# Thermal Energy Storage Performance of Tetrabutylammonium Acrylate Hydrate as Phase Change Materials
## 3 Results and Discussion
### In the System Using an Ultrasonic Transducer  
In this section, we discuss the results in the system with ultrasonic vibration. The inflow temperature \(\mathrm{T_{in}}\), outflow temperature \(\mathrm{T_{out}}\) and thermal energy storage medium temperature \(\mathrm{T_{PCM}}\) were measured. Figure 9a,b shows the time evolutions of \(\mathrm{T_{in}}\), \(\mathrm{T_{out}}\) and \(\mathrm{T_{PCM}}\) in the ultrasonic vibration system (28 kHz and 56 kHz). Time zero was defined as the time at which the circulating water was started to flow. Figure 8: Time evolution of thermal energy storage rate and density in the agitated system (**a**,**b**) depict the thermal energy storage rate and density, respectively. The slope of the T\({}_{\text{PCM}}\) first decrease was similar to that of the static system. However, when the slope changed from negative to positive, the T\({}_{\text{PCM}}\) was about 284 K, which was higher than that of the static and agitated system. This is because the hydrate nucleation occurred at a higher temperature than in the static system. In an ultrasonic vibration system, hydrate nucleation would occur at a higher temperature due to the effects of cavitation or acceleration of ultrasonic vibration. The slope of the T\({}_{\text{PCM}}\) increase is not much different from that of the static system at 28 kHz and appears to be more gradual at 56 kHz. This was because of relatively high T\({}_{\text{PCM}}\), which results in a relatively slow hydrate growth rate and low heat of formation during hydrate nucleation. The increase in T\({}_{\text{PCM}}\) changed from a rise to a fall at around 288 K, and then T\({}_{\text{PCM}}\) slowly decreased. This was because the slope of the T\({}_{\text{PCM}}\) change turned from positive to negative because hydrate was generated and covered the heat exchange coil surface as the static system. Figure 10a-c shows the pictures of the crystal growth during this system. As shown in Figure 10a-c, hydrate was formed on the heat transfer surface near the bottom of the container. As time went by, the formed hydrate piled up on the bottom of the container. Figure 11a shows time evolutions of thermal energy storage rate in the system using the ultrasonic vibration, which depends on the frequency of 28 kHz and 56 kHz. The thermal energy storage rate \(\dot{q}\) in the static system is also shown for comparison. Time zero was defined as the time at which the circulating water is started to flow. Here, \(\dot{q}\) was proportional to the difference between T\({}_{\text{in}}\) and T\({}_{\text{out}}\) and thus shows almost the same trend as T\({}_{\text{out}}\) change in the static system. In addition, the slope of change in the thermal energy storage rate was similar to that of the static system. However, as for the 28 kHz ultrasonic vibration, the maximum value of \(\dot{q}\) after the increase was about 1.5 times larger than that of the static system. This was because the hydrate was detached from the heat exchange coil by cavitation, which increased the growth rate of the hydrate. On the other hand, the maximum value of \(\dot{q}\) at 56 kHz was almost the same as that of the stationary system. Considering the size of hydrate adhesion, the cavitation effect is stronger at lower frequencies. This was why the maximum value of \(\dot{q}\) at 56 kHz was larger than that of \(\dot{q}\) at 28 kHz. After the peak of \(\dot{q}\), the ultrasonic vibration system maintained a larger \(\dot{q}\) for a relatively longer time than the static system. This was because the hydrate growth was continued for a relatively long time after the hydrate covered the heat exchange coil due to the effects of cavitation. Figure 11b shows the time evolution of the thermal energy storage density. The result of the static system is also shown in Figure 11b. Time zero was defined as the time at which the circulating water is started to flow. As shown in Figure 11b, \(\overline{q}\) in the ultrasonic vibrated system started increasing a bit earlier than the static system.