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An advanced analytical model of the Diffusion Absorption Refrigerator cycle
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 6 0 5 e6 1 2
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An advanced analytical model of the Diffusion Absorption Refrigerator cycle Giuseppe Starace*, Lorenzo De Pascalis Department of Engineering for Innovation, University of Salento, LECCE, Italy
article info
abstract
Article history:
The results about the performance of a new DAR’s thermodynamic model are compared
Received 7 March 2011
with the predictions of Zohar et al. (2009). The main difference is due to an accurate
Received in revised form
modeling of the refrigerant composition, assumed there as pure ammonia. A sensitivity
29 October 2011
analysis shows that, as the generator temperature increases, the rich solution mass
Accepted 6 November 2011
flowrate reduces more than that of the refrigerant one, and COP decreases. This happens as
Available online 15 November 2011
the absorption temperature increases as well, due to the lower absorption of ammonia in the weak solution. COP was found to increase when the ammonia concentration decreases.
Keywords:
In addition, for lower heat fluxes supplied to the generator, the heat dissipation toward
Adsorption
ambient dominates and COP becomes small; when the heat flux overtakes a threshold, the
Diffusion absorption refrigerator
evaporator reaches its maximum heat transfer, that remains constant for any further
Diffusion system
increase of heat supplied. COP presents its highest values over a limited range of the
Analytical model
generator’s operating conditions.
Refrigeration cycle
ª 2011 Elsevier Ltd and IIR. All rights reserved.
Mode`le analytique de pointe du cycle frigorifique a` absorption a` diffusion Mots cle´s : Adsorption ; Re´frige´rateur a` absorption a` diffusion ; Syste`me a` diffusion ; Mode`le analytique ; Cycle frigorifique
1.
Introduction
The Diffusion Absorption Refrigerator (DAR) cycle was introduced in 1928 by Von Platen and Munters (1928) and uses a binary mixture of ammonia (refrigerant) and water (absorbent) as working fluids in solution with either hydrogen or helium as auxiliary inert gas. The inert gas plays its role to reduce the partial pressure of the refrigerant in the evaporator according to Dalton’s law and to allow the fluid to evaporate
producing the cooling effect. The main characteristic of the DAR is of having no moving parts: a thermally driven pump (also referred to as the generator) acts to circulate the fluid in place of a mechanical device (this is the reason why it is both quiet and reliable). Nowadays, the refrigerator is commercially available only in a small cooling power range up to 100 W, where heat is supplied to the generator by electrical heating cartridges or a direct flame. These characteristics make the DAR small and simple to be built, but not really
* Corresponding author. Dipartimento di Ingegneria dell’Innovazione, Corpo O, via per Monteroni, snc e 73100 Lecce, Italy. Tel.: þ39 0832 297753; fax: þ39 0832 297777. E-mail address: [email protected] (G. Starace). 0140-7007/$ e see front matter ª 2011 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2011.11.007
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Nomenclature A COP cp C_ p;min h _ m p Q_ R T U x y DTmax
2
heat transfer area, m coefficient of performance specific heat at constant pressure, J kg1 K1 minimum heat capacity, J K1 s1 specific enthalpy, J kg1 mass flowrate, kg s1 pressure, Pa heat transfer, W gas constant, J kg1 K1 temperature, K global heat transfer coefficient, W m2 K1 molar concentration of ammonia in liquid solution molar concentration of ammonia in vapor solution maximum temperature difference between refrigerated air and refrigerant in the evaporator, K
