed separated by different velocity curves. For example, the region between the minimum bubbling velocity curve and segregation velocity curve at S=0.9 corresponds to the partially segregated regime.

In the magnetic-last mode, segregation magnetic gradient values at S=0.1 and S=0.9 are used to define the position of magnetized bubbling, partial and complete segregation regions. The phase diagram reflects three distinct regimes: below the magnetic gradient corresponding to S=0.1 the magnetized bubbling regime is found, between S=0.1 and S=0.9 partial segregation of the bed is observed, and above S=0.9 the complete segregation regime is situated.

Phase diagrams for both the magnetic-first and magnetic-last modes are thus generated, illustrating fluidized bed behaviour under upward and downward magnetic gradients.

4.4. Process Intensification for Industrial Applications

The findings of this study have significant implications for industrial fluidized bed operations, particularly those handling large and/or dense magnetically susceptible particles. The obtained phase diagrams indicate the zones for mixing, segregation and stabilized operations in a magnetically fluidized bed operation. Hence, a MFB can be operated as a completely mixed bed for efficient contact process and enhanced heat and mass transfer processes, as a completely segregated bed for selective catalyst oxidation or reduction process, or as a stabilized bed for stabilized operation requirements in pharmaceutical industries.

5. Conclusion

CFD-DEM simulations confirm that magnetic fields promote uniform particle distribution, and provide flexibility in controlling fluidization regimes. Phase diagrams illustrate how MFBs can operate as fully mixed, segregated, or stabilized beds depending on the applied magnetic field and gas velocities. These capabilities make MFBs versatile for industrial applications, as precise control over particle behaviour is offered. This work lays the foundation for comparison of the obtained phase diagrams and thus operating regime position for different particle types.

6. References:

1. Zhu Q et al. Chemical Engineering Journal, 2021.
2. Buelens LC et al. Industrial & Engineering Chemistry Research, 2019.
3. Pinto-Espinoza J. Oregon State University, 2003.
4. Wang B et al. Powder Technology, 2022.