Experimental energetic analysis of the subcooler system in a two-stage refrigeration facility driven by a compound compressor.
The high environmental impact associated wit the refrigeration sector favors, from the point of view of energy efficiency, the use of more efficient refrigeration methods. Two-stage compression refrigeration systems, first developed in the 19th century, are among these methods and are now an efficient and readily available solution, since they allow cold to be produced with coefficient of performance (COP) and cooling capacities that are higher than those resulting from single-stage compression systems.
The first analyses of these systems, most of which were conducted from a theoretical point of view, focused on the energetic optimization of the interstage level and its relation to the evaporating and condensing temperatures. Examples of such studies include the works of Rasi (1955), Czaplinksy (1959), Arora and Dhar (1971), Domanski (1995), Zubair et al. (1996), and Ouadha et al. (2005). Research on two-stage compression cycles, especially with compound compressors, currently focuses on their application in air-conditioning systems with [CO.sub.2] (Celik 2004; Cavallini et al. 2005), in commercial refrigeration with hydrofluorocarbons (HFCs) (Torrella et al. 2009), and in high-efficiency heat pumps with HFCs (Zehnder 2004) and [CO.sub.2] (Agrawal and Bhattacharyya 2007; Agrawal et al. 2007), where the improvement in energy efficiency in relation to single-stage systems can be as much as 20% (Zehnder 2004).
Continuing with a series of publications in HVAC&R Research (Llopis et al. 2007) devoted to two-stage compression refrigeration plants and their interstage configurations, this work focuses on the analysis of one of the most used two-stage cycles--that with subcooler. In this configuration, part of the liquid refrigerant leaving the condenser is expanded to the intermediate pressure and then evaporated to achieve a degree of subcooling in the rest of refrigerant flowing to the evaporator and, thus, increasing the specific cooling capacity. Furthermore, this cycle can be used with zeotropic refrigerant mixtures, since it avoids problems associated with the distillation of the refrigerant and with retention of the lubricant oil in intermediate tanks. The experimental plant used in this work is the same as that used by Llopis et al. (2007) to analyze the direct liquid-injection system, where the effect of the desuperheating between the compression stages was examined. R-404A, one of the most widely-used refrigerants in Europe for low-temperature applications, is used to carry out the analysis.
The aim of this work is to complement the experimental research on two-stage refrigerating cycles and to present and analyze from experimental data the effects of the subcooler system on the main parameters of a real facility: cooling capacity, compressor power consumption, and COP. Furthermore, with this work we delve deeply into the knowledge of one of the most efficient and used two-stage cycles in medium capacity refrigerating applications.
EXPERIMENTAL PLANT DESCRIPTION AND TEST PROCEDURE
The experimental plant used in this work, which is presented in Figure 1, consists of three fluid loops in which the main loop is the refrigerant loop and the others are auxiliary systems that allow the behavior of the system to be studied under different operating conditions.
[FIGURE 1 OMITTED]
The refrigerant circuit (Figure 2), whose working fluid is the refrigerant R-404A, corresponds to a two-stage compression cycle with a liquid subcooling system. It consists of an isolated brazed-plate exchanger with a heat-transfer surface area of 0.29 [m.sup.2] and a thermostatic expansion valve whose bulb is placed at the refrigerant vapor outlet of the subcooler (P11, Figure 2). The refrigerant is driven by a 4 kW semi-hermetic compound compressor with six cylinders (bore: 50.8 mm; stroke: 31.8 mm), four of which correspond to the low compression stage and the rest to the high one. The refrigerant from the high compression stage (P1, Figure 2) is condensed in an isolated brazed-plate heat exchanger with a heat-transfer surface area of 0.62 [m.sup.2], and it feeds the liquid receiver of the facility (P3, Figure 2). The liquid refrigerant that leaves the receiver (P4, Figure 2) is divided into two currents: the main one, which flows to the evaporator through the subcooler (P5, Figure 2) and the secondary one, which is expanded by a thermostatic expansion valve to the interstage pressure (P10, Figure 2) and used to subcool the main refrigerant current (by evaporating the refrigerant in the subcooler). It is then used to produce a moderate desuper-heating between the compression stages. The evaporator is an isolated brazed-plate heat exchanger with a heat-transfer surface area of 1.2 [m.sup.2], and it is controlled by a thermostatic expansion valve with external equalization. This facility has an accumulation tank to avoid problems rising from liquid suction in the compressor at the evaporator exit. The superheat vapor at the evaporator exit (P7, Figure 2) is compressed to the intermediate pressure in the low-compression stage (P8 to P9, Figure 2) and is cooled slightly using the vapor refrigerant coming from the sub-cooler (P11, Figure 2). After entrance to the compressor at the intermediate pressure (P12, Figure 2), the refrigerant cools the electric motor and enters the high compression stage.
