# A Novel Liquid-Solid Fluidized Bed of Large-Scale Phase-Changing Sphere for Thermal Energy Storage
## 4 Results and Discussion  
### Fluidization Status  
With the conventional theories on predicting the minimum fluidization velocity, for instance, the one shown in [PERSON] et al. [32], it is estimated that the PCM spheres should start fluidizing at a flow rate of 10.27 L/min. However, the spheres are found to remain stationary until the flow rate goes above 20 L/min. This indicates the theories used to predict the fluidization of micro-to-small solid particles are no longer appliable. Actually, the conventional theories were developed for particles of size in the range from a few micrometers to less than a millimeter, while the sphere in the present study is 25 mm in diameter. In addition, the internal diameter of the fluidized bed is 75 mm, only 3 times that of the sphere diameter, which may result in the flow field deviating a lot from small particles fluidized in a larger vessel. Both these factors contribute the higher initial fluidization velocity. As shown in Figure 4, between 20 L/min and 30 L/min, the fluidization is not stable as it is observed that the spheres would clog from upside down, forming a pattern with the spheres sticking neatly to the internal wall of the cylinder and leaving a hollow channel in the middle. This phenomenon is similar to the undesirable channel flow appearing in conventional small-particle fluidized bed. Moreover, if the flow rate exceeds 38 L/min,  
Figure 3: Image-processing technique. (Red circles denote makers of the detected capsules). the expansion of the solid phase would increase too much, leading the lowest level of the spheres to reach the bottom of the fluidized bed (950 mm in height). Therefore, only the flow rate between 30 and 38 L/min would be used during energy-storage tests, within which the spheres are able to fluidize stably. The fluidization statuses at certain instants as the flow rate increases from 31.3 L/min to 37.3 L/min are shown in Figure 5. Because the size of the spheres is relatively large compared to the tube diameter, the slugging and bubbling modes are indistinguishable, and hereafter it will be called slug mode since 'bubbles' are barely visible. It is worth noting the slug mode here is not a bad condition as the term'slug' for the conventional fluidization bed of small particles usually indicates the fluidization has deteriorated. The lowest level where the solid phase can reach, though manifesting fluctuating nature with time, increases with the flow rates. By taking the average positions of the lowest level throughout a whole phase-changing duration and dividing it by the height of the fixed bed (0.346 m), the expansion ratio (\(ER\)) can be obtained. The \(ER\) for melting and solidifying at multiple flow rates is demonstrated in Figure 6. As expected, the \(ER\) increases with the increase in flow rates (from 1.7 to 2.2 as the flow rate increases from 31.3 L/min to 37.3 L/min). A higher \(ER\) beyond this range can also be possible with higher flow rates but this is limited by the length of the fluidization bed. The averaged \(ER\)s for melting and solidifying are similar at the same flow rate and the small difference shown in Figure 6 can be attributed to the measurement uncertainty. Moreover, during the test, no apparent difference can be observed from the instantaneous expansion ratio no matter whether the PCM spheres are going through melting or solidifying. It is thus speculated that the small-scale phase-changing status inside the PCM spheres merely impacts the macroscopic fluidization status. The pressure drops caused by the flow resistance for fixed as well as fluidized bed are compared in Figure 7, where the pressure drop values are averaged through a whole phase-changing process and the error bars shown are the standard deviation of the collected pressure drop signal instead of errors. As might be expected, the pressure drops for both fixed and fluidized beds increase with the increasing flow rate [33].