Optimization Analysis of Low Temperature Air Source Heat Pump System
A low temperature air source heat pump system, using a triplecylinder two stage rolling piston compressor with variable volume ratio (referred to as two stage compressor with variable volume ratio), can work and show better economic efficiency at the outdoor ambient temperature of as low as 35°C. Compared with the conventional singlestage compression air source heat pump system, the low temperature air source heat pump system with variable volume ratio twostage compression twostep throttling interstage incomplete cooling cycle has the following differences:
1) In the twostage compression twostep throttling interstage incomplete cooling cycle, the throttling pressure drop shared by each stage is significantly smaller than that of the conventional singlestage compression cycle; in the twostage compression onestep throttling interstage incomplete cooling cycle, the branched throttling pressure drop and the branched mass flow rate are also significantly smaller than the conventional singlestage compression system.
 2) The evaporation temperature of a low temperature twostage compression system is significantly lower than that of conventional singlestage compression system, which causes great differences in thermophysical properties of refrigerants in low pressure side such as gas density and liquid dynamic viscosity with conventional singlestage compression system.
 3) During the heating operation, the refrigerant is further subcooled before entering the outdoor heat exchanger (evaporator), thus inlet quality and enthalpy of refrigerant in the evaporator are significantly reduced. The mass flow rate of refrigerant is reduced at the same as the heat exchange capacity.
 4) At a low outdoor ambient temperature, the displacement of compressor in the triplecylinder operation mode is greatly increased compared with the conventional singlestage compression air source heat pump system. The mass flow rate of refrigerant is remarkably increased.
Therefore, component design and selection of an air source heat pump system using a twostage compressor with variable volume ratio is of certain difference from that of a conventional singlestage compression air source heat pump system.
This chapter will analyze these differences and their influencing factors to provide design guidance for a variable volume ratio twostage compression air source heat pump system.
Optimization Analysis of Electronic Expansion Valve
General mass flow rate correlation of electronic expansion valve
The general mass flow rate correlation of the electronic expansion valve (EEV) is
where M = mass flow rate of refrigerant, kg/s A = flow cross section area of EEV, m^{2 }p = inlet density of refrigerant, kg/m^{3 }Дp = throttling pressure drop, Pa Co = flow coefficient
For the flow coefficient Co of refrigerant, there is no empirical correlation with high prediction accuracy. Here, the Wile empirical correlation with experimental correction factor is applied, that is
where v = specific volume of outlet twophase refrigerant
k_{c} = experimental correction factor, for R22, R410A and R32, k_{c} = 1.11.2
The flow cross section area of the EEV can be calculated according to the structural parameters of the valve body. The flow cross section area of an EEV with an ideal conical valve head as shown in Figure 5.1 is expressed as follows
where A = flow cross section area of EEV, mm^{2 }h = valve head lift of EEV, mm a = valve head taper angle of EEV D = inner diameter of valve seat of EEV, mm
FIGURE 5.1
Schematic diagram of flow passage for electronic expansion valve with conical valve head
The head lift of EEV (axial displacement from valve closing to valve opening) can be expressed as
where H = valve head maximum lift of EEV, mm n = number of pulse no = valve closing pulse number N = valve full opening pulse number
When the flow cross section area A of the EEV is known, the expression corresponding to the number of pulses of EEV can be obtained from the Equation (5.3) and Equation (5.4), that is
Optimization of firststep and secondstep electronic expansion valves for twostage compression twostep throttling cycle
In the twostage compression twostep throttling interstage incomplete cooling cycle heat pump system, the pressure drop shared by the firststep and second step EEVs will be significantly lower than that of the conventional single stage compression heat pump system. Therefore, under the same operating
TABLE 5.1
Flow cross section area of EEV for variable volume ratio twostage compression twostep throttling heat pump system with a rated heating capacity of 4 kW
R410A 
R410A 
R134a 
R134a 
R32 
R32 