efficient with very low COPs and, therefore, with high primary energy consumptions per unit of heat removed. Since the 1930s, the DAR cycle was studied and many authors have proposed papers on its performance and optimization. Up to now, a number of commercial DARs have been investigated. Results showed COPs of 0.2e0.3 and cooling powers between 16 W and 62 W at about 18 to 6 C obtained with temperatures of heat supplied to the generator in the range of 160 and 230 C (Keizer, 1979; Bourseau et al., 1987; Gutierrez, 1988; Jakob et al., 2008). Some methods to calculate graphically and/or numerically or to evaluate experimentally the properties of the working fluids circulating in the refrigerator were carried out by Reistad (1968), Kouremenos and Stegou-Sagia (1988), Chen et al. (1996), Srikhirin and Aphornratana (2002), Al-Shemmeri and Wang (2003) and Maiya (2003). Some of these works present models based on very limiting assumptions and their results frequently diverge from DAR real behavior. Actually when authors compare and fit analytical predictions with their experimental data in order to model the performance of the device, the results of their models can be only referred to those particular cases of DAR circuits. Zohar et al. (2005) proposed a complex thermodynamic model that explored the DAR performance. He and his coauthors found that the maximum COP values reachable with a DAR cycle can be obtained when the ammonia concentrations in rich and weak solutions are respectively 0.25e0.30 and 0.10, and that the generator’s temperature is approximately 200 C. The assumption was that the vapor exiting the rectifier is pure ammonia and no traces of water are present. This is rarely true, due to the not full efficiency of the rectifier in the process of separating the water from the ammonia. In addition to that, it must be pointed out that the temperature of the saturated liquid solution strongly depends on ammonia concentration. For instance, at 25 bar a reduction from 1.00 to 0.90 of the ammonia molar concentration in the liquid solution causes the effect of an increase of the liquid saturation
Subscripts 1.11 states of working solutions a absorption conditions air refrigerated air in evaporation chamber c condensation conditions e evaporation conditions H highest temperature in generator H,d heat dissipated at the highest temperature in the generator I,a intermediate temperature in the absorber I,c intermediate temperature in the condenser I,r intermediate temperature in the rectifier ig auxiliary inert gas l saturated liquid state L lowest temperature in evaporator L,max maximum evaporator heat transfer p weak solution r rich solution refr refrigerant v saturated vapor state
temperature from 57.95 to 63.17 C, of higher temperatures at the condenser and of a decrease of the DAR performance. The aim of the present study is to provide a thermodynamic model of the DAR cycle (shown in Fig. 1) with no pure
Fig. 1 e Schematic diagram of the DAR cycle, adapted from Dometic, 2004.
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ammonia as refrigerant assumptions. Several runs of the model were carried out to investigate its potential and to perform a sensitivity analysis to some input parameters.
2.
The DAR model
