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Analytical studies on the performance of cascaded refrigeration-heat pump systems with different working fluid combinations
Heat Recover3' Systems Vol. 2, No. 3. pp. 233-245, 1982
0198-7593/82/030233-13503.00/0 © 1982 Pergamon Press Ltd
Printed in Great Britain.
ANALYTICAL STUDIES ON THE PERFORMANCE OF CASCADED REFRIGERATION-HEAT PUMP SYSTEMS WITH DIFFERENT WORKING FLUID COMBINATIONS S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY Refrigeration and Air-conditioning Laboratory, Department of Mechanical Engineering. Indian Institute of Technology, Madras. India Abstract-~ascading of vapour-compression refrigeration and heat pump systems to produce both cooling and heating for industrial applications is an interesting possibility. As a first step in this direction, a detailed thermodynamic analysis of an idealised hybrid systems is made for various combinations of working fluids R12 or R22 on the refrigeration system and RI 1, R21 or R12BI on the heat pump system. Charts and correlations are presented to facilitate the estimation of performance parameters such as COP, isentropic compression work and cooling and heating capacities. For the temperature ranges considered, overall COPs in the range of 9.5-4.0 can be achieved.
INTRODUCTION
CASCADING of vapour-compression refrigeration systems for producing very low temperatures is a well known technique. However, with the prevailing energy shortages and the need to recover the expended energy to the maximum possible extent, one can envisage the use of cascade systems for the dual task of providing both refrigeration and heat. In a variety of industries such as food, dairy, chemicals, etc., which demand both cooling and heating at various stages of processing operations, a cascaded refrigerationheat pump system operating between the required temperature limits can contribute to optimum utilisation of energy. An added advantage of such a system would be the absence of the need for external cooling of the condenser of the refrigeration system. This would result in considerable savings in capital equipment costs due to elimination of cooling towers, blowers, pumps, etc. Additionally, savings are achieved in recurring costs for the high-grade electrical energy to operate the above equipment and cooling-water costs. Apart from the savings in the energy required for the heating system, use of expensive boilers is also avoided. Although refrigeration systems and heat pumps have been analysed individually, literature on coupled systems is lacking. Heat pumps for low-temperature applications such as space heating have been extensively studied [1-3]. However, considerable work needs to be carried out in the area of high-temperature heat pumps for industrial use. Steimle [4] points out that 'The development of heat pumps and their applications, particularly for industrial heating, is in its infancy' and also emphasises that looking towards total energy systems, the Rankine cycle heat pumps are of great interest. Recently, preliminary experimental studies on such systems have been reported [5-6]. Experiments on solar-assisted industrial heat pumps operating with R11 and R114 are being carried out at the authors' laboratory. A detailed thermodynamic analysis of heat pump systems working with various working fluids is made by Holland [7]. Computational procedures for estimation of the thermodynamic performance of single-stage refrigeration systems [8, 9] and of cascade systems for production of very low temperatures [10] have been reported in literature. The first step in the development of hybrid equipment which delivers both cold and heat is a thermodynamic analysis of the idealised system which facilitates the selection of suitable working fluids, identification of optimum operating conditions and prediction of performance characteristics. In this paper, such an analysis is presented for working fluids and parameter ranges of practical interest. While conventional refrigerants R12 and R22 are considered for the refrigeration system, R21, R11 and R12B1 are chosen for 233
234
S. SRINIVASA MURTHY and M. V, KRISHNA MURTHY
w,% Oe, at
Qc, at ~¢:::~(0e2 a~ t e,,Pc~ ~
[
[ tez,Pe2 :~,w2 exchanger J ~
Compressor1 ~
! t
I
Compressor2
e
tcz,Pc~
3
] ooo.o..I
.>1 Expn.valve1
(~cz G'F
Expn. volve 2
Fig. 1. Schematic diagram of cascaded refrigeration-heat pump system.
the heat pump system. The coefficients of performance, heat and work quantities are determined for various combinations of the above working fluids. Charts have been prepared for easy estimation of the performance parameters. Correlations which facilitate quick calculation of the above quantities are also presented. DESCRIPTION OF THE SYSTEM
Figure 1 shows the schematic of the idealised system consisting of the refrigeration and the heat pump subsystems cascaded at the heat exchanger. The various heat quantities and temperature and pressure levels are indicated in the figure. The following simplifying assumptions have been made to carry out the anlysis: (a) The thermodynamic cycles of both refrigerauon and heat pump systems follow the standard cycle involving isentropic compression, isenthalpic expansion and absence of superheating of the suction vapour or of subcooling of the condensed liquid. (b) Pressure drops in piping, heat exchangers, compressor valves, etc., are neglected. (c) The heat exchanger formed by the condenser of the refrigeration system and the evaporator of the heat pump system is ideal, i.e.. Qc! = Qe2.
(1)
The thermodynamic cycle is represented on p-h scales in Fig. 2. THEORETICAL CONSIDERATIONS
Based on the assumptions listed earlier, the following relations applicable to both refrigeration and heat pump systems are derived: For the cooling capacity of the evaporators one can write, Q, = thAh~,
(2)
where rh = (l;'r/v)/V.
(3)
A combination of equations (2) and (3) yields Qe = l;'r/vq~,
(4)
where q= is the 'volurr~tric heat of evaporation' defined as q, = Ahffv.
(5)
Similarly for the heating capacity of the condensers, one can write Qc = l?r/vqc,
(6)
Analytical studies on the cascaded refrigeration-heat pump
235
"2"
0..
Specitic en~halpy, hlkJ. kg -1) Fig. 2. Idealised thermodynamic cycle for refrigeration or heat pump subsystem.
where q¢ is the 'volumetric heat of condensation' defined as, (7)
q, = A h , / v .
Also, for the idealised system, the isentropic work of compression is, W = Q o - Qo,
(8)
for 1 kW of refrigeration load Q~I, equation (4) gives 171 = 1/(r/vt q~l)
(9)
which in conjunction with equation (6) results in, (10)
Q,I = q,l/q~l
Equations (1), (4) and (10) yield, (1 1)
~'2 = (q¢l/q~l)(1/rl,2 q~2)
which together with equation (6) gives, (12)
Q¢2 = (q¢l/qeO(qcE/q~2).
