Second Law Study of the Einstein Refrigeration Cycle

8/11/2019 Second Law Study of the Einstein Refrigeration Cycle

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1 Copyright 1999 by ASME

Proceedings of theRenewable and Advanced Energy Systems for the 21 st Century

April 11-15, 1999, Lahaina, Maui, Hawaii

SLA-2

SECOND LAW STUDY OF THE EINSTEIN REFRIGERATION CYCLE

Sam V. Shelton, Ph.D.Assoc. Professor

G.W.W. School of Mechanical EngineeringGeorgia Institute of Technology

Atlanta, Georgia [email protected]

Andrew Delano, Ph.D.

Design EngineerHewlett-Packard, Inc.3400 East Harmony Road, MS 69Fort Collins, Colorado 80528-9599

[email protected]

Laura A. Schaefer

Ph.D. StudentG.W.W. School of Mechanical EngineeringGeorgia Institute of Technology

Atlanta, Georgia [email protected]

Keywords: Second Law, Absorption, Einstein Cycle, Coefficient of Performance

ABSTRACTAfter formulating the theory of relativity, Albert Einstein

spent several years developing absorption refrigeration cycles.In 1930, he obtained a U.S. patent for a unique single pressure

absorption cycle. The single pressure throughout the cycleeliminates the need for the solution pump found inconventional absorption cycles. The Einstein cycle utilizesbutane as a refrigerant, ammonia as a pressure equalizingfluid, and water as an absorbing fluid. This cycle isdramatically different in both concept and detail than the betterknown ammonia-water-hydrogen cycle.

Recent studies have shown that the cycles COP is 0.17,which is relatively low compared to two-pressure cycles. Thislimits the cycle to refrigeration applications where simplicity,compactness, silent operation, and low cost are the importantcharacteristics. Improved efficiency would open up otherpotential applications.

In this study, a comprehensive second law analysis of thecycle was carried out on each component and process todetermine the thermodynamic source of the low efficiency.The results show that the reversible COP for the cycle is 0.58,and that the component with the largest irreversibility is thegenerator. The entropic average temperatures for the heatflows into and out of the cycle are 353 K for the generator, 266K for the evaporator, and 315 K for the absorber/condenser.The COP degradations from the ideal due to irreversibilities

are 0.12 for the evaporator, 0.11 for the absorber/condenser,and 0.17 for the generator. The generator irreversibility is dueto the inherent temperature difference in the internal heatexchange. The results show that there is a large potential for

increasing the cycles efficiency through design changes toraise the low generator temperature and to reduce the largegenerator irreversibilities.

NOMENCLATURESymbolsCOP Coefficient of Performanceh Enthalpy (kJ)m Mass (kg)Q Heat Transfer (kJ)S Entropy (kJ/K)T Temperature ( C, K)x Liquid Concentrationy Vapor Concentration

Subscripts# State Point as Identified in Figure 1a Ammoniab Butanef Liquidg Vapor


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gi Generator, Internali Component iil Internal Liquidiv Internal Vaporrev Reversibles Entropic

SuperscriptsRate

Average

INTRODUCTIONCurrent refrigeration cycles used in air conditioning,

refrigeration, and heat pump equipment are two-pressurecycles where a temperature difference between a condenser andevaporator is established by a pressure difference. Acompressor establishes this pressure difference in vapor-compression cycles, or a solution pump in absorption cycles.These two-pressure cycles require mechanical devices withmoving parts and access to shaft or electrical power to drivethe compressor or pump. This compressor or pump addssignificantly to the system costs, reduces reliability, generatesnoise, and limits portability. In addition, these refrigerationsystems must be connected to a fuel burning power generatingfacility which converts only 25 to 35 percent of this fuel topower. The one exception to this is the Platen and Munterscycle using hydrogen gas to establish a lower refrigerantpartial pressure in the evaporator, while maintaining a higherrefrigerant pressure in the condenser. Because of its lowefficiency and limited temperature lift, it has very limitedcommercial application.