[FIGURE 2 OMITTED]
The refrigeration load is provided with an auxiliary system that works with an ethylene-glycol mixture (50/50 percent by volume). It consists of a 500-liter secondary fluid tank heated with electrical resistors controlled by a proportional--integral--derivative (PID) regulator and an inverter drive for the pump to control the flow rate. This allows the evaporating pressure level to be regulated. Another auxiliary system is used to control the condensing pressure. This system consists of a loop working with water that absorbs the heat released by the refrigerant in the condenser, which is cooled again using air-cooled heat exchangers. These heat exchangers are controlled by an inverter drive for the fan motor in order to obtain the required temperature level. Another inverter drive is used to regulate the water flow rate.
The thermodynamic states of the working fluids are obtained with 17 type T thermocouples placed over the pipe surface properly isolated from the environment and 10 piezoelectric pressure transducers. The mass flow rate of the refrigerant at the condenser outlet is obtained using a Coriolis mass flowmeter, and the volumetric flow rates of the fluids in the auxiliary systems are measured with two magnetic volumetric flowmeters. The compressor power consumption is obtained using a digital wattmeter, and its speed is measured with a calibrated signal from the inverter drive. All the sensors were calibrated, and their uncertainties can be checked in Table A1. The thermodynamic states of the refrigerant and the water are evaluated using the REFPROP database (Lemmon et al. 2002), and the properties of the ethylene-glycol mixture are obtained with interpolated polynomials from the 2005 ASHRAE Handbook--Fundamentals (ASHRAE 2005).
APPENDIX A Table A1. Measurement Device Uncertainties Physical Measurement Measurement and Calibrated Variable Device Calibration Range Uncertainty Temperature Type T 220-380 K [+ or -]0.1 K thermocouples Pressure Pressure gauges 0-1000 kPa 0-3000 kPa [+ or -]10 kPa [+ or -] 30 kPa Refrigerant mass Coriolis mass 0-6 kg*[min.sup.-1] [+ or -] flow rate flowmeter 0.22% of reading Secondary fluid Magnetic 0-4 [+ or -] volumetric flow volumetric [m.sup.3]*[min.sup.-1] 0.33% of rates flowmeter reading Compressor power Digital 0-6 kW [+ or -]0.5% consumption wattmeter of reading Compressor speed Inverter signal 0-1500 rpm [+ or -]1.3% of reading
The secondary refrigerant mass flow rate used to produce the subcooling in the main current of refrigerant in the high-pressure line is obtained indirectly from an energetic balance at the subcooler using Equation 1 with the nomenclature of Figure 2. The validity of the results is evaluated according to the difference in the heat transferred by the refrigerant and the secondary fluid in the evaporator, where there was a maximum disagreement of 4.1%, and in the condenser, with a maximum disagreement of 3.9%.
[m.sub.L] = [m.sub.H] * [[[h.sub.11] - [h.sub.10]]/[[h.sub.11] - [h.sub.5]]] (1)
The results of this work are based on four experimental tests at a constant compressor speed (1450 rpm) using the refrigerant R-404A, which are presented in Tables A2-A5 in the appendix of this paper. The facility behavior working with and without the subcooler system was analyzed over a range of evaporating pressures with a constant condensing pressure (18.3 bar) and also over a range of condensing pressures with a constant evaporating pressure (1.6 bar) with the same reheating at low-stage suction. In this paper, the two-stage cycle working without intermediate systems is referred to as the base configuration, and the two-stage cycle working with the subcooler system is called the subcooler configuration. Furthermore, in order to analyze the dependence of the interstage working pressure, an additional test was carried out in which the ratio of condensing and evaporating refrigerant mass flow rates were varied while operating at constant condensing ([P.sub.k] = 18.4 bar) and evaporating pressures ([P.sub.o] = 1.8 bar).
