A new ejector-absorber cycle to improve the COP of an absorption refrigeration system

Applied Energy 30 (1988) 37-51

A New Ejector-Absorber Cycle to Improve the COP of an Absorption Refrigeration System

Li-Ting C h e n Department of Power Mechanical Engineering,National Tsing-Hua University, Hsinchu, 300 Taiwan

ABSTRACT A modified ejector-absorber absorption refrigeration cycle is presented and analysed. Results for an R-22/DME-TEG system with a 0"5 heat-exchanger effectiveness and a 0"85 nozzle (diffuser) efficiency are computed for the conventional as well as the modified cycle. A considerable improvement in COP is observed for the latter.

NOTATION A E G H P Q T V X p

Area (m2). Efficiency, effectiveness. Mass flow rate (kg/s). Enthalpy (kJ/kg). Pressure (N/m2). Heat quantity (k J). Temperature (K). Velocity (m/s). Concentration of refrigerant in solution. Density (kg/m3).

Subscripts

A C D

Absorber. Condenser. Diffuser. 37

Applied Energy 0306-2619/88/$03"50 © 1988 Elsevier Applied Science Publishers Ltd,

England. Printed in Great Britain

38

E G H HE L M N opt P PC R S sat W

Li-Ting Chen

Evaporator. Generator. High side. Heat-exchanger. Low side. Mixing tube. Nozzle. optimum value. Pump. Precooler. Refrigerant. Strong solution. At saturation. Weak solution.

INTRODUCTION Absorption refrigeration is, in principle, an attractive method for using heat energy directly for cooling purposes. Extensive studies have been reported in the literature on the selection of refrigerant-absorbent combinations 1-~ and on the analysis of the cycle performance.S- 11 The basic absorption refrigeration system, shown in Fig. 1, consists of four major components: (1) generator; (2) condenser; (3) evaporator; and (4) absorber. The basic cycle is not used in practice because of a low COP value 8 =.

Condenser

"

1

I

lhrottle

valve

I

Generator

I

~l.~1

~.2._lEvaporator

~1~ Pressure reducing valve

I

I 13 +"

Absorber

I1 Solution pump Fig. 1. Basic absorption refrigeration system.

A new ejector-absorber cycle 12

I

39

Condenser

Ev°'at°r7

./

Generator

I ,, ~ •

re(racing valve

~

I I ! I ~ _

I -

13 X

"

~

16

Throttle

er

i

pump

Fig. 2.

Conventional absorption refrigeration system.

owing to the irreversible losses in the strong and weak solution streams between the generator and the absorber. Figure 2 shows a widely-used conventional cycle which has two additional components: a heat-exchanger between the strong and weak solution streams and a precooler between liquid going to the evaporator and the vapour coming from it. The COP of the conventional cycle is improved considerably as compared with the basic cycle. For a conventional cycle, the high-side pressures in the condenser and the generator are essentially equal, as are the low-side pressures in the evaporator and the absorber. These two pressure sides are separated by an expansion valve and a pressure-reducing valve• The use of these two throttle valves is a source of inefficiency in the process since they degrade the energy with no useful work being recovered. For a limited absorber temperature, the absorption efficiency increases with increasing absorber pressure. The energy associated with the expansion of the high-pressure weak solution can be used, in principle, to do such pumping work. This energy-recovery process can be accomplished by using an ejector instead of a pressure-reducing valve. 11 The scope of this investigation is to present an analysis of an ejector-absorber cycle by considering appropriate component efficiencies. ANALYSIS OF A C O N V E N T I O N A L CYCLE Given the generator, condenser, absorber and evaporator temperatures, along with the cooling load, the state-point properties and the quantities of heat supplied and rejected in the cycle are calculated as described below.

Li-Ting Chen

40

The high-side pressure, Pn, in the generator and condenser is calculated from the condenser temperature: PH = PH(Tc)

(1)

The low-side pressure, PL, in the absorber and evaporator is calculated from the given evaporating temperature, TE: PL = PL(TE)

(2)

The equilibrium refrigerant fractions in the strong and the weak solutions are then given by XAE "= XAE(TA, PL)

(3)

XGE = XGE(TG, PH)

(4)

and

The precooler-evaporator loop The enthalpies for the v a p o u r and liquid states, namely calculated by the following equations: for the v a p o u r state for the liquid state

H12 and Hx, are

H12 = H12(PH, To) H 1 --Hl(Tc)sa t

(5) (6)

In the evaporator, the temperature at the exit of the evaporator is T4 ~-- T 3

(7)

The enthalpy at state 4 is given by //4 = H4(T4, P2)

(8)

Using the definition of effectiveness, Epc, for the precooler, we get Tz = 7"1 - (T1 - T4)Epc

(9)