Over 65 years ago, Albert Einstein and Leo Szilardobtained a U.S. patent for a pump-less absorption refrigerationcycle (Einstein, 1930). This cycle operates with an evaporator,a combined condenser/absorber, and a generator at a singleuniform pressure. It utilizes butane as a refrigerant, ammoniaas a pressure equalizing fluid, and water as an absorbing fluid.In the evaporator, the partial pressure on the entering liquidbutane is reduced by ammonia vapor, allowing it to evaporateat a lower temperature. In the condenser/absorber, the partialpressure on the vapor butane coming from the evaporator isincreased when the ammonia vapor is absorbed by liquidwater, thus allowing the butane to condense at a higher

temperature. Liquid butane and liquid ammonia-water areimmiscible and naturally separate. The ammonia is thenseparated from the water in a generator by the application of heat. Fluid flow in the cycle is accomplished with a heatdriven bubble pump and gravity.

In this study, a first and second law thermodynamic modelof the Einstein refrigeration cycle was used to investigate thecycles performance characteristics. Two regenerative heatexchangers not included in the Einstein patent were added to

improve performance. These are a generator internal regenera-tive heat exchanger and an evaporator pre-cooler. Theammonia-butane and ammonia-water fluid mixture propertieswere modeled with a cubic equation of state and fitted to thelimited available experimental data using mixing rules.

As described below, the cycle COP was calculated throughboth first and second law analyses. The entropic averagetemperatures, the ideal reversible COP, the entropy generationin each process, and the irreversible COP degradations fromthe reversible COP for each component are analyzed.

CYCLE DESCRIPTIONFigure 1 shows a schematic of the Einstein refrigeration

cycle. In the Einstein cycle, ammonia acts as an inert gas tolower the partial pressure over the refrigerant, butane. Waterlater provides separation by absorbing the ammonia.

Starting in the evaporator, liquid butane arrives from thecondenser/absorber. In the evaporator, the partial pressureabove the butane is reduced by ammonia vapor flowing fromthe generator. With its partial pressure reduced, the butaneevaporates near the saturation temperature of its partialpressure, cooling itself and the ammonia, and providingexternal refrigeration. The ammonia-butane vapor mixture

leaves the evaporator and enters the pre-cooler where it coolsthe hot vapor ammonia that is counter-flowing from thegenerator. The now superheated ammonia-butane mixtureflows out of the pre-cooler into the condenser/absorber, whichis continuously cooled by an environmental heat sink.Meanwhile, liquid water from the generator is sprayed into thecondenser/absorber. With its affinity for ammonia vapor, thiswater absorbs the vapor ammonia from the ammonia-butanemixture. The absorption of the ammonia vapor increases the

2

Q evaporator

1

6 3

4

5

7

9

5

Q condenser

Q generator

Reservoir

Condenser/Absorber

G e n e r a t o r

E v a p o r a t o r

Pre-Cooler

B u

b b l e P u m p

Qbub pump

Figure 1 Einstein Refrigeration Cycle Schematic


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partial pressure on the butane vapor to nearly the totalpressure, allowing it now to condense at butanes saturationtemperature for the total pressure. Note that this is higher thanbutanes saturation temperature at the partial pressure in theevaporator. The butane and the ammonia water separate dueto their respective density differences and the fact thatammonia-water is immiscible with butane at thecondenser/absorbers temperature and pressure. Since liquidbutane is less dense than liquid ammonia-water, it is the topliquid and is siphoned back to the evaporator. Meanwhile, theammonia-water mixture leaves from the bottom of thecondenser/absorber and enters the solution heat exchanger.Here, the mixture is pre-heated by the internal regenerativeheat exchanger before being heated by an external heat source.

Inside the generator, heat is applied to the strongammonia-water solution, driving off ammonia vapor where it

rises and is carried to the evaporator. The remaining weak ammonia-water solution is pumped up to a reservoir via abubble pump. In the reservoir, any residual ammonia vaporfrom the bubble pump is sent to the condenser/absorber. Thisvapor flow into the condenser is small (Delano, 1998), and hasbeen neglected in this analysis of the cycle. The weak ammonia water solution falls to the generator internalregenerative heat exchanger where it gives up its heat to thestrong ammonia-water solution coming from the condenser.Finally, this water is sprayed into the condenser/absorber.

While the overall pressure of the cycle is constant, thereare slight pressure variations within the cycle necessary forfluid motion. These are due to height variations and are not

large enough to significantly affect property evaluation.