In the generator, heat (Q_ H in Fig. 1) is supplied to the rich solution to reach the state 2. The hot refrigerant and absorbent vapor mixture arises in the capillary and, at point 4, is separated from the remaining weak liquid solution that returns in the shell of the capillary (state 3). The vapor at state 5, goes through the rectifier and is cooled down to separate most of the absorbent fluid. The remaining near-pure ammonia vapor at state 6 moves toward the condenser where condenses (7). Then it flows to the evaporator entrance (9) after a cooling in the gas heat exchanger (gas HX). The uncondensed refrigerant flows to a reservoir through the gas bypass. At the evaporator entrance, the liquid refrigerant reduces its partial pressure as it mixes with the auxiliary inert gas arriving from the absorber through the gas HX. The resulting mixture leaves the evaporator and the following preheating in the gas HX allows the refrigerant to become a saturated vapor (state 10). Then, the gas-vapor mixture passes through the reservoir, entering the absorber coil from the bottom by flowing upward in a counter-current arrangement to the weak solution, which enters the absorber coil from the top (state 8) through the liquid solution heat exchanger (liquid HX). The refrigerant vapor is absorbed in the weak solution. The resulting rich solution flows to the reservoir. Then it leaves the reservoir (11) toward the generator. The inert gas is not absorbed and returns to the evaporator. Fig. 1 schematizes the DAR circuit. The weak solution (state 3 þ 5) is not reheated in the generator before entering the liquid HX because it passes through a separated pipe. Referring to the Fig. 1, the analytical thermodynamic model presented here is based on the following assumptions: pressure drops along the pipes are negligible; hydrostatic pressures are negligible; the liquid solution (state 3) and the vapor bubbles (state 4) exit the capillary and leave the generator at the same temperature (i.e., T3 ¼ T4 ); the generator is not completely thermally insulated, so a part Q_ H;d of the supplied heat, depending on a variable heat exchanger efficiency, dissipates toward the ambient; in the state 6 the whole refrigerant flowrate is condensed (i.e., no flow in the gas bypass) and becomes a saturated liquid (i.e., no sub-cooling in the condenser); the refrigerant and the rich solution leave respectively the condenser and the reservoir at the same temperature, as the cooling medium is ambient air (i.e., T7 ¼ T11 ); refrigerant and inert gas mixing at the entrance of the evaporator is adiabatic; the refrigerant leaves the gas HX in state 10 as saturated vapor; no absorption takes place inside the reservoir. To extend the model applicability to most of the real situations, no assumptions were made on the pureness of
ammonia vapor in state 6 (i.e., the solution does contain water vapor). In order to determine the state of the working solutions at each point of the cycle, the relations among temperature, pressure, concentration and enthalpy described by Pa´tek and Klomfar (1995) were used. In Table 1 the state properties of the working fluids are resumed. The input parameters to the model are: the temperature of the rich solution entering the generator, T1 ; the temperature reached by the rich solution after heating, T2 ; the temperature of the weak solution and the vapor leaving the generator, T3 ¼ T4 ; the temperature of the refrigerant leaving the rectifier, T6 ; the temperature of the refrigerant leaving the condenser, T7 ;
Table 1 e State properties of working fluids. State 1
2 3
4
5
6
7
8
8,ig 9
10
10,ig
11
Property
Value
p h x p x p h x p h y p T h x p h x p h x p T x p h p T h x p h y p h
p 1 ¼ pc h1 ¼ hl ðT1 ; x1 Þ T1 ¼ Tðpa ; x1 Þ0x1 (by iterations) p 2 ¼ pc x2 ¼ x12 p 3 ¼ pc h3 ¼ hl ðT3 ; x3 Þ T3 ¼ Tðpc ; x3 Þ0x3 (by iterations) p 4 ¼ pc h4 ¼ hv ðT4 ; y4 Þ T4 ¼ Tðpc ; y4 Þ0y4 (by iterations) p 5 ¼ pc T5 ¼ Tðpc ; x5 Þ h5 ¼ hl ðT5 ; x5 Þ y4 ¼ yðpc ; x5 Þ0x5 (by iterations) p 6 ¼ pc h6 ¼ hv ðT6 ; y6 Þ T6 ¼ Tðpc ; y6 Þ0y6 (by iterations) p 7 ¼ pc h7 ¼ hl ðT7 ; x7 Þ x7 ¼ y6 T8 ¼ Tðp8 ; x8 Þ0p8 (by iterations) h8 ¼ hl ðT8 ; x8 Þ0T8 (by iterations) x8 ¼ x3 p8;ig ¼ pc h8;ig ¼ cp;ig ,T8;ig p 9 ¼ pe T9 ¼ Tðp9 ; x9 Þ h9 ¼ hl ðT9 ; x9 Þ x9 ¼ y6 T10 ¼ Tðp10 ; y10 Þ0p10 ¼ pe (by iterations) h10 ¼ hv ðT10 ; y10 Þ y10 ¼ y6 p10;ig ¼ pc pe h10;ig ¼ cp;ig ,T10;ig
