Evaluation of a novel liquid-flooded Ericsson cycle cooler for vending machine applications.
This paper presents a parametric study of a liquid-flooded Ericsson cooler (LFEC). The LFEC was described in Hugenroth et al. (2007), where a thermodynamic analysis of the cycle was presented. This analysis assumed ideal gas and constant specific heats for the gas and liquid. The liquid-flooded Ericsson cooler (LFEC) is a modification of the basic reverse Ericsson cycle that overcomes the substantial practical difficulties of achieving isothermal compression and expansion processes. In the LFEC, isothermal compression and expansion are approached by mixing a nonvolatile liquid with a noncondensable gas during the compression and expansion processes. The term "flooded" comes from the notion that the compressor and expander are flooded with large quantities of liquid. Liquid mass flow rates may be significantly greater than gas mass flow rates. This is in contrast to oil injection schemes in some types of positive displacement compressors where the principle purpose is to improve sealing of the leakage paths and the reduction of friction within the compressor, and the oil flow rates represent only about 1% to 5% of the total flow by mass. A practical approach for achieving liquid flooding would be to utilize oil as the liquid in combination with compressors/expanders that would tolerate high oil volumes, such as scroll compressors.
Scroll compressors are fixed volume ratio machines. This allows them to tolerate liquid flooding since a finite gas volume remains in the discharge pockets when the fluid is ejected through the discharge port. Off-the-shelf scroll compressors have been shown to operate with reasonable efficiency for hundreds of hours under liquid flooded conditions (Hugenroth 2006, Hugenroth, et al. 2008). Hugenroth (2006) contains a detailed discussion of liquid flooded compression theory and practical considerations.
The motivation of LFEC research is the elimination of HFC refrigerants, which are potent greenhouse gases. Gas cycles, such as the Ericsson cycle, can use environmentally benign working fluids, such as air, argon, xenon, or helium. Replacement of HFC refrigerants with natural working fluids would reduce the direct impact of refrigerant leakage on global warming. However, in order to not increase the indirect global warming impact due to burning of fossil fuels for electricity generation, alternatives to vapor compression systems should have equal or better operating efficiencies.
The particular applications being considered for the LFEC technology were vending machine bottle coolers with a cooling capacity of 380 W. These bottle coolers are free standing units that are approximately the size of full sized refrigerators used in U.S. homes. They have a single swing-open glass door and shelving for holding bottled or canned drinks. While the bottle cooler was the primary application of interest, the analysis applies to any system operating with the same sink and source temperatures. The goal of the study was to determine the operating parameter values (e.g. pressures, mass flow rates) that minimize the required efficiency of various components in the system while meeting the specified COP and capacity requirements.
A schematic of a LFEC is shown in Figure 1. Two arrangements are shown. The arrangement in Figure 1a is being called a Type 1 liquid-flooded Ericsson cooler (LFEC1). The LFEC1 is how the concept was originally conceived. Hugenroth et al. (2008) reported on the experimental work of a system using this arrangement. However, it was later found that the COP is greater for the arrangement shown in Figure 2b. This is being called a Type 2 liquid-flooded Ericsson cooler (LFEC2). Therefore, the LFEC2 is the focus of this study.
[FIGURE 1 OMITTED]
In Figure 1b, the solid lines correspond to liquid flows while the dashed lines are gas flows. A solid line next to a dashed line indicates a liquid gas mixture. The liquid and the gas are separate substances (e.g. oil and nitrogen). No phase change occurs for the fluids in the system.
The components to the left of the regenerator are on the hot side. (i.e. temperatures are at or above ambient) while the components on the right side are on the cold side (i.e. temperatures are below ambient).
The system operates as follows: Starting at state point 1, a low pressure high temperature gas flows into the hot side mixer where it mixes with liquid coming from state point 9. The gas and liquid are different substances and are assumed noncondensable and nonvolatile, respectively. The liquid and gas mixture (state point 2) enters the compressor where they are compressed simultaneously. The liquid absorbs much of the heat of compression, such that the temperature of the fluid mixture at state point 3 is much lower than it would be for a dry compression process. This occurs because the thermal capacitance of the liquid is greater than that of the gas, and intimate thermal contact between the liquid and gas is achieved. For sufficient liquid flooding the process is nearly isothermal. The fluid mixture then enters the hot side heat exchanger where heat is rejected from the system. The fluid flow at state point 10 enters the hot side separator where the liquid and gas streams are separated. The high pressure gas stream (state point 4) enters the regenerator where heat is rejected to the low pressure stream. The gas exits the separator as a cold high pressure stream (state point 5). The gas then enters the cold side mixer where it mixes with the high pressure liquid stream (state point 13). This mixture is discharged from the mixer (state point 6) before entering the expander. The fluid mixture exits the expander as a low pressure low temperature liquid and gas mixture. The temperature of the fluid is higher than it would be for a dry expansion process. The liquid and gas mixture enters the cold side heat exchanger where heat is absorbed from the refrigerated space. The fluid stream at state point 12 enters the cold side separator where the liquid and gas are separated. The low pressure low temperature gas at state point 8 then enters the regenerator where it absorbs heat from the high pressure gas stream.