PROPERTY MODELAccurate working property models are available for the

ammonia-water mixtures needed in this study, but none werefound for the required ammonia-butane. Therefore, forconsistency, the vapor-liquid equilibrium thermodynamicproperties of both the ammonia-butane and ammonia-water

mixtures were modeled with the Patel-Teja cubic equation of state (Patel, 1980) in conjunction with the Panagiotopoulosand Reid mixing rules (Panagiotopoulos and Reid, 1986).These mixing rules allow the equation of state to be fitted to

experimental mixture data. For the ammonia-butane mixture,the equation of state was fitted to the experimental data of Wilding et al. (1996). For the ammonia-water mixture, theequation of state was fitted to the experimental data of Gillespie et al. (1987).

Typical property model results for ammonia-butane areshown on a temperature-concentration plot in Figure 2. Thepressure in this case is taken at four bars, which is the totaloperating pressure at which the cycle was analyzed. Note thatthe property model shows an azeotrope as well as theappearance of a liquid-liquid equilibrium. This liquid-liquidseparation disappears at lower pressures, which agrees with theexperimental data.

Figure 3 shows the ammonia-water property model resulton a temperature-concentration diagram. Again, the totalpressure is taken at 4 bars, and the results agree very well withthe Gillespie et al. (1987) experimental data. A more detaileddescription of the agreement between the property models andthe experimental data is given in Delano (1998).

SECOND LAW ANALYSISThe first and second laws can be combined to provide a

relationship for the reversible COP of a three-temperaturereservoir heat pump in terms of only the constant temperature

reservoir temperatures. Due to irreversibilities such as fluidmixing and heat transfer across a finite temperature difference,the COP rev is degraded to the actual COP. Using the conceptof direct second law analysis (Alefeld, 1990), it is possible tocalculate the amount by which each process in a system of interest degrades the systems reversible COP.

This approach is different in detail to carrying out anexergy or availability analysis where the loss of work due toirreversible entropy generation is calculated. Since no work isrequired or produced by the Einstein cycle, work is not a

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0240

250

260

270

280

290

300

310

320

T

( K

)

Condenser/Absorber

Evaporator

ammonia concentration (molar)

P = 4 bar

Figure 2 T-x-x-y Diagram for Ammonia-Butane

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0250

275

300

325

350

375

400

425

x,y ammonia

T

( K

)

Condenser/Absorber

Generator

Figure 3 T-x-y Diagram for Ammonia-Water, P=4 bar


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commodity of interest. The effect on the COP is of interest.This COP is the ratio of the desired output, which is therefrigeration heat absorbed, to the input paid for, which isthe driving high temperature generator heat input. This directsecond law approach directly calculates the degradation of thisCOP due to irreversible entropy generation in the various cycle

processes.For the Einstein refrigerator, direct second law analysisbegins by applying the first and second law to a control volumeencompassing the entire system, with only heat crossing theboundary, as shown in Figure 1.

0QQQ condenseroverall,generatorevaporator (1)

k k

s,condenser

condenser

s,generator

overall,generator

s,evaporator

evaporator STQ

T

Q

T

Q(2)

In the previous equation, k S represents the entropygeneration of each process, k , occurring within the system, and

overall,generatorQ is the heat added to the overall generator

subsystem. The temperatures T evaporator,s , T condenser,s , andT generator,s are defined to be the entropic average temperaturesat which heat flows across the defined control volumes (Heroldet al., 1996). The condenser/absorber and the evaporatorexchange heat with their respective heat sinks and source atconstant temperatures. Therefore, their entropic average

temperatures are merely equal to T evaporator and T condenser , whichare fixed at 315 K and 266 K. However, the generator fluidreceives its heat at a varying temperature, starting at theinternal heat exchanger exit at T 7i to the maximum generatortemperature, T 8, as shown in Figure 7b. Calculation of theexact entropic average temperature for this desorbing processis complex, and was therefore estimated as the numericalaverage of the entering and leaving temperatures. The errorintroduced by this calculation is minimal for this smalltemperature range, as demonstrated by Alefeld (1993).

