## 4 Simulation Results
Moreover, as shown in Figure 11, the crushing and polymerization of particle-groups in PCPM make the pressure fluctuation more violent. This property alleviates the problem of too flat pressure drop predicted by the TM. Figure 8: The change of the total particle number during the simulation of PCPM. Figure 7: The change of bed height over observation time. (**a**) experimental result given by [PERSON] et al. (2018) (reused with permission from Elsevier); (**b**) simulation results. Figure 9: Particle-group crushing amount at different time instants during the simulation of PCPM. phenomenon when the number of particles is increased. Influenced by the wake vortexes of the large bubble in the middle region of the bed, airflow escapes from the small bubbles below to the large bubble. At the same time, the particles aggregating at the top of the small bubbles are collapsing. This process causes the disappearance of small bubbles and the growth of large bubble. Because of the thick layer of aggregated particles at the top of the bed, the large bubble cannot pass through the bed quickly. Squeezed by the top layer particles, the bubble almost transforms into rectangular in shape and becomes large enough to completely fill the cross-section of the bed. Until 1.68 s, cracks appear in the top layer of the bed and the gas trapped in the large bubble escapes quickly. Figure 13 shows the evolution of particle distribution at the later stage. The phenomenon of bubble merging along the transverse direction can be observed from these figures. In this process, the bubbles on the left and right sides near the walls grow rapidly due to the vertical bubble merging. Soon two slender bubbles are formed on the left and right sides. The particle groups between the two bubbles gradually thin and disappear under the influence of air flow on both sides, and finally the two bubbles merge horizontally. In the case shown in the figures, since the two bubbles have reached the top layer of the bed by the time they finally merge, so the complete merging morphology is not seen. These results reflect the complexity of the fluidization pattern change in dense particle flow systems. It suggests that the heterogeneous mesoscale structures have great influence on gas-solid flows. In addition to the traditional spherical bubbles, there are also bubbles with complex structures, which will play a leading role in the dynamic behavior of the whole bed. At last, Figure 14 shows some results obtained at coarse grain ratios \(l=2\) and \(l=3\). As can be seen, in the initial stage of simulation (\(t=0.4\)s), the bed experienced uniform expansion under the effect of gas velocity. The bed morphology simulated by the coarse grain system with \(l=2\) is relatively close to that of the original system. However, when the coarse grain ratio increases to \(l=3\), the bed shows a morphology between the scattered bed and the bubbling bed. Although the bubbles generated are very small, the whole bed is still in a fluidized state. In the middle stage of simulation (\(t=6.44\)s), the system with coarse grain ratio \(l=2\) can still keep a similar state to the original system, while the result of \(l=3\) is seriously distorted. Accordingly, the coarse grain ratio of the simulation system needs to be carefully selected. Excessive coarse grain will make the coarse grain system severely deviate from the original system, and proper coarse grain will greatly reduce the simulation time. For the current simulation, when the coarse grain ratio is \(l=2\), the simulation time of the coarse grain system is about 10% of the original system. Figure 12: Snapshots of particle distribution obtained by the PCPM for a two dimensional fluidized bed at the very early stage: the phenomenon of bubble merging along the vertical direction and rectangular bubble formation. (**a**) 1.00 s. (**b**) 1.04 s. (**c**) 1.08 s. (**d**) 1.12 s. (**e**) 1.16 s. (**f**) 1.20 s. (**g**) 1.32 s. (**h**) 1.44 s. (i) 1.56 s. (**j**) 1.68 s. (**k**) 1.80 s.