The path just described, traced by the dashed line, is referred to as the gas loop. The path traced by the solid line on the hot side of the system is referred to as the hot liquid loop, and the path traced by the solid line on the cold side of the system is referred to as the cold liquid loop.
Completing the hot liquid loop starting at state point 14, the liquid exits the hot side separator at high pressure. It passes through a hydraulic motor to lower its pressure, recovering shaft work during the process. The liquid exiting the hydraulic motor (state point 9) enters the hot side mixer, as described previously. Similarly, on the cold side of the system the liquid exiting the cold separator (state point 11) is at low pressure. A pump is used to increase the pressure of the liquid to the high side system pressure (state point 13).
The reason for using a liquid gas mixture is that, in principle, the work required to compress the gas is substantially reduced because of the higher specific volume that results from the liquid absorbing the heat of compression. Similarly, an increase in expander work output will occur, in theory. When the rotating machinery in the system has an adiabatic efficiency of 100% and the heat exchangers have effectiveness values of 100%, then the COP of the system approaches the Carnot COP as the liquid flooding rate increases [Hugenroth, 2006]. In addition, the gas loop processes are identical to the Ericsson refrigeration cycle.
The LFEC Type 1 and 2 are novel system concepts developed by this paper's authors. As stated, the motivation of the research was the elimination of HFC refrigerants, which are potent global warming gases. Additional, information about LFEC systems can be found in the literature shown in the References section.
CYCLE MODEL DEVELOPMENT
A numerical model was developed to simulate the LFEC2. Several improvements were made over the model developed for the LFEC1 analysis that was presented in Hugenroth et al. (2007). These include:
* The impact of pressure drop on cycle performance
* Modeling of gas in the liquid line due to incomplete separation
* Modeling of liquid in the gas line due to incomplete separation
* Real gas flooded compression and expansion modeling
* Real gas modeling of the heat exchangers and regenerator
* Allowing for temperature dependence of liquid specific heat and specific volume
While the effect of small liquid droplets of oil in the gas loop was modeled, the effect of oil vapor in the gas loop was neglected. Oil vapor in the gas loop was estimated to be a maximum of 0.3% of the total flow in the gas loop (Hugenroth 2006).
Real Gas Liquid Flooded Compression and Expansion
Real gas flooded compression and expansion were modeled by employing a control volume analysis assuming negligible kinetic and potential energy changes and steady state operation. It was further assumed that the flow was homogeneous (the liquid and gas move through the control volume at the same speed), and the oil and gas are in thermal equilibrium. A mathematical description of the cycle simulation including flooded compression and expansion processes is given in the Appendix.
Modeling of the Remaining Components in the System
The remaining components in the LFEC system model include hot and cold side heat exchangers, a regenerator, hot and cold side mixers, hot and cold side separators, a hydraulic motor, and a pump. Effectiveness models were used for the heat exchangers. The temperature of the liquid and gas exiting the separators is assumed to be equal to the fluid inlet temperature. The mixer model implements an adiabatic mixing process. The pump and hydraulic motor were modeled in the same manner as the compressor and expander, respectively, to account for gas in the liquid loops due to incomplete separation in the separators.
For all components in the system, excluding the rotating machinery, pressure drops are accounted for by specifying a pressure drop across each component in the system. This simple approach was used so that the sensitivity of the cycle performance to pressure drop could be investigated.
Highly accurate real gas equations of state were used for all of the gaseous fluids considered (Klein, 2006). The oil used in the modeling and the experimental work (Hugenroth et al. 2008) was 60 SUS alkyl-benzene oil. Specific heat data were obtained for the oil using differential scanning calorimetry and a curve fit for the data is given in the Appendix.
In practice, the separators used in a real system will not perform perfect separation. Therefore, gas remains in the liquid loop flows while liquid is entrained in the gas loop flow. The presence of a secondary fluid in the primary fluid flows will result in different properties for the combined flow. The LFEC2 simulation calculates the change in the fluid mixture properties due to fluid carryover using a model that is presented in the Appendix.
Performance parameters for the model are presented in this section. The cooling capacity ([Q.sub.in]) is
[Q.sub.in] = [H.sub.12] - [H.sub.7] (1)
where H is the enthalpy and the subscript refers to the state points shown in Figure 1b.
