# Eulerian-Eularian Model for Agglomeration Behavior of Combusted Iron Particles
## 1 Introduction
Therefore, it is crucial to understand the process of inter-particle cohesion by solid bridge force in the DRI method, which causes defluidization of fluidized bed combustion plants. Thus, different approaches to numerical simulations, such as the two-fluid method and the discrete element method (DEM), provide tools to investigate the fluidization phenomena that take place in fluidized bed combustion. The numerical model simulation strategy developed by [PERSON] et al. uses two fluid approaches based on the Eularian-Eulatian technique to predict agglomeration. The established modeling technique is verified using experimental data from the literature for a simplified two-dimensional geometry of a pilot-scale fluidized bed combustor [18]. Another numerical model based on the DEM approach was developed by [PERSON] et al. [12] to investigate metallic solid bridge forces in agglomeration. This model encompasses a surface diffusion mechanism that considers the surface roughness. Further, particle sintering in agglomeration is analyzed by [PERSON] et al. [19; 20] with a CFD-DEM simulation. Their study incorporates the effect on the agglomerate sizes by temperature and gas velocity. There are several studies that have utilized CFD-DEM simulations to investigate the sintering behavior of iron/iron oxide fines in fluidized beds. However, the high computing cost makes it challenging to simulate large-scale experiments using the CFD-DEM approach. The computer simulation cost of the DEM is significantly affected by the enormous number of particles in the micron-sized cohesive iron/iron oxide powder. To overcome this challenge and to expand the modeling capability to a large/industrial scale, the two-fluid modeling approaches can be applied. However, there is very little research work conducted using the two-fluid approach to simulate agglomeration in fluidized beds for the production of iron/iron oxide powder. Even the available literature does not provide proper agglomeration behavior with significant parameters, like solid pressure. They do not provide solid fraction variations with defluidization in the fluidized bed, which is crucial for understanding the agglomeration patterns in the fluidized bed. In this model, solid fraction variation aligned with the solid pressure variation is analyzed in detail and validated with the CFD-DEM study. Moreover, this study provides a cost-effective multiphase CFD model that can be scaled up for industrial-level reactors to predict agglomeration. Therefore, in this study, a simplified yet comprehensive CFD 3D numerical model using the Eularian-Eularian method was developed using AVL Fire advanced simulation software (2024 R1) and user-defined FORTRAN subroutines. The gas phase of the model was modeled using the inbuilt AVL Fire algorithms, while the solid phase was developed explicitly using user-defined subroutines and coupled with the software AVL Fire. In this work, defluidization behavior of iron particles were analyzed at various temperatures in a controlled adiabatic and reduced atmosphere. It is crucial to understand the process of sintering iron particles in DRI method. When in the DRI process, sintering can also occur at lower temperatures due to chemical reactions of converting iron oxide to metallic iron [6]. This model includes a variety of temperature settings, from low to high, to analyze the micron-sized iron particle sintering in the fluidized bed. Further, the paper provides a detailed explanation modeling procedure and the application of solid bridge force into the model in Section 2. Section 3 of this paper includes a detailed description of the geometry of the reactor and other parameters. Section 4 covers the numerical results achieved with this model and validation of the results with CFD-DEM model results produced for the same experiment. Section 5 outlines the conclusions drawn from the previous section of results and discussion and the intended future work of this model.