## 4 Simulation Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Physical Quantities** & **Units** & **Data set** \\ \hline Particle Density & kg/m\({}^{3}\) & 1150 \\ Particle diameter & mm & 1.5 \\ Stiffness & N/m & 800 \\ Coefficient of friction & — & 0.3 \\ Coefficient of restitution & — & 0.9 \\ Gas density & kg/m\({}^{3}\) & 1.28 \\ Gas viscosity & N \(\times\) s/m\({}^{2}\) & \(1.7\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical properties for the first simulation case. crushing and separated, thus reducing the drag force required for suspension of these particles. These results indicate that the PCPM can better capture the phenomena of bubbles popping out of the bed and particle-group crushing than the TM. Figure 5: Snapshots of particle distribution in a two dimensional fluidized bed. Upper: simulation results obtained by the traditional coarse grain DEM-CFD method. Middle: experimental results given by [PERSON] et al. [18] (reused with permission from Elsevier). Bottom: simulation results obtained by the current dynamic coarse grain DEM-CFD method. **(a)** 0.16 s. **(b)** 0.20 s. **(c)** 0.24 s. **(d)** 0.28 s.  
The above is just an apparently qualitative comparison. We now compare the simulation results of the two methods and the experimental results quantitatively. Figure 6 shows the pressure drop at the 45 mm horizontal section above the fluidized bed distributor. It can be seen that both the PCPM and TM predicted the periodic fluctuation of the pressure. However, in terms of amplitude, the result of PCPM is closer to the experimental result. The result of TM shows rather flat pressure valleys which indicates a long duration of low pressure, while the PCPM improves this low pressure effect. Figure 7 shows the change of bed height over observation time. The bed height predicted by the PCPM is slightly higher than that of the TM, as shown in this figure. This phenomenon is mainly caused by the consideration of particle-group crushing. That is, when the bubbles move to the top of the bed during the bed moving, the particles in the top layer will be blown higher due to the reduction of their sizes caused by particle-group crushing. Although there are some differences between the two simulation results and experimental result, both the simulations are acceptable. The dynamic variations of the total particle number and particle-group crushing amount during the simulation of PCPM are shown in Figures 8 and 9. These results indicate that the collisions between particles cause violent crushing and polymerization of particle-groups during the simulation, and thus the total particle number presents a dynamic fluctuation. Next, we redo the above simulations at a coarse grain ratio \(l=2\). The particle-group distribution predicted by the PCPM and TM are shown in Figure 10. The results of both PCPM and TM show a qualitative agreement with the experimental results about the distribution of the particles. Hence, the macroscopic flow properties of the fluidized bed obtained from the coarse grain models can be regarded to be equivalent to the original particle system to some extent. Still, there are several differences between the results of the two methods. First, the particle distribution predicted by the TM is relatively homogeneous, while that predicted by the PCPM shows strong aggregations. Second, the top layer of the bed predicted by the TM changes mildly when the particles rise. By contrast, the PCPM can capture the drastic movement of the top layer particles when the bubbles come out of the bed. Finally, the PCPM is capable of showing the presence of multiple bubbles in the bed compared to the TM. These results indicate that the PCPM is better that the TM in describing the heterogeneity  
Figure 6: Pressure drop at the 45 mm horizontal section above the fluidized bed distributor. (a) experimental result given by [PERSON] et al. (2018) (reused with permission from Elsevier); (b) simulation results. of the particle distribution in the fluidized bed.