The heat rejected ([Q.sub.out]) is
[Q.sub.out] = [H.sub.10] - [H.sub.3] (2)
The cooling coefficient of performance (COP) is defined as
COP = [[Q.sub.in]/[W.sub.net]] (3)
The second law efficiency is defined as
[[eta].sub.II] = ([COP]/[[COP.sub.carnot]]) (4)
The entropy generation rate is
[S.sub.gen] = [DELTA]S - [[Q.sub.i]/[T.sub.i]] (5)
The heat transfer rate term ([Q.sub.i]) was zero except for the hot and cold heat exchangers, and [T.sub.i] corresponded to either the ambient or cold space temperature.
Three parametric studies were performed to study impacts of different system parameters and operating conditions on design requirements for a fixed cooling capacity. The first two studies focused on the bottle cooler (i.e. vending machine) application that was the motivation for the research program. This application required a COP of 1.25 with a cooling capacity of 380 W (1297 Btu/hr). The ambient and cold space temperatures were 32.2[degrees]C (90[degrees]F) and 2[degrees]C (35.6[degrees]F), respectively. In order to attain a COP of 1.25 the rotating machinery in the system (i.e. compressor, expander, pump, hydraulic motor) must operate at some minimum adiabatic efficiency. This minimum efficiency will vary depending on system pressure drops, fluid carryover, heat exchanger effectiveness, and system operating pressures. The first parametric study investigated the sensitivity of the required rotating machinery efficiency to changes in the other system parameters. Table 1 summarizes the input parameters used for the study. For each case, the [C.sub.ratio] values for the compressor and expander and the compressor pressure ratio were optimized. [C.sub.ratio] is a dimensionless parameter defined as
[C.sub.ratio] = [[[m.sub.l][c.sub.l]]/[[m.sub.g][c.sub.p, g]]] (6)
Table 1. Inputs for Sensitivity Study Case Figure [[eta].sub.m], [[epsilon].sub.reg] [[epsilon].sub.hx] [[eta].sub.p] 1 2 n/a 0.81-0.9 0.85 2 3 n/a 0.85 0.81-0.9 3 4 n/a 0.85 0.85 4 5 n/a 0.85 0.85 5 6 n/a 0.85 0.85 6 7 0.8-0.9 0.85 0.85 7 8 n/a 0.85 0.85 8 9 n/a 0.85 0.85 Case [[eta].sub.elec] [x.sub.c], [y.sub.c] [P.sub.2], [DELTA]P, [x.sub.e] kPa (psia) kPa (psia) 1 0.9 0.01 0.01 500 (72.5) 5 (0.73) 2 0.9 0.01 0.01 500 (72.5) 5 (0.73) 3 0.86-0.95 0.01 0.01 500 (72.5) 5 (0.73) 4 0.9 0-0.05 0.01 500 (72.5) 5 (0.73) 5 0.9 0.01 0-0.05 500 (72.5) 5 (0.73) 6 0.9 0.01 0.01 500 (72.5) 5 (0.73) 7 0.9 0.01 0.01 200-1000 5 (0.73) (29.0-145.0) 8 0.9 0.01 0.01 500 (72.5) 5-30 (0.73-4.35)
In words, it is the ratio of the liquid's thermal capacitance rate to gas's thermal capacitance rate. Using [C.sub.ratio] eliminates the need to consider changes in mass flow rates and specific heats of the fluids independently. Nitrogen and 60 SUS alkyl-benzene oil were used in the analysis.
The second parametric study looked at the cycle performance for different working fluid pairs. Six potentially viable working fluid pairs were considered in the analysis. These were nitrogen/alkyl-benzene, nitrogen/30% aqueous ethylene glycol, xenon/alkyl-benzene, xenon/30% aqueous ethylene glycol, helium/alkyl-benzene, and helium/30% aqueous ethylene glycol. The input parameters are shown in Table 2.
Table 2. Model Input Parameters for Working Fluids Comparison COP [T.sub.[infinity]], [T.sub.ref], [[epsilon].sub.reg] [degrees]C [degrees]C ([degrees]F) ([degrees]F) 1.25 32.2 (90.0) 2.0 (35.6) 0.85 COP [[epsilon].sub.hx] [[eta].sub.elec] [x.sub.c], [y.sub.c] [x.sub.e] 1.25 0.85 0.9 0.01 0.01 COP [P.sub.2], [DELTA]P, kPa (psia) kPa (psia) 1.25 500 (72.5) 5 (0.73)
The third study looked at the LFEC2 performance for a range of source temperatures (i.e. cold space temperature). This was done to gain an initial understanding of the suitability of the technology for other applications ranging from comfort cooling to low temperature refrigeration. Four fluid working pairs were considered. These were nitrogen/alkyl-benzene, nitrogen/ethanol, helium/alkyl-benzene, and helium/ethanol. The aqueous ethylene glycol solution was not considered since the freezing point is too high. The freezing point for the 60 SUS alkyl-benzene oil was not known. However, at low temperatures the oil would be very viscous. In addition, property data at low temperatures was not available. For these reasons, when alkyl-benzene oil was used in the analysis a low temperature limit of -43[degrees]C (-45.4[degrees]F) was specified. At the pressures used in the analysis xenon condenses at about -45[degrees]C (-49[degrees]F). The model in its current form was not able to handle a condensable gas. Ethanol, which remains liquid from - 114.1[degrees]C (237.4[degrees]F) to 78.5[degrees]C (173.3[degrees]F) at ambient pressure, is considered a candidate liquid for low temperature operation. However, the vapor pressure of ethanol is high enough that some evaporation and condensation is expected to occur on the hot side of the system. The real fluid model in its current form does not account for this effect.
