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The second law analysis of absorption cooling cycles
Heat Recover)' Systems & CHP Vol. 8, No. 6, pp. 549-558, 1988 Printed in Great Britain.
0890-4332/88 $3.00 + .00 Pergamon Press plc
THE SECOND LAW ANALYSIS OF ABSORPTION COOLING CYCLES NILOFERE~RICAN The Technical University of Istanbul, Department of Mechanical Engineering, Gfimfi~suyu, Istanbul, Turkey (Received 24 April 1988) Abstract--The second law of thermodynamics has recently been applied to various components and cycles by a theoretical approach. However, the application of this law practically is not common because the relevant concepts do not seem to be very important yet. In this study, the second law will be applied to absorption cooling cycles by defining two new effectiveneues of the system for two working fluids and the choice of working fluids will be based on this law. Besides permitting more realistic performance concepts from the economic and thermodynamic points of view, the second law analys/s of absorption cooling cycles also offers an alternativeabsorbent/cooling combination (lithium bromide/water), which does not destroy the ozone layer.
NOMENCLATURE a am Abs b b. B Con Ev Gen h H HE Mp P Q R s so S T u° v W X y y"
Redlich-Kwong constant (equation 7) Redlich-Kwong constant for binary mixtures (equation 9) absorber Redfich-Kwong constant (equation 8) Redlich-Kwong constant for binary mixtures (equation 10) exergy condenser evaporator generator molar enthalpy enthalpy heat exchanger mass flow rate of strong solution pressure heat universal gas constant molar entropy ideal gas state molar entropy entropy temperature ideal gas state molar internal energy molar volume power mole fraction concentration (or mass fraction) of refrigerant concentration (or mass fraction) of solvent
Greek symbols A difference operator effectiveness Subscripts A absorber c critical C condenser E evaporator f flow G generator HE heat exchanger i inlet I outlet 0 environmental p strong solution Pm pump 549
550 R S TV
N. E~RICAN refrigerantfluid solventfluid throttling valve
INTRODUCTION Most of the absorption cooling cycle studies are based upon two principles: (1) choosing a suitable refrigerant/absorbent combination; (2) obtaining the best performance according to the first law of thermodynamics. The criteria for choosing refrigerant/absorbent combinations, which include toxicity, chemical stability and corrosiveness, solubility of the refrigerant in the solvent, viscosity of the solution, the boiling and melting points of the refrigerant and the solvent and the latent heat of vaporization of refrigerant are widely discussed in the literature [5]. Thermodynamic properties of solutions have also been studied and the results are presented in various published works such as the one approaching the choice of fluid by means of the Redlich-Kwong equation of state [6]. The equations derived from the Redlich-Kwong equation of state. P =
RT v-b
a v ( v + b ) T t~'2
(1)
are as follows: For the pure fluid, h=u °+Pc+
3aT-~/2 -~ lnlv/(v+b)l
Iv-bl aT-3121n v + b . s = s° + R ln --R-T- + ~ I t---(---
(2) (3)
Here, u ° and s o are ideal gas state internal energy and entropy, respectively. For the multicomponent fluid, the Redlich-Kwong equation of state is assumed to have the form: RT P =- V -- b m
a v (v + b . ) T t/:"
(4)
Performing phase equilibrium calculations and using equation (4) leads to: h = Xsu ° + Xs u° + Pv + ~
3a.
. I v In ~
(5)
and v - b,[ a. . [ v I 1 Xsl s = X , s ° + Xss°s + R In RTX~I + ~ l n v---'~[ + RXs n
(6)
Here, Xs and X , are mole fractions of solvent and refrigerant, respectively. In these equations a, b, a , and b. are constants defined as: a = 0.42748 R2/T~'S/P,
(7)
b = 0.08664 RT,/P,.
(8)
a, = aRX~ + 2(1 -- kRs)(anas)l/2 XRXs + asX2s b, = b,XR + bsXs .
(9) (10)
Subscript R refers to refrigerant and subscript S refers to solvent. Coefficient k ~ accounts for the unlikely interaction of a refrigerant molecule and a solvent molecule, and its values for different fluid combinations have been given in reference [6]. From the table in the mentioned reference, the coefficient kRs for ammonia/water combination, the most common fluid combination used in absorption cooling cycles and also investigated in this study, equals -0.3.