For Qcl = 1, equations (8) and (10) yield, (13)
W1 = (qcl - q~l)/q~l
and equations (1), (8), (10) and (12) give, W2 = (q,1/q~l)[(qc2 - qe2)/qe2].
(14)
The individual coefficients of performance of the cooling and heating systems are given respectively by, (COP)t = 1/W1 = q ~ / ( q ¢ l - qel)
(15)
(COP)2 = Q ¢ 2 / w 2 = q¢2/(q¢2 - q~2).
(16)
and
The total performance of the dual-purpose cascaded system may be represented by an overall COP defined based on the conventional practice that, COP = (desired commodity)/(expenditure) which results in (COP)o = (Q~I
+ Q¢2)/(WI +
W2)-
(17)
In case the system operates as heat pump only, drawing energy from a cold source (e.g.,
236
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
in winter from the ambient), the C O P is defined as, (COP)h r = Q,z/(W~ + W2).
(18)
In the above calculations, the volumetric heat quantities q, can be derived from the thermodynamic property data for the working fluids. The swept volume I), is dependent on the compressor dimensions and its speed. The volumetric efficiency r/,., is a function of the clearance volume and the pressure ratio in the following familiar form: q,
=
1 -
C[(pc/p~)
t:
-
1].
(19)
One may be reminded here that the pressure ratio itself is a function of the operating temperatures t, and t c. One may observe from equations (10) and (12)-(18) that a knowledge of l? and qv is not needed for the thermodynamic analysis of the cascaded system. However, when a selection of suitable compressors for the system is being made, these data will be essential. SELECTION O F WORKING FLUIDS
The common refrigerants Rl2 and R22 are chosen as the working fluids on the refrigeration side. For the selection of working fluids on the heat pump side, the various candidates listed in Table 1 in the ascending order of their critical temperatures are considered. In selecting the working fluids for vapour compression systems, it is an established practice to ensure that the operating temperatures and pressures are not close to the critical values. Since the present study involves industrial heat pumps suitable for operating at temperatures up to 110°C, keeping in mind that invariably 10-15°C of superheat is experienced at the end of compression, the first 23 refrigerants in Table 1 are discarded. Of the remaining six candidate refrigerants, Rl14, R600 and R113 have the disadvantage that they demand high degrees of superheat at the evaporator to avoid wet Table 1. Critical properties of candidate working fluids S1. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Refrigerant R50 RI4 RII50 R503 R23 RI3 R744 R170 R504 R13BI R115 R502 R1270 R22 R290 R500 R245 R12 R152a RC318 R717 R600a R142b R114 R600 R12B1 R21 RII Rl13
Chemical formula CH, CF4 CH2CH 2 CHF3/CCF 3 CHF3 CCIF3 CO2 CH3CH 3 CH2F2/CHF2CF 3 CBrFa CF3CFaCI CHCIF2/CCIF2CF3 CH:CHCH2 CHCIFa CH3CH2CH3 CCIFz/CH3CHF2 CH3C2Fs CCl2F2 CHaCHF2 C4Fa NHa CH(CHa) a CHaCCIF2 C2C12F 4 CH~CH2CH2CH 3 CBrCIF2 CHClaF CC|aF CCI2FCCIF2
Critical temperature [°C]
Critical pressure [bar]
-82.50 -45.67 9.90 19.50 26.30 28.83 31.04 32.23 66.39 67.00 79.94 90.00 91.76 96.00 96.81 105.50 106.96 112.00 113.50 115.33 133.00 134.98 t37A l 145,72 152,01 154.50 178.50 198.00 214.11
46.41 37.44 51.17 43.43 49.70 38.68 73.77 48.94 47.61 39.65 31.58 42.68 46.27 49.77 42.57 44.26 31.37 41.76 44.95 27.83 114.25 36.48 41.23 32,62 37,97 41.23 5t.89 44.13 34.40
Analytical studies on the cascaded refrigeration-heat pump
237
compression. The performance of the remaining working fluids, i.e., R12B1, R21 and R11 which seem to be suitable for high temperature heat pump applications are analysed in this paper.
RESULTS AND DISCUSSION Keeping in mind the temperature levels encountered in conventional refrigeration and air-conditioning practice, and the need for thermal energy at medium high-temperature levels, the following temperature ranges are chosen for the present study: (a) Evaporation temperature for the refrigeration system (tel) = - 4 0 - 1 0 °C. (b) Intermediate temperature: (tot or re2) = 20-60°C. (c) Condensation temperature for the heat pump system (to2) = 70-110°C. Using the published thermodynamic data [11-14] for R12, R22, Rll, R21 and R12B1, the values of qc, qc and pressure ratio are computed for the temperature ranges mentioned above. These data are presented in the form of ready-to-use charts in Figs 3-7. In order to facilitate quick estimation of the performance for the complete range of parameters and for the working fluids considered, the computed performance data is correlated by making a multiple regression analysis. Linear and power curves are tried
~000
20
qc+
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\
\\\ "~
2000
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.\
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/// I
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,,:,~ ...,,,"i~/tc~('C) L. " < t ~r. " ~ .. \ . < " ~ .
I
-30 -20 -10 Evaporation temperature, te~{°C}
I
i
0
Fig. 3. Chart giving pressure ratio and volumetric heat quantity data for RI2.
10
238
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
25t~
5000
T ....
qeL_[
I
R22
/Pe,
1
Condensation temp. tc~(*C)
20~ ,?
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¢y
.~ 15 o ==
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J= (J
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I0
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-50
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-30
L
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-20
t
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Evaporation temperature, tew{'C ) Fig. 4. Chart giving pressure ratio and volumetric heat quantity data for R2!
10
Analytical studies on the cascaded refrigeration-heat pump
23q
L IX -
117 11,'1,7 II,'A 'L Ik////' ~All~,',
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-
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25
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Rll
i
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,/72~
¢11
lO
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.~
=.=G
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Condensation temp. tcz('C) = 7 0 ~ 80 -.~
2000
"i,Y l
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-/
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~ , .".g..' ."... ,~.,.c, ,2, 500
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"" ...~.. ~.~"~~.. "~..'.._ -~"---L>~--~ •--..~ ; ~ . . ~ _ . . - _ . . ~
0
10
I
i'l
I
I
30 t,O Evaporation temperature, tez(*C)
I
50
I
60
Fig. 5. Chart giving pressure ratio and volumetric heat quantity data for RI 1.