Table 3 shows the input parameters used in the real fluid analysis when the source temperature was varied.
Table 3. Model Input Parameters for Different Source Temperatures ([T.sub.ref]) and Working Fluids [eta] (all [T.sub.[infinity], [T.sub.ref] [[epsilon].sub.reg] rotating [degrees]C machinery) ([degrees]F) 0.85 32.2 (90) N/A 0.85 [eta] (all [[epsilon].sub.hx] [[eta].sub.elec] [x.sub.c], [y.sub.c] rotating [x.sub.e] machinery) 0.85 0.85 0.9 0.01 0.01 [eta] (all [P.sub.2], [[DELTA]P, rotating kPa (psia) kPa (psia) machinery) 0.85 500 (72.5) 5 (0.73)
RESULTS AND DISCUSSION
The following results are for the first parametric study, which uses the input parameters from Table 1. In Figures 2-4 the rotating machinery efficiency required to maintain a COP of 1.25 is shown as a function of other system parameters. The amount of change in the required rotating machinery efficiency indicates how sensitive the cycle is to changes in the independent parameter. In Figure 2 the rotating machinery adiabatic efficiency is shown as a function of the regenerator and heat exchanger effectiveness values. A ten percentage point change in the effectiveness for either the regenerator or the heat exchangers results in roughly a one-half percentage point change in the required rotating machinery efficiency. This indicates that the cycle COP is much more sensitive to changes in rotating machinery efficiency than it is to changes in heat exchanger effectiveness.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Figure 3 shows the variation in required rotating machinery efficiency when the electric motor efficiency varies. The motor was assumed to be external to the system (i.e. not hermetic). This figure shows that increasing the motor efficiency from 86% to 95% will allow for the rotating machinery efficiency to be decreased only 1.4 percentage points.
In experimental work performed for the LFEC1 (Hugenroth et al. 2008) it was found that gas bubbles remained in the liquid stream. It is unlikely that this effect could be totally eliminated in a commercial system. The sensitivity of the LFEC2 performance to fluid carryover is shown in Figure 4, where the required rotating machinery efficiency is shown as a function of the gas and liquid carryover. In the analysis the mass fraction of gas carried into the hot and cold liquid loops were assumed equal. For the liquid carryover, the liquid in the gas leaving the hot separator ([y.sub.c]) was specified. The oil remaining in the gas coming from the cold separator was determined from Equation (A27). The impact of the oil in the gas loop was found to be almost negligible. The gas in the oil loops, however, had a more significant impact.
In Figure 5, the hydraulic motor and pump efficiencies are equal to each other, and vary from 0.8 to 0.9. This is plotted against the compressor and expander efficiency required to attain a COP of 1.25. The cycle performance is much more sensitive to the compressor and expander efficiency than to that of the hydraulic motor and pump. This occurs because the compressor and expander consume and produce much more power. Therefore, losses in these components have a more significant impact on the cycle performance.
[FIGURE 5 OMITTED]
Figure 6 shows the rotating machinery efficiency required to attain a COP of 1.25 as the compressor inlet pressure varies. As the pressure increases, the required efficiency decreases. A minimum was reached at about 900 kPa (130.5 psi). This behavior is a consequence of the fact that a fixed pressure drop of 5 kPa (0.73 psi) was assumed across each component in the system, with the exception of the rotating machinery. If the pressure drops were zero then the required efficiencies for the rotating machinery would increase monotonically with increasing inlet pressure (Hugenroth 2006). This occurs because the gas compression work is a function of pressure ratio while the liquid compression work is a function of pressure differential (Hugenroth 2006, Hugenroth et al. 2007). For a fixed pressure ratio, the pressure differential decreases as the nominal system pressure decreases (i.e. reduced low or high side system pressures). Therefore, the losses associated with the compressor and expander decrease.