Second law analysis of absorption cooling cycles
551
The detailed explanation of the equations (1-10) are also presented in reference [3]. It is obvious that the Redlich-Kwong equation of state for fluid combinations cannot be applied to the lithium bromide/water pair because lithium bromide, the solvent of this combination, is in solid form when it is in pure state. For the determination of thermodynamic properties of lithium bromide/water combination, offered as an alternative working fluid in this study, diagrams in reference [7] will be used. Another point to be noticed is that the lithium bromide/water combination has some limiting properties which involve special conditions for refrigeration. For example, in cooling systems in which LiBr-H20 is used, the temperature must be above 0°C because the refrigerant fluid, water, solidifies below this temperature and the system will not work. The other limiting properties and the working conditions belonging to this combination are described in detail and proved by the means of diagrams in the reference mentioned above [7]. The absorption cooling system investigated here is the simplest and most basic one (Fig. 1). It is extensively referred to in the literature [5], but it is useful to describe it briefly. There are four main components in an absorption cooling system: generator; condenser; absorber and evaporator. The refrigerant fluid leaves the generator at point (1) in a vapour state and condenses at To (environmental temperature) in the condenser up to point (2). During its condensation, the refrigerant fluid gives off Qc (condensation heat) to the environment. Then it undergoes an isenthalpic expansion in throttling valve I (2-3). Here, its pressure drops to the pressure in the evaporator and the absorber. The evaporation of the refrigerant fluid, which begins in throttling value I, continues in the evaporator at T~ (evaporator temperature) until point (4) and produces the cooling effect of the cycle by removing Q~ from the environment. When the evaporation is completed, refrigerant fluid is in a saturated vapour state and it enters into the absorber. Meanwhile the weak solution, formed by evaporation of refrigerant fluid in generator, undergoes an isenthalpic expansion in throttling value II (7-8) and comes into absorber. Here, the weak solution absorbs the refrigerant fluid coming from the evaporator and a strong solution occurs. Then the solution is pumped to the generator. ANALYSIS
The first law analysis The first law analysis of absorption cooling cycle leads to a coefficient of performance (COP) and it is defined as the ratio of cooling effect Q~ (heat added to the refrigerant in evaporator) to the input heat QG (heat added to the mixture in generator) [6]: ~E =
h4 -- h2 =
(l l)
l
(h, - hT) -~ - - ( h 7
XA- Xo
- h~)
Throttling volve
I
®
1
3 Condenser
Evoporotor
I I
--
-rhnatt~ ] votve n
4
J6
-
~6
Fig. 1. Schematic diagram of the absorption cooling cycle.
ot
552
N. EORICAN
Here, Xa and Xo are the mole fractions of refrigerant fluid leaving the absorber and generator, respectively. Details about the definition of C O P and its changes according to different working conditions for ammonia/water systems, experimentally and theoretically, are given and shown in the diagrams in reference [6]. The second law analysis
For the second law analysis of absorption cooling cycles in this study, the key word is e x e r g y . This concept is described by Brzustowski and Golem [8] as "generalized thermodynamic potential, equal to the maximum work which could possibly be extracted from a thermodynamic system in a given state in any process which brings the system into equilibrium with its environment. It is also equal to" they add, "minimum amount of work which could possibly be expended to bring the system from a state of equilibrium with the environment to some required state." After deriving exergy from Gibbs--Duhem equation, they reach several definitions of it. Equation: B:-=
(fi
-
T0~) - (fio - To'o)
(12)
is one of these definitions and it will be enlarged in this study. Here the subscript f refers to the flowing exergy [8]. Now, let us define the exergy flow rate change in the components of the absorption cooling cycle, using equation (12). It is the difference in exergy rates between the inlets and the outlets of the components [2, 4]: 03) A ~ = (fi, - r o ~ ) - (fio - r o ~ o ) - ( f i , -
(14)
r0£) + 0% - r0~o)
A~ = (fir, _ To~,) - ( f i , - r o £ )
05)
~,),
(16)
A~E = M , [ h , - h3 - T0(s3 - s,)]
(17)
A B c = Mt[h2 - h, - To(s, - s2)]
(18)
~z} = (fi, - fi,) - r o ( £ SO:
s,)]
(19)
A~A --- M , ( h s - h,) + g , ( h 5 - hs) - To[M,(s4 - ss) + g p ( s s - ss)]
(20)
M , ( h , - h , ) + M , ( h , - h6) - To[M,(s7 - s, ) + g , ( s 6 -
M , [ - To(s2 - s3)]
(21)
A/}rv. = M , [ - To(s7 - ss)].
(22)
ABrvl
=
By assuming that energy given to the pump is negligible, its exergy flow rate difference equals to zero:
A/b. = ~.
= M, (h6 - W~) = 0.
(23)
Here, M, and Mp are the mass flow rates of the refrigerant fluid and the strong solution, respectively. For ammonia/water systems, the criterion for the quality of solution is the concentration of refrigerant fluid (ammonia), while it is concentration of solvent (lithium bromide) in lithium bromide/water systems. So, in the former system, the strong solution is assumed as the one which is pumped from the absorber and in the second system, the one passing through the throttling valve II. Effectiveness
Effectiveness in an absorption cooling cycle may be defined using two different approaches. One is the ratio of the aim to the cost. In such a cycle, the aim is the cooling effect (Qe) and the cost for obtaining this aim is the input heat (Q~). From the point of view based on the second law,
Second law analysis of absorption cooling cycles Table I. Working conditions of lithium bromide/water system Gen Abs Con. Ev TCC) P(kPa)
80 3.169
25 0.710
25 3.169
2 0.710
553
Table 2. Working conditions of ammonia/water system Gen Abs Con. Ev T('C) P(kPa)
100 1000.0
25 462.5
25 1000.0
2 462.5
the aim is to obtain the greatest amount of exergy change in the evaporator by paying for it with the least exergy change in the other components. So, I The exergy fl°w rate difference in evap°rat°r I El = Total exergy flow rate difference in other components
(24)
can be defined and may be named as "the qualitative effectiveness". Another approach is related to the directions of exergy flow rate differences. In the evaporator, generator and the first throttling valve the exergy flow rate increase while it decreases in the condenser, absorber and the second throttling valve. If effectiveness is defined as the ratio of all exergy leaving the process to all exergy entering it: ]A~E + AB~ + A / I r v j E2= ABA+ ABc + A ~ I '
(25)
may be written. Here, the essence is the amount of exergy. So, equation (25) may be named as "the quantitative effectiveness". A NUMERICAL EXAMPLE FOR COMPARISON OF LiBr-H20 SYSTEM WITH A NH3-H20 SYSTEM For a refrigeration at T = 2°C in an environment in which To -- 25°C, the working conditions for both of the systems (lithium bromide/water and ammonia/water systems) are given in Table 1 and Table 2. In order to reduce the amount of heat given to the generator, a heat exchanger has been installed between the generator and the absorber (Fig. 2). Exergy flow rate differences in the heat exchanger can be defined similarly to equations (17-23): A/~HE= (Mp - l)(h7 - T0ST)+ M p ( h 9 - T0sg) - ( M p - 1)(hi0 -- Toslo) -- M p ( h 6 - Tos6).