240
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
25
OUUU
-.--.--- qc 2
-- I
--
qe z
R21
%/Pc
I,
/.h I/// //.71/,
~OOG -
2 0 ~
Condensation temperature tc2['C)=70 ~..
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300(
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0 10
J
n .... I A 20 30 Evaporation t e m p e r a t u r e ,
1
/.0
~
i
50
60
te2( C )
Fig, 6. Chart giving pressure ratio and volumetric heat quantity data for R21.
Analytical studies on the cascaded refrigeration-heat pump
-
25 - - 5 0 0 0
241
qcz
-
------qe2
--
R12B1
P°'I"e i
__
Condensation temp. tcz{°C)= 20
-
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-
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,
"~3000
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/
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--7,
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,
/
-
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.= /
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/
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5-
0
-
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10
1000
[.
L
O,
20
30
Evaporation
/,0 temperature,
50
60
tea('C)
Fig. 7. Chart giving pressure ratio and volumetric heat quantity data for RI2B1.
and the correlations which give the best fit are presented. In carrying out this numerical exercise, in addition to those mentioned earlier, the following condition is assumed to hold good: t~ = t~2. (20) This is because the At across the heat exchanger would not only depend on the characteristics of the working fluids but also on the type and design of the heat exchanger and hence any particular numerical value for At would have to be assumed arbitrarily. For establishing qualitatively the thermodynamic feasibility of the concept, it is felt that the above assumption may be acceptable. However, it should be emphasised here that the charts given in Figs 3-7 are useful in estimating the performance even when a At exists.
242
S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY
Table 2. Correlation coefficients for equation (21) for COP Working fluid
u0
RI2 R22 RI1 R21 R12BI
a~
Multiple correlation
-8.96866 -9.43952 -8.61366 - 8.47636 -7.88992
0.97174 0.96733 0.97137 0.96289 0.97133
a~
22428 903137 11691 6788 507083
7.72735 7.55036 7.53501 7.48785 6.11777
For instance, if one assumes At = 5~C, i.e., t¢1 = 4 0 C and t~2 = 3 5 C (say), one can take the values of q¢1, qcl, qe2 and qc2 from charts at the above temperatures and obtain Qc2, Wl, w2 and (COP)o from equations (12)-(14) and (17) respectively. The individual coefficients of performance for the refrigeration and heat p u m p systems, which are dependent only on the evaporation and condensation temperatures are expressed as power curves, thus, C O P = ao t~ ~t~-"
(21)
where the values of a 0 . . . a2 for temperatures in degrees Kelvin are given in Table 2. The individual work requirements for the refrigeration and heat p u m p systems, for 1 k W of cooling load are linearly correlated in terms of temperatures as, Wt = ao + a t t ~ + a2t~
(22)
W2 = ao + at t~t + a2 t~t + a3 to2
(23)
and
where the coefficients ao .. • a3 are listed in Table 3 to yield work in kW for temperatures in degrees Celsius. An energy balance of the complete system gives the expression for the quantity of heat available at high-temperature level at the condenser of the heat p u m p as, Qc2 ---(1 + Wt + w2)
(24)
Using equations (15)-(17), the overall C O P may be expressed as, (COP)o =
(COP)t + ( C O P ) ~ ( W 2 / W t )
(25)
1 -+- ( W 2 / W I )
which can be calculated from correlations (21 I-(23). The (COP)hp is estimated using equation (18) together with correlations (22) and (23). Thus the correlations (22) and (23) would enable one to quickly estimate the complete performance of the cascaded refrigeration-heat p u m p system. In Fig. 8. a n o m o g r a m based on equation (19) is given for the pressure ratios expected for the working fluids and temperature ranges considered here. For known isentropic
Table 3. Correlation coefficients for equations (22) and (23) for isentrop~c work Working fluid RI2 R21 R22-RI 1 RI2-Ril R22-R21 R 12-R21 R22-RI2BI R12-RI2BI
ao
a~
-0.10550
-0.00770
-0.10105 -0.35151 -0.35581 -0.33188 - 0.32559 -0.39665 -0.40109
-0.00711 -0.00455 -0.00459 -0.00452 - 0.00463 -0.00440 -0.00445
a2
a~
0.00733 0.00728 -0.00092 -0.00087 - 0.001D3 - 0.00102 -0.00090 -0.00084
Multiple correlation 0.98123
0.00650 0.00654 0.00630 0.00626 0.00735 0.00738
0.98369 0.98668 0.98546 0.98350 0.97708 0.97072 0.96939
Analytical studies on the cascaded refrigeration-heat pump
J
/
i/,.,,
//;l/y If///// i
1
2
3
/.
Pressure ratio, pc/Pe
/
5
243
t,0
//,//
'°°
,
,_
'
'
6 78910
20
lOO
90
80
7o
60
Volumetric efficiency, ,/o
sO
40
Fig. 8. Nomogram for determination of volumetric efficiency.
