## 2 Materials and Methods  
### Measurement Method  
This method is suitable for single-stage centrifugal chillers, but can also be applied to two-stage chillers by simply bypassing the economizer of the two-stage unit and closing the secondary stage suction. Figure 2 shows the refrigerant flow chart of a single-stage centrifugal chiller. The sub-cooled liquid refrigerant flows out from the bottom of the condenser. Its main part enters the evaporator after being throttled by an orifice, where it is distributed axially by the distributor at the bottom of the evaporator. The vapor-liquid two-phase refrigerant flows upward across the tube bundle, absorbing the heat of the cold water in the tubes and evaporating. The temperature of the cold water decreases. The evaporated gaseous refrigerant and a small amount of entrained droplets flow out from the top outlet of the evaporator and are drawn into the compressor and compressed into high-pressure superheated vapor, then return to the condenser, where it is condensed by the cooling water in tubes and subcooled. In addition, there are two refrigerant auxiliary circuits, one of which enters the motor chamber after passing through a throttling orifice, which cools the motor and then flows back to the evaporator from the bottom of the motor chamber. There is also an orifice on the motor return pipe to make the pressure in the motor chamber slightly higher than that in the evaporator. In another auxiliary circuit, the refrigerant enters the oil cooler through a thermal expansion valve (TXV). It cools the lubricating oil of the transmission system and returns to the evaporator. The superheated vapor from the oil cooler enters the evaporator and mixes with the refrigerant vapor in the evaporator and then is drawn into the compressor. As shown in the dashed box in Figure 2, assuming that there is no hot gas bypass at the condenser outlet and ignoring the kinetic energy of the outlet liquid, the energy balance equation of the refrigerant is given by Equation (1). \[m_{v}h_{0,evo}+m_{l}h_{0,elo}-(m_{v}+m_{l})h_{sub}=Q_{e}+Q_{motor}+Q_{oil} \tag{1}\]  
where \(m_{v}\), \(m_{l}\) are the vapor and liquid flow rate from the evaporator, respectively; \(m_{l}\) is the amount of liquid entrainment; \(Q_{e}\), \(Q_{motor}\) and \(Q_{oil}\) are the cooling capacity of evaporator, the heat dissipation rate of motor and the heat dissipation rate of oil cooler, respectively; \(h_{0,evo}\) and \(h_{0,do}\) are the total enthalpy of the refrigerant vapor and liquid at the outlet of the evaporator (i.e., the inlet of the compressor), respectively; \(h_{sub}\) is the enthalpy of liquid refrigerant at the outlet of the condenser. The total enthalpy of vapor \(h_{0,evo}\) and liquid droplets \(h_{0,elo}\) at the outlet of the evaporator can be calculated by Equations (2) and (3), respectively [17]. \[h_{0,evo}=h_{evo}+\frac{u_{evo}^{2}}{2\times 1000} \tag{2}\]  
\[h_{0,elo}=h_{elo}+\frac{u_{elo}^{2}}{2\times 1000} \tag{3}\]  
where \(h_{evo}\) is the enthalpy of refrigerant vapor at the evaporator outlet, determined by the suction pressure and temperature; \(h_{elo}\) is the enthalpy of refrigerant saturated liquid at the evaporator outlet, determined by the suction temperature. \(u_{evo}\), \(u_{elo}\) is the vapor and droplets velocity, respectively. In Equations (2) and (3), 1000 is a unit conversion constant. It is assumed here that the velocity of droplets \(u_{elo}\) is equal to that of the vapor \(u_{evo}\), i.e., there is no slip between the vapor and liquid phase. Calculations show that when the  
Figure 2: Refrigerant flow chart of a single-stage centrifugal chiller. droplet velocity varies from 0 to \(u_{evo}\), its impact on the liquid entrainment factor is less than 0.1%. Usually, a subcooling tube bundle is arranged at the bottom of the condenser and the outlet liquid enthalpy can be determined by pressure and temperature.