(26)
As the effectiveness of a heat exchanger [1] must be less than one, the exergy flow rate difference in exchanger is negative. Thus, equation (25) takes the form: E2 =
A/~AABE+ A/~ + A/)TV, + A/Jc + A/~rvl, + A/~,e
(27)
"
Now let us investigate the behaviour of the solution (Fig. 3). The weak solution leaves the generator (10) in liquid state, while the strong one is in the same state when it leaves the absorber
To
From
condenser
evopomtor
TI O~
Heot exchonger
Q4,
8
.
W,.,,,
Fig. 2. Absorption cooling cycle with heat exchanger. H.R.S. 8 'b---E
o~
N. E(~RICAN
554
~
9
Y~o Y7
Y9 Ys
Ye
Ys
PG
Mass fraction of refrigeront fluid Fig. 3. States of solution in the cycle.
(5). During the operation in the pump the strong solution remains in the liquid state (6). In the heat exchanger heat is given off by the strong solution and it reaches the liquid state again (9). Consequently, the weak solution is deep in the liquid state when it enters the throttling valve (7). Here, it becomes wet vapour (8). With the help of this knowledge the thermodynamic properties of both the refrigerant and the solution can be determined (Tables 3 and 4). The properties which Table 3 shows are d e ~ by using the diagrams in reference [7]. It must be noted that these diagrams have n o t been drawn in SI units. Table 3. Properties of refriserant fluid and solution at the main points of lithium bromide/water system y" P T h s kgi.,iBr/kg kPa °C kJ k8- i kJ kg- 1K solution I 2 3 4 5 6 7 8 9 10
3.169 3.169 0.710 0.710 0.710 3.169 3.169 0.710 3.169 3.169
80 25 2 2 25 25 58 55 45 80
2670.00 104.89 104.89 2505.20 243.43 243.43 305.15 305.15 277.66 350,00
8.95 0.37 0.38 9.10 2.13 2.13 1.90 1.88 2.31 2.05
0.00 0.00 0.00 0.00 0.51 0.51 0.66 0.66 0.51 0.66
Table 4. Properties of refriserant fluid and solution at the main points of ammonia/water system P kPa I 2 3 4 5 6 7 8 9 10
1080.00 1080.00 462.50 462.50 462.50 1000.00 1000.00 467.50 1000.00 1000.00
T °C
b kJ kg- I
s kJ k 8 - *K
Y kgNH3/kg solution
100 25 2 2 25 25 75 60 50 100
1665.40 289.20 289.20 1445.60 91.53 91.53 242.80 242.80 205.02 422.13
5.6392 1.0915 I. 1100 5.3108 0.9100 0.9100 1.3400 1.1800 1.2300 1.6200
0.00 0.00 0.00 0.00 0.56 0.56 0.30 0.30 0.56 0.30
Second law analysis of absorption cooling cycles
555
2.I 2. Z
~
1.6
"i'~
1.4
(t," .
0.6 0.4
°7,
+Z
,
0 0.10 0.20
0.40
I
0.60
I
I
0.80
f
q.r., 0.10 0.20
Ammonia concentration (Kg Nil 3 Kg" =~ution)
Ammonia
0.40
0.60
0.1~)
ccf,;~,Itration (Kg NH 3 Kg -~sotution)
Fig. 4. Entropy-concentration diagram for ammonia/water combination (drawn according to the Redlich-Kwong equation).
The necessary values and methods for determination of the properties shown on Table 4 are presented in references [5, 6, 9]. Also, entropy-concentration diagrams including liquid and vapour lines for ammonia/water combination, according to the Redlich-Kwong equation of state, have been drawn for use in this study (Fig 4a and b). From the detailed explanations in references [5, 6, 9] the mass flow rates are as follows: for lithium bromide/water system: Mpf4.18kgh
-l
and for ammonia/water system:
Mp = 2.70 kg h- I. The first law analysis According to equation (11)
(COP)us,-M2offi0.915 (COP)NH}-H20= 0.631 The second law analysis The exergy flow rate differences [equations (17)-(23) and equation (26)] for lithium bromide/ water system: A~r ffi 4998.87 kJ h -I, A/~c = 5121.95 kJ h -I, A~o = 4428.30 kJ h -I, A/~A ffi 4317.14 kJ h -I, A/~rvl ffi 2.98 kJ h - i,
N. F_X;RICAN
556
A[~rv,l =
-- 18.95 kJ h - I,
A / ~ = 0.00, AB,e = - 110.04 kJ h -1. For ammonia/water system: A ~ E = 2408.24 kJ h-~, A/~c = - 2 7 3 1 . 4 1 kJ h-t, A/~c = 3405.54 kJ h -~, AB A = -3011.531 kJ h -],
A[~rv= = Al~rvn = ABe,
=
5.51 kJh -I, - 81.06 kJ h-), 0.00,
A~uE = -- 114.054 kJ h-L The qualitative effectiveness (equation 24): (~l)uBr-.2o = 0.987, ((;I)N,3- "20 = 0.980. The quantitative effectiveness (equation 27):
((Z)UB,-H20=
0.976,
(E2)NH3-H20 = 0.954.
CONCLUSIONS The lithium bromide/water system has more advantages than the ammonia/watex system from the points of view of both the first law and the second law, as it is s ~ n from the calculations above and the Figs 5-10, in spite o f its involving a noticeable amount of solution. As the amount of
!
E2
I 0.9
p/i, 0.8
0.8
J
0.7 0.6 5
i
r 0.6
15
0.4
4
To • Z S ' C T~ • 2 " C
TO ,ZSoC
0.3
T~ , 2 " C 0.2
. . . . LiBr
--NH
O.I
I
I
60
I
70
I
90
I
II0 tnlW~Um
I,
I:~I0
- HzO 3 - HzO I
150
T~ ('C)
Fig. 5. Qualitative and quantitative effectivenesses as a function o f generator temperature.
. . . . LiBr - H~O . . . . NHz~ - Hz-O
0.2
o
t
60
I
70
I
90
I
IiO
I
i~o
I
15o
Generator temperature T~ ('C} Fig. 6. Coefficient of performance as a function of ~ n c r a t o r temperature.
Second law analysis
557
o f absorption cooling cycles
27 25
w
23
!
.~"5
17
"t
15
0.8 0,7 "E o
15
II
|
,
J°
0.6 0.5
i
• 25%
- ~ LtBr - H20 ~ N H 3 - H20
3 -
I
I
60
I
70
I
90
I
I10
I
130
o. 3 -
~ :
0.2
i
o.I
150
To • 40"C
r~-
.... LiBr - H20 ~ N H 3 - H20
I
80
I
I00
C-enerotor temperature Te (*C)
I
120
c~rl~r
Fig. 7. Mass flow rate o f strong solution as a function o f generator temperature.
IO'C
I
140
~
160
~ (*c)
Fig. 8. Qualitative and quantitative effectivenesses as a function o f generator temperature.
solution (in other words, mass flow rate Mp) increases, the exergy flow rate difference in the second throttling valve increases absolutely [equation (22)]. Consequently, both of the effectivenesses decrease, but this result does not remove the lithium bromide/water combination's advantages. Mp is inversely proportional to the generator leaving temperature (To). This result has been shown for
54
l
~J
5(:
I
I
•
~"
4e
~
42
O.~
O.E 22 To • 4 0 e C
O.~
TE • IO'C
IO'C
O.:"
- HzO - HzO
""" I
80
I
90
I
IfO
I
1:30
I
l~g3
I
170
Genera(or temperature T~ ('C) Fig. 9. Coefficient o f performance as a function of generator temperature,
14
~
l
2= I
80
t
90
~
----LiBr - HzO NH3 - Hz0
I10
I
130
C.ammtor t e ~ m
I
150
i
170
T~ ('C)
Fig. 10. Mass flow rate o f strong solution as a function o f generator temperature.
558
N. Et~RICAN
both of the combinations and the effectiveness has been calculated for the same temperatures (see Figs 5-10). When the operation is repeated for different refrigeration conditions, it is observed that the effectiveness and C O P values o f lithium bromide/water are higher than those of the ammonia/water combination. The principal problem that makes using L i B r - H , O in absorption cooling cycles difficult is its limiting property which prevents application for the refrigeration conditions below 0°C. Taking into consideration the fact that lithium bromide/water solution does not harm the ozone layer and it undergoes the operations in the cooling cycles almost perfectly from the point of view of the second law, and has also high C O P values, it is realistic to draw a conclusion suggesting this combination as an alternative one. REFERENCES 1. T. A Brzustowski and P. J. Golem, Second law analysis of energy processes part lI: the parformance of simple heat exchangers, Trans. CSME 4, 219-226 (1976-1977). 2. A. N. E~rican and A. Karakul, Second law analysis of a solar powered rankine cycle/vaporcompressioncycle, Heat Recovery Systems 6, 135-141 0986). 3. A. Bejan, General criterion for rating heat exchanger performance, J. Heal Mass Transfer 21, 655-658 (1978). 4. A. Bejan, The concept of irreversibility in heat exchanger design: counterflow heat exchangers for gas-to-gas application Trans. ASME 99, 374-380 (1977). 5. F. Bosnjakovic, Technical Thermodynamics (Translated by P. L. Blackshear) Holt, Rinehart and Winston, New York (1965). 6. Adolfo L. Gomez and G. Ali Mansoori, Thermodynamic equation of state approach for the choice of working fluids of absorption cooling cycles, Sol. Energy 31, 557-566 (1983). 7. A. L6wer, Thermodynamische eigenschaften und warme diagramme des binaren systems lithium bromid/wasser, Kaltetechnik 13 Jahrgang Heft 5/1961. 8. T. A. Brzustowski and P. J. Golem, Second law analysisof energy processes: part one: exergy--an introduction, Trans. CSME 4, 209-218 (1976--1977). 9. G. J. Van Wylen and R. E. Sonntag, Fundamentals of Classical Thermodynamics, John Wiley, New York (1976).
0890-4332/88 $3.00 + .00 Pergamon Press plc
THE SECOND LAW ANALYSIS OF ABSORPTION COOLING CYCLES NILOFERE~RICAN The Technical University of Istanbul, Department of Mechanical Engineering, Gfimfi~suyu, Istanbul, Turkey (Received 24 April 1988) Abstract--The second law of thermodynamics has recently been applied to various components and cycles by a theoretical approach. However, the application of this law practically is not common because the relevant concepts do not seem to be very important yet. In this study, the second law will be applied to absorption cooling cycles by defining two new effectiveneues of the system for two working fluids and the choice of working fluids will be based on this law. Besides permitting more realistic performance concepts from the economic and thermodynamic points of view, the second law analys/s of absorption cooling cycles also offers an alternativeabsorbent/cooling combination (lithium bromide/water), which does not destroy the ozone layer.
NOMENCLATURE a am Abs b b. B Con Ev Gen h H HE Mp P Q R s so S T u° v W X y y"
Redlich-Kwong constant (equation 7) Redlich-Kwong constant for binary mixtures (equation 9) absorber Redfich-Kwong constant (equation 8) Redlich-Kwong constant for binary mixtures (equation 10) exergy condenser evaporator generator molar enthalpy enthalpy heat exchanger mass flow rate of strong solution pressure heat universal gas constant molar entropy ideal gas state molar entropy entropy temperature ideal gas state molar internal energy molar volume power mole fraction concentration (or mass fraction) of refrigerant concentration (or mass fraction) of solvent
Greek symbols A difference operator effectiveness Subscripts A absorber c critical C condenser E evaporator f flow G generator HE heat exchanger i inlet I outlet 0 environmental p strong solution Pm pump 549
550 R S TV
N. E~RICAN refrigerantfluid solventfluid throttling valve
INTRODUCTION Most of the absorption cooling cycle studies are based upon two principles: (1) choosing a suitable refrigerant/absorbent combination; (2) obtaining the best performance according to the first law of thermodynamics. The criteria for choosing refrigerant/absorbent combinations, which include toxicity, chemical stability and corrosiveness, solubility of the refrigerant in the solvent, viscosity of the solution, the boiling and melting points of the refrigerant and the solvent and the latent heat of vaporization of refrigerant are widely discussed in the literature [5]. Thermodynamic properties of solutions have also been studied and the results are presented in various published works such as the one approaching the choice of fluid by means of the Redlich-Kwong equation of state [6]. The equations derived from the Redlich-Kwong equation of state. P =
RT v-b
a v ( v + b ) T t~'2
(1)
are as follows: For the pure fluid, h=u °+Pc+
3aT-~/2 -~ lnlv/(v+b)l
Iv-bl aT-3121n v + b . s = s° + R ln --R-T- + ~ I t---(---
(2) (3)
Here, u ° and s o are ideal gas state internal energy and entropy, respectively. For the multicomponent fluid, the Redlich-Kwong equation of state is assumed to have the form: RT P =- V -- b m
a v (v + b . ) T t/:"
(4)
Performing phase equilibrium calculations and using equation (4) leads to: h = Xsu ° + Xs u° + Pv + ~
3a.
. I v In ~
(5)
and v - b,[ a. . [ v I 1 Xsl s = X , s ° + Xss°s + R In RTX~I + ~ l n v---'~[ + RXs n
(6)
Here, Xs and X , are mole fractions of solvent and refrigerant, respectively. In these equations a, b, a , and b. are constants defined as: a = 0.42748 R2/T~'S/P,
(7)
b = 0.08664 RT,/P,.
(8)
a, = aRX~ + 2(1 -- kRs)(anas)l/2 XRXs + asX2s b, = b,XR + bsXs .
(9) (10)
Subscript R refers to refrigerant and subscript S refers to solvent. Coefficient k ~ accounts for the unlikely interaction of a refrigerant molecule and a solvent molecule, and its values for different fluid combinations have been given in reference [6]. From the table in the mentioned reference, the coefficient kRs for ammonia/water combination, the most common fluid combination used in absorption cooling cycles and also investigated in this study, equals -0.3.
Second law analysis of absorption cooling cycles
551
The detailed explanation of the equations (1-10) are also presented in reference [3]. It is obvious that the Redlich-Kwong equation of state for fluid combinations cannot be applied to the lithium bromide/water pair because lithium bromide, the solvent of this combination, is in solid form when it is in pure state. For the determination of thermodynamic properties of lithium bromide/water combination, offered as an alternative working fluid in this study, diagrams in reference [7] will be used. Another point to be noticed is that the lithium bromide/water combination has some limiting properties which involve special conditions for refrigeration. For example, in cooling systems in which LiBr-H20 is used, the temperature must be above 0°C because the refrigerant fluid, water, solidifies below this temperature and the system will not work. The other limiting properties and the working conditions belonging to this combination are described in detail and proved by the means of diagrams in the reference mentioned above [7]. The absorption cooling system investigated here is the simplest and most basic one (Fig. 1). It is extensively referred to in the literature [5], but it is useful to describe it briefly. There are four main components in an absorption cooling system: generator; condenser; absorber and evaporator. The refrigerant fluid leaves the generator at point (1) in a vapour state and condenses at To (environmental temperature) in the condenser up to point (2). During its condensation, the refrigerant fluid gives off Qc (condensation heat) to the environment. Then it undergoes an isenthalpic expansion in throttling valve I (2-3). Here, its pressure drops to the pressure in the evaporator and the absorber. The evaporation of the refrigerant fluid, which begins in throttling value I, continues in the evaporator at T~ (evaporator temperature) until point (4) and produces the cooling effect of the cycle by removing Q~ from the environment. When the evaporation is completed, refrigerant fluid is in a saturated vapour state and it enters into the absorber. Meanwhile the weak solution, formed by evaporation of refrigerant fluid in generator, undergoes an isenthalpic expansion in throttling value II (7-8) and comes into absorber. Here, the weak solution absorbs the refrigerant fluid coming from the evaporator and a strong solution occurs. Then the solution is pumped to the generator. ANALYSIS
The first law analysis The first law analysis of absorption cooling cycle leads to a coefficient of performance (COP) and it is defined as the ratio of cooling effect Q~ (heat added to the refrigerant in evaporator) to the input heat QG (heat added to the mixture in generator) [6]: ~E =
h4 -- h2 =
(l l)
l
(h, - hT) -~ - - ( h 7
XA- Xo
- h~)
Throttling volve
I
®
1
3 Condenser
Evoporotor
I I
--
-rhnatt~ ] votve n
4
J6
-
~6
Fig. 1. Schematic diagram of the absorption cooling cycle.
ot
552
N. EORICAN
Here, Xa and Xo are the mole fractions of refrigerant fluid leaving the absorber and generator, respectively. Details about the definition of C O P and its changes according to different working conditions for ammonia/water systems, experimentally and theoretically, are given and shown in the diagrams in reference [6]. The second law analysis
For the second law analysis of absorption cooling cycles in this study, the key word is e x e r g y . This concept is described by Brzustowski and Golem [8] as "generalized thermodynamic potential, equal to the maximum work which could possibly be extracted from a thermodynamic system in a given state in any process which brings the system into equilibrium with its environment. It is also equal to" they add, "minimum amount of work which could possibly be expended to bring the system from a state of equilibrium with the environment to some required state." After deriving exergy from Gibbs--Duhem equation, they reach several definitions of it. Equation: B:-=
(fi
-
T0~) - (fio - To'o)
(12)
is one of these definitions and it will be enlarged in this study. Here the subscript f refers to the flowing exergy [8]. Now, let us define the exergy flow rate change in the components of the absorption cooling cycle, using equation (12). It is the difference in exergy rates between the inlets and the outlets of the components [2, 4]: 03) A ~ = (fi, - r o ~ ) - (fio - r o ~ o ) - ( f i , -
(14)
r0£) + 0% - r0~o)
A~ = (fir, _ To~,) - ( f i , - r o £ )
05)
~,),
(16)
A~E = M , [ h , - h3 - T0(s3 - s,)]
(17)
A B c = Mt[h2 - h, - To(s, - s2)]
(18)
~z} = (fi, - fi,) - r o ( £ SO:
s,)]
(19)
A~A --- M , ( h s - h,) + g , ( h 5 - hs) - To[M,(s4 - ss) + g p ( s s - ss)]
(20)
M , ( h , - h , ) + M , ( h , - h6) - To[M,(s7 - s, ) + g , ( s 6 -
M , [ - To(s2 - s3)]
(21)
A/}rv. = M , [ - To(s7 - ss)].
(22)
ABrvl
=
By assuming that energy given to the pump is negligible, its exergy flow rate difference equals to zero:
A/b. = ~.
= M, (h6 - W~) = 0.
(23)
Here, M, and Mp are the mass flow rates of the refrigerant fluid and the strong solution, respectively. For ammonia/water systems, the criterion for the quality of solution is the concentration of refrigerant fluid (ammonia), while it is concentration of solvent (lithium bromide) in lithium bromide/water systems. So, in the former system, the strong solution is assumed as the one which is pumped from the absorber and in the second system, the one passing through the throttling valve II. Effectiveness
Effectiveness in an absorption cooling cycle may be defined using two different approaches. One is the ratio of the aim to the cost. In such a cycle, the aim is the cooling effect (Qe) and the cost for obtaining this aim is the input heat (Q~). From the point of view based on the second law,
Second law analysis of absorption cooling cycles Table I. Working conditions of lithium bromide/water system Gen Abs Con. Ev TCC) P(kPa)
80 3.169
25 0.710
25 3.169
2 0.710
553
Table 2. Working conditions of ammonia/water system Gen Abs Con. Ev T('C) P(kPa)
100 1000.0
25 462.5
25 1000.0
2 462.5
the aim is to obtain the greatest amount of exergy change in the evaporator by paying for it with the least exergy change in the other components. So, I The exergy fl°w rate difference in evap°rat°r I El = Total exergy flow rate difference in other components
(24)
can be defined and may be named as "the qualitative effectiveness". Another approach is related to the directions of exergy flow rate differences. In the evaporator, generator and the first throttling valve the exergy flow rate increase while it decreases in the condenser, absorber and the second throttling valve. If effectiveness is defined as the ratio of all exergy leaving the process to all exergy entering it: ]A~E + AB~ + A / I r v j E2= ABA+ ABc + A ~ I '
(25)
may be written. Here, the essence is the amount of exergy. So, equation (25) may be named as "the quantitative effectiveness". A NUMERICAL EXAMPLE FOR COMPARISON OF LiBr-H20 SYSTEM WITH A NH3-H20 SYSTEM For a refrigeration at T = 2°C in an environment in which To -- 25°C, the working conditions for both of the systems (lithium bromide/water and ammonia/water systems) are given in Table 1 and Table 2. In order to reduce the amount of heat given to the generator, a heat exchanger has been installed between the generator and the absorber (Fig. 2). Exergy flow rate differences in the heat exchanger can be defined similarly to equations (17-23): A/~HE= (Mp - l)(h7 - T0ST)+ M p ( h 9 - T0sg) - ( M p - 1)(hi0 -- Toslo) -- M p ( h 6 - Tos6).
(26)
As the effectiveness of a heat exchanger [1] must be less than one, the exergy flow rate difference in exchanger is negative. Thus, equation (25) takes the form: E2 =
A/~AABE+ A/~ + A/)TV, + A/Jc + A/~rvl, + A/~,e
(27)
"
Now let us investigate the behaviour of the solution (Fig. 3). The weak solution leaves the generator (10) in liquid state, while the strong one is in the same state when it leaves the absorber
To
From
condenser
evopomtor
TI O~
Heot exchonger
Q4,
8
.
W,.,,,
Fig. 2. Absorption cooling cycle with heat exchanger. H.R.S. 8 'b---E
o~
N. E(~RICAN
554
~
9
Y~o Y7
Y9 Ys
Ye
Ys
PG
Mass fraction of refrigeront fluid Fig. 3. States of solution in the cycle.
(5). During the operation in the pump the strong solution remains in the liquid state (6). In the heat exchanger heat is given off by the strong solution and it reaches the liquid state again (9). Consequently, the weak solution is deep in the liquid state when it enters the throttling valve (7). Here, it becomes wet vapour (8). With the help of this knowledge the thermodynamic properties of both the refrigerant and the solution can be determined (Tables 3 and 4). The properties which Table 3 shows are d e ~ by using the diagrams in reference [7]. It must be noted that these diagrams have n o t been drawn in SI units. Table 3. Properties of refriserant fluid and solution at the main points of lithium bromide/water system y" P T h s kgi.,iBr/kg kPa °C kJ k8- i kJ kg- 1K solution I 2 3 4 5 6 7 8 9 10
3.169 3.169 0.710 0.710 0.710 3.169 3.169 0.710 3.169 3.169
80 25 2 2 25 25 58 55 45 80
2670.00 104.89 104.89 2505.20 243.43 243.43 305.15 305.15 277.66 350,00
8.95 0.37 0.38 9.10 2.13 2.13 1.90 1.88 2.31 2.05
0.00 0.00 0.00 0.00 0.51 0.51 0.66 0.66 0.51 0.66
Table 4. Properties of refriserant fluid and solution at the main points of ammonia/water system P kPa I 2 3 4 5 6 7 8 9 10
1080.00 1080.00 462.50 462.50 462.50 1000.00 1000.00 467.50 1000.00 1000.00
T °C
b kJ kg- I
s kJ k 8 - *K
Y kgNH3/kg solution
100 25 2 2 25 25 75 60 50 100
1665.40 289.20 289.20 1445.60 91.53 91.53 242.80 242.80 205.02 422.13
5.6392 1.0915 I. 1100 5.3108 0.9100 0.9100 1.3400 1.1800 1.2300 1.6200
0.00 0.00 0.00 0.00 0.56 0.56 0.30 0.30 0.56 0.30
Second law analysis of absorption cooling cycles
555
2.I 2. Z
~
1.6
"i'~
1.4
(t," .
0.6 0.4
°7,
+Z
,
0 0.10 0.20
0.40
I
0.60
I
I
0.80
f
q.r., 0.10 0.20
Ammonia concentration (Kg Nil 3 Kg" =~ution)
Ammonia
0.40
0.60
0.1~)
ccf,;~,Itration (Kg NH 3 Kg -~sotution)
Fig. 4. Entropy-concentration diagram for ammonia/water combination (drawn according to the Redlich-Kwong equation).
The necessary values and methods for determination of the properties shown on Table 4 are presented in references [5, 6, 9]. Also, entropy-concentration diagrams including liquid and vapour lines for ammonia/water combination, according to the Redlich-Kwong equation of state, have been drawn for use in this study (Fig 4a and b). From the detailed explanations in references [5, 6, 9] the mass flow rates are as follows: for lithium bromide/water system: Mpf4.18kgh
-l
and for ammonia/water system:
Mp = 2.70 kg h- I. The first law analysis According to equation (11)
(COP)us,-M2offi0.915 (COP)NH}-H20= 0.631 The second law analysis The exergy flow rate differences [equations (17)-(23) and equation (26)] for lithium bromide/ water system: A~r ffi 4998.87 kJ h -I, A/~c = 5121.95 kJ h -I, A~o = 4428.30 kJ h -I, A/~A ffi 4317.14 kJ h -I, A/~rvl ffi 2.98 kJ h - i,
N. F_X;RICAN
556
A[~rv,l =
-- 18.95 kJ h - I,
A / ~ = 0.00, AB,e = - 110.04 kJ h -1. For ammonia/water system: A ~ E = 2408.24 kJ h-~, A/~c = - 2 7 3 1 . 4 1 kJ h-t, A/~c = 3405.54 kJ h -~, AB A = -3011.531 kJ h -],
A[~rv= = Al~rvn = ABe,
=
5.51 kJh -I, - 81.06 kJ h-), 0.00,
A~uE = -- 114.054 kJ h-L The qualitative effectiveness (equation 24): (~l)uBr-.2o = 0.987, ((;I)N,3- "20 = 0.980. The quantitative effectiveness (equation 27):
((Z)UB,-H20=
0.976,
(E2)NH3-H20 = 0.954.