The enthalpy of the sub-cooled liquid at state 2 is calculated by the same equations as for saturated liquid at temperature T z, i.e. H 2 = H2(PH, T2)

(10)

Further, for the throttling process from state 2 to state 3, we have H 3= H E

(11)

A heat balance across the precooler yields H 5 = H 4 + (H~ - H2)

(12)

A n e w e j e c t o r - a b s o r b e r cycle

41

The refrigerant flow rate per tonne (1 tonne - 3500 W) is calculated by a heat balance across the evaporator, i.e. GR = 3500/(/-/4 - H3)

kg/s-ton

(13)

The heat rejected in the condenser is given by Qc = GR(H,2 - H,)

(14)

The absorber-generator loop This loop includes the absorber, the heat-exchanger and the generator. As states 6, 9 and 5 are already defined, we can evaluate the following properties: H 6 = H6(PL, TA)

(15)

H9 = Hg(PH, T~)

(16)

X 6 = XA

(17)

X 9 = X~

(18)

where X A and X G are the refrigerant fractions in the strong and weak solutions, respectively, and they can be calculated 11 by using

x~-x~

EA

(19)

J(A -- J(GE

and EG

XAE--XG

(20)

where E A = absorber effectiveness and E~ = generator effectiveness. The mass-flow rates of strong and weak solutions are calculated by making an absorbent balance over the absorber, i.e. Gs = GR(I - XG)/(XA -- XG)

(21)

and Gw = Gs - GR

(22)

The enthalpy at state 8 is calculated for the saturated liquid state, i.e. H s = Hs(Pn, XA)

(23)

Qe = Gs(PH - PLFP6

(24)

7"7 = TA

(25)

The pumping energy, and

42

Li-Ting Chen

A heat balance across the heat-exchanger yields Hlo = H9 - (H8 - Hv)Gs/Gw

(26)

At this stage a check on the heat-exchanger's effectiveness is carried out. An upper limit of 1.0 is set for the effectiveness of an ideal cycle, while it is specified by Erie for an actual cycle. If the actual effectiveness EHE = (T9 -- Tlo)/(T9 - Tv)

(27)

exceeds the upper limit, the foregoing calculations are corrected for the limiting heat-exchanger's effectiveness. Note that Tlo is calculated from HIO = Hxo(Pn,/'1o )

(28)

since Hl o is k n o w n from eqn (26). F o r the throttling process from state 10 to 11, H11 = H1 o

(29)

The heat rejected in the absorber is calculated by making a heat balance over the absorber, i.e. QA ~- GwHH + GRHs = GsH6

(30)

The heat input to the generator, in W / t o n units, is given by Qc = GwH9 + GRHI: - GsH8

(31)

COP and overall heat balance The C O P of the system is given by C O P = QE/Qo

(32)

A final check is made by performing an overall energy balance: Q~ + Q~ + QP = Qc + QA q- E r r o r

(33)

The error term, as determined from eqn (33), should be close to zero.

ANALYSIS OF THE EJECTOR-ABSORBER CYCLE A schematic arrangement of the ejector-absorber cycle is shown in Fig. 3. The weak solution leaving the heat-exchanger flows from state 10 to state 11 through a nozzle and mixes with refrigerant v a p o u r in the mixing tube of the ejector. The mixture leaves the diffuser at the absorber pressure, PA = P6. The analysis of the ejector-absorber cycle differs only in the absorbergenerator loop.

43

A new ejector-absorber cycle 12

]

Condenser

Evaporator

G en era to r

e,c=ong

'e

~J6 Absorber Solution pump

Fig. 3.

A new ejector-absorber absorption refrigeration system.

Absorber-generator loop The analytical ejector-absorber model is shown in Fig. 4. The following assumptions were applied when deriving the governing equations for each section in the ejector: 1. 2. 3. 4. 5. 6. 7.

There is no external heat transfer. The weak solution flows through the nozzle from the generator pressure, PH, to the evaporator pressure, PL. The pressure drop and m o m e n t u m of the vapour refrigerant flow are negligible. There is no wall friction. All fluid properties are uniform over the cross-section after complete mixing at the exit of the mixing tube. Potential energy is negligibly small. The fluid is incompressible.

Nozzle flow The exit velocity from a reversible nozzle is calculated ~2 from 1/21 = 2(Px o - P1 x)/Pw

(34)

The actual leaving kinetic energy is determined from the definition of nozzle efficiency, E N. Hence 1/21 = EN2(PH -- PL)/Pw

(35)

44

Li- Ting Chen

V11~0

weok solution GW, PH ....

10

Nozzle

R r grant oR

5

Mixing Tube

t

Diffuser

l

lvs'

t

A 6'

TA,% :PA,XA Absorber 6 strongsolution GS Fig. 4. The analytical ejector-absorber model.

The mass flow rate is Gw = p w V x l A l l

(36)

where A 11 is the nozzle exit area and Pw is the density of the weak solution.

Flow in the mixing tube The mixture mass-flow rate is G~ = Gw + GR

(37)

and

G. + Gw = A'5 V~p'5

(38)

where A~ = cross-sectional area of the mixing tube, V~ = mixture velocity and p~ = mixture density.

A new ejector-absorber cycle

45

A momentum balance over the mixing tube yields

GwVtl + PllA'5 = (Gw + GR)V'5 + P'sA'5

(39)

Combining eqns (36), (38) and (39), we can obtain the expression for the pressure rise in the mixing tube from "l)T=-?TT_~pwVii ; - - PI' - 2(~-~1~ -- 2(Gw--I--GR"]2(P-~-w''](~']\ Gw I # \ p s , ] \ A s I #

(40)

where the density ratio, Pw/P'5, can be written as

r

Pw= 1 p; L

,_

if,owl

(aw + G,)IGw [ \ p,.] -~ Gw-+-G.

(41)

if a homogeneous two-phase mixture model were used and PR is the refrigerant's vapour density. Diffuser flow

The energy equation is


1

g

= p~6(P; - P;)

(42)

where ED is the diffuser efficiency. The mass-flow rate in the diffuser is G~ = G; = Gw + GR

(43)

and the diffuser exit velocity is l/Z --

1

A'6p'6

!

G6

(44)

with p;

=

p;

(45)

The absorber

The absorber pressure is

PA= P6= P'6

(46)

The equilibrium refrigerant fraction in the strong solution then is XAE = XAE(TA,PA)

(47)

The mass-flow rate of the strong solution is Gs = G~

(48)

46

Li-Ting Chen

The optimum mixing section area The equation expressing the total pressure-rise across the ejector can be obtained by combining eqns (38), (40), (42) and (44): (49)

TS-~ -7~- - 2AMN--

~pwVi~ \ Uw } \Ps } where AMN = A 11/A'5 and AMo = A'5/A'6.

Equation (49) shows that the actual absorber pressure depends on both the operating conditions and the ejector geometry. For given conditions the optimum mixing section area ratio, AMN, can be found by maximising PA subject to eqn (49). Thus, differentiating eqn (49) with dPA = 0, we obtain the expression for the o p t i m u m area ratio as A

(AMN)°pt =

1 ~ PW

Gw + GR'~ 2

(50)

[2--ED(1--"MO'](~5)(-G-- w- ; RESULTS A N D DISCUSSION The cycle performance is obtained by solving eqns (1)-(50). Equilibriumstate thermodynamic properties of the refrigerant-absorbent solutions are required for the analysis. Freon-22 and D M E - T E G are used as the working fluids in this study. The P - T - X equations developed by Blutt and Sadek 1 have been used to determine these properties. A computer program, based on iterative procedures, was developed to solve these simultaneous equations. The following values were used in the computation: Effectiveness of the precooler Effectiveness of the heat-exchanger Nozzle efficiency Diffuser efficiency Area ratios Range of generator temperatures Range of absorber and condenser temperatures Evaporator temperature

Epc = 0.5 EHE = 0.5

eN=0-85 E o = 0"85

A'5/A'6 = AMo = 0"1 AI1/A'5 = AMN = 0"01--0"3 To = 120-180°C TA = Tc = 30-50°C

5°C

The effect of the ejector area ratio, AMN, on the system's COP is investigated and the result is shown in Fig. 5. It shows an optimum value of A MN,as indicated byeqn (50). This optimum A MNgives a maximum COP value

.4 new ejector-absorber cycle

47

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o= ",n .o

~

T~ °

/

~

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I.~

-;g T.

~' ILl

o 0

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~.~

~-

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1

d

~.

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o

1

o

I

o.

o

""

Q

"1 d/V d

3VX

I I I/

87 0

°~

II

0

o ~

IoO I

0

tl

ii

el

I

l

I

I

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I

I

1

o"

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~

o'

o-

~"

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g

dOD

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¢,. 0

o.

~

cs

~

0

•

¢.q

Li- Ting Chen

48

.9 .8 .7 .6 .5 0

--present cycle .... conventional cycle

.4 .3

o2

o~

I

130

I

t

140

I

150

160

I

170

I

I

180

190

200

TG ('C)

Fig. 7.

The effect of generator temperature on COPopt for a water-cooled system (TA = Tc =40°C). 1.0

0.9--

--present cycle .... conventional cycle

0.a0.70.6t3_ 0

O.~-

I

1

0.3/

/

/

J

f

f

0.2 £ 0.1 120

I

130

I

160

I

150

I

160

I

170

I

180

I

190

200

TO ('C) Fig. 8.

The effect of generator temperature on COPop t for an air-cooled system (T A = T c = 50°C).

49

A new ejector-absorber cycle

TG=120"C

1.4 1.2 1.c

0.8

0 ¢J

0.6 ....

conventional cycle

0.4f ~ O.2

I

0 30

~- ~. ~ .

"t

1

35

1

40

45

50

TA ,TC ('C) Fig. 9. The effect of heat rejection temperature

o n COPop t

for To = 120°C.

of 0.85 while the COP of the conventional cycle is 0.678. The variations of absorber pressure ratio, PA/PL,and equilibrium concentration, XAE, with AMN are shown in Fig. 6. The maximum values of PA/PLand XAE occur at AMN= (AMN)opt, To = 120°C and Tc = 40°C. To investigate the variation of COPopt with generator temperature, two values of the absorber and condenser temperatures, 40°C and 50°C, are selected to represent the water-cooled and the air-cooled systems,

1.6 TG=150"C

1./~ 1

.

2

~

1.0 o

a. 0

0.8

--

~

~ , ~

0.6 -

~ "" ~

0,4 -

present cycle - - - - c o n v e n t ionol cycle

'

~ ~--..

0.2-

30

35

4 TA ,TC ('C)

45

"1

Fig. 10. The effect of heat rejection temperature on COPopt for To = | 50°C.

50

Li-Ting Chen

respectively. The results are shown in Figs 7 and 8. For water-cooled systems, a m a x i m u m COPop t value o f 0.86 is observed at To = 130°C, while it is 0-74 for a conventional cycle with TC = 150°C. For air-cooled systems, a m a x i m u m COPop t value of 0"53 is observed at Tc = 160°C, while for the conventional cycle, a value of 0"44 is obtained with To = 180°C. The influence of the heat rejection temperature on the performance is studied by varying the absorber and the condenser temperatures. It is clear from earlier results that for air-cooled systems with their higher heat rejection temperatures the COP values are lower than those corresponding to water-cooled systems. There is also an upper temperature limit for heat rejection above which the air system cannot function for a given generator temperature. Figure 9 shows the variation of COP with the absorber and condenser temperatures for a TC of 120°C. Similar results for a generator temperature of 150°C are shown in Fig. 10. The COP decreases with an increasing heat-rejection temperature for both cycles. CONCLUSIONS In the present study a new rejector-absorber cycle is presented and also analysed. Results have been computed for conventional as well as for the present systems by taking representative values of the system's parameters. The actual c o m p o n e n t performances are taken into account by defining efficiency parameters. F r o m the results it is observed that a considerable improvement in COP is obtained with the present cycle when compared with that of the conventional cycle. The present study also shows that the geometric parameters of the ejector design have considerable effects on the system's performance and it is recommended that the detailed analysis be used in conjunction with coupled ejector-parameters to arrive at optimum operating conditions. REFERENCES 1. G. F. Zellhoefer, Summer and winter air conditioning by low pressure steam, Heating, Piping and Air Conditioning, 2 (1973), pp. 265-70. 2. G. F. Zellhoefer, Solubility ofhalogenated hydrocarbon refrigerants in organic solvents, Industrial and Engineering Chemistry, 29 (1937), pp. 548-51. 3. W. R. Hainsworth, Refrigerants and absorbents, Part 1, Refrigeration Engineering, 48 (1944), pp. 201 2 5. 4. R. M. Buffington, Qualitative requirements for absorbent-refrigerant combinations, Refrigeration Engineering, 57 (1949), pp. 343-5, 384, 386, 388. 5. R. T. Ellington, G. Kinst, R. E. Peck and J. F. Reed, The absorption cooling process, Research Bulletin, Institute of Gas Technology, Chicago, IL, No. 14, 1957.

A new ejector-absorber cycle

51

6. R. A. Macriss, Selecting refrigerant absorbent fluid systems for solar energy utilization, A S H R A E Trans., 82 (1976), pp. 975-88. 7. G.A. Manscori and V. Patil, Thermodynamic basics for the choice of working fluids for solar absorption cooling systems, Solar Energy, 22 (1979), pp. 483-91. 8. E. P. Whitlow, Trends of efficiencies in absorption refrigeration machines, A S H R A E Journal, 8 (1966), pp. 13: 44-8. 9. W. F. Stoecker and L. D. Reed, Effect of operating temperatures on the coefficient of performance of aqua-ammonia refrigerating systems, A S H R A E Trans., 77 (1971), pp. 1:163-73. 10. E. P. Whitlow, Relationship between heat source temperature, heat sink temperature, and coefficient of performance for solar powered absorption air conditioners, A S H R A E Trans., 82 (1976), pp. 1:950-8. 11. J.R. Blutt and S. E. Sadek, A gravity independent vapor absorption refrigerator, NASA CR-836, 1967. 12. E.G. Cravalho and J. L. Smith, Engineering Thermodynamics (1981), pp. 406-18.