Optimization of main and branched electronic expansion valves for two-stage compression one-step throttling cycle

Two-stage compression one-step throttling interstage incomplete cooling cycle (referred to Figure 2.7) and two-stage compression two-step throttling interstage incomplete cooling cycle' (referred to Figure 2.9) are widely applied to engineering practice. In the two heat pump cycle systems under ideal operating conditions(no heat transfer temperature difference, no pressure drop in the heat exchanger and complete separation of gas and liquid in the flash- tank), the suction, discharge and intermediate pressures of the one-step throttling cycle shown in Figure 2.7 are the same as those of the two-step throttling cycle shown in Figure 2.9. The mass flow rate of the refrigerant flowing through the branched EEV and the main EEV in the one-step throttling cycle obey the Equation (2.34) and the Equation (2.36), respectively, where the entrainment ratio E = 0. Because the mass flow rate of refrigerant flowing through the condenser in two-step throttling cycle is the same as that flowing through the first-step EEV, the mass flow rate of the refrigerant flowing through the second-step EEV also satisfies Equation (2.36) where the entrainment ratio E = 0. Therefore, when the heating capacity is the same, the ideal one-step throttling cycle and the two-step throttling cycle have the following similarities:

• 1) The state of the inlet and outlet refrigerants of the branched and main EEVs in one-step throttling cycle are the same as those of the first-step and second-step EEVs in two-step throttling cycle, respectively, except for the inlet pressure of the main and the second-step EEVs. According to Equation (5.2), the flow coefficient and the inlet refrigerant density in Equation (5.1) are correspondingly identical between the above two systems;
• 2) The throttling pressure drop of the branched EEV in the one-step throttling cycle corresponding to Equation (5.1) is the same as the throttling pressure drop of the first-step EEV in two-step throttling cycle;
• 3) The refrigerant mass flow rate of the main EEV in the one-step throttling cycle is the same as that of the second-step EEV in the two-step throttling cycle.

However, the following differences exist:

• 1) The throttling pressure drop of the main EEV in one-step throttling cycle is the sum of the throttling pressure drops of the first-step and the second-step EEVs in the two-step throttling cycle;
• 2) The refrigerant mass flow rate of the branched EEV in the one-step throttling cycle is equal to that of the first-step EEV in the two-step throttling cycle multiplied by the first-step throttling quality (flash quality).

From the above analysis, combined with Equation (5.1) and Equation (2.34), it can be deduced that when the heating capacity is constant, under ideal operating conditions, the ratio of the flow cross section area of branched EEV in the one-step throttling cycle to the flow cross section area of the first-step EEV in the two-step throttling cycle is equal to the first-step throttling quality (flash quality). In addition, the ratio of the flow cross section area of the main EEV in the one-step throttling cycle to the that of the second-step EEV in the two-step throttling cycle is equal to the square root of the ratio of the second-step throttling pressure drop to the total throttling pressure drop.

Taking the variable volume ratio two-stage compression one-step throttling interstage incomplete cooling heat pump cycle as an example, the flow cross section areas of the branched and main EE Vs of heat pump system are calculated as described above. The results are listed in Table 5.6. The rated heating capacity of heat pump is 12kW and other calculation conditions are the same as Table 5.1. When calculating, firstly the flow cross section areas of the branched and main EEVs in one-step throttling cycle with the rated heating capacity of 4kW are calculated referred to Table 5.1; then, according to the Equation (5.1), the flow cross section area of the EEV of one-step throttling cycle of 12kW is converted.

TABLE 5.6

Flow cross section area of EEV for variable volume ratio two-stage compression one-step throttling heat pump system with rated heating capacity of 12 kW

Similarly, the selection design of EEV can be processed after calculating the above mentioned flow cross section area.

For comparison, referring to Table 5.5, the calculation results of the flow cross section area of EEV in the single-stage heat pump system of 12 kW are listed in Table 5.7. According to Tables 5.5 and 5.7, when the heating capacity is the same, the flow cross section area of the branched EEV of the variable volume ratio two-stage compression one-step throttling interstage incomplete cooling heat pump system is much smaller than that of the single- stage heat pump system and that of the two-step throttling heat pump system. In addition, the flow cross section area of the main EEV of the variable volume ratio two-stage compression one-step throttling interstage incomplete cooling heat pump system is smaller than that of the single-stage heat pump system and that of the two-step throttling heat pump system.

TABLE 5.7

Flow cross section area of EEV for single-stage heat pump system with rated heating capacity of 12 kW

In the the single-stage compression heat pump, the outlet subcooling of condenser is generally greater than that of the two-stage compression interstage incomplete cooling heat pump, resulting in a decrease in the inlet temperature of EEV, and increases in the inlet density and flow coefficient. In addition, the outlet specific enthalpy of the condenser decreases while the inlet specific enthalpy of the condenser increases (as the discharge temperature of single-stage compression is higher), so the specific heating capacity increases and actual mass flow rate is reduced compared with the theoretical calculation result. It can be known from Equation (5.1) that the actual flow cross section area of EEV of the single-stage compression heat pump will be smaller than the theoretical calculation result. Therefore, the actual ratio of the flow cross section areas of the first-step EEV and the second-step EEV of two-stage compression two-step throttling heat pump to that of the EEV of single-stage compression heat pump, or the actual ratio of the flow cross section areas of the branched EEV and the main EEV of the two-stage compression one-step throttling heat pump to that of the EEV of single-stage compression heat pump, will be larger than the theoretical calculation result.