# A Multi-Scale Hybrid CFD-DEM-PBM Description of a Fluid-Bed Granulation Process

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## Abstract

**:**

## 1. Introduction, Motivation and Objectives

#### 1.1. 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.

## 2. Background

## 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

Particle properties | |

Shear modulus | 1 × 10${}^{6}$ Nm${}^{-2}$ |

Poisson’s ratio | $0.25$ |

Density | 1030 kgm${}^{-3}$ |

Particle-particle interactions | |

Coefficient of restitution | $0.2$ |

Coefficient of static friction | $0.5$ |

Coefficient of rolling friction | $0.01$ |

Granulator walls | |

Material | Steel |

Shear modulus | 7.6 × 10${}^{8}$ Nm${}^{-2}$ |

Poisson’s ratio | $0.29$ |

Density | 7800 kgm${}^{-3}$ |

Particle-wall interactions | |

Coefficient of restitution | $0.2$ |

Coefficient of static friction | $0.5$ |

Coefficient of rolling friction | $0.01$ |

#### 3.3. Population Balance Model for FBG

**x**,

**z**,t) is the population distribution function,

**x**is the vector of internal co-ordinates used to express the particle size, z is the vector of external co-ordinates used to represent spatial position of the particles and t is the time. The term $\frac{\partial}{\partial \mathbf{x}}\left[F(\mathbf{x},\mathbf{z},t)\frac{d\mathbf{x}}{dt}\right]$ accounts for the rate of change of particle distribution due to change in particle size. The term $\frac{\partial}{\partial \mathbf{z}}\left[F(\mathbf{x},\mathbf{z},t)\frac{d\mathbf{z}}{dt}\right]$ accounts for the rate of change of particle distribution with respect to spatial co-ordinates. ${R}_{formation}$ and ${R}_{depletion}$ stand for particles being formed and depleted respectively due to aggregation and breakage.

#### 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 [48]).
- A simple aggregation kernel has been formulated based on collision frequency and collision efficiency (adapted from [46]).
- 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 [47]).
- Liquid addition has been captured in EDEM${}^{\mathrm{TM}}$ 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${}^{\mathrm{TM}}$.
- The geometry has been meshed using ICEM-CFD${}^{\mathrm{TM}}$.
- The mesh file has been imported within FLUENT${}^{\mathrm{TM}}$.
- 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${}^{\mathrm{TM}}$ is coupled with EDEM${}^{\mathrm{TM}}$ 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${}^{\mathrm{TM}}$ 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${}^{\mathrm{TM}}$ 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${}^{\mathrm{TM}}$.
- The material properties, particle-particle and particle-wall interaction parameters as given in Table 1 have been set in EDEM${}^{\mathrm{TM}}$.
- The initial PSD has been created in EDEM${}^{\mathrm{TM}}$.
- The liquid particles have been created in EDEM${}^{\mathrm{TM}}$ (the liquid addition starts at 0.2 s).
- Once the EDEM${}^{\mathrm{TM}}$ simulation is set up, initialize the solution in FLUENT${}^{\mathrm{TM}}$.
- Run the calculation.

#### 4.2. Model Geometry

#### 4.3. Multi-Scale Model Results

**Figure 3.**Velocity contour plots. (

**a**) Velocity distribution over 0 s–0.5 s; (

**b**) Velocity distribution over 0.5 s–1.0 s; (

**c**) Velocity distribution over 1.0 s–1.5 s; (

**d**) Velocity distribution over 1.5 s–2.0 s.

**Figure 4.**Plots for particle liquid content distribution. (

**a**) Liquid content over 0 s–0.5 s; (

**b**) Liquid content over 1.5 s–2.0 s.

**Figure 5.**EDEM${}^{\mathrm{TM}}$ snapshots of liquid content. (

**a**) Particle liquid content at time = 1 s; (

**b**) Particle liquid content at time = 2 s.

**Figure 7.**EDEM${}^{\mathrm{TM}}$ snapshots of particle diameter. (

**a**) Particle diameter at time = 1 s; (

**b**) Particle diameter at time = 2 s.

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix. Effect of PSD on Collision Frequency

**Figure A2.**Collision frequency versus particle size for each distribution based on DEM simulations. (

**a**) D1; (

**b**) D2; (

**c**) D3; (

**d**) D4.

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**MDPI and ACS Style**

Sen, M.; Barrasso, D.; Singh, R.; Ramachandran, R.
A Multi-Scale Hybrid CFD-DEM-PBM Description of a Fluid-Bed Granulation Process. *Processes* **2014**, *2*, 89-111.
https://doi.org/10.3390/pr2010089

**AMA Style**

Sen M, Barrasso D, Singh R, Ramachandran R.
A Multi-Scale Hybrid CFD-DEM-PBM Description of a Fluid-Bed Granulation Process. *Processes*. 2014; 2(1):89-111.
https://doi.org/10.3390/pr2010089

**Chicago/Turabian Style**

Sen, Maitraye, Dana Barrasso, Ravendra Singh, and Rohit Ramachandran.
2014. "A Multi-Scale Hybrid CFD-DEM-PBM Description of a Fluid-Bed Granulation Process" *Processes* 2, no. 1: 89-111.
https://doi.org/10.3390/pr2010089