# Eulerian-Eularian Model for Agglomeration Behavior of Combusted Iron Particles
## 4 Results and Discussion
### Solid Bed Hydrodynamics  
In a proper bubbling fluidized bed, bubbles originate at the bottom of the solid bed and rise to the top, increasing in bubble size until their buoyancy force exceeds the solid drag force. The buoyancy force rises as the bubble diameter increases, causing the bubbles to climb to the surface of the solid substrate and burst. This situation recurs in the fluidized bed reactor to enhance fuel mixing capabilities for improved combustion. As the bubble ascends, solid particles move, resulting in the formation of zones with lower solid fraction. However, when agglomeration occurs, it affects the bubble growth in the fluidized bed, driving the bed toward defluidization. This numerical model has the capability to analyze the strength of the solid bridge force for various temperatures and four different agglomeration force models. Figure 3 illustrates the normalized bed pressure drop profiles over time for each sintering force model temperature varying from 500 \({}^{\circ}\)C to 1000 \({}^{\circ}\)C. The standard deviation (STD) of the pressure drop curves was calculated from 0.5 s to 15 s. At low temperatures (e.g., 500 \({}^{\circ}\)C), the cohesive force impact was observed to be negligible in any sintering force model. This can be identified in the snapshots of Figure 4, as both cohesive and non-cohesive cases have healthy bubbling behavior at 500 \({}^{\circ}\)C. Comparatively, the standard deviation was increased in the three-micro contact-point model (C = 0.417) at 650 \({}^{\circ}\)C compared with the 500 \({}^{\circ}\)C model cases despite there being no agglomeration visible in Figure 4b. This is because even with reduced sintering force, the bed may have difficulty maintaining bubbling at temperatures exceeding 650 \({}^{\circ}\)C. Additionally, when C = 0.417 (three-micro contact-point model) at 1000 \({}^{\circ}\)C, a consistent reduction in pressure drop is observed after 8 s. It is further demonstrated by the snapshots in Figure 4d. Images captured at 1000 \({}^{\circ}\)C with a C value of 0.417 display blue areas indicating minimal solid presence and channeling caused by particle sintering. The void fraction snapshots from the CFD-DEM model performed by [PERSON] et al. provide similar evidence to this discussion. However, there are some distinctions in the three-micro contact-point model (C = 0.417) at 1000 \({}^{\circ}\)C in the CFD-DEM study, as it shows good bubbling hydrodynamics in the CFDDEM study even with a higher STD value. In this study, agglomeration occurred after 8 s, which shows significant pressure reduction. To illustrate that behavior, 15 s of run time was maintained in this study [26]. In sintering force models at higher temperatures (i.e., 800 \({}^{\circ}\)C and 1000 \({}^{\circ}\)C), the fluctuations of the pressure drop increased gradually, showing higher standard deviation (STD) values. This notable variation proposes an increase in bubble sizes, resulting in more extreme bed dynamics. The sintering force models of a smooth surface (C = 1) and the nine-microcontact-point model (C = 1.251) had significant differences in terms of the magnitude (approximately 2.4 to 3 times) compared with the three-micro contact-point  
Figure 4: Solid fraction variation. Figure 3: Pressure drop variation with time. model (C = 0.417). Hence, the rate of particle clumping was high when in higher sintering force models (C \(\geq\) 1), leading to inhomogeneity in the bed. This scenario can be well captured in a three-micro contact-point model sintering model at 1000 \({}^{\circ}\)C. Then, when the sintering force was further increased by applying the smooth surface model (C = 1) and the nine-microcontact-point model (C = 1.251) at the maximum temperature used in this study (i.e., 1000 \({}^{\circ}\)C), the pressure drop and the standard deviation (STD) decreases rapidly, clearly indicating particle agglomeration in Figures 3d and 4d.