## 4 Experimental Results and Discussion
### Bubble Dynamics
#### 4.4.1 Fluidization Index (F.I.) The fluidization quality can be examined through a vital parameter, a fluidization index (F.I.). This index is the ratio of minimum bubble rise velocity (U\({}_{mft,b}\)) and the minimum fluidization or incipient velocity of fluidization (U\({}_{mft,f}\)). This parameter provides information about the maximum expansion of the fluidized bed. [PERSON] and [PERSON] [38] investigated the fluidization index for the fluidization of different sizes of powders and found that the index is maximum for Gardart group A particles. It was established previously that the bed could grasp more fluidizing air between the minimum fluidization velocity and bubbling rise velocity point for higher F.I. This means that there is less likelihood of bubbles formation at the surface of the static bed for initial superficial velocities increments between these two points (U\({}_{mft,b}\) and U\({}_{mft,f}\)) [39]. Most of the researchers have investigated the fluidization behavior of F.I with different types of solid particles. In this study fluidization index is evaluated for three different types of distributor plates to observe the hydrodynamic behavior of fluidized bed under different operational conditions. It has been predicted that under similar operating conditions, the minimum bubbling rise velocity (U\({}_{mft,b}\)) and F.I. are found to be maximum for perforated plate and minimum for 45\({}^{\circ}\) slotted plate distributor. However, for the hybrid plate distributor, F.I and U\({}_{mft,b}\) is found to be in between perforated and 45\({}^{\circ}\) slotted plate. Such behavior is owing to the bubble dynamic within the fluidized zone, as different sizes of bubbles form as they emerge through the distributor plates. Moreover, the further collapse and amalgamation of these bubbles are quite different for different distributor plate as they move up the column of a gasifier. A high-speed camera is installed during the experimentation to record the fluidization phenomena. With the help of slow-motion flicks of the phenomena, the bubble rise velocity is calculated by measuring the time a bubble travels from the bottom to the surface of the bed, where it erupts for each distributor plate. It can be observed from the graphs below in Figure 9 that for the perforated distributor plate, the bubble rise velocity ratio is found to be highest (1.211) for the superficial velocity of U\({}_{mft}\), the particle size of 590 \(\upmu\)m and the initial bed height of 10 cm. In contrast, the bubble rise velocity ratio for a 45\({}^{\circ}\) slotted plate was slightly less (1.026) owing to the larger bubble size. The intermediate bubble rise velocity ratio (1.10) was observed for the hybrid plate distributor due to the intermediate-size air bubbles experiencing medium drag force during their upward path. Figure 9 shows that the bubble rise velocity ratio (F.I.) is maximum for perforated plate distributor flowed by hybrid plate. The lowest fluidization index (F.I.) is found for a 45\({}^{\circ}\) distributor plate. It is also found that increasing superficial air velocity for each distributor plate increases the bubble rise velocity but not in a linear trend. The drag force of bubbles increases with the square of the velocity as the velocity increases; hence, the bubble velocity is not in the same order as superficial air velocity. As sand and air both act as a fluid in the fluidization phenomena so the object, which is a bubble here, can experience drag force with a square of the velocity according to the relation below:  
\[\text{F}_{\text{D}}=0.5\ \text{\rho V}^{2}\ \text{A}\ \text{C}_{\text{D}}\]  
where F\({}_{\text{D}}\) is the drag force of the bubbles, \(\rho\) is the density of the fluid, A is the reference area, V is the relative velocity of the object (bubbles) in the fluid, and C\({}_{\text{D}}\) is the drag coefficient. For the perforated distributor plate, there is more fluidization air to grasp within the bed for a range of superficial air velocities compared to the other two plates.