exponent coefficient, pressure ratio and per cent clearance, this can be used to determine the volumetric efficiency. Generally, the temperature of the cooling load tel, at the evaporator of the refrigeration system and that of the heating load t¢2, at the condenser of the heat pump system are known depending on the practical needs. The intermediate temperature tct or to2, has to be chosen suitably. It is well known that the (COP)t of refrigeration system increases sharply as tc~ is decreased. However, this necessitates the heat pump to upgrade the energy over a larger temperature differential thereby causing an equally sharp fall in (COP)2. It is beneficial to aim at maximum value for (COP)o. To illustrate the above trends, the performance of the individual systems is shown in Fig. 9 as a function of the intermediate temperature at the extreme operating temperatures. One may observe that there is very little difference in the performances of different working fluids over the ranges of temperatures considered. However, on the heat pump side, a marginal advantage is exhibited by R21 and RI1 compared to R12B1, in particular at higher values of to2"
As an example, the (COP)o of R I 2 - R l l cascaded system is also shown in Fig. 9. Since both (COPh and (COP)2 vary equally sharply, but in opposite directions, the overall COP which is a function of both does not vary significantly with the intermediate temperature. This trend is particularly true when the overall temperature differential (fez -- tel } is large. However, a slight improvement in (COP)o may be seen somewhere in the middle of the intermediate temperature range, i.e., between 30°C and 50°C. Operation in this range would have the added practical advantage in that the pressure ratios in both subsystems will not have unnecessarily large values. Identical trends are observed in the performance of all working fluids considered here. Based on the (COP)o, the difference in performance among the six combinations of refrigerants is not significant. Hence, one may select a proper working fluid combination
244
S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY
3O ---
( COP )~
I\
(cop I,
2s~
--'--
,o _I-R.,R21
o o20_ =
(COP)o
i
0
E '~IS ¢3.
I
,R12-Rll~ '~ 10 ~-t=, .t~,
'-
10, 70 / I0,110~
,,, " " ~ ' ~ . ~
~
-40- j 70 ~ " ' ~ / ~ ~
o
0
I
-
I
~
1
~ez"i10c "~. i ~-R 11,R 21
x~. " ~ R
12 B1
I
20 30 40 SO 60 Intermedioae temperature , tel or tez(C)
70
Fig. 9. Performance of cascaded refrigeration-heat pump system.
on the basis of practical considerations such as operating pressures, physical size of the compressors, availability of refrigerants etc. Selection of the refrigerant RI2 or R22 for the refrigeration system may be carried out as in established practices followed in commercial refrigeration and air-conditioning. Among the three candidate refrigerants for the heat pump system, at a given operating temperature, R11 exerts the lowest pressure while R12BI offers the highest value. However, R11 has the disadvantage of having the highest specific volume, which necessitates larger-sized compressors. While the compressors for the refrigerauon side are readily available, one may experience difficulty in finding suitable compressors for high-temperature heat pump operation. The major factors which contribute to this situation are high discharge temperafures which cause lubricant and refrigerant breakdown, large pressure ratios and of course the relatively small heat pump market. Even though the cascading technique overcomes the drawback of large pressure ratios, development of high-temperature, long-life lubricants is essential. The prevailing energy crisis has drawn considerable attention of industrialists and scientists towards the heat pump applications and one can foresee greater demands in near future. An interesting possibility is the use of conventional R t2 and R22 compressors for high-temperature heat pump applications using other working fluids with high-temperature lubricants. Thermodynamic performance of such systems are being studied by the authors where it is observed that R21 and RI2BI can be used successfully with R I2 and R22 refrigeration compressors for high-temperature heat pump applications. It is obvious that in a practical situation, the heating and cooling loads may not balance exactly. However, depending upon the specific case. the cascade system may be operated to provide one of the effects (e.g. cooling) completely, while the heat available from the system could form a significant fraction of the total heating load thus contributing to the overall energy economy.
Analytical studies on the cascaded refrigeration-heat pump
245
CONCLUDING REMARKS
A thermodynamic analysis of idealised cascade refrigeration-heat pump systems is made. Charts and correlations which are useful in estimating the performance of such a hybrid system are presented. It is observed that on the basis of overall COP, any combination of R12 or R22 on the refrigeration system and Rll, R21 or R12B1 on the heat pump system may be adopted. For the low and high temperature limits of 10°C and 70°C, a (COP)o of about 9.5 can be achieved while for the extreme limits of -40°C and 110°C, the (COP)o would be in the vicinity of 4.0. Although the intermediate temperature does not exert any significant influence on the overall performance, on practical considerations it is beneficial to operate in the middle range of 30-50°C. NOMENCLATURE ao. • • a3 C COP Ah ~h P Q q t At
¢
I: W rh, ? Subscripts c e hp 0 1
2
correlation coefficients in equations (21)-(23) volumetric clearance ratio coefficient of performance specific enthalpy difference [kJ kg- 1] mass flow rate [ k g s - l ] saturation vapour pressure [bar] heating/cooling capacity [kW] volumetric heat quantity [kJ m - 3] temperature ['°C] temperature difference across the heat exchanger [°C] swept volume of compressor [m 3 s- tl specific volume [m 3 kg- 1] isentropic work [kW] volumetric efficiency isentropic expansion coefficient condenser evaporator heat pump operation only cascade system refrigeration subsystem heat pump subsystem REFERENCES
1. The Electric Heat Pump, Proc. German~American Col~ on Technol. and Applications, Vulkan, Essen (October 1980). 2. H. Kirn and A. Hadenfeldt, Wiirmepumpen, C. F. Muller, Karlsruhe (1976). 3. D. A. Reay and D. B. A. Macmichael. Heat Pumps: Theory, Design and Applications, Pergamon Press, Oxford (1979). 4. F. Steimle, Int. J. Refrig. 3, 9-18 (1980). 5. G. Laroche, Int. J. Refrig. 3, 347-351 (1980). 6. H. Kruse, Int. J. Refrig., 4, 119--125 (1981). 7. F. A. Holland, Ind. Chem. Engr., 22, 3-38 (1980). 8. J. A. Schofield, ASHRAE Trans., 76, Part I, 52-63 (1970). 9. C. Y. Chan and G. G. Haselden, Int. J. Refrig., 4, 131-134 (1981). 10. H. Auracher, Kiiltechnik-Klimatisierung, 22, 295-302 (1970). 11. U. K. Rombusch and H. Giesen, Kiiltetechnik-Klimatisierung, 18, 37-40 0966). 12. Thermodynamic Properties of Refrigerants, ASHRAE Inc., New York (1969). 13. I. S. Badyikes, Proc. XII Int. Cong. Refrig. Madrid (1967). 14. R. DSring, Proc. X I V Int. Cong. Refrig., Moscow (1975).
0198-7593/82/030233-13503.00/0 © 1982 Pergamon Press Ltd
Printed in Great Britain.
