# Thermal Energy Storage Performance of Tetrabutylammonium Acrylate Hydrate as Phase Change Materials
## 3 Results and Discussion
### For Industrial Utilizing of TBAAc Hydrate as PCM  
As written in Section 3.1, a range of the practical solid-phase fraction is from 40 to 50% [37]. The thermal energy storage density of ice is 140 MJ m\({}^{-3}\) when the solid phase fraction is 45%. As for TBAB hydrate, it has a thermal energy storage density of 100 MJ/m\({}^{3}\) when the solid phase fraction is 50% [33]. We regarded these values as a target thermal energy storage density. Given the thermal energy storage during nighttime of 10 h, the required time for thermal energy storage should be shortened. This was why the time to reach the target values was compared to each other system. In addition, the amount of the used electric power was estimated for more practical evaluation. Table 3 shows the time that was needed to achieve the target thermal energy storage density. As for the target of 140 MJ/m\({}^{3}\), it was achieved only when the rotation rates of agitation were 300 rpm and 600 rpm. When the rotation rates were 300 rpm or 600 rpm, it was 5.9 h or 2.9 h to achieve the target, respectively. Concerning the consumed electric power to achieve the target, it was 58 MJ/m\({}^{3}\) and 29 MJ/m\({}^{3}\), respectively. As for the target of 100 MJ/m\({}^{3}\), it was achieved in all systems where an external force was applied. When the rotation rates were 300 rpm and 600 rpm, it took about a third of the time of  
Figure 12: Time evolutions of thermal energy storage rate and density in all systems. (**a,b**) depict the thermal energy storage rate and density, respectively. the ultrasonic vibration system. However, the consumed electric power by the external force to achieve the target was 45 MJ/m\({}^{3}\), 24 MJ/m\({}^{3}\), 15 MJ/m\({}^{3}\) for the agitation system (100 rpm, 300 rpm, 600 rpm), and 5 MJ/m\({}^{3}\) for the ultrasonic vibration system at both frequencies (28 kHz, 56 kHz), respectively. Therefore, when the target of thermal energy storage density is 100 MJ/m\({}^{3}\), the agitation system (300 rpm, 600 rpm) is more suitable for storing thermal energy in a short time, and the ultrasonic vibration system is more suitable as an external force for reducing the amount of electricity used. In this study, the thermal energy storage density in the agitated system was greatly improved by adding agitation. On the other hand, the amount of electricity used for agitation became larger than other systems. The agitation intensity was almost the same as that in a general low-viscosity agitation. However, the agitation Reynolds number was 25,000 at 600 rpm. This was due to the fact that the impeller power number of the three propeller blades was 1, which was smaller than that of other agitation blades [39]. Therefore, even if the agitation intensity was a general value, the agitation Reynolds number became larger, and energy consumption also became larger. It will be possible to optimize the rotations and electric power consumption by selecting a more suitable agitator at the similar experimental apparatus. The thermal energy storage density in the ultrasonic vibration system was not as large as that in the agitation system. The reason for this result is that it was difficult to resonate the ultrasonic transducer. To resonate the ultrasonic transducer, it is necessary to provide a natural frequency, but this frequency varies slightly depending on the environment in which the ultrasonic transducer is placed, for example, the materials in contact. Also, the natural frequency is also expected to change during the transformation of the aqueous solution into hydrate. Therefore, it is possible that the ultrasonic transducer was not able to resonate properly in this experimental system. A possible solution to solve this problem is to use a device that automatically follows the resonant frequency and keeps giving the resonant frequency to the transducer.