# Numerical Analysis on the Performance of a Heat Pump Powered by Surface Water Freezing
## 3 Results and Analysis
### Effect of Evaporation Temperature  
Figure 8a shows the effect of evaporation temperatures on the exhaust temperature \(T_{\rm r}\) from the compressor. Because the water freezing and its latent heat released increase in the evaporator at a lower evaporation temperature, the heat exchange between water and refrigerant and the evaporation capacity of the refrigerant also increase, which results in a larger evaporation pressure and \(T_{\rm r}\). The lower the evaporation temperature, the higher \(T_{\rm r}\) is. During working time, on the one hand, the freeze contributes to increasing heat exchange and refrigerant evaporation in the evaporator. On the other hand, the thermal resistance due to the ice layer tends to decrease heat exchange. Finally, the quasi-equilibrium state is obtained when both trends intersect. In the same evaporation temperature condition, \(T_{\rm r}\) sharply increases at first. Then, \(T_{\rm r}\) is almost constant after 15 min due to approaching a stable state. In the stable state, \(T_{\rm r}\) values are about 102.7 \({}^{\circ}\)C, 103.9 \({}^{\circ}\)C, and 105.1 \({}^{\circ}\)C, corresponding to the evaporation temperatures of \(-3\)\({}^{\circ}\)C, \(-5\)\({}^{\circ}\)C, and \(-7\)\({}^{\circ}\)C.  
Because the ice and its latent heat increase in the evaporator with working time and lower evaporation temperature, the evaporation capacity increases, which results in a larger isentropic power \(w\) consumed by the compressor. Figure 8a also shows the effects of evaporation temperatures on \(w\), which are similar to those on \(T_{\rm r}\). The lower the evaporation temperature, the higher the isentropic power \(w\) is. In the same evaporation temperature conditions, during working time, \(w\) sharply increases at first. Then, \(w\) is almost constant in  
Figure 8: Effect of evaporation temperature with time (**a**) on \(T_{\rm r}\) and \(w\), (**b**) on \(Q\) and _COP_.  
Figure 7: Curve of ice content fitting.  
the stable state after 15 minutes. In the stable state, \(w\) is about 144.65, 155.45, and 166.50, corresponding to the evaporation temperatures of \(-3\)\({}^{\circ}\)C, \(-5\)\({}^{\circ}\)C, and \(-7\)\({}^{\circ}\)C.  
Figure 8b shows the effect of evaporation temperatures on the heating capacity \(Q\). The lower the evaporation temperature, the higher \(Q\) is. This is because the evaporation capacity in the evaporator increases due to more water being iced and its latent heat released at lower evaporation temperatures. As working time progresses and the more heat obtained and refrigerant evaporated in the evaporator, the \(Q\) of the condenser sharply increases at first. Then, the \(Q\) is almost constant after 15 minutes due to approaching the stable state. In the stable state, \(Q\) is about 435.32 kW, 454.83 kW, and 475.87 kW, corresponding to the evaporation temperatures of \(-3\)\({}^{\circ}\)C, \(-5\)\({}^{\circ}\)C, and \(-7\)\({}^{\circ}\)C.  
Figure 8b also shows the effect of evaporation temperatures on the system heating performance coefficient \(COP\). The higher the evaporation temperature, the greater the \(COP\) is. This is because the \(w\) of the compressor decreases. Although a higher evaporation temperature means a larger heating capacity, \(w\) is also larger and its increase rate is higher than that of \(Q\). As the working time progresses, in the same evaporation temperature conditions, \(COP\) sharply decreases at first. Then, \(COP\) is almost constant in the stable state after 15 minutes, which depends on the change in \(w\) and \(Q\). In the stable state, \(COP\) is about 3.02, 2.94, and 2.86, corresponding to the evaporation temperatures of \(-3\)\({}^{\circ}\)C, \(-5\)\({}^{\circ}\)C, and \(-7\)\({}^{\circ}\)C, respectively. The \(COP\) of the heat pump recommended in this paper is a little lower than that of the traditional surface water source heat pump because \(COP\) is positively correlated with the evaporative temperature.  
Based on the analysis above, the optimal time to deice the evaporator should be about 15 min.