## 2 Materials and Methods
### Measurement Method
It should be noted that for chillers with throttling orifices, a certain amount of refrigerant vapor may be entrained in the outlet of the condenser when the load is low. Due to the condensation heating of entrained hot vapor, the outlet subcooling is reduced or even no outlet subcooling. For the latter case, Equation (1) above is not applicable. The presence of refrigerant vapor can generally be determined by checking the subcooling degree at the condenser outlet or whether there are bubbles in the outlet pipe. For chillers with adjustable throttling flow area devices, such as floating ball valves, where the floating ball is above the lowest position, it can be considered that the condenser outlet is liquid refrigerant. The evaporator cooling capacity \(Q_{e}\) is calculated by Equation (4) according to the water temperature difference between the inlet and outlet and the water pressure drop. \[Q_{e}=\rho_{ev}V_{evo}c_{ev}(t_{evi}-t_{evo})+V_{evo}\Delta p_{ev} \tag{4}\]  
Based on the energy balance of the motor, ignoring the heat dissipation from the motor's case, the heat dissipation of motor \(Q_{motor}\) is equal to its power loss, as described by Equation (5). \[Q_{motor}=W_{in}(1-\eta_{e}) \tag{5}\]  
The transmission parts are cooled by the lubricating oil, which then dissipates heat to the refrigerant in the oil cooler, so the heat dissipation of the oil cooler \(Q_{oil}\) is equal to the power loss of the transmission parts \(Q_{mech}\), given in Equation (6). \[Q_{oil}=Q_{mech} \tag{6}\]  
The energy balance of the compressor is described by Equation (7). \[(m_{v}+m_{l})h_{0,evo}-(m_{v}h_{0,evo}+m_{l}h_{0,elo})=W_{comp} \tag{7}\]  
where \(W_{comp}\) is the input power of the compressor; the total discharge enthalpy of compressor \(h_{0,evo}\) is given in Equation (8). \[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{8}\]  
The vapor enthalpy at the compressor outlet \(h_{evo}\) is determined by the discharge temperature and pressure. According to Equation (7), given the discharge enthalpy and input power of the compressor, the amount of liquid entrainment \(m_{l}\) can be calculated and, conversely, if it is assumed that there is no liquid drawn into the compressor, the discharge enthalpy and temperature of the compressor without liquid entrainment can be calculated using Equation (7). So, the difference between the measured compressor discharge temperature and the calculated value without liquid carryover reflects the amount of liquid entrainment. The input power of the compressor in Equation (7) is calculated by Equation (9) according to the motor efficiency and the transmission power loss. \[W_{comp}=W_{in}\eta_{e}-Q_{mech} \tag{9}\]  
By adding Equations (1) and (7) and using Equations (5), (6) and (9), the following equation can be obtained:  
\[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]0The energy balance of the condenser can be written as:  
\[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]1  
Therefore, Equation (10) can also be expressed as Equation (12). \[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]2  
The condenser heat exchange capacity \(Q_{c}\) is calculated by Equation (13). \[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]3  
According to Equations (7) and (10) and by using Equation (9), \(m_{l}\) can be obtained by the following equation:  
\[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]4  
The above equation uses the heat exchange rate of the evaporator and the electric power input of the compressor to calculate the liquid entrainment rate \(m_{l}\). By using Equation (11), another expression for calculating the amount of liquid entrainment can be obtained, as described in Equation (15). \[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]5  
Since Equation (15) uses both heat exchange capacities of evaporator and condenser to calculate the liquid entrainment rate, generally, the result from Equation (15) has higher accuracy than that from Equation (14).