[FIGURE 6 OMITTED]
Since the capacity was fixed, the mass flows in the system remained relatively constant as the compressor inlet pressure varied. If the system geometry were assumed constant then the pressure drop tends to decrease as the system pressures increased, due to the decrease in the fluid specific volume. Therefore, the assumption that the pressure drop remained constant with increasing compressor inlet pressure is conservative. The end result for a real LFEC2 system is that an optimum compressor inlet pressure exists.
The effect of pressure drop on the required rotating machinery efficiency is shown in Figure 7. The impact is substantial. A pressure drop across each component of just 3 kPa means that the adiabatic efficiencies of the rotating machinery must increase by about 1.4%.
[FIGURE 7 OMITTED]
In each of the simulation runs in the parametric study, the pressure ratio and [C.sub.ratio] values for the compressor and expander were optimized independently. For Cases 1 through 6, the values for pressure ratio and [C.sub.ratio] did not vary a great deal. The optimum pressure ratio tended to be about 3.7 while the optimum compressor and expander [C.sub.ratio] values were about 10.3 and 7.3, respectively. These values and the compressor inlet pressure dictate the displacement volume and volume ratio for the compressor and expander. The displacement volumes and built in volume ratios are important from a system design standpoint. The average values for Cases 1 through 6 are shown in Table 4. The shaft speed was fixed at 58 Hz.
Table 4. Average Displacement Volume and Volume Ratio for Parametric Study Cases 1 through 6 Displacement Discharge Volume, Volume Ratio Volume, [mm.sup.3]/rev [mm.sup.3]/rev ([in.sup.3]/rev) ([in.sup.3]/rev) Compressor 15500 (0.946) 4700 (0.287) 3.3 Expander 4100 (0.251) 13100 (0.799) 3.2
The relative size difference between the compressor and expander is found by comparing the compressor displacement volume with the expander discharge volume. The expander is slightly smaller than the compressor because the gas on the expander side has a lower specific volume due to its lower temperature. The pressure drops in the system also result in a smaller pressure ratio across the expander. Because of this, the expander volume ratio is slightly smaller.
Figures 8 through 11 show the variation in optimum pressure ratio, [C.sub.ratio], and displacement volumes as a function of the compressor inlet pressure, and the per component pressure drop. These results are for Cases 7 and 8 (Table 1) where the large variation in the system pressures resulted in larger variations for the optimum pressure ratio and [C.sub.ratio] values. Consequently, the compressor and expander displacement volume and volume ratios vary more substantially.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The results of the second parametric study (Table 2 inputs), which investigated the effects of varying the working fluid pairs, are shown in Table 5. The parameter a in Table 5 relates the volume of the liquid at the compressor or expander inlet to the total inlet volume. That is
a = [[V.sub.l]/[V.sub.dis]] (7)
Table 5. Comparison of Design Parameters for Different Working Fluid Pairs to Achieve a COP of 1.25 Nitrogen Nitrogen Xenon Xenon Working Fluid Alkyl-benzene 30% Alkyl-benzene 30% Pairs Ethylene Ethylene Glycol Glycol (Aqueous) (Aqueous) [a.sub.c] 0.042 0.037 0.040 0.041 [a.sub.e] 0.099 0.097 0.161 0.137 [C.sub.ratio,c] 12.47 10.83 15.60 15.68 [C.sub.ratio,e] 6.90 8.42 7.51 8.49 [eta] * 0.87 0.87 0.85 0.85 [P.sub.ratio] 3.7 3.6 4.6 4.3 [V.sub.ratio,c] 3.2 3.2 4.2 3.9 [V.sub.ratio,e] 3.2 3.1 4.2 4.1 [V.sub.dis,c], 15,500 15,500 11,400 11,800 [mm.sup.3] [V.sub.dis,c], 0.946 0.946 0.696 0.720 [in.sup.3] [V.sub.dis,e], 4000 4100 2200 2300 [mm.sup.3] [V.sub.dis,e], 0.244 0.250 0.134 0.140 [in.sup.3] Helium Helium Working Fluid Alkyl-benzene 30% Pairs Ethylene Glycol (Aqueous) [a.sub.c] 0.034 0.035 [a.sub.e] 0.095 0.087 [C.sub.ratio,c] 14.34 14.62 [C.sub.ratio,e] 10.58 12.02 [eta] * 0.87 0.87 [P.sub.ratio] 3.4 3.4 [V.sub.ratio,c] 3.0 3.0 [V.sub.ratio,e] 2.9 2.9 [V.sub.dis,c], 16,700 16,800 [mm.sup.3] [V.sub.dis,c], 1.019 1.025 [in.sup.3] [V.sub.dis,e], 4800 4800 [mm.sup.3] [V.sub.dis,e], 0.293 0.293 [in.sup.3] * All rotating machinery
The use of xenon instead of nitrogen resulted in a two percentage point reduction in the required efficiency for the rotating machinery. No improvement was found with helium. However, this was not the case at lower source temperatures, as will be shown. The use of the aqueous ethylene glycol mixture did not strongly affect the required rotating machinery efficiency. The required displacement volume using xenon was smaller than when nitrogen was used. However, the required volume ratio with xenon increased.
