Optimization Analysis of Low Temperature Air Source Heat Pump System

A low temperature air source heat pump system, using a triple-cylinder 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 single-stage compression air source heat pump system, the low temperature air source heat pump system with variable volume ratio two-stage compression two-step throttling interstage incomplete cooling cycle has the following differences:

1) In the two-stage compression two-step throttling interstage incomplete cooling cycle, the throttling pressure drop shared by each stage is significantly smaller than that of the conventional single-stage compression cycle; in the two-stage compression one-step throttling interstage incomplete cooling cycle, the branched throttling pressure drop and the branched mass flow rate are also significantly smaller than the conventional single-stage compression system.

• 2) The evaporation temperature of a low temperature two-stage compression system is significantly lower than that of conventional single-stage 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 single-stage 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 triple-cylinder operation mode is greatly increased compared with the conventional single-stage 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 two-stage compressor with variable volume ratio is of certain difference from that of a conventional single-stage 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 two-stage 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, m² p = inlet density of refrigerant, kg/m³ 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 two-phase refrigerant

k_c = experimental correction factor, for R-22, R-410A and R-32, k_c = 1.1-1.2

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, mm² 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 first-step and second-step electronic expansion valves for two-stage compression two-step throttling cycle

In the two-stage compression two-step throttling interstage incomplete cooling cycle heat pump system, the pressure drop shared by the first-step 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 two-stage compression two-step throttling heat pump system with a rated heating capacity of 4 kW

	R-410A	R-410A	R-134a	R-134a	R-32	R-32
	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 first-step EEV; x,,_in. quality after second-step EEV: M_c, mass flow rate of first-step EEV, kg/h; M_e, mass flow rate of second-step EEV, kg/h; pi, inlet density of first-step EEV, kg/m³; vj, outlet specific volume of first-step EEV, m³/kg; dp, pressure drop of first-step EEV, кРа; Сод, flow coefficient of first-step EEV; p2, inlet density of second-step EEV, kg/m³; ’2, outlet specific volume of second-step EEV, m³/kg; dp2, pressure drop of second-step EEV, kPa; Co,2, flow coefficient of second-step EEV; Ai, flow cross section area of first-step EEV, mm²; Л2, flow cross section area of second-step EEV, mm²

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 single-stage compression heat pump system.

Take the two-step throttling interstage incomplete cooling heat pump cycle using a two-stage 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 first-step and the second-step 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 first-step and the second-step 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 first-step and the second-step EEVs of R-134a are obviously larger than those of R-410A and R-32, wherein the system with R-32 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 R-410A, R-134a and R-32 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 R-32, R-410A and R-134a heat pump systems, respectively.

For comparison, the calculation results of the flow cross section area of the EEV of the single-stage 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 first-step and second-step EEVs of the two-stage compression two-step 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 first-step and second-step EEVs at evaporation temperature of 0°C

TABLE 5.4

Pulse number of first-step and second-step EEVs at evaporation temperature of -30°C_

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 first-step and second-step EEVs of the two-stage compression two-step throttling interstage incomplete cooling cylce heat pump are larger than those of the EEV of the single-stage compression heat pump with the same heating capacity.

TABLE 5.5

Flow cross section area of EEV for single-stage heat pump system with rated heating capacity of 4 kW