Now, equation 2 is multiplied by T condenser and subtractedfrom equation 1. After some rearrangement, the followingequation is produced:

ov,gen

k k

evapcond

condevap

evap

evapcond

s,gen

conds,gen

ov,gen

evap

Q

S

TT

TT

T

TT

T

TT

Q

Q (3)

The first term in square brackets on the right side inequation 3 is the COP rev for a thermally-driven refrigeratoroperating between three temperature reservoirs. Equation 3may thus be rewritten as follows:

k k n,degradatiorev COPCOPCOP (4)

where

overall,gen

k

evaporatorcondenser

condenserevaporatork n,degradatio

Q

STT

TTCOP (5)

Equation 5 conveniently shows how much the entropygeneration of each process, k , inside the control volume of

Figure 1 degrades the reversible COP to the actual irreversibleCOP. This allows for an absolute evaluation of the degradationimpact on the cycle COP for each irreversible process.

THERMODYNAMIC MODELTo create a thermodynamic model of the Einstein cycle,

the overall cycle was divided into 5 separate control volumes:the evaporator, the pre-cooler, the condenser/absorber, thegenerator, and the internal generator. Next, the massconservation and first and second law equations were writtenfor each control volume. Each control volume was assumed tooperate under steady state conditions with no fluid friction.

Figure 4 shows the control volume for the evaporator.Conserving mass for both the ammonia and the butane foundin the evaporator yields the following equations, with thesubscripts referring to the Figure 4 state points:

422,a33,a mmxmy (6)

2

3

4

ControlVolume

Qevaporator

Figure 4 The Evaporator


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22,b33,b mxmy (7)

Conservation of energy for this same evaporator controlvolume in Figure 4 yields:

442133evaporator hmhmhmQ (8)

Furthermore, the second law entropy generation for theevaporator is:

evaporator

evaporator442133evaporator T

QsmsmsmS (9)

where T evaporator is constant.The pre-cooler (Figure 5) is insulated so that the only heat

transfer occurs between the entering streams and exiting

streams. Since the conservation of mass will be satisfiedbetween the evaporator and condenser/absorber, the onlyequation necessary for the pre-cooler is the conservation of energy.

442163541133 hmhmhmhmhmhm (10)

The entropy generated by the pre-cooler due to heattransfer across any finite temperature difference is:

541133442163precool smsmsmsmsmsmS (11)

In this study, the effect of non-ideal heat exchange isaccommodated simply with the use of pinch points. Since it isa three stream heat exchanger, there are two pinch points inthe pre-cooler. One is between the vapor mixture entering at

state point 3 and the liquid leaving at state point 2. A secondexists between the vapor mixture leaving at state point 6 and

the liquid entering at state point 5.

32 TT (12)

56 TT (13)

In the Einstein refrigeration cycle, the condenser andabsorber are combined into a single component where bothprocesses occur simultaneously as shown in Figure 6. Since

63 mm , conservation of mass for the condenser/absorbercontrol volume in Figure 6 yields the following equations:

g83971 mmmmm (14)

g8g8,i33,i99,i77,i11,i mymymxmxmx (15)

Conserving energy for this same control volume yields theheat transfer from the condenser:

g8g863997711cond hmhmhmhmhmQ (16)

The second law entropy generation for the control volumein Figure 6 is:

cond

condg8g863997711cond T

QsmsmsmsmsmS (17)

21

5

6

4

3

Figure 5 The Pre-Cooler

Control Volume

1

6

7

9

Qcondenser

Condenser/Absorber

8g

Figure 6 The Condenser/Absorber


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In the generator, shown in Figure 7a, ammonia rich waterarriving from the condenser is heated. Conserving mass andenergy flow for the generators control volume yields:

9g847 mmmm (18)

g8g8,a499,a77,a mymmxmx (19)

77g8g89955bubpumpgen hmhmhmhmQQ (20)

The entropy generated by the generator is:

s,gen

bpmpgen77g8g89955gen

T

QQsmsmsmsmS (2 1)

To account for the generators internal heat exchanger,another control volume is necessary (Figure 7b). Conservationof mass and energy yield the following equations:

giv7gil mmmm 5 (22)

77,agivgi,agilgi,a mxmymxm 5 (23)

givgiv897799gilgil55 hmhmhmhmhmhm

(24)

The subscript ( ) giv denotes the vapor entering the bottomof the control volume at the i interface and the subscript ( ) gidenotes the liquid flowing down the wall out of the bottom of the control volume interface at i.

