# A Novel Liquid-Solid Fluidized Bed of Large-Scale Phase-Changing Sphere for Thermal Energy Storage
## 4 Results and Discussion
### Heat-Storage Characteristics  
Since the temperature difference between the inlet and outlet of the fluidized bed is not accurate enough to represent the process of heat storage as explained in Section 3.1, the PCM melting or solidifying status inside spheres reflected by the brightness are adopted to indicate the heat-storage process. However, this method inevitably involves one major shortcoming for the heat-releasing stage. The moment when the brightness reaches a plateau (Figures 8b and 9b) during solidifying does not indicate the end of full solidification. This is because, during the heat-releasing stage, the PCM solidifies from the outer portion of the sphere towards the center; the solidified PCM would block the light and after a while the brightness would not change even though the solidification has not finished. Fortunately, the moment can still be utilized as an indicator of how quickly the solidified PCM accumulates enough to completely block the light, and an indicator of the solidifying rate before brightness reaches the plateau. Hereafter, this moment is referred to as when solidification has been visually finished, with 'visually' implying the end of solidification is visually determined. Moreover, the brightness of spheres at the same phase-changing stage with identical solid and liquid fraction of PCM might be different due to the uneven distribution of incident light as well as reflection and refraction of the plexiglass tube. This brings great oscillating features to the detected brightness and uncertainty in precisely determining the instant when the phase-changing finishes. Figure 8: Variation of brightness along with PCM melting or solidifying for a fixed bed. Figure 7: Flow resistance across the bed. The variations in average brightness along with time are shown in Figure 8 for the fixed bed. The brightness is normalized between 0 and 1 by the maximum and minimum values. Since the maximum and minimum values might be different for different flow rates due to the oscillating feature, discrimination of the end phase-changing should be based on when the curves stop descending or climbing, not by the absolute value of the Y-axis. The shallow blue bars mark the range of the instants when brightness for multiple flow rates is unchanged; that is when the melting has finished or the solidifying has visually finished. The width of the blue bar includes both the measurement errors and the influence of varying flow rates. Although the instantaneous brightness demonstrates fluctuations, it can be observed from Figure 8a that the time required for melting lies between 1430 s and 1550 s. The increasing flow velocity leads to a higher heat-transfer rate between the external surface of the sphere and the flowing fluid and it can be expected that the melting inside can be accelerated. However, this trend is not so obvious as the flow rates increase from 20.6 L/min to 37.3 L/min, due to the uncertainty brought by the brightness fluctuations and small range of flow rates covered. Meanwhile, the time required for finishing solidifying visually lies between 900 s and 1000 s for the tested flow rates. It is worth noting that if the solidifying duration is shorter than melting duration, it does not mean that the heat is released faster than the it is absorbed, since the solidification only ends visually. The normalized brightness under the seven flow rates which can fluidize the PCM spheres stably are illustrated in Figure 9a,b, for melting and solidifying, respectively. As the flow rate increases, the melting or solidifying is expected to be accelerated considering the enhanced heat transfer outside and inside the PCM spheres. However, this trend is not strictly obeyed because of the small range of flow rates covered and brightness uncertainty.