0 
30 
0 
30 
0 
30 

0.8 
0.4 
0.8 
0.4 
0.8 
0.4 

200.3 
231.1 
182.2 
198.8 
308.6 
367.5 

17.11 
10.29 
14.14 
3.42 
16.55 
11.06 

0.203 
0.247 
0.198 
0.264 
0.159 
0.187 

0.122 
0.236 
0.097 
0.200 
0.094 
0.197 

71.9 
62.3 
79.0 
72.4 
46.7 
39.2 

57.3 
46.9 
63.4 
53.3 
39.3 
31.9 

980. G 
980.6 
1147.9 
1147.9 
896.3 
896.3 

0.0047 
0.0066 
0.0092 
0.0168 
0.0052 
0.0068 

1397.7 
1635.8 
684.9 
829 
1456.1 
1652.6 

0.725 
0.727 
0.788 
0.794 
0.694 
0.695 

1096.G 
1127.1 
1246.5 
1283.4 
994.9 
1015.7 

0.0048 
0.0233 
0.0074 
0.0457 
0.0051 
0.0265 

535.1 
827.4 
182.2 
246.5 
525.6 
868.8 

0.767 
0.791 
0.820 
0.859 
0.731 
0.754 

0.52G 
0.420 
0.703 
0.581 
0.366 
0.288 

0.G0G 
0.381 
1.008 
0.685 
0.462 
0.280 
Note: t_{e}, evaporation temperature, °C; R_{v}, volume ratio of compressor; g_{m},c ■ specific heating capacity, kJ/kg; tpr, intermediate temperature, °C; xft, quality after firststep EEV; x,,_{in}. quality after secondstep EEV: M_{c}, mass flow rate of firststep EEV, kg/h; M_{e}, mass flow rate of secondstep EEV, kg/h; pi, inlet density of firststep EEV, kg/m^{3}; vj, outlet specific volume of firststep EEV, m^{3}/kg; dp, pressure drop of firststep EEV, кРа; Сод, flow coefficient of firststep EEV; p2, inlet density of secondstep EEV, kg/m^{3}; ’2, outlet specific volume of secondstep EEV, m^{3}/kg; dp2, pressure drop of secondstep EEV, kPa; Co,2, flow coefficient of secondstep EEV; Ai, flow cross section area of firststep EEV, mm^{2}; Л2, flow cross section area of secondstep EEV, mm^{2}
conditions and at the same heating capacity, the flow cross section area of each step of the EEV will be larger than that of the conventional singlestage compression heat pump system.
Take the twostep throttling interstage incomplete cooling heat pump cycle using a twostage compressor with variable volume ratio as an example. When the subcooling is 5°C, the evaporation temperature and volume ratio are as shown in Table 5.1 (other parameters are the same as Table 2.2), and the rated heating capacity of heat pump is 4 kW, the flow cross section areas of the firststep and the secondstep EEVs are calculated according to Equation (5.1). The calculation results are listed in Table 5.1, where the correction factor k_{c} in Equation (5.2) is 1.15.
As shown in Table 5.1, when the evaporation temperature is 0°C and 30°C, the flow cross section areas of the firststep and the secondstep EEVs are relatively close for the same refrigerant. However, when the refrigerant is different, the flow cross section areas of the EEVs differ considerably due to the difference in pressure drop and thermophysical properties. For example, the flow cross section areas of the firststep and the secondstep EEVs of R134a are obviously larger than those of R410A and R32, wherein the system with R32 has the smallest flow cross section areas.
The structural parameters of the three EEVs with conical valve head are listed in Table 5.2. The flow cross section area of the corresponding EEV can be obtained by the Equation (5.3) and Equation (5.4). The variation of flow cross section area with the pulse number is shown in Figure 5.2.
TABLE 5.2
Structural parameters of EEV with conical valve head
EEV1 
1.3 
10 
2.5 
50 
500 
EEV2 
1.6 
10 
2.5 
50 
500 
EEV3 
2 
13 
2.5 
50 
500 
By substituting the flow cross section area in Table 5.1 into Equation (5.5), the pulse numbers of the EEVs 1, 2 and 3 corresponding to R410A, R134a and R32 are calculated in turn. The calculation results of the evaporation temperatures of 0°C and 30°C are listed in Tables 5.3 and 5.4, respective^. As can be seen from Tables 5.3 and 5.4, the EEVs 1, 2 and 3 are suitable for the R32, R410A and R134a heat pump systems, respectively.
For comparison, the calculation results of the flow cross section area of the EEV of the singlestage compression air source heat pump with a rated heating capacity of 4 kW are shown in Table 5.5. In addition, the flow cross section areas of the firststep and secondstep EEVs of the twostage compression twostep throttling interstage incomplete cooling cycle air source heat pump system calculated in Table 5.1 is compared with that of the EEVs of single stage compression heat pump system. The results are listed in Table 5.5.
TABLE 5.3
Pulse number of firststep and secondstep EEVs at evaporation temperature of 0°C
R410A 
R134a 
R32 