Table A2. Experimental Data of Base Configuration--Evaporation Pressure Variation Test at Constant Condensing Pressure [P.sub.H] [P.sub.i], [P.sub.o], RU, RTOT, bar bar bar [degrees]C [degrees]C EST-1 18.189 5.096 1.589 0.899 11.051 EST-2 18.394 5.690 1.899 0.976 9.184 EST-3 18.107 6.006 2.093 1.200 10.937 EST-4 18.439 6.354 2.341 1.304 7.978 EST-5 18.292 6.754 2.590 1.459 7.688 EST-6 18.299 7.246 2.934 1.815 7.494 SUB, [M.sub.o], [M.sub.k], [Q.sub.o] [Q.sub.k] W, kW [degrees]C kg/s kg/s kW kW EST-1 0.299 0.02723 0.02723 2.487 4.926 3.118 EST-2 0.448 0.03379 0.03379 3.143 5.936 3.488 EST-3 0.395 0.03771 0.03771 3.615 6.688 3.737 EST-4 0.385 0.04333 0.04333 4.221 7.396 3.951 EST-5 0.386 0.04874 0.04874 4.914 8.225 4.215 EST-6 0.485 0.05773 0.05773 6.127 9.644 4.524 COP EST-1 0.798 EST-2 0.901 EST-3 0.967 EST-4 1.068 EST-5 1.166 EST-6 1.354 Table A3. Experimental Data of Base Configuration--Condensing Pressure Variation Test at Constant Evaporating Pressure [P.sub.H], [P.sub.i], [P.sub.o], RU, RTOT, bar bar bar [degrees]C [degrees]C EST-1 21.197 5.490 1.591 0.898 11.454 EST-2 19.071 5.185 1.581 0.887 11.107 EST-3 18.189 5.096 1.589 0.899 11.051 EST-4 16.806 4.923 1.583 0.726 11.061 EST-5 15.788 4.852 1.583 0.710 11.091 EST-6 14.661 4.752 1.577 0.737 10.966 SUB, [M.sub.o], [M.sub.k], [Q.sub.o], [Q.sub.k], W,kW [degrees]C kg/s kg/s kW kW EST-1 0.317 0.02476 0.02476 2.030 4.198 3.019 EST-2 0.283 0.02629 0.02629 2.324 4.689 3.087 EST-3 0.299 0.02723 0.02723 2.487 4.926 3.118 EST-4 0.379 0.02783 0.02783 2.675 5.132 3.120 EST-5 0.289 0.02834 0.02834 2.830 5.325 3.089 EST-6 0.200 0.02849 0.02849 2.975 5.453 3.059 COP EST-1 0.672 EST-2 0.753 EST-3 0.798 EST-4 0.857 EST-5 0.916 EST-6 0.973 Table A4. Experimental Data of Subcooler Configuration--Evaporating Pressure Variation Test at Constant Condensing Pressure [P.sub.H], [P.sub.i], [P.sub.o], RU, RTOT, bar bar bar [degrees]C [degrees]C EST-1 18.265 5.701 1.578 0.69 9.837 EST-2 18.412 6.259 1.863 1.29 10.724 EST-3 18.313 6.292 1.899 1.47 10.473 EST-4 18.577 6.778 2.078 1.21 12.226 EST-5 18.435 6.826 2.181 1.35 10.243 EST-6 18.369 7.599 2.717 2.08 10.020 EST-7 18.546 7.907 2.913 2.11 10.910 SUB, [M.sub.o], [M.sub.k], [Q.sub.o], [Q.sub.k], W,kW [degrees]C kg/s kg/s kW kW EST-1 0.394 0.02388 0.03476 3.448 5.947 3.262 EST-2 0.542 0.03047 0.04243 4.247 7.168 3.655 EST-3 0.575 0.03129 0.04313 4.351 7.311 3.722 EST-4 0.423 0.03551 0.04799 4.865 8.073 4.040 EST-5 0.660 0.03751 0.04909 5.094 8.218 4.029 EST-6 0.776 0.05466 0.06437 7.095 10.671 4.524 EST-7 0.630 0.06308 0.07116 7.974 11.800 4.664 COP EST-1 1.057 EST-2 1.162 EST-3 1.169 EST-4 1.204 EST-5 1.265 EST-6 1.568 EST-7 1.710 Table A5. Subcooler Configuration--Condensing Pressure Variation Test at Constant Evaporating Pressure [P.sub.H], [P.sub.i], [P.sub.o], RU, RTOT, bar bar bar [degrees]C [degrees]C EST-1 15.428 5.308 1.587 0.660 9.001 EST-2 16.987 5.534 1.579 0.675 9.441 EST-3 18.265 5.701 1.578 0.689 9.837 EST-4 19.730 5.902 1.585 0.708 10.900 EST-5 21.047 6.049 1.580 0.648 11.424 EST-6 22.748 6.326 1.585 0.656 11.556 SUB, [M.sub.o], [M.sub.k], [Q.sub.o], [Q.sub.k], W, kW [degrees]C kg/s kg/s kW kW EST-1 0.244 0.02618 0.03587 3.836 6.464 3.306 EST-2 0.342 0.02467 0.03527 3.585 6.182 3.266 EST-3 0.394 0.02388 0.03476 3.448 5.947 3.262 EST-4 0.473 0.02278 0.03376 3.253 5.641 3.209 EST-5 0.531 0.02223 0.03250 3.127 5.307 3.157 EST-6 0.526 0.02202 0.03241 3.048 5.104 3.168 COP EST-1 1.160 EST-2 1.098 EST-3 1.057 EST-4 1.014 EST-5 0.990 EST-6 0.962