p
pa ¼
h x
h11 ¼ hl ðT11 ; x11 Þ x11 ¼ x1
_ r ½xr RNH3 þ ð1 xr ÞRH2 O m p _ ig Rig þ m _ r ½xr RNH3 þ ð1 xr ÞRH2 O c m
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the temperature of the refrigerant and of the auxiliary gas leaving the gas HX, T10 ¼ T10;ig ; the operating pressure, pc ; the heat supplied to the generator, Q_ H ; the temperature of air in the refrigerated chamber, Tair ; _ air . the refrigerated air mass flowrate, m The condition T10 ¼ T10;ig allows to determine the temperature of the refrigerant (as saturated liquid) and the auxiliary gas in the evaporator, T9 ¼ T9;ig . A large number of input variables is necessary to describe the real working operations of the DAR cycle. Most of previous models use fewer input values and, despite the easiness of use, results remain affected by too many assumptions. A great number of input variables, on the contrary, allows to run the model here proposed according to the real DAR cycle operation and to perform better predictions. In Fig. 2, detailed schemes of the evaporator and of the gas HX are shown: hatched contours indicate the presence of thermal insulation. For all the heat exchangers shown in Fig. 1, considering positive the heat supplied to the working solution, and referring to the scheme of the evaporator of Fig. 2, total mass, ammonia mass and energy balances can be written as: 8 _3þm _4 _1¼m > < 4 y45 x5 6 _ _4 m m ¼ 6 Rectifier y6 x5 > > : Q_ ¼ m _ 5 h5 þ m _ 6 h6 m _ 4 h4 I;r _ 6 ðh7 h6 Þ Condenser Q_ I;c ¼ m
x1 ¼ x2 ¼ x11 ¼ xr
(10)
x3 ¼ x8 ¼ xp
(11)
(2)
y6 ¼ x7 ¼ x9 ¼ y10 ¼ yrefr
(12)
(3)
pc pe yrefr RNH3 þ 1 yrefr RH3 O _ refr _ ig ¼ m m pe Rig
(1)
8 _7¼m _9¼m _ 10
8 _ 11 ¼ m _1
Fig. 2 e Scheme of the evaporator and of the gas HX.
if if
(5)
Q_ L Q_ L;max Q_ L > Q_ L;max
where:
(4)
_ 4 h4 jT4
_ _ 11 h11 m _ 10 h10 m _ 8 h8 þ m _ ig h8;ig m _ ig h10;ig Q I;a ¼ m _ 11 h11 m _ 10 h10 m _ 8 h8 þ m _ ig h8;ig m _ ig h10;ig þ Q_ L Q_ L;max Q_ I;a ¼ m
Absorber
if if
Q_ L Q_ L;max Q_ L > Q_ L;max
Q_ L;max ¼ C_ p;min ,DTmax
_1¼m _2¼m _ 11 ¼ m _r m
(7)
_8¼m _p m
(8)
_7¼m _9¼m _ 10 ¼ m _ refr _6¼m m
(9)
(13)
(14)
(6)
(15)
The terms hi jTj ¼Tk and hi jTj
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Table 2 e Differences between the assumptions of the present model and the Zohar’s one. Zohar model
Temperature of the gas mixture in the evaporator
Assumption of a fixed reduction in the fluid temperature along the tube Input value
Thermal insulation of the generator
No heat losses toward the ambient
Fluid composition at the output of the rectifier Weak solution entering the absorber (state 8)
Pure ammonia Equilibrium state
f¼
Q_ L Q_ H
_r m _ refr m
3.
Predictions
3.1.
Comparison with Zohar et al. (2009) model
The evaporator and the gas HX are treated as a single control volume (Fig. 1): the input value is T10 ¼ T10,ig Heat losses (Q_ H;d ) are taken into account with some assumptions of heat transfer toward the ambient Mixture of water and ammonia Not necessarily in the equilibrium state
Advantages Flexible and better description of the real operation of the cycle None
More realistic conditions
More realistic conditions More flexible model
(16)
The maximum differences in results between the Zohar et al. (2009) model and the one here presented are 8.5% in terms of xp , 6.1% of xr and 2.0% of COP. They are due to the pure ammonia as refrigerant (i.e., yrefr ¼ 1) assumption in the model of Zohar et al. (2009). The model here presented, actually, shows an ammonia molar concentration at the vapor refrigerant exit from the rectifier different from 1 (yrefr ¼ 0:985). Considering pure ammonia as refrigerant, therefore, leads to no significant errors when the generator temperatures are approximately up to 170 C; errors increase with T2 , due to a greater water evaporation rate in the generator.