The LFEC2 system is complex compared to vapor compression systems typically used in vending machines. In addition, the components used in the system require relatively high performance to achieve the target COP of 1.25. This makes the commercial viability of the LFEC2 for vending machine applications questionable.
In light of the results for near ambient refrigeration, other source temperatures were investigated to see how the LFEC2 cycle performance varied. For example, it was not known if the technology would be suitable for comfort cooling or low temperature refrigeration, for which numerous applications exist.
Figure 12 summarizes the results of the LFEC2 performance when operating at other source temperatures. It can be seen that the cycle second law efficiency peaks at temperatures much lower than the 2[degrees]C used for vending machine applications. The peak efficiency occurs at a source temperature of approximately -112[degrees]C (-169.6[degrees]F) when helium is used and - 92[degrees]C (-133.6[degrees]F) when nitrogen is used.
[FIGURE 12 OMITTED]
At source temperatures in this range, cascade vapor compression systems are often used. These systems are much more complex than simple vapor compression systems. Therefore, it is possible that the LFEC2 system would be commercially viable for low temperature use, not only because this is where the cycle is most efficient, but also because the complexity of the LFEC2 system is, arguably, on par with cascade vapor compression systems. However, additional research is required to validate this hypothesis.
Three parametric studies were performed for a LFEC2 system. The first study investigated the adiabatic efficiency sensitivity of the rotating machinery to changes in other system parameters. A COP of 1.25 was specified as a requirement in the analysis. The results showed that the adiabatic efficiencies were relatively insensitive to changes in heat exchanger and regenerator effectiveness values, motor efficiency, and liquid and gas carryover; assuming reasonable values of these parameters were used. As a corollary, the results show that the COP of the LFEC2 is very sensitive to small changes in the adiabatic efficiencies of the compressor and expander. The adiabatic efficiency of the rotating machinery was found to be quite sensitive to pressure drops in the system.
The use of xenon as the system refrigerant for near ambient refrigeration reduced the required rotating machinery efficiency by about two percentage points, compared to nitrogen and helium. Little performance difference was found between using alkyl-benzene oil and aqueous ethylene glycol as the system liquid. Using reasonable effectiveness values and pressure drops it was found that the rotating machinery efficiency needed to be in the range of 85% to 87% to achieve a COP of 1.25. These values are feasible. However, substantial improvement in adiabatic efficiencies and, therefore, COP would be quite difficult to attain.
The effect of decreasing the source temperature was also studied. It was found that the second law efficiency of the LFEC2 increases substantially as the source temperature decreased. The maximum second law efficiency occurred at approximately -112[degrees]C (-169.6[degrees]F) when helium and ethanol were used as the working fluids. For low temperature applications the complexity of the LFEC2 is more akin to that of competing technologies such as cascade vapor compression systems. Therefore, the LFEC2 is more likely to be commercially viable for these applications.
The authors would like to thank Tecumseh Products Company for sponsoring this research.
Liquid Flooded Compression and Expansion Modeling
The first law for an arbitrary differential control volume is
[delta]W + [delta]Q = dH (A1)
Steady-state steady-flow operation, chemical equilibrium, and no changes in kinetic or potential energy are assumed. If the control volume contains liquid and gas, the terms in Equation (A1) can be separated into liquid and gas terms giving
[delta][W.sub.g] + [delta][Q.sub.g] + [delta][W.sub.l] + [delta][Q.sub.l] = d[H.sub.g] + d[H.sub.l] (A2)
Since the process is assumed adiabatic,
[delta][Q.sub.g] + [delta][Q.sub.l] = 0 (A3)
Therefore, Equation (A2) can be rewritten as
[delta][W.sub.total] = [delta][W.sub.g] + [delta][W.sub.l] = [m.sub.g]d[h.sub.g] + [m.sub.l]d[h.sub.l] (A4)
Integrating Equation (A4) across the control volume gives
[W.sub.total] = [m.sub.g][DELTA][h.sub.g] + [m.sub.l][DELTA][h.sub.l] (A5)
where the [DELTA]h terms represent the enthalpy at the outlet minus that of the inlet. Equation (A5) simply states that the total power is equal to the enthalpy change of the gas, times the gas flow rate, plus the enthalpy change of the liquid, times the liquid flow rate. Where, for the present analysis, the power corresponds to the liquid flooded compression power. Typically, the inlet condition and outlet pressure are known. However, the outlet temperature is unknown, leaving the outlet enthalpy unknown, and Equation (A5) unsolvable without additional information.
