# Thermal Energy Storage Performance of Tetrabutylammonium Acrylate Hydrate as Phase Change Materials
## 3 Results and Discussion
### Comparison in All Systems  
Figure 12a shows a comparison in the time evolution of the thermal energy storage rate in all systems. In the agitated system, the thermal energy storage rate, \(\dot{q}\), increased earlier than the other systems; \(\dot{q}\) increased at 1 h, 0.6 and 0.4 h for a rotation rate of 100 rpm, 300 rpm and 600 rpm, respectively. The forced convection generated by the agitation increased the convective heat transfer coefficient. This was why the temperature of the thermal energy storage medium dropped relatively earlier and hydrate formation occurred earlier, resulting in the early increase of \(\dot{q}\). In addition, this forced convection caused rapid hydrate formation in the entire container, which released huge heat in a short period. This was why \(\dot{q}\) increased vertically. As the rotation rate increased, \(\dot{q}\) increased more.  
Figure 11: Time evolutions of the thermal energy storage rate and density in the system using an ultrasonic vibration. (**a**,**b**) depict the thermal energy storage rate and density, respectively.  
Figure 10: Optical observation changing in the container with ultrasonic vibration of 28 kHz. (**a**–**d**) are the pictures at 2 h, 2.5 h, 3 h and 5 h after cooling water started to be circulated, respectively.  
The maximum values of \(\dot{q}\) after the vertical increase were 47 kW m\({}^{-3}\), 54 kW m\({}^{-3}\) and 69 kW m\({}^{-3}\) for a rotation rate of 100 rpm, 300 rpm and 600 rpm, respectively. These values are 5 to 8 times larger than that of a static system.  
In the ultrasonic vibration system, the maximum of \(\dot{q}\) was 14 kW m\({}^{-3}\), which is about 1.5 times larger than that of the static system, when the frequency was 28 kHz. This was because cavitation detached the adhesion between hydrate and heat exchanger coil, which could be the thermal resistance. As for the system with 56 kHz frequency, the maximum values of \(\dot{q}\) were almost the same as in the static system. This was because the effect of the cavitation was not as big as 28 kHz [38]. In summary, the agitation increased the rate of heat and mass transfer by creating forced convection, thereby shortening the hydrate formation time and increasing the hydrate growth rate. On the other hand, ultrasonic vibration kept the hydrate growth longer by the effect of cavitation.  
Figure 12b shows a comparison in the time evolution of thermal energy storage density, \(\overline{\eta}\), in all systems. In the agitated system, \(\overline{\eta}\) increased earlier and quicker than the other systems. This was because T\({}_{\text{PCM}}\) decreased quicker by the forced convection, which caused the quicker hydrate formation and growth for the entire container. In the ultrasonic vibration system, the \(\overline{q}\) increase appeared to be relatively longer than the other systems. This was because the cavitation enabled hydrate to grow after hydrate covered the surface of the heat exchanger coil. The static system, the agitated system (rotation rate of 100 rpm, 300 rpm and 600 rpm), and the ultrasonic vibrated system (frequency of 28 kHz and 56 kHz) had the thermal energy storage density of 96 MJ/m\({}^{3}\), 121 MJ/m\({}^{3}\), 159 MJ/m\({}^{3}\), 183 MJ/m\({}^{3}\), 126 MJ/m\({}^{3}\), and 111 MJ/m\({}^{3}\), respectively. Assuming TBAAc hydrate has the heat for formation and decomposition of approximately 200 MJ/m\({}^{3}\), each solid phase fraction is 48%, 61%, 80%, 92%, 63%, and 55%, respectively.