(17)
3.2.
ambient in the generator using Eq. (14)) considers the temperature reduction of the working solution changing its state from 2 to 3 and 4. This is a measure of the imperfect insulation of the generator. In Eq. (15), _ air ,cp;air ; m _ refr ,cp;refr Þ is the minimum value C_ p;min ¼ minðm between heat capacities of the refrigerated air and the refrigerant in the evaporator, and DTmax ¼ Tair T9 is the maximum temperature difference. The performance of the DAR cycle can be calculated in terms of COP and mass flowrates ratio f: COP ¼
T2 and T3 ¼ T4 as input variables
The analytical model was set up with Labview v.8.6 (National Instruments, 2009). In order to test the model consistency, a comparison with results provided by Zohar et al. (2009) was performed. The differences between the assumptions of the model here developed and the Zohar’s one are reported in Table 2. To guarantee a correct comparison, the same operating conditions and working fluids have been adopted:
fluids: ammonia and water; auxiliary inert gas: hydrogen; operating pressure pc ¼ 15:5 bar; maximum evaporator cooling capacity Q_ L;max Q_ L ; temperature of the working solution leaving the generator T3 ¼ T4 ¼ T2 5 C; condensing temperature T7 ¼ 40 C; evaporator inlet temperature T9 ¼ 5 C. Comparisons between weak and rich solution concentrations are depicted in Fig. 3 as temperature T2 goes from 150 to 160 C; COP variations are shown in Fig. 4.
Sensitivity analysis
In Fig. 5, a decrease of mass flowrates ratio f with T2 is shown. This happens as a more intense reduction of the rich solution mass flowrate than that of the refrigerant mass flowrate is present; at higher temperatures this yields to a higher quantity of refrigerant produced per mass of rich solution. Anyway,
xp , xr
Generator’s capillary
Present model
Solution concentrations,
Issue
0.6 0.5 0.4 0.3 0.2 0.1 0.0
xp (Proposed model) xr (Proposed model) xp (Zohar et al.) xr (Zoharet al.)
148 150 152 154 156 158 160 162 Generator temperature,T2 [°C] Fig. 3 e Comparison between the present and the Zohar et al. (2009) models in terms of solution concentrations vs. T2 at constant heat power supplied to the generator.
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0.35
COP
0.33
COP (Proposed model) COP (Zohar et al.)
0.31 0.29 0.27 0.25 148 150 152 154 156 158 160 162 Generator temperature,T2 [°C]
Fig. 4 e Comparison between the present and the Zohar et al. (2009) models in terms of COP vs. T2 at constant heat power supplied to the generator.
the reduction of the refrigerant mass flowrate leads to the COP decrease shown in Fig. 6 for different temperatures of the refrigerant leaving the rectifier. As expected, increasing T6 leads to a reduction of the purity of ammonia in the refrigerant and COP increases as a consequence. Thus, a raise in the rectifier temperature causes an increase in COP, an increase in the water content of the refrigerant, a decrease of the evaporation pressure and an increase of the temperature glide in the evaporator (see also Grossman et al., 1995). This happens because the latent heat of water is higher than that of ammonia. The DAR cycle performance is influenced by the absorption temperature T11 as well. Assuming a fixed geometry of the absorber, T11 results strongly influenced by the ambient temperature (Fig. 7): higher ambient temperatures lead to lower absorption rates of the refrigerant in the absorbent. This, in turn, leads to a decrease of the ammonia concentration in the rich solution entering the generator and, therefore, to a decrease of the refrigerant mass separating from the liquid solution that produces a cooling effect at the evaporator. COP values decrease as well. The heat Q_ H supplied to the generator, as well as the generator and absorption temperatures, influences the DAR
_ r, m _ refr Fig. 5 e Mass flowrates ratio f and mass flowrates m as functions of the generator temperature T2 .
Fig. 6 e COP as a function of the generator temperature T2 for different ammonia concentrations in refrigerant.
cycle performance. COP actually depends on Q_ H for three reasons: 1. the thermal insulation of the generator is not perfect (a part of Q_ H is dissipated toward the ambient); 2. a minimum value of Q_ H is needed to realize the two-phase flow regime in the capillary of the generator, i.e. bubbles begin to form at the inner surface of the tube walls only when a certain value of heat supplied is reached (Jakob et al., 2008); 3. the dimensional and geometrical characteristics limit the maximum evaporator heat transfer. Reasons no. 1 and 2 imply that the working solutions in the generator need a minimum value of heat Q_ H;d supplied to start the cycle. The reason 3 implies that the physical configuration of the evaporator allows the refrigerant to exchange up to a Q_ L;max . Therefore, when this limit is reached, an increase Q_ H þ DQ_ H of heat supplied to generator will not correspond to an increase of energy stored in the fluid; the exceeding power DQ_ H will be dissipated toward the ambient through the absorber. The COP, then, begins to decrease. In Fig. 8, COP and Q_ L are depicted as functions of Q_ H . The heat Q_ L is calculated up to Q_ L;max using Eq. (4). The left field of the graph represents the operation of DAR dominated by the
Fig. 7 e Coefficient of performance COP as a function of the absorption temperature T11 .
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Fig. 8 e COP and Q_ L as functions of the heat Q_ H supplied to the generator.
heat dissipation and flow regime behaviors; the right field that dominated by the evaporator heat transfer limit. These behaviors are important for the design of a DAR cycle. The designer has to carefully take into account the influence of the heat supplied to the generator and the physical configuration of the evaporator. Consequences will be evident for the DAR performance.
4.
Conclusions
An advanced thermodynamic analytical model of the Diffusion Absorption Refrigerator was developed with no assumptions made on the composition of the refrigerant leaving the rectifier. The model was compared with the one by Zohar et al. (2009). The differences between the predictions of the two models vary in the range from 2.0% to 8.5% and are certainly due to the main difference in the assumption concerning the ammonia content in the refrigerant flow. This was assumed as 1 by the Zohar et al. (2009) and, in the present model, comes out form calculations (for the case here reported the value is 0.985). Differences are much less consistent when the generator temperatures are low; mismatches in results increase with T2 due to a greater water evaporation rate in the generator. Compared with the other models in literature (Reistad, 1968; Kouremenos and Stegou-Sagia, 1988; Chen et al., 1996; Srikhirin and Aphornratana, 2002; Al-Shemmeri and Wang, 2003; Maiya, 2003; Zohar et al., 2005,2009), the one presented here uses a higher number of inputs and this lets to describe more real working operations in a wide range of the DAR cycles. The high number of input values leads to an increase of model’s accuracy but, on the other hand, to an higher complexity in use. Some efforts will be done in the future by the authors to reduce the computation complexity, even referring, for real cases, to the results of simulations (to be performed with CFD codes) or to experimentals of heat transfer in real devices. The model was also used to carry out a sensitivity analysis of the DAR cycle performance. The results showed that, as the
611
generator temperature increases, the rich solution mass flowrate decreases more than the refrigerant one. This leads to a decrease of the mass flowrates ratio and to a reduction in COP. The pureness of ammonia in refrigerant is another leading parameter that influences the DAR cycle performance: a higher water content in refrigerant causes a higher COP value. Some problems, on the other hand, could occur in the circuit with water freezing in the evaporator, when a too low evaporation pressure is reached. On the contrary, the COP decreases as the absorption temperature increases, because of the reduction in the absorption rate of the ammonia in the weak solution. The DAR performance is influenced as well by the heat flux supplied to generator: for a small heat power, the heat dissipation toward the ambient and the reduced fluid mass flowrates in the generator dominate and COP values become very small. Vice versa, if Q_ H exceeds the value that allows the evaporator to exchange its maximum power, Q_ L remains constant and COP begins to reduce. As a result, the COP shows its maximum values over a limited range of the heat power supplied to the generator. In the next future an experimental validation campaign will be performed on an instrumented DAR commercial refrigerator.
references
Al-Shemmeri, T., Wang, Y., 2003. Theoretical investigation and parameter study of a diffusion absorption refrigeration system. In: Proceedings of the 21st IIR International Congress of Refrigeration August, Washington D.C., 17e22. Bourseau, P., Mora, J.C., Bugarel, R., 1987. Coupling of absorptiondiffusion refrigeration machine and a solar flat-plate collector. Int. J. Refrigeration 10 (4), 209e216. Chen, J., Kim, K.J., Herold, K.E., 1996. Performance enhancement of a diffusion absorption refrigerator. Int. J. Refrigeration 19, 208e218. Dometