## 4 Simulation Results  
Two simulation cases are performed to test the dynamic coarse grain DEM-CFD method. In the first simulation case, a two-dimensional fluidized bed with 90 mm width and 500 mm height is considered. The geometry is discretized as \(18\times 100\) cells by setting the grid size to be 5 mm. Gas is injected from the base, where the superficial velocity is set to be 0.9 m/s. The number of solid particles is 4080. All the particles have equal size and are assumed to be spheres with sphericity equal to 1. The physical properties of the particles and gas are illustrated in Table 2. The time step size used in the simulations is 0.05 ms. Because the simulation conditions are very similar with those adopted in the experiments made by [PERSON] et al. (2018), we can compare our simulation results with the experimental ones. Before we start the simulations, some comparative studies are made to demonstrate that the EMMS drag force model fits our need. Both the EMMS drag force model and the famous Wen and Yu drag force model are used to the present simulation case. The original DEM-CFD method is used to generate simulation results. Both qualitative and quantitative comparisons show that the EMMS results are more consistent with the experimental ones. These facts as well as the research work done by many other researchers give us the reason to believe that the EMMS drag force model fits our need. Although the particle-group crushing and polymerization model is proposed for particle-groups, we are still curious whether the simulation results will be improved if it is applied to original particles. For this purpose, we first directly use our dynamic coarse grain DEM-CFD method to the original particles under the assumption that the particles are divisible. In this case, each particle is treated as a particle-group. Figure 5 shows the results obtained by the current method together with those obtained by experiments and traditional coarse grain DEM-CFD method. For facilitating the comparisons, we call our dynamic coarse grain DEM-CFD method involving the particle-group crushing and polymerization model as PCPM and the traditional coarse grain DEM-CFD method as TM for short. The results show that the particles are in the fluidized state. Bubbles are generated periodically at the bottom of the bed and gradually rise and swell. The bubble nose is getting thinner and thinner. When the maximum bed height is reached, the top particles begin to fall back and the bubbles eventually disappear. No particles can flee from the computational domain. They will bounce when they collide with the wall. The particle-wall interactions are modeled by using springs, dashpots and friction sliders as introduced in Section 2. This consideration prevents the particles from going through the solid wall. On the other hand, if the gas velocity is too high, the particles may escape from the outlet of the fluidized bed. But for the simulation cases we considered, the gas velocity is moderate and the gravitational force prevents the particles escape from the outlet. By comparison, the results obtained by the PCPM are more consistent with the experimental results than those obtained by TM. That is the PCPM has the ability to improve the simulation results of the original DEM-CFD method (TM with a coarse grain ratio equal to 1). The transverse and longitudinal sizes and positions of the large bubbles predicted by the PCPM are much closer to the experimental results. Therefore, it appears that the PCPM can simulate the macroscopic flow properties of the fluidized bed. The particles at the top layer have a longer suspension time, which indicates that the particles at the top of the bed are