For reversible adiabatic flooded compression the process is isentropic, that is
[m.sub.g][DELTA][s.sub.g] + [m.sub.l][DELTA][s.sub.l] = 0 (A6)
In Equation (A6) the outlet entropies are unknown. However, using the assumption that the liquid and gas are in thermal equilibrium, the only unknown is the outlet temperature. Therefore, Equation (A6) can be solved iteratively for this temperature. The temperature determined from solving Equation (A6) can be applied to Equation (A5), which gives the reversible or ideal liquid flooded compression power ([W.sub.ideal]). The adiabatic efficiency for flooded compressor is defined as
[[eta].sub.c] = [[W.sub.ideal]/[W.sub.actual]] = [[[m.sub.g][DELTA][h.sub.g, s] + [m.sub.l][DELTA][h.sub.l, s]]/[[m.sub.g][DELTA][h.sub.g] + [m.sub.l][DELTA][h.sub.l]]] (A7)
where [W.sub.actual] is the actual compression power. Once the actual power is known the actual outlet temperature and enthalpies can be found by iteratively solving Equation (A5).
The compressor model developed to this point is generic in that it does not represent a specific type of compressor, such as a scroll or screw compressor. In the overall LFEC2 model, the compressor is modeled as a positive displacement machine, since the displacement rate is fixed by the displacement volume and shaft speed, which are supplied as inputs. Specifics of liquid-flooded compression as it relates to positive displacement compressors can be found in Hugenroth et al. (2007).
The compressor model requires the following inputs: liquid and gas properties, inlet temperature, inlet and outlet pressures, displacement volume, shaft speed, adiabatic efficiency, and volume fraction of liquid entering the inlet. The basic model outputs are outlet temperature, liquid flow rate, gas flow rate, and power. Additional outputs are available, such as built in volume ratio, effective volume ratio, gas compression power, liquid compression power and others. The liquid-flooded expander is analogous to the compressor and was modeled in the same manner. The adiabatic efficiency for the expander is defined as
[[eta].sub.e] = [[W.sub.actual]/[W.sub.ideal]] (A8)
Alkyl-Benzene Oil Properties
Equation (A9) shows the curve fit for the specific heat of the 60 SUS alkyl-benzene oil. The raw data are available in Hugenroth (2006).
[c.sub.l] = 5.186T + 337.1 (A9)
In Equation (A9) T is in Kelvin (K) and [c.sub.l] is in J/kg-K.
A single room-temperature density measurement was made for the 60 SUS alkyl-benzene oil. Published data for density as a function of temperature were available for 150 and 300 SUS alkyl-benzene oils. These relationships are linear. The 60 SUS alkyl-benzene oil density was assumed to vary at the same rate with respect to temperature as the 150 and 300 SUS alkyl-benzene oils. The resulting density relationship is
[[rho].sub.l] = -0.6670T + 1051 (A10)
where T is in K and [[rho].sub.l] is in [kg/m.sup.3]. The oil was assumed to be incompressible, so that
[du.sub.l] = [c.sub.l]dT (A11)
[dh.sub.l] = [c.sub.l]dT + dP/[[rho].sub.l] (A12)
d[s.sub.l] = [[c.sub.l]/T]dT (A13)
Equations (A11), (A12), and (A13) can be integrated analytically after substitution of the specific heat and density curve fits (Equations (A9) and (A10). The resulting expressions are
[u.sub.l] = 2.593 [T.sup.2] + 337.1 T (A14)
[h.sub.l] = [u.sub.l] + P/[[rho].sub.l] (A15)
[s.sub.l] = 5.186(T - 298) + 337.1 ln[T/298] (A16)
where T is in K and P is in Pa. To evaluate internal energy and enthalpy at any T and P, the reference state for integration of the internal energy and enthalpy expressions was chosen as [T.sub.ref] = [P.sub.ref] = 0. For the entropy expression, integration was performed from a reference state of 298 K to an arbitrary T value.
Fluid Carryover Modeling
The gas entrained in the hot liquid flow was accounted for by specifying the fraction of gas flow through the compressor that was carried into the hot oil loop ([x.sub.c]). That is,
[x.sub.c] = [[m.sub.g, hotliquid]/[m.sub.g, c]] (A17)
where, [m.sub.g,c] is the total gas flow through the compressor, and [m.sub.g,hotliquid] is the mass of gas carried into the hot liquid loop. The fraction of the gas flow through the expander that is carried into the cold oil loop ([x.sub.e]) was defined in a similar manner. The amounts of gas in the hot and cold oil loops are independent of each other. However, the amount of gas entering the gas loop from the hot separator must equal the amount of gas entering the gas loop from the cold separator. This requirement means that
[m.sub.g, c](1 - [x.sub.c]) = [m.sub.g, e](1 - [x.sub.e]) (A18)
Were this not the case, then gas would accumulate on one side of the system.