The entropy generated by the generators internal heatexchanger is accounted for with equation 21, which includesthe internal heat exchanger. The internal heat exchanger inthe generator also requires a pinch point:

97 TT (25)

To circulate the working fluids without a mechanicalpump, the Einstein cycle relies on a bubble pump. The bubblepump is a heated tube communicating with the generator andthe higher reservoir. The liquid in the generator initially fillsthe lower part of the tube. Heat is applied at the bottom of thetube at a rate sufficient to evaporate some of the liquid in thetube. The resulting vapor bubbles rise in the tube. The bulk density of the fluid in the tube is reduced relative to the liquidin the generator, thereby creating an overall buoyancy lift.

This buoyancy lift causes liquid and vapor to flow upward inthe tube carrying fluid from the generator to the reservoir.A model of the bubble pump was created using the

conservation of mass, momentum and energy, assuming thatthe bubble pump operated in the slug flow regime. The resultsof this model showed the energy requirement of the bubblepump to be about ten percent relative to that of the generator.Since the bubble pump has a relatively small effect, details of the analysis are omitted here, but can be found in Delano(1998).

CYCLE OPERATING CONDITIONS

Einsteins patent (Einstein, 1930), specified ammonia,water, and butane as the working fluids. The operatingconditions for the cycle were chosen in this study to be at asystem pressure of 4 bar, a condenser/absorber temperature of 315 K, an evaporator temperature of 266 K, and a maximumgenerator temperature, T 8, of 375 K. These were chosen to beconsistent with a refrigerator using ambient air as a heat sink and producing ice-making conditions, as discussed below.

C o n

t r o l

V o

l u m e

5

Qgenerator

B u b

b l e

P u m p

Reservoir

G e n e r a t o r

7

9

8

8f

Qbubble pump

8g

(a) Total Control Volume

C o n t r o

l V o l u m e 7

98 f

7i

5

(b) Internal Control Volume

Figure 7 The Generator


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The temperature for the condenser/absorber was chosen tobe 43C, or 315 K, so that heat could be rejected to the ambientair. Next, the behavior of the ammonia-butane mixture, shownin Figure 2, was studied to select a system pressure andevaporator temperature. As seen in Figure 2, pure butane at a

pressure of 4 bar condenses at 315 K. The addition of ammonia allows the mixture to boil as low as 266 K.Therefore, the system pressure was chosen to be 4 bar and theevaporator temperature 266 K. This -7C evaporator allows theproduction of ice.

To select a maximum generator outlet temperature, thebehavior of the ammonia-water mixture at the system pressure,as shown in Figure 3, was studied. To generate ammoniavapor, the nearly 50/50 ammonia-water mixture flowing fromthe condenser/absorber at 315 K is heated, driving off mostlyammonia vapor, but also some unwanted water vapor. Heatingthe ammonia-water to 375 K reduces the mass concentration of ammonia in the liquid from about 0.5 to under 0.2, and doesnot generate a significant amount of water vapor. Lowertemperatures would reduce the amount of the desorbedammonia vapor, and higher temperatures would boil unwantedwater vapor. Therefore, the maximum generator temperaturewas selected to be 375 K.

Figure 2 shows that at a fixed system pressure, thecharacteristics of the ammonia-butane mixture constrains theevaporator and condenser/absorber temperatures to a minimum

and a maximum respectively. These extreme temperatureswere used to produce the maximum temperature lift.

For the case studied here, infinitely large heat exchangerswere assumed by making the pinch points for both heatexchangers zero. Finally, all mass flow rates were normalizedto the mass flow rate into the bubble pump, since this flow ratecan be controlled by heat input to the bubble pump. Withspecification of ammonia-water-butane fluids, the evaporator,condenser/absorber, and generator temperatures, zero heat

exchanger pinch points, and a bubble pump mass flow rate of 10 g/s, the refrigeration cycle model is fully developed.

RESULTSTo simultaneously solve the large set of nonlinear

equations in both the refrigeration cycle thermodynamic modeland the Patel-Teja cubic equation of state property model, the

Engineering Equation Solver software was used (Klein andAlvarado, 1997).

Table 1 provides the important results of this base case.Note that the scaling parameter is the bubble pump mass flowrate, taken arbitrarily in this case.

Utilizing equation 5, Table 2 shows the irreversibledegradations calculated for the various processes.

