## 4 Results and Discussions
### Numerical Results and Discussions  
Figures 6 and 7 illustrate the growth dynamics of the fluidized zone of the immersed granular stack. As we can see, there are different grain dynamics depending on the initial density of the material. The loose stack rapidly fluidized from the injection zone to the top of the granular layer in a turbulent manner with a uniform overall expansion.  
Figure 5: Experimental observation of the evolution (from 1 to 4) of the fluidized zone height.  
Figure 6: Transitional phases of destabilization by homogeneous fluidization of an initially loose sand stack.  
Conversely, for the same material in a dense state, there was a mass takeoff of the stack, which added to the propagation of an instability of the wavy porosity type from bottom to top of the stack with fast kinetics, which decompacted the medium.  
CFD and EDEM (two particulate methods) were coupled to carry out a numerical study of the destabilization mechanism observed during the previous experimental study of the destabilization of an immersed granular material by homogeneous fluidization. According to the results, the same destabilization scenario of the immersed granular material was observed. A marked difference in behavior during the transient regime has been highlighted: a loose stack fluidizes from the injection zone to the top of the granular layer while for the same material in a dense state, there is a takeoff of the material without deformation. This mechanism of destabilization, which led to a fluidization of the medium in the loose state case, could be explained by the imbalance between the contact forces induced by the flow on the grains and the apparent weight of the granular stack. On the other hand, the effect of the resultant forces and the confinement imposed by the side walls can give a solid body behavior to the granular stack in the dense case and cause a vertical takeoff of the material.  
The numerical and experimental studies have noted that for the loose granular stack, porosity wave instability propagates from the base to the top. Then, there begins a bed expansion process with eruptions on the surface. Moreover, by observing the behavior of the bed during the experimental phase, it is clear that the numerical observations show good agreement with the experimental observations. However, other more in-depth studies devoted to these numerical and experimental observations are in progress and will be the subject of further submissions in the near future.  
However, we have represented, in Figure 8, the fluidized bed height evolution as a function of the time for a fluidization rate of U = 0.07 m\(\cdot\)s\({}^{-1}\). It is important to mention that the fluidized bed height increased linearly with the time until reaching a state where its variation remained almost stationary.  
Retrieved data from image sequences also allowed us to plot, in Figure 9, the variation of the maximum fluidized bed height H\({}_{\rm f}\) as a function of the fluidization rate U. Indeed, in the case of dense granular stack, we have, at the very beginning of the fluidization process, a fixed bed regime where the height of the bed varies only when the velocity reaches a given value (U = 0.07 m\(\cdot\)s\({}^{-1}\)). This corresponds well to the phenomenon observed during the homogeneous fluidization process of a dense granular stack where, in order to fluidize the material, the grains must first be disentangled in the granular stack. They retain a solid body behavior in a first phase. Subsequently we attend, because of the imposed geometric confinement by the walls, to the vertical takeoff of the material and the fluidization of the bed during which the height of the bed increases progressively with the flow rate. It should  
Figure 7: Transitional phases of destabilization by homogeneous fluidization of an initially dense sand stack.  
also be noted that the higher the flow rate increases, the fluctuations of the height of the bed become very important.