EXPERIMENTAL DATA ANALYSIS
This section is devoted to presenting and discussing the experimental results of the two-stage compression system working with the subcooler configuration. The experimental performance is analyzed through a comparison with the two-stage compression system working in a single-stage configuration without using intermediate-stage cooling (base configuration). The refrigerant fluid used to carry out the test was R-404A in an evaporating temperature range between -36[degrees]C and -21[degrees]C and a condensing temperature range of 31[degrees]C to 49[degrees]C.
Figure 3 presents a schematic diagram of the facility, and Figure 4 presents a simplified comparison of the main differences between the thermodynamic cycles for both configurations, which are analyzed and discussed above in the paper by considering the following assumptions:
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
* Equality of evaporating pressures/temperatures
* Equality of condensing pressures/temperatures
* Equality of specific suction volume at low compression stage
The interstage pressures in both tests are presented in Figures 5a and 5b. Experimental results show that the interstage pressure in the subcooler configuration is always higher than that reached in the base configuration. The increment in the pressure is caused by the amount of refrigerant injected between compression stages. In this cycle, the refrigerant is used to obtain a degree of subcooling in the liquid refrigerant that goes to the evaporator. This increment in the interstage pressure was observed when Llopis et al. (2007) analyzed the direct liquid-injection system experimentally. They found that the interstage pressure in a compound compressor is a linear function of the ratio of condensing and evaporating refrigerant mass flow rates, represented by Equation 2. In Equation 2, M represents the ratio of condensing and evaporating refrigerant mass flow rates, b is the slope of compressor volumetric efficiency linear approximation ([R.sub.v] = 1-b*t), t is the compression ratio, [R.sub.v] is the volumetric efficiency, [v.sub.suc, H] is the specific suction volume at the high compression stage, and [P.sub.i] is the inter-stage pressure of the two-stage cycle. The procedure for obtaining Equation 2 can be checked in Llopis et al. (2007).
[FIGURE 5 OMITTED]
[dM/M] = [b * ([t.sub.H]/[R.sub.v,H] + [t.sub.L]/[R.sub.v,L]) - [[d[v.sub.suc,H]/d[P.sub.i]]/[v.sub.suc,H]] * [P.sub.i]] * [[d[P.sub.i]]/[P.sub.i]] (2)
The relation represented by Equation 2 was verified by means of an experimental test in which the ratio between the condensing and evaporating refrigerant mass flow rates was varied (subcooling degree variation test) while operating at constant condensing ([P.sub.k] = 18.4 bar) and evaporating ([P.sub.o] = 1.8 bar) pressures at a fixed compressor speed (1450 rpm). The results concerning the interstage working pressure are represented in Figure 6, which shows the linear dependence of the ratio between refrigerant mass flow rates and the interstage pressure, which rises as the amount of refrigerant used in the subcooler increases.