For the ideal process, the reversible COP using equation 3is 0.57. Including the degradations of all the processes resultsin an actual COP of 0.17. The generator contributes thelargest irreversible degradation. This is due to heat transferacross the inherent temperature difference in the internal heatexchanger. In this regenerative heat exchanger, the liquidentering the generator from the condenser/absorber at 315 K isheated to approximately 325 K. This fluid is heated by the hotfluid side starting at the peak generator temperature of 375 Kand decreasing down to 315 K at the exiting zero pinch point.This produces a large temperature difference of 55 K at oneend of the heat exchanger, decreasing to zero at the other end.

The mixing of ammonia and butane in the evaporatorcauses its degradation to be relatively high as well, at 0.12.Likewise, the mixing of water and ammonia occurring in thecondenser/absorber causes the third largest degradation to theCOP. The pre-cooler contributes relatively minor degradations.

Table 1 Base Case Results for Pressure = 4 bars

Parameter ValueCOP ideal 0.57COP 0.17

genratorQ 7.09 kW

bubblepumpQ 0.76 kW

absorber / condenserQ -9.18 kW

evaporatorQ 1.33 kW

1m 3.8 g/s

3m 8.5 g/s

4m 4.6 g/s

7m 14.7 g/s

9m 9.6 g/s

bpm 10 g/s

Tevaporator 266 KTcondenser/absorber 315 KTgenerator, max 375 K

generator,s 352.9 KTgenerator,internal 325.4 KT4 278.1 K

Table 2 Degrading of Reversible COP

Process COP degradationPre-cooler 0.007Condenser/Absorber 0.106Evaporator 0.119

Generator/Bubble Pump 0.173Total 0.405


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DISCUSSIONA question arises as to the value of adding the generator

internal regenerative heat exchanger, which is the singleirreversible process occurring in the generator/bubble pump,and the largest irreversibility in the cycle. It was inserted intothe cycle in order to reduce the generator external heat

requirement and to increase the COP. If it is removed, thegenerator irreversibility will be reduced. This appears to be acontradiction.

However, the entropic average temperature for thegenerator heat input will also be reduced with the removal of the generator internal heat exchanger, thereby reducing theCOP rev. Specifically, without the internal heat exchanger, theexternal generator heat input will start at T 7 (315 K), ending atthe maximum generator temperature of 375 K, for an averageof 345 K, rather than the 352.9 K with the internal heatexchanger. In addition, the exiting fluid temperature leavingthe generator and entering the condenser will rise from 315 Kto 375 K. This will increase the condenser irreversibility since

it will have to reject this additional high quality thermalenergy to the 315 K sink. The effect of removing the generatorheat exchanger will be to reduce the COP rev, add to thecondenser irreversibility, and decrease the generatorirreversibility. The net effect will cause a reduction in theresulting COP.

The internal regenerative heat exchanger has an inherenttemperature difference at one end due to a large difference inthe thermal masses of the two streams. This regenerative heatexchanger is not present in the original Einstein cycle, but wasadded to improve the COP. The fact that this addedcomponent causes a large irreversibility is not contradictorywith its intent to improve the overall cycle efficiency. Itsaddition raises the entropic average temperature for thegenerator heat input and therefore the reversible COP, fromwhich the irreversibilities degrade performance. It alsoreduces the temperature of the steam flowing to the absorber,thereby reducing the irreversibility in that component.

The evaporator irreversibility is due to mixing theammonia vapor with the butane to reduce the partial pressureof the butane, thereby reducing its boiling temperature. This isa fundamental characteristic of the process. However, usingother fluids might reduce the magnitude of the irreversibility.

The combined condenser/absorber irreversibility is duesolely to the mixing of the liquid water flowing from the

generator and the ammonia coming from the evaporator. Thismixing process is necessary to absorb and remove theammonia vapor from the butane-ammonia mixture to increasethe partial pressure of the butane, thereby increasing thecondensing temperature. This allows the thermal energyabsorbed in the low temperature evaporator to be rejected at ahigher temperature, thereby pumping thermal energy up atemperature hill.

The pre-cooler heat exchanger between the condenser/ absorber and the evaporator also contributed a small

irreversibility of 0.01. This is due to the imbalance of thethermal masses, but the irreversibility is essentially negligible.This heat exchanger was added to improve the cycle COP,which it does by changing the stream temperatures to make thecondenser/absorber and evaporator reject and receive heat atconstant temperatures. This is similar to the generator internal

heat exchanger effect discussed above.