ANALYTICAL STUDIES ON THE PERFORMANCE OF CASCADED REFRIGERATION-HEAT PUMP SYSTEMS WITH DIFFERENT WORKING FLUID COMBINATIONS S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY Refrigeration and Air-conditioning Laboratory, Department of Mechanical Engineering. Indian Institute of Technology, Madras. India Abstract-~ascading of vapour-compression refrigeration and heat pump systems to produce both cooling and heating for industrial applications is an interesting possibility. As a first step in this direction, a detailed thermodynamic analysis of an idealised hybrid systems is made for various combinations of working fluids R12 or R22 on the refrigeration system and RI 1, R21 or R12BI on the heat pump system. Charts and correlations are presented to facilitate the estimation of performance parameters such as COP, isentropic compression work and cooling and heating capacities. For the temperature ranges considered, overall COPs in the range of 9.5-4.0 can be achieved.
INTRODUCTION
CASCADING of vapour-compression refrigeration systems for producing very low temperatures is a well known technique. However, with the prevailing energy shortages and the need to recover the expended energy to the maximum possible extent, one can envisage the use of cascade systems for the dual task of providing both refrigeration and heat. In a variety of industries such as food, dairy, chemicals, etc., which demand both cooling and heating at various stages of processing operations, a cascaded refrigerationheat pump system operating between the required temperature limits can contribute to optimum utilisation of energy. An added advantage of such a system would be the absence of the need for external cooling of the condenser of the refrigeration system. This would result in considerable savings in capital equipment costs due to elimination of cooling towers, blowers, pumps, etc. Additionally, savings are achieved in recurring costs for the high-grade electrical energy to operate the above equipment and cooling-water costs. Apart from the savings in the energy required for the heating system, use of expensive boilers is also avoided. Although refrigeration systems and heat pumps have been analysed individually, literature on coupled systems is lacking. Heat pumps for low-temperature applications such as space heating have been extensively studied [1-3]. However, considerable work needs to be carried out in the area of high-temperature heat pumps for industrial use. Steimle [4] points out that 'The development of heat pumps and their applications, particularly for industrial heating, is in its infancy' and also emphasises that looking towards total energy systems, the Rankine cycle heat pumps are of great interest. Recently, preliminary experimental studies on such systems have been reported [5-6]. Experiments on solar-assisted industrial heat pumps operating with R11 and R114 are being carried out at the authors' laboratory. A detailed thermodynamic analysis of heat pump systems working with various working fluids is made by Holland [7]. Computational procedures for estimation of the thermodynamic performance of single-stage refrigeration systems [8, 9] and of cascade systems for production of very low temperatures [10] have been reported in literature. The first step in the development of hybrid equipment which delivers both cold and heat is a thermodynamic analysis of the idealised system which facilitates the selection of suitable working fluids, identification of optimum operating conditions and prediction of performance characteristics. In this paper, such an analysis is presented for working fluids and parameter ranges of practical interest. While conventional refrigerants R12 and R22 are considered for the refrigeration system, R21, R11 and R12B1 are chosen for 233
234
S. SRINIVASA MURTHY and M. V, KRISHNA MURTHY
w,% Oe, at
Qc, at ~¢:::~(0e2 a~ t e,,Pc~ ~
[
[ tez,Pe2 :~,w2 exchanger J ~
Compressor1 ~
! t
I
Compressor2
e
tcz,Pc~
3
] ooo.o..I
.>1 Expn.valve1
(~cz G'F
Expn. volve 2
Fig. 1. Schematic diagram of cascaded refrigeration-heat pump system.
the heat pump system. The coefficients of performance, heat and work quantities are determined for various combinations of the above working fluids. Charts have been prepared for easy estimation of the performance parameters. Correlations which facilitate quick calculation of the above quantities are also presented. DESCRIPTION OF THE SYSTEM
Figure 1 shows the schematic of the idealised system consisting of the refrigeration and the heat pump subsystems cascaded at the heat exchanger. The various heat quantities and temperature and pressure levels are indicated in the figure. The following simplifying assumptions have been made to carry out the anlysis: (a) The thermodynamic cycles of both refrigerauon and heat pump systems follow the standard cycle involving isentropic compression, isenthalpic expansion and absence of superheating of the suction vapour or of subcooling of the condensed liquid. (b) Pressure drops in piping, heat exchangers, compressor valves, etc., are neglected. (c) The heat exchanger formed by the condenser of the refrigeration system and the evaporator of the heat pump system is ideal, i.e.. Qc! = Qe2.
(1)
The thermodynamic cycle is represented on p-h scales in Fig. 2. THEORETICAL CONSIDERATIONS
Based on the assumptions listed earlier, the following relations applicable to both refrigeration and heat pump systems are derived: For the cooling capacity of the evaporators one can write, Q, = thAh~,
(2)
where rh = (l;'r/v)/V.
(3)
A combination of equations (2) and (3) yields Qe = l;'r/vq~,
(4)
where q= is the 'volurr~tric heat of evaporation' defined as q, = Ahffv.
(5)
Similarly for the heating capacity of the condensers, one can write Qc = l?r/vqc,
(6)
Analytical studies on the cascaded refrigeration-heat pump
235
"2"
0..
Specitic en~halpy, hlkJ. kg -1) Fig. 2. Idealised thermodynamic cycle for refrigeration or heat pump subsystem.
where q¢ is the 'volumetric heat of condensation' defined as, (7)
q, = A h , / v .
Also, for the idealised system, the isentropic work of compression is, W = Q o - Qo,
(8)
for 1 kW of refrigeration load Q~I, equation (4) gives 171 = 1/(r/vt q~l)
(9)
which in conjunction with equation (6) results in, (10)
Q,I = q,l/q~l
Equations (1), (4) and (10) yield, (1 1)
~'2 = (q¢l/q~l)(1/rl,2 q~2)
which together with equation (6) gives, (12)
Q¢2 = (q¢l/qeO(qcE/q~2).
For Qcl = 1, equations (8) and (10) yield, (13)
W1 = (qcl - q~l)/q~l
and equations (1), (8), (10) and (12) give, W2 = (q,1/q~l)[(qc2 - qe2)/qe2].
(14)
The individual coefficients of performance of the cooling and heating systems are given respectively by, (COP)t = 1/W1 = q ~ / ( q ¢ l - qel)
(15)
(COP)2 = Q ¢ 2 / w 2 = q¢2/(q¢2 - q~2).
(16)
and
The total performance of the dual-purpose cascaded system may be represented by an overall COP defined based on the conventional practice that, COP = (desired commodity)/(expenditure) which results in (COP)o = (Q~I
+ Q¢2)/(WI +
W2)-
(17)
In case the system operates as heat pump only, drawing energy from a cold source (e.g.,
236
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
in winter from the ambient), the C O P is defined as, (COP)h r = Q,z/(W~ + W2).
(18)
In the above calculations, the volumetric heat quantities q, can be derived from the thermodynamic property data for the working fluids. The swept volume I), is dependent on the compressor dimensions and its speed. The volumetric efficiency r/,., is a function of the clearance volume and the pressure ratio in the following familiar form: q,
=
1 -
C[(pc/p~)
t:
-
1].
(19)
One may be reminded here that the pressure ratio itself is a function of the operating temperatures t, and t c. One may observe from equations (10) and (12)-(18) that a knowledge of l? and qv is not needed for the thermodynamic analysis of the cascaded system. However, when a selection of suitable compressors for the system is being made, these data will be essential. SELECTION O F WORKING FLUIDS
The common refrigerants Rl2 and R22 are chosen as the working fluids on the refrigeration side. For the selection of working fluids on the heat pump side, the various candidates listed in Table 1 in the ascending order of their critical temperatures are considered. In selecting the working fluids for vapour compression systems, it is an established practice to ensure that the operating temperatures and pressures are not close to the critical values. Since the present study involves industrial heat pumps suitable for operating at temperatures up to 110°C, keeping in mind that invariably 10-15°C of superheat is experienced at the end of compression, the first 23 refrigerants in Table 1 are discarded. Of the remaining six candidate refrigerants, Rl14, R600 and R113 have the disadvantage that they demand high degrees of superheat at the evaporator to avoid wet Table 1. Critical properties of candidate working fluids S1. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Refrigerant R50 RI4 RII50 R503 R23 RI3 R744 R170 R504 R13BI R115 R502 R1270 R22 R290 R500 R245 R12 R152a RC318 R717 R600a R142b R114 R600 R12B1 R21 RII Rl13
Chemical formula CH, CF4 CH2CH 2 CHF3/CCF 3 CHF3 CCIF3 CO2 CH3CH 3 CH2F2/CHF2CF 3 CBrFa CF3CFaCI CHCIF2/CCIF2CF3 CH:CHCH2 CHCIFa CH3CH2CH3 CCIFz/CH3CHF2 CH3C2Fs CCl2F2 CHaCHF2 C4Fa NHa CH(CHa) a CHaCCIF2 C2C12F 4 CH~CH2CH2CH 3 CBrCIF2 CHClaF CC|aF CCI2FCCIF2
Critical temperature [°C]
Critical pressure [bar]
-82.50 -45.67 9.90 19.50 26.30 28.83 31.04 32.23 66.39 67.00 79.94 90.00 91.76 96.00 96.81 105.50 106.96 112.00 113.50 115.33 133.00 134.98 t37A l 145,72 152,01 154.50 178.50 198.00 214.11
46.41 37.44 51.17 43.43 49.70 38.68 73.77 48.94 47.61 39.65 31.58 42.68 46.27 49.77 42.57 44.26 31.37 41.76 44.95 27.83 114.25 36.48 41.23 32,62 37,97 41.23 5t.89 44.13 34.40
Analytical studies on the cascaded refrigeration-heat pump
237
compression. The performance of the remaining working fluids, i.e., R12B1, R21 and R11 which seem to be suitable for high temperature heat pump applications are analysed in this paper.
RESULTS AND DISCUSSION Keeping in mind the temperature levels encountered in conventional refrigeration and air-conditioning practice, and the need for thermal energy at medium high-temperature levels, the following temperature ranges are chosen for the present study: (a) Evaporation temperature for the refrigeration system (tel) = - 4 0 - 1 0 °C. (b) Intermediate temperature: (tot or re2) = 20-60°C. (c) Condensation temperature for the heat pump system (to2) = 70-110°C. Using the published thermodynamic data [11-14] for R12, R22, Rll, R21 and R12B1, the values of qc, qc and pressure ratio are computed for the temperature ranges mentioned above. These data are presented in the form of ready-to-use charts in Figs 3-7. In order to facilitate quick estimation of the performance for the complete range of parameters and for the working fluids considered, the computed performance data is correlated by making a multiple regression analysis. Linear and power curves are tried
~000
20
qc+
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\
\\\ "~
2000
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.\
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I
,./isxK.
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/// I
l
"
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,,:,~ ...,,,"i~/tc~('C) L. " < t ~r. " ~ .. \ . < " ~ .
I
-30 -20 -10 Evaporation temperature, te~{°C}
I
i
0
Fig. 3. Chart giving pressure ratio and volumetric heat quantity data for RI2.
10
238
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
25t~
5000
T ....
qeL_[
I
R22
/Pe,
1
Condensation temp. tc~(*C)
20~ ,?
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/
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¢y
.~ 15 o ==
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J= (J
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-50
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-30
L
I
-20
t
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0
Evaporation temperature, tew{'C ) Fig. 4. Chart giving pressure ratio and volumetric heat quantity data for R2!
10
Analytical studies on the cascaded refrigeration-heat pump
23q
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117 11,'1,7 II,'A 'L Ik////' ~All~,',
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-
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Rll
i
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._
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\ II/i'ti',',.',
-
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,/72~
¢11
lO
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go ", ,oo~ ~51/,7," "~--~,~PT.,' ,'
.~
=.=G
AYiA' .'
Condensation temp. tcz('C) = 7 0 ~ 80 -.~
2000
"i,Y l
#
-/
i
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~ , .".g..' ."... ,~.,.c, ,2, 500
~"".
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"" ...~.. ~.~"~~.. "~..'.._ -~"---L>~--~ •--..~ ; ~ . . ~ _ . . - _ . . ~
0
10
I
i'l
I
I
30 t,O Evaporation temperature, tez(*C)
I
50
I
60
Fig. 5. Chart giving pressure ratio and volumetric heat quantity data for RI 1.
240
S. SRINIVASAMURTHY and M. V. KRISHNA MURTHY
25
OUUU
-.--.--- qc 2
-- I
--
qe z
R21
%/Pc
I,
/.h I/// //.71/,
~OOG -
2 0 ~
Condensation temperature tc2['C)=70 ~..
,o "x~.~.
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90 ,~
_
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300(
oQ.¢a
1 1 0 % . ~
[ ~. ~"
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/
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////7,"
~,ooo'.
./ /
/ / / /
--
, - ' ~ " ~''>'
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/
""
/
tc,('c) ~ "~
-~.~--. --.~,~ -.~.._ ~......
0 10
J
n .... I A 20 30 Evaporation t e m p e r a t u r e ,
1
/.0
~
i
50
60
te2( C )
Fig, 6. Chart giving pressure ratio and volumetric heat quantity data for R21.
Analytical studies on the cascaded refrigeration-heat pump
-
25 - - 5 0 0 0
241
qcz
-
------qe2
--
R12B1
P°'I"e i
__
Condensation temp. tcz{°C)= 20
-
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,
"~3000
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/
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--7,
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,
/
-
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.= /
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/
/ /
/
5-
0
-
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10
1000
[.
L
O,
20
30
Evaporation
/,0 temperature,
50
60
tea('C)
Fig. 7. Chart giving pressure ratio and volumetric heat quantity data for RI2B1.
and the correlations which give the best fit are presented. In carrying out this numerical exercise, in addition to those mentioned earlier, the following condition is assumed to hold good: t~ = t~2. (20) This is because the At across the heat exchanger would not only depend on the characteristics of the working fluids but also on the type and design of the heat exchanger and hence any particular numerical value for At would have to be assumed arbitrarily. For establishing qualitatively the thermodynamic feasibility of the concept, it is felt that the above assumption may be acceptable. However, it should be emphasised here that the charts given in Figs 3-7 are useful in estimating the performance even when a At exists.
242
S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY
Table 2. Correlation coefficients for equation (21) for COP Working fluid
u0
RI2 R22 RI1 R21 R12BI
a~
Multiple correlation
-8.96866 -9.43952 -8.61366 - 8.47636 -7.88992
0.97174 0.96733 0.97137 0.96289 0.97133
a~
22428 903137 11691 6788 507083
7.72735 7.55036 7.53501 7.48785 6.11777
For instance, if one assumes At = 5~C, i.e., t¢1 = 4 0 C and t~2 = 3 5 C (say), one can take the values of q¢1, qcl, qe2 and qc2 from charts at the above temperatures and obtain Qc2, Wl, w2 and (COP)o from equations (12)-(14) and (17) respectively. The individual coefficients of performance for the refrigeration and heat p u m p systems, which are dependent only on the evaporation and condensation temperatures are expressed as power curves, thus, C O P = ao t~ ~t~-"
(21)
where the values of a 0 . . . a2 for temperatures in degrees Kelvin are given in Table 2. The individual work requirements for the refrigeration and heat p u m p systems, for 1 k W of cooling load are linearly correlated in terms of temperatures as, Wt = ao + a t t ~ + a2t~
(22)
W2 = ao + at t~t + a2 t~t + a3 to2
(23)
and
where the coefficients ao .. • a3 are listed in Table 3 to yield work in kW for temperatures in degrees Celsius. An energy balance of the complete system gives the expression for the quantity of heat available at high-temperature level at the condenser of the heat p u m p as, Qc2 ---(1 + Wt + w2)
(24)
Using equations (15)-(17), the overall C O P may be expressed as, (COP)o =
(COP)t + ( C O P ) ~ ( W 2 / W t )
(25)
1 -+- ( W 2 / W I )
which can be calculated from correlations (21 I-(23). The (COP)hp is estimated using equation (18) together with correlations (22) and (23). Thus the correlations (22) and (23) would enable one to quickly estimate the complete performance of the cascaded refrigeration-heat p u m p system. In Fig. 8. a n o m o g r a m based on equation (19) is given for the pressure ratios expected for the working fluids and temperature ranges considered here. For known isentropic
Table 3. Correlation coefficients for equations (22) and (23) for isentrop~c work Working fluid RI2 R21 R22-RI 1 RI2-Ril R22-R21 R 12-R21 R22-RI2BI R12-RI2BI
ao
a~
-0.10550
-0.00770
-0.10105 -0.35151 -0.35581 -0.33188 - 0.32559 -0.39665 -0.40109
-0.00711 -0.00455 -0.00459 -0.00452 - 0.00463 -0.00440 -0.00445
a2
a~
0.00733 0.00728 -0.00092 -0.00087 - 0.001D3 - 0.00102 -0.00090 -0.00084
Multiple correlation 0.98123
0.00650 0.00654 0.00630 0.00626 0.00735 0.00738
0.98369 0.98668 0.98546 0.98350 0.97708 0.97072 0.96939
Analytical studies on the cascaded refrigeration-heat pump
J
/
i/,.,,
//;l/y If///// i
1
2
3
/.
Pressure ratio, pc/Pe
/
5
243
t,0
//,//
'°°
,
,_
'
'
6 78910
20
lOO
90
80
7o
60
Volumetric efficiency, ,/o
sO
40
Fig. 8. Nomogram for determination of volumetric efficiency.
exponent coefficient, pressure ratio and per cent clearance, this can be used to determine the volumetric efficiency. Generally, the temperature of the cooling load tel, at the evaporator of the refrigeration system and that of the heating load t¢2, at the condenser of the heat pump system are known depending on the practical needs. The intermediate temperature tct or to2, has to be chosen suitably. It is well known that the (COP)t of refrigeration system increases sharply as tc~ is decreased. However, this necessitates the heat pump to upgrade the energy over a larger temperature differential thereby causing an equally sharp fall in (COP)2. It is beneficial to aim at maximum value for (COP)o. To illustrate the above trends, the performance of the individual systems is shown in Fig. 9 as a function of the intermediate temperature at the extreme operating temperatures. One may observe that there is very little difference in the performances of different working fluids over the ranges of temperatures considered. However, on the heat pump side, a marginal advantage is exhibited by R21 and RI1 compared to R12B1, in particular at higher values of to2"
As an example, the (COP)o of R I 2 - R l l cascaded system is also shown in Fig. 9. Since both (COPh and (COP)2 vary equally sharply, but in opposite directions, the overall COP which is a function of both does not vary significantly with the intermediate temperature. This trend is particularly true when the overall temperature differential (fez -- tel } is large. However, a slight improvement in (COP)o may be seen somewhere in the middle of the intermediate temperature range, i.e., between 30°C and 50°C. Operation in this range would have the added practical advantage in that the pressure ratios in both subsystems will not have unnecessarily large values. Identical trends are observed in the performance of all working fluids considered here. Based on the (COP)o, the difference in performance among the six combinations of refrigerants is not significant. Hence, one may select a proper working fluid combination
244
S. SRINIVASA MURTHY and M. V. KRISHNA MURTHY
3O ---
( COP )~
I\
(cop I,
2s~
--'--
,o _I-R.,R21
o o20_ =
(COP)o
i
0
E '~IS ¢3.
I
,R12-Rll~ '~ 10 ~-t=, .t~,
'-
10, 70 / I0,110~
,,, " " ~ ' ~ . ~
~
-40- j 70 ~ " ' ~ / ~ ~
o
0
I
-
I
~
1
~ez"i10c "~. i ~-R 11,R 21
x~. " ~ R
12 B1
I
20 30 40 SO 60 Intermedioae temperature , tel or tez(C)
70
Fig. 9. Performance of cascaded refrigeration-heat pump system.
on the basis of practical considerations such as operating pressures, physical size of the compressors, availability of refrigerants etc. Selection of the refrigerant RI2 or R22 for the refrigeration system may be carried out as in established practices followed in commercial refrigeration and air-conditioning. Among the three candidate refrigerants for the heat pump system, at a given operating temperature, R11 exerts the lowest pressure while R12BI offers the highest value. However, R11 has the disadvantage of having the highest specific volume, which necessitates larger-sized compressors. While the compressors for the refrigerauon side are readily available, one may experience difficulty in finding suitable compressors for high-temperature heat pump operation. The major factors which contribute to this situation are high discharge temperafures which cause lubricant and refrigerant breakdown, large pressure ratios and of course the relatively small heat pump market. Even though the cascading technique overcomes the drawback of large pressure ratios, development of high-temperature, long-life lubricants is essential. The prevailing energy crisis has drawn considerable attention of industrialists and scientists towards the heat pump applications and one can foresee greater demands in near future. An interesting possibility is the use of conventional R t2 and R22 compressors for high-temperature heat pump applications using other working fluids with high-temperature lubricants. Thermodynamic performance of such systems are being studied by the authors where it is observed that R21 and RI2BI can be used successfully with R I2 and R22 refrigeration compressors for high-temperature heat pump applications. It is obvious that in a practical situation, the heating and cooling loads may not balance exactly. However, depending upon the specific case. the cascade system may be operated to provide one of the effects (e.g. cooling) completely, while the heat available from the system could form a significant fraction of the total heating load thus contributing to the overall energy economy.
Analytical studies on the cascaded refrigeration-heat pump
245
CONCLUDING REMARKS
A thermodynamic analysis of idealised cascade refrigeration-heat pump systems is made. Charts and correlations which are useful in estimating the performance of such a hybrid system are presented. It is observed that on the basis of overall COP, any combination of R12 or R22 on the refrigeration system and Rll, R21 or R12B1 on the heat pump system may be adopted. For the low and high temperature limits of 10°C and 70°C, a (COP)o of about 9.5 can be achieved while for the extreme limits of -40°C and 110°C, the (COP)o would be in the vicinity of 4.0. Although the intermediate temperature does not exert any significant influence on the overall performance, on practical considerations it is beneficial to operate in the middle range of 30-50°C. NOMENCLATURE ao. • • a3 C COP Ah ~h P Q q t At
¢
I: W rh, ? Subscripts c e hp 0 1
2
correlation coefficients in equations (21)-(23) volumetric clearance ratio coefficient of performance specific enthalpy difference [kJ kg- 1] mass flow rate [ k g s - l ] saturation vapour pressure [bar] heating/cooling capacity [kW] volumetric heat quantity [kJ m - 3] temperature ['°C] temperature difference across the heat exchanger [°C] swept volume of compressor [m 3 s- tl specific volume [m 3 kg- 1] isentropic work [kW] volumetric efficiency isentropic expansion coefficient condenser evaporator heat pump operation only cascade system refrigeration subsystem heat pump subsystem REFERENCES
1. The Electric Heat Pump, Proc. German~American Col~ on Technol. and Applications, Vulkan, Essen (October 1980). 2. H. Kirn and A. Hadenfeldt, Wiirmepumpen, C. F. Muller, Karlsruhe (1976). 3. D. A. Reay and D. B. A. Macmichael. Heat Pumps: Theory, Design and Applications, Pergamon Press, Oxford (1979). 4. F. Steimle, Int. J. Refrig. 3, 9-18 (1980). 5. G. Laroche, Int. J. Refrig. 3, 347-351 (1980). 6. H. Kruse, Int. J. Refrig., 4, 119--125 (1981). 7. F. A. Holland, Ind. Chem. Engr., 22, 3-38 (1980). 8. J. A. Schofield, ASHRAE Trans., 76, Part I, 52-63 (1970). 9. C. Y. Chan and G. G. Haselden, Int. J. Refrig., 4, 131-134 (1981). 10. H. Auracher, Kiiltechnik-Klimatisierung, 22, 295-302 (1970). 11. U. K. Rombusch and H. Giesen, Kiiltetechnik-Klimatisierung, 18, 37-40 0966). 12. Thermodynamic Properties of Refrigerants, ASHRAE Inc., New York (1969). 13. I. S. Badyikes, Proc. XII Int. Cong. Refrig. Madrid (1967). 14. R. DSring, Proc. X I V Int. Cong. Refrig., Moscow (1975).