[FIGURE 6 OMITTED]
Modification of the interstage level implies an alteration in the compression rates of each stage, which in turn results in the modification of the volumetric efficiencies; this leads to variations in the refrigerant mass flow rates throughout the cycle, as analyzed by Llopis et al. (2007).
The first energetic parameter that is affected by the use of the subcooler system is the cooling capacity of the cycle, for which the experimental measurements, as well as those for the specific cooling capacity, are presented in Figure 7a and Figure 7b for the evaporating and condensing variation tests respectively. (The average estimated error in the cooling capacity is 3.6%.)
[FIGURE 7 OMITTED]
Experimental measurements show that the cooling capacity of the subcooler cycle is always higher than that reached by the base configuration; its difference is amplified as both the condensing and evaporating pressures increase. The specific cooling capacity of the subcooler cycle is higher too; however, the bigger the total compression ratio is, the greater its difference becomes.
This difference in cooling capacities could be analyzed by expressing them for both cycles, as presented in Equations 3 and 4 (subcooler configuration denoted with *), taking into account that the specific cooling capacity for the base configuration ([q.sub.0]) is a term of the specific cooling capacity of the subcooler cycle. The total specific cooling capacity of the subcooler configuration is composed of the specific cooling capacity of the base cycle plus the difference in enthalpy due to the liquid subcooling ([DELTA][h.sub.Subc]).
[Q.sub.o] = [m.sub.L] * [q.sub.o] (3)
[Q*.sub.o] = [m*.sub.L] * [q.sub.o,Subc] = [m*.sub.L]x * ([q.sub.o] + [DELTA][h.sub.Subc]) (4)
Accordingly, the difference in cooling capacities between the cycles depends on the mass flow rate modification due to the interstage pressure change, and on the degree of subcooling achieved in the subcooler, as presented in Equation 5.
[Q*.sub.o]-[Q.sub.o] = ([m*.sub.L]-[m.sub.L])*[q.sub.o] + [m*.sub.L][DELTA][h.sub.Subc] (5)
The difference in cooling capacities for both cycles, represented by Equation 5, could be expressed as a function of the operating pressures and other energetic parameters, as represented by Equation 7. To expand, the following relations and assumptions have been considered: relation between the refrigerant mass flow rate with the volumetric efficiency; linear function of the volumetric efficiency with the pressure ratio ([R.sub.v] = a-b*t); effectiveness of the subcooler (Equation 6) (in which the difference in enthalpy due to the subcooling at the condenser outlet and due to the refrigerant glide are neglected); equal specific suction volume at the low-stage ([v.sub.suc,L]) for both cycles. In Equation 7, [V.sub.G,L] represents the geometric volumetric flow rate at the low-compression stage, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the specific enthalpy of saturated liquid at condensing pressure, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the specific enthalpy of saturated liquid at interstage pressure in the subcooler configuration.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Equation 7 is composed of two terms. The first term represents the reduction in cooling capacity due to the decrease in the mass flow rate through the evaporator because the increased interstage pressure. This term is always negative when the subcooler system is used, and implies that the lower the evaporating temperature is, the higher the reduction in cooling capacity induced by the reduction in mass flow rate. This result is the same as that observed when using the direct liquid-injection system (Llopis et al. 2007). However, the second term in Equation 7 is always positive and represents the increase in cooling capacity due to the subcooling of the liquid refrigerant at high pressure.
The term corresponding to the subcooling depends on the subcooler efficiency (Equation 6), the experimental evolutions of which are presented in Figure 8a and 8b for the evaporating and condensing variation tests, respectively. The experimental results show that the subcooler efficiency largely depends on the evaporating temperature rather than on the condensing pressure. This fact is related to the dependence of the refrigerant mass flow rates on the pressure levels, where the influence of the evaporating pressure on the mass flow rate is stronger than that exerted by the condensing pressure, as previously analyzed by Cabello et al. (2007).