CONCLUSIONSThe Einstein cycle is a three temperature thermal heat

pump with no work input or output. It receives high temp-erature driving heat which is used to pump heat from a lowrefrigeration temperature to an ambient rejection temperature.The refrigeration application analyzed in this study usesbutane-ammonia-water working fluids with the driving heatinput temperature varying from 325 K to 375 K. The entropicaverage temperature for this driving heat input is 342 K. Thisis a relatively low driving heat source temperature. The

refrigeration temperature from which heat is pumped wasselected to be 266 K and the single heat rejection temperaturewas selected to be 315 K. The COP of this cycle is low relativeto two-pressure absorption cycles, which require a liquidsolution pump. A second law analysis gives insight into thefundamental reasons for the low COP.

The reversible COP was found to be at 0.57. This meansthat even if the cycle could be made reversible, it still could notreach the COP of advanced two-pressure absorption cycles.This is due primarily to the low generator heat input entropicaverage temperature of 342 K.

This reversible COP is degraded by three primaryirreversibilities: 1) the generator internal regenerative heatexchanger, 2) the evaporator mixing, and 3) the absorbermixing. They degrade the reversible COP by 0.17, 0.12, and0.11 respectively, down to 0.17.

The cycle demonstrates a creative approach to achievingrefrigeration with no work requirement, though at a relativelow COP. The second law analysis shows the source of thislow performance to be primarily due to a low generatortemperature. This should be investigated to determine how thecycle and working fluids might be changed to raise thegenerator heat input temperature and various achievetemperature lifts.

These developments could make the cycle competitive

with current commercial technology in various applicationssuch as residential heat pump space cooling and heating. Thecycle can achieve first law heating efficiencies over 100percent, and reduce summer peak air conditioning loads onelectrical power plants. Other applications are possible wherelow cost and reliability are important, such as remoteinstallations and developing countries without an electricalinfrastructure. Silent operation is also a benefit.


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REFERENCESAlefeld, G., 1990, What Are Thermodynamic Losses andHow to Measure Them, A Future For Energy , J. Necco, ed.,World Energy Symposium, Firenze, Italy.

Alefeld, G., and Radermacher, R., 1993, Heat Conversion

Systems , CRC Press, Boca Raton, FL, p. 64.

Delano, A., 1998, Design Analysis of the EinsteinRefrigeration Cycle, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, Georgia.

Einstein, A., and Szilard, L., 1930, Refrigeration (Appl:16 Dec. 1927; Priority: Germany, 16 Dec. 1926) Pat. No.1,781,541 (United States).

Gillespie, P.C., Wilding, W.V. and Wilson,G.M., 1987,Vapor-liquid equilibrium measurements on the ammonia-water system from 313 K to 589 K, Experimental Results

From the Design Institute for Physical Property Data , C.Black, ed., AIChE Symposium Series, Vol. 83, No. 256.

Herold, K., Radermacher, R., and Klein, S. A., 1996, Absorption Chillers and Heat Pumps , CRC Press, Boca Raton,FL, p. 13.

Klein, S.A., and Alvarado, F.L., 1997, Engineering EquationSolver , Version 4.4, F-Chart Software, Middleton, Wisconsin.

Palmer, S.C. and Shelton, S.V., 1996, Effect of EvaporatorDesign Pressure on Dual-Pressure Absorption Heat PumpPerformance Proceedings of the International Ab-Sorption

Heat Pump Conference , R. Radermacher, ed., Vol. 1, pp. 231-236.

Patel, N.C., 1980, The Calculation of ThermodynamicProperties and Phase Equilibria Using a New Cubic Equationof State, Ph.D. Thesis, Loughborough University of Technology, Loughborough, Leicestershire, United Kingdom.

Pangiotopoulos, A.Z., and Reid, R.C., 1986, New MixingRule for Cubic Equations of State for Highly Polar,Asymmetric Systems, Equations of State: Theories and

Applications , K.C. Chao and R. Robinson, ed., American

Chemical Society, Washington, D.C., pp. 571-585.

Wilding, W.V., Giles, N.F., and Wilson, L.C., 1996, PhaseEquilibrium Measurements on Nine Binary Mixtures,

Journal of Chemical Engineering Data , Vol. 41, pp. 1239-1251.

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Second Law Study of the Einstein Refrigeration Cycle