1. Introduction, Motivation and Objectives
- Present a hybrid CFD-DEM-PBM framework using dynamic two-way coupling.
- Incorporate multi-scale information such that the model can be used to study the detailed process dynamics.
- Study the heterogenous particle velocity distribution and liquid binder distribution.
- Study the evolution of average particle diameter and particle liquid content with time.
3. Multi-Scale Model Development
3.1. CFD Model for the Fluidizing Medium
- Flow near wall is laminar and the velocity varies linearly with the distance from wall.
- A no slip boundary condition has been set at the wall.
- A velocity inlet boundary condition has been used for the air entering the geometry.
- An outlet-vent boundary condition has been used at the geometry exit.
3.2. Discrete Element Model
|Shear modulus||1 × 10 Nm|
|Coefficient of restitution|
|Coefficient of static friction|
|Coefficient of rolling friction|
|Shear modulus||7.6 × 10 Nm|
|Coefficient of restitution|
|Coefficient of static friction|
|Coefficient of rolling friction|
3.3. Population Balance Model for FBG
3.4. Information Exchange in the Coupling Framework
- The PBM considers aggregation only, breakage and consolidation has not been incorporated since FBG processes are low shear processes with reduced consolidation and breakage (similar approach has been followed by ).
- A simple aggregation kernel has been formulated based on collision frequency and collision efficiency (adapted from ).
- The collision efficiency in the aggregation kernel is size independent, non-mechanistic and conditional based on the liquid content of the powder particles (adapted from ).
- Liquid addition has been captured in EDEM by creating particles which get deleted from the system upon contact.
- A reasonable number of collisions occur among the particles between any two subsequent time steps.
- The PBM is solved a reasonable number of times such that there is a more consistent distribution of the particle size (as described in Section 4.3)
3.5. Model Outputs
4. Results and Discussion
4.1. Simulation Procedure
- The geometry has been made using ANSYS Design Modeler.
- The geometry has been meshed using ICEM-CFD.
- The mesh file has been imported within FLUENT.
- The mesh has been converted into Polyhedra domain.
- The gravity is defined in the correct direction and a transient simulation is selected.
- The flow model has been selected to be viscous laminar.
- The coupling server has been started.
- The FLUENT is coupled with EDEM for the desired fluid domain by selecting the Eulerian-Eulerian option.
- The coupling server will automatically import the geometry with the specified direction of gravity in EDEM and set the source terms in x-momentum, y-momentum and z-momentum calculation. The value of the simulation parameters of the coupling interface has been set as follows:
- Sample points: The number of points used by FLUENT to calculate the volume fraction of the fluid cell. This value has been set at 10, which means that a large particle can transfer its volume between 10 cells. This particular parameter decides the stability and speed of the simulation. A higher value of sample point may increase the stability but decrease the simulation speed.
- Relaxation factor: The relaxation factors again help with stability and convergence of the solution. Reducing the value helps to increase stability and achieve convergence. Both momentum-MTM-under-relaxation factor and volume under-relaxation factor have been set at 0.7.
- The inlet fluid velocity has been defined as 30 m/s.
- The custom contact model and custom factory (for PBM calculation) have been imported within EDEM.
- The material properties, particle-particle and particle-wall interaction parameters as given in Table 1 have been set in EDEM.
- The initial PSD has been created in EDEM.
- The liquid particles have been created in EDEM (the liquid addition starts at 0.2 s).
- Once the EDEM simulation is set up, initialize the solution in FLUENT.
- Run the calculation.
4.2. Model Geometry
4.3. Multi-Scale Model Results
Conflicts of Interest
Appendix. Effect of PSD on Collision Frequency
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