## 2 Materials and Methods
### Uncertainty Analysis  
The uncertainty of \(E_{fg}\) is calculated by the uncertainty propagation equation according to the uncertainty of each parameter [19]. Taking Equation (14) as an example, the uncertainty of \(E_{fg}\) is calculated by the following Equation (21). \[ \begin{array}{ll}u\Big{(}E_{fg}\Big{)}&=\sqrt{\left(\frac{\partial E_{fg}}{ \partial E_{fg}}\right)^{2}\left(u\left(W_{in}\right)\right)^{2}+\left(\frac{ \partial E_{fg}}{\partial E_{\text{J}}}\right)^{2}\left(u\left(\eta_{e} \right)\right)^{2}+\left(\frac{\partial E_{fg}}{\partial E_{\text{J}}}\right) ^{2}\left(u\left(Q_{mech}\right)\right)^{2}+\left(\frac{\partial E_{fg}}{ \partial E_{\text{J}}}\right)^{2}\left(u\left(V_{ew}\right)\right)^{2}}\\ &+\left(\frac{\partial E_{fg}}{\partial E_{\text{J}}}\right)^{2}\left(u\left( t_{ew}\right)\right)^{2}+\left(\frac{\partial E_{fg}}{\partial E_{\text{J}}} \right)^{2}\left(u\left(t_{ew}\right)\right)^{2}+\left(\frac{\partial E_{fg}}{ \partial E_{\text{J}}}\right)^{2}\left(u\left(t_{success}\right)\right)^{2}+ \left(\frac{\partial E_{fg}}{\partial E_{\text{J}}}\right)^{2}\left(u\left(t_ {diss}\right)\right)^{2}}\\ &+\left(\frac{\partial E_{fg}}{\partial t_{is}}\right)^{2}\left(u\left(t_{ obj}\right)\right)^{2}+\left(\frac{\partial E_{fg}}{\partial p_{act}}\right)^{2} \left(u\left(p_{succ}\right)\right)^{2}+\left(\frac{\partial E_{fg}}{\partial p _{is}}\right)^{2}\left(u\left(p_{dis}\right)\right)^{2}+\left(\frac{\partial E _{fg}}{\partial p_{c}}\right)^{2}\left(u\left(p_{c}\right)\right)^{2}\\ &+\left(\frac{\partial E_{fg}}{\partial p_{c}}\right)^{2}\left(u\left(\Delta p _{e}\right)\right)^{2}\\ \end{array}  \tag{21}\]  
The experimental data processing and uncertainty calculation are all based on the Engineering Equation Solver (EES) [20]. The thermal properties of refrigerant and water are calculated by the EES built-in program. The authors examined the accuracy of the  
Figure 4: Evaporator inlet and outlet water temperature at 700 RT and 581 kg charge. Figure 5: Condenser inlet and outlet water temperature at 700 RT and 581 kg charge. EES thermal property calculations and compared the difference between the \(E_{fg}\) calculated using Refprop 9.1 (Gaithersburg, USA) [21] and the results from EES. It was found that the difference is generally much less than 0.1%. So, it is reasonable to ignore the EES thermal property calculation error. Table 2 shows the entrainment factor \(E_{fg}\) and its uncertainty under 700 RT and 581 kg of charge, including the results using Equation (14) (Method 1) and Equation (15) (Method 2). The table also shows the impact on the \(E_{fg}\) results if the uncertainty of the transmission power loss is doubled. As shown in the table, the calculated \(E_{fg}\) value of Equation (15) is about 2% lower than that of Equation (14). The difference is related to the system thermal balance, the better the system thermal balance, the smaller the difference between the two methods will be. Since the thermal balance of this experimental point is \(-0.23\%\) (the thermal balance of all test points is within \(-0.80\%\)\(\sim\)\(-0.18\%\)), the difference between the two methods is small. The thermal balance of the system can partly reflect the reliability of the measurement results, so it is recommended that the thermal balance of the experimental points be within 1%. As shown in the table, the relative uncertainties of \(E_{fg}\) for methods one and two are 24% and 22%, respectively. Since the results from the two methods are very close to each other for a system with good thermal balance and the accuracy of Method 2 is higher, it is recommended to use Method 2 (Equation (15)) to calculate \(E_{fg}\). As can be seen from the table, if the uncertainty of the transmission power loss is doubled, the relative uncertainty of the \(E_{fg}\) of methods one and two will increase to 29% and 27%, respectively. Therefore, the transmission power loss has a great impact on the uncertainty of \(E_{fg}\).