## 3 Results
This is an important study because it is the pressure difference of the particles at the inlet and outlet that drives them into the reactor. It is evident from the graph that the pressure at the mixture outlet is zero, while the pressure inside the reactor after 15 s is almost 1.5 kPa at any height. Since the height of the particle bed is much lower compared to the height of the reactor, the pressure differences along the height are almost the same. It is also noticeable from the figure that up to 2 s, the pressure inside the reactor is also zero, because the particles are settling on the bed during this period in the reactor. After the settling period is over, an instantaneous spike in pressure can be seen, the magnitude of which is different at different heights. This is because when the air is injected through the bed, at that moment, it experiences the resistance from the particle bed. The magnitude of the pressure spike is its highest (6.2 kPa) at air inlet and its lowest (1.9 kPa) at the top of the reactor for a 7 m height. The particle inside the bed begins to move upward as a result of this pressure buildup. The bed stabilizes after 15 s when the fast fluidization regime is fully developed. Figure 4: Variation of mass flow rate with respect to time at the outlet of the reactor. Figure 5: Variation of static pressure with time at different heights. The particle volume fraction is an important parameter because it helps to understand the fractional distribution of the solid particle at different heights during different time intervals. The volume fraction of solid particles with respect to time at different heights is shown in Figure 6. The volume fraction of solids is much lower because of the small volume occupied by them, as compared to the volume of the reactor. However, the surge in volume fraction is noticed initially at a height of 0.5 m and 0.75 m. The maximum volume fraction is observed at a height of 0.5 m at 2 s. This happens because of the gathering of the particles at the bottom planes of the reactor, as a result of particle movement. The particle volume fraction at higher planes is not affected at that instant due to the small number of particles transferred from the bottom. A stable particle distribution is observed after 28 s when the oscillations in volume fraction are reduced. The velocity of the gas phase (air) plays an important role in fluidizing the bed as well as lifting the particles from the bed to the outlet. Figure 7 shows the transient variation in air velocity along different heights of the reactor. It can be observed from the graph that the initial velocity of air at the air inlet is 0 and after 2 s it is 2.5 m/s, according to the boundary condition. The velocity of air at a height of 0.25 m increases due to the internal turbulence created by the particles injected  
Figure 6: Variation in volume fraction with time at different heights. Figure 7: Variation in air velocity with time at different heights. into the reactor for 1 sec. However, this decreases as the particles get settled down at the bed. As the bed settles and the velocity of air at the inlet is increased gradually up to the terminal velocity, there is a sudden spike in the velocity, which can be seen in the graph along with the different heights of the reactor. This happens because of the turbulence created by the particle and the increasing air velocity at the inlet. However, once stable circulation is achieved, the velocity becomes constant to maintain the continuous flow of the particles to the outside. Figure 8 gives the particle velocity profile at different heights of the reactor with time. The velocity of the particles depends on the air velocity from the bottom of the reactor. Initially, the particle velocity is zero at all the heights of the reactor, but it gradually increases with the increment in the air velocity. The maximum variation in the velocity is observed at the outlet of the reactor.