# A Novel Liquid-Solid Fluidized Bed of Large-Scale Phase-Changing Sphere for Thermal Energy Storage
## 1 Introduction  
Since the heat conduction is the main mode of heat transfer in solid phase, the heat-transfer rate during the solid-liquid phase-changing process is not high enough and thus the energy-absorbing or -releasing rate is usually weak. Therefore, it is a consensus that the application of latent heat storage has been hindered greatly and a lot of related research efforts have been devoted to improving the heat transfer during energy storage. Improving the effective thermal conductivity of the phase-changing material (PCM) is a common and straightforward way, as the improvement contributes to not only the solid phase but also the liquid phase of PCM. This can be realized via the addition of materials with extreme high thermal conductivity, for instance, metal skeleton [1, 2], nano-metal particles [3], expanding heat-transfer area by fins and heat pipe [4, 5, 6], foam metal or foam graphite [7, 8]. However, these additives sacrifice energy-storage density as well as material stability [9, 10, 11]. In addition, the melting process can sometimes be retarded because of the interference between the additives and the natural convection of melted PCM [12, 13]. The PCM capsule/element/sphere, which is featured with the PCM capsule by a solid shell, divides the PCM and heat-transfer fluid into two sides, helps mitigate the stratification of compound PCM and thus maintains the PCM stability [14, 15, 16, 17]. The encapsulationgreatly increases the heat-transfer area and improves the whole heat-transfer rate, and this effect can be enlarged with the downsizing of the capsule. However, adopting a small PCM capsule would severely reduce the energy-storage density because of the thickness of the shell. Moreover, the small capsule has been proved to increase the subcooling of the PCM, thus deteriorating the performance of the whole energy storage system [18,19]. Different from the convention of packing the capsules or particles in a fixed bed to store energy, it occurred to multiple researchers that the fluidized bed may function as a good candidate to improve the heat-transfer rate as well as make the energy storage uniform across the bed. One of the recent representatives is [PERSON] et al. [20], who employed the CaO/CaCO\({}_{3}\) thermochemical cycle to store the solar heat with a fluidized bed and examined the influence of acoustic waves on the fluidization status. The particles were in Group C of Geldart's classifications [21] with a Sauter diameter of 4 \(\upmu\)m.  
The model and experimental investigations of the CaO/Ca(OH)\({}_{2}\) fluidized bed reactor have been explored by [PERSON] et al. [22,23], with particle sizes between 200 to 400 \(\upmu\)m. They claimed that the results offer encouraging support for the scaling-up application of the CaO/Ca(OH)\({}_{2}\) fluidized bed for thermochemical energy storage. [PERSON] et al. [24,25] developed a one-dimensional numerical model to predict the performance of a fluidized bed using MgO/Mg(OH)\({}_{2}\) as reaction materials to store thermochemical energy. The particles they used were in Group B of Geldart's classifications with a mean diameter of 240 \(\upmu\)m. Experiments were performed to validate their model and multiple influential factors were analyzed. [PERSON] et al. [26] found that the time cost by solidifying and melting can be greatly reduced by the fluidized bed than the fixed bed. They concluded that the reason is the enhanced heat transfer between the external wall of PCM particles and heat-transfer fluid. They also found that the heat-transfer rate between the PCM particles and the deployed heat exchange tubes can be improved by the fluidization [27]. However, the particles they adopted were in the size range between 0.2 and 2 mm, and PCM only occupies 30% of the particle mass. The above studies of fluidized bed for energy storage all used small-scale particles (\(\sim\)2 mm), and the contents of energy-storage material as well as energy-storage density were thus not high.