Hot liquid in the gas loop was specified as the fraction of the hot liquid flow through the compressor that was entrained into the gas loop. That is,
[y.sub.c] = [[m.sub.l, gasloop]/[m.sub.l, c]] (A19)
The fraction of the cold liquid entering the gas loop ([y.sub.e]) is defined similarly. The amount of liquid entering the gas loop from the hot and cold sides must be equal to prevent accumulation of liquid on one side of the system. This requires that
[m.sub.l, c][y.sub.c] = [m.sub.l, e][y.sub.e] (A20)
In practice the assumption made in Equation (A20) is not strictly true. Due to a number of factors such as, differences in pressure, temperature and normal manufacturing variability, one of the gas streams exiting the separators will always contain more liquid than the other. This difference is negligible as far as cycle performance is concerned. However, for a commercial system a means would have to be in place to prevent accumulation of liquid on one side of the system over time.
The total enthalpy rate terms in the LFEC2 model include the effect of liquid in the oil loop and gas in the liquid loops. That is,
[H.sub.i] = [m.sub.g, c](1 - [x.sub.c])[h.sub.g, i] + [m.sub.l, c][y.sub.c][h.sub.l, i] (gas loop) (A21)
[H.sub.i] = [m.sub.g, c][x.sub.c][h.sub.g, i] + [m.sub.l, c](1 - [y.sub.c])[h.sub.l, i] (hot liquid loop) (A22)
[H.sub.i] = [m.sub.g, e][x.sub.e][h.sub.g, i] + [m.sub.l, e](1 - [y.sub.e])[h.sub.l, i] (cold liquid loop) (A23)
where the subscript i refers to a specific state point in the system (see Figure 1b).
a = liquid volume fraction
c = specific heat
COP = coefficient of performance
[C.sub.ratio] = ratio of liquid to gas capacitance rates
H = enthalpy rate
h =specific enthalpy
m = mass flow rate
P = pressure
[P.sub.ratio] = pressure ratio
Q = heat transfer rate
S = entropy rate
s = entropy
T = temperature
u = specific internal energy
W = work rate (power)
x = gas mass fraction in liquid loop
y = oil mass fraction in gas loop
actual = actual process
c = compressor
e = expander
elec = electric motor
g = gas
gen = generation
hx = heat exchanger
ideal = ideal process
in = in
l = liquid
m = motor
out = out
p = pump
ref = refrigerated space
reg = regenerator
s = isentropic
total = total
1, 2, 3 ... i = state points
[infinity] = ambient space
[DELTA] = change
[epsilon] = effectiveness
[eta] = adiabatic efficiency
[[eta].sub.II] = second law efficiency
[rho] = density
Hugenroth, J., Liquid Flooded Ericsson Cycle Cooler, A Thesis, Purdue University, 2006.
Hugenroth, J., Braun, J., Groll, E., King, G., Thermodynamic analysis of a liquid-flooded Ericsson cycle cooler, International Journal of Refrigeration, Vol. 10, pp. 1176-1186, 2007.
Hugenroth, J., Braun, J., Groll, E., King, G., Experimental investigation of a liquid-flooded Ericsson cycle cooler, International Journal of Refrigeration, Vol. 31, pp. 1241-1252, 2008
Klein, S., Engineering Equation Solver (EES), F-Chart Software, 2006.
Omar Abdelaziz, University of Maryland, College Park, MD: What is the model accuracy? How would that be reflected in estimated rotating machine efficiency?
Jason Hugenroth: The model developed for the Liquid-Flooded Ericsson Cycle Cooler was a thermodynamic model only. The cycle simulation does not predict the rotating machinery efficiency based on a set of operating conditions. Rather, for a given set of operating conditions, it determines what the efficiency needs to be to achieve a specified COP. In this regard, the model predictions are nearly exact. There will be insignificant errors due to imperfections in the fluid property data and roundoff errors.
Jason Hugenroth, PhD, PE
Associate Member ASHRAE
James Braun, PhD
Eckhard Groll, PhD
Galen King, PhD
Jason Hugenroth is the owner of InvenTherm, a research and development consulting company. This research was completed while he was a student at Purdue University, West Lafayette, IN. James Braun, Eckhard Groll, and Galen King are professors in the School of Mechanical Engineering, Purdue University.
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|Author:||Hugenroth, Jason; Braun, James; Groll, Eckhard; King, Galen|
|Date:||Jul 1, 2009|
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