CONCLUSIONS The lithium bromide/water system has more advantages than the ammonia/watex system from the points of view of both the first law and the second law, as it is s ~ n from the calculations above and the Figs 5-10, in spite o f its involving a noticeable amount of solution. As the amount of
!
E2
I 0.9
p/i, 0.8
0.8
J
0.7 0.6 5
i
r 0.6
15
0.4
4
To • Z S ' C T~ • 2 " C
TO ,ZSoC
0.3
T~ , 2 " C 0.2
. . . . LiBr
--NH
O.I
I
I
60
I
70
I
90
I
II0 tnlW~Um
I,
I:~I0
- HzO 3 - HzO I
150
T~ ('C)
Fig. 5. Qualitative and quantitative effectivenesses as a function o f generator temperature.
. . . . LiBr - H~O . . . . NHz~ - Hz-O
0.2
o
t
60
I
70
I
90
I
IiO
I
i~o
I
15o
Generator temperature T~ ('C} Fig. 6. Coefficient of performance as a function of ~ n c r a t o r temperature.
Second law analysis
557
o f absorption cooling cycles
27 25
w
23
!
.~"5
17
"t
15
0.8 0,7 "E o
15
II
|
,
J°
0.6 0.5
i
• 25%
- ~ LtBr - H20 ~ N H 3 - H20
3 -
I
I
60
I
70
I
90
I
I10
I
130
o. 3 -
~ :
0.2
i
o.I
150
To • 40"C
r~-
.... LiBr - H20 ~ N H 3 - H20
I
80
I
I00
C-enerotor temperature Te (*C)
I
120
c~rl~r
Fig. 7. Mass flow rate o f strong solution as a function o f generator temperature.
IO'C
I
140
~
160
~ (*c)
Fig. 8. Qualitative and quantitative effectivenesses as a function o f generator temperature.
solution (in other words, mass flow rate Mp) increases, the exergy flow rate difference in the second throttling valve increases absolutely [equation (22)]. Consequently, both of the effectivenesses decrease, but this result does not remove the lithium bromide/water combination's advantages. Mp is inversely proportional to the generator leaving temperature (To). This result has been shown for
54
l
~J
5(:
I
I
•
~"
4e
~
42
O.~
O.E 22 To • 4 0 e C
O.~
TE • IO'C
IO'C
O.:"
- HzO - HzO
""" I
80
I
90
I
IfO
I
1:30
I
l~g3
I
170
Genera(or temperature T~ ('C) Fig. 9. Coefficient o f performance as a function of generator temperature,
14
~
l
2= I
80
t
90
~
----LiBr - HzO NH3 - Hz0
I10
I
130
C.ammtor t e ~ m
I
150
i
170
T~ ('C)
Fig. 10. Mass flow rate o f strong solution as a function o f generator temperature.
558
N. Et~RICAN
both of the combinations and the effectiveness has been calculated for the same temperatures (see Figs 5-10). When the operation is repeated for different refrigeration conditions, it is observed that the effectiveness and C O P values o f lithium bromide/water are higher than those of the ammonia/water combination. The principal problem that makes using L i B r - H , O in absorption cooling cycles difficult is its limiting property which prevents application for the refrigeration conditions below 0°C. Taking into consideration the fact that lithium bromide/water solution does not harm the ozone layer and it undergoes the operations in the cooling cycles almost perfectly from the point of view of the second law, and has also high C O P values, it is realistic to draw a conclusion suggesting this combination as an alternative one. REFERENCES 1. T. A Brzustowski and P. J. Golem, Second law analysis of energy processes part lI: the parformance of simple heat exchangers, Trans. CSME 4, 219-226 (1976-1977). 2. A. N. E~rican and A. Karakul, Second law analysis of a solar powered rankine cycle/vaporcompressioncycle, Heat Recovery Systems 6, 135-141 0986). 3. A. Bejan, General criterion for rating heat exchanger performance, J. Heal Mass Transfer 21, 655-658 (1978). 4. A. Bejan, The concept of irreversibility in heat exchanger design: counterflow heat exchangers for gas-to-gas application Trans. ASME 99, 374-380 (1977). 5. F. Bosnjakovic, Technical Thermodynamics (Translated by P. L. Blackshear) Holt, Rinehart and Winston, New York (1965). 6. Adolfo L. Gomez and G. Ali Mansoori, Thermodynamic equation of state approach for the choice of working fluids of absorption cooling cycles, Sol. Energy 31, 557-566 (1983). 7. A. L6wer, Thermodynamische eigenschaften und warme diagramme des binaren systems lithium bromid/wasser, Kaltetechnik 13 Jahrgang Heft 5/1961. 8. T. A. Brzustowski and P. J. Golem, Second law analysisof energy processes: part one: exergy--an introduction, Trans. CSME 4, 209-218 (1976--1977). 9. G. J. Van Wylen and R. E. Sonntag, Fundamentals of Classical Thermodynamics, John Wiley, New York (1976).