[FIGURE 8 OMITTED]
The next parameter that varies is the compressor power consumption, which is always higher when the subcooler system is used. In this case, the compression work in the low-stage decreases due to the reduction in refrigerant mass flow rate through the evaporator. However, the increment in the compression power consumption is mainly caused by the increase in the compression work in the high-stage due to the rise in the refrigerant mass flow rate. In contrast to what was observed when the direct liquid-injection system was analyzed (Llopis et al. 2007), in the subcooler configuration (with the bulb of the expansion valve of the subcooler placed at the outlet of the subcooler), the temperature level of the refrigerant at the entry to the compressor at the high-stage is higher than that measured in the direct liquid-injection system and similar to that measured in the base configuration. Therefore, the heat absorbed by the refrigerant inside the compressor does not change significantly with regard to the base configuration. Nevertheless, it is worth mentioning that the subcooler system has a secondary function of producing a certain degree of desuperheating between compression stages and, consequently, the high discharge temperature is reduced. In the experimental tests, a reduction in the high discharge temperature of 15[degrees]C at an evaporating temperature of -36[degrees]C was registered; nonetheless, this temperature difference was null at an evaporating temperature of -21[degrees]C.
Finally, the most important difference between the two-stage cycle working with the bubcooler configuration in relation to the base one is the energetic efficiency of the plant, the experimental results of which are depicted in Figure 9a and 9b for the evaporating and condensing pressure variation tests, respectively. (The average estimation error in COP values is 2.9%). Observing Figures 9a and 9b, the energetic improvement achieved when using the subcooler system is obvious. In this case, despite the fact that the compressor power consumption increases, the increase in cooling capacity is higher and, therefore, the COP is enhanced over the whole operation range of the facility. As represented in Figure 9b, the higher the condensing pressure is, the more prominent the improvement, related to the slight increment in subcooler efficiency (Figure 8b). On the other hand, the COP improvement decreases when the evaporating pressure descends (Figure 9a), even with an increase in the subcooler efficiency (Figure 8a). This is because, at low evaporating pressures, the drop in cooling capacity due to the reduction in the refrigerant mass flow rate becomes more important than at high pressures (Equation 6).
[FIGURE 9 OMITTED]
This paper presents an experimental comparison between a two-stage refrigerating cycle with a subcooler system and a two-stage refrigerating cycle without the intermediate system. The analysis was carried out for a two-stage refrigerating facility with a semi-hermetic compound compressor and R-404A as the working fluid.
Experimental results show that the interstage pressure is always higher when the subcooler is used than when it is not. This interstage pressure increase is a consequence of the increase in the ratio of condensing/evaporating refrigerant mass flow rates in the two-stage cycle when the subcooler is used, where their relation is a linear dependent function.
The intermediate pressure increase when the subcooler is used produces a modification in the cooling capacity of the two-stage cycle due to two main effects. First, the cooling capacity tends to be reduced because of the reduction in the refrigerant mass flow rate through the evaporator (as a consequence of the pressure ratio increase in the low stage). Second, the cooling capacity tends to increase due to the subcooling of the refrigerant in the subcooler. The composition of these effects results in an increment in the cooling capacity in relation to the cycle without subcooler, where the increment is a function of the efficiency of the subcooler.
The experimental tests show that the efficiency reached by the subcooler is strongly influenced by the evaporating pressure, since this variable is the one that exerts the greatest effect on the refrigerant mass flow rates. However, the efficiency is nearly constant when the condensing pressure is varied.
Finally, the compressor power consumption is always higher when the subcooler is used, because of the increase in the amount of refrigerant to be compressed in the high stage; however, no significant differences in relation to the base configuration were measured concerning the heat absorbed by the refrigerant in the compressor cooling at the interstage level. The global result of the increase in the cooling capacity and in the increment in the compressor power consumption is a gain in COP of the two-stage cycle. This increase becomes lower when the evaporating pressure descends, and that rises when the condensing pressure increases.
a = constant of compressor volumetric efficiency linear approximation
b = slope of compressor volumetric efficiency linear approximation
h = enthalpy, kJ*[kg.sup.-1]
M = ratio of condensing and evaporating refrigerant mass flow rates
P = pressure, bar
Q = heat transferred, kW
[q.sub.o] = specific cooling capacity, kJ*[kg.sup.-1]
[R.sub.v] = volumetric efficiency
RMU = superheating degree in suction line, [degrees]C
RU = superheating degree at evaporator, [degrees]C
SUB = subcooling degree at condenser outlet, [degrees]C
t = compression ratio
T = temperature, [degrees]C
[V.sub.G] = geometric volumetric flow rate, [m.sup.3]*[s.sup.-1]
W = compressor power consumption, kW
[upsilon] = specific volume, [m.sup.3]*[kg.sup.-1]
[epsilon] = subcooler effectiveness
[DELTA] = increment
Base = refers to the two-stage configuration without interstage systems
disch = compressor discharge
H = high compression stage
i = interstage level
k = condenser
l = saturated liquid
L = low compression stage
o = evaporator
S,l,out = subcooler liquid outlet
Subc = refers to the two-stage configuration with the subcooler system
suc = compressor suction
S,v,out = subcooler vapor outlet
Agrawal N., S. Bhattacharyya. 2007. Studies on a two-stage transcritical carbon dioxide heat pump cycle with flash intercooling. Applied Thermal Engineering 27(2-3):299-305.
Agrawal N., S. Bhattacharyya, and J. Sarkar. 2007. Optimization of two-stage transcritical carbon dioxide heat pumps. Int. J. of Thermal Sciences 46(2):180-87.
Arora C.P., P.L. Dhar. 1971. Optimization of multistage refrigerant compressors. Proceedings of the 13th International Conges of Refrigeration, Paris, France, pp. 693-700.
ASHRAE. 2005. 2005 ASHRAE Handbook--Fundamentals. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
Cabello R., J. Navarro, R. Llopis, and E. Torrella. 2007. Analysis of the variation mechanism in the main energetic parameters in a single-stage vapour compression plant. Applied Thermal Engineering 27(1):167-76.
Cavallini, A., L. Cecchinato, M. Corradi, E. Fornasieri, C. Ziliio. 2005. Two-stage transcritical carbon dioxide cycle optimisation: A theoretical and experimental analysis. Int. J. Refrigeration 28:1274-83.
Celik, A. 2004. Performance of two-stage [CO.sub.2] refrigeration cycles. Doctoral thesis, Faculty of the Graduate School of the University of Maryland, College Park.
Czaplinsky, S. 1959. Uber den optimalen Zwischendruck bei Kalteprozessen. Allgemeine Warmetechnik 91(9): 3-6.
Domanski, P.A. 1995. Theoretical evaluation of the vapor compression cycle with a liquid-line/suction-line heat exchanger, economizer, and ejector. National Institute of Science and Technology, Interagency Report 5606, National Institute of Standards and Technology, Gaithersburg, MD.
Lemmon, E.W., M.O. McLinden, and M.L. Huber. 2002. REFPROP NIST Standard Reference Database 23, v.7.0. National Institute of Standards and Technology, Gaithersburg, MD.
Llopis R., E. Torrella, R. Cabello, and J.A. Larumbe. 2007. Experimental energetic analysis of the liquid injection effect in a two-stage refrigeration facility using a compound compressor. HVAC&R Research 13(5):819-31.
Ouadha A., M. En-Nacer, L. Adjlout, and O. Imine. 2005. Exergy analysis of a two-stage refrigeration cycle using two natural substitutes of HCFC22. International Journal of Exergy 2(1):14-30.
Rasi, A. 1955. La pression intermediare la plus correcte pour les cycles frigorifiques a deux phases. Proceedings of the 9th International Congress of Refrigeration, Paris, France, pp. 3032-39.
Torrella E., R. Llopis, and R. Cabello. 2009. Experimental evaluation of the inter-stage conditions of a two-stage refrigeration cycle using a compound compressor. International Journal of Refrigeration 32(2):307-15.
Zehnder, M. 2004. Efficient air-water heat pumps for high temperature lift residential heating including oil migration aspects. Doctoral thesis, Ecole Polytechnique Federale de Lausanne, Laussane, Switzerland.
Zubair, S.M., M. Yaqub, S.H. Khan. 1996. Second-law-based thermodynamic analysis of two-stage and mechanical-subcooling refrigeration cycles. International Journal of Refrigeration 19(8):506-16.
Enrique Torrella, PhD
Rodrigo Llopis, PhD
Ramon Cabello, PhD
Received July 8, 2008; accepted October 20, 2008
Enrique Torrella is a professor in the Department of Applied Thermodynamics, Polytechnic University of Valencia, Valencia, Spain. Rodrigo Llopis and Daniel Sanchez are lecturers and Ramon Cabello is a professor in the Department of Mechanical Engineering and Construction, Campus de Riu Sec, Jaume I University, Castellon, Spain.