First step 
Second step 
First step 
Second step 
First step 
Second step 

EEV1 
349 
403 
471 
 
250 
308 
EEV2 
282 
321 
370 
 
208 
252 
EEV3 
189 
212 
239 
329 
145 
172 
TABLE 5.4
Pulse number of firststep and secondstep EEVs at evaporation temperature of 30°C_
R410A 
R134a 
R32 

First step 
Second step 
First step 
Second step 
First step 
Second step 

EEV1 
282 
259 
386 
458 
204 
200 
EEV2 
233 
215 
309 
361 
173 
169 
EEV3 
1G0 
150 
204 
234 
125 
123 
FIGURE 5.2
Flow cross section area of EEV with conical valve head varies with pulse number
From Table 5.5, the flow cross section areas of the firststep and secondstep EEVs of the twostage compression twostep throttling interstage incomplete cooling cylce heat pump are larger than those of the EEV of the singlestage compression heat pump with the same heating capacity.
TABLE 5.5
Flow cross section area of EEV for singlestage heat pump system with rated heating capacity of 4 kW
Refrigerant 

R410A 
R410A 
R134a 
R134a 
R32 
R32 

Condensation temperature (°C) 
45 
45 
45 
45 
45 
45 
Outlet subcooling of condenser (°C) 
5 
5 
5 
5 
5 
5 
Evaporation temperature (°C) 
0 
30 
0 
30 
0 
30 
Specific heating capacity (kJ/kg) 
202.9 
240 
182.9 
202.3 
311.8 
378.2 
Quality after EEV 
0.3042 
0.4376 
0.284 
0.4355 
0.2388 
0.3526 
Mass flow rate (kg/h) 
70.97 
60.00 
78.73 
71.18 
46.18 
38.08 
Inlet density of EEV (kg/m^{3}) 
980.0 
980.6 
1147.9 
1147.9 
896.3 
896.3 
Outlet specific volume of EEV (m^{3}/kg) 
0.0107 
0.0424 
0.0202 
0.0988 
0.0115 
0.0467 
Pressure drop of EEV (kPa) 
1932.8 
2463.2 
867.1 
1075.5 
1981.7 
2521.4 
Flow coefficient of EEV 
0.730 
0.753 
0.796 
0.853 
0.699 
0.724 
Flow cross section area of singlestage EEV (mm^{2}) 
0.439 
0.318 
0.616 
0.466 
0.308 
0.217 
Flow cross section area ratio of firststep EEV to singlestage EEV 
1.199 
1.319 
1.141 
1.246 
1.188 
1.325 
Flow cross section area ratio of secondstep EEV to singlestage EEV 
1.381 
1.196 
1.637 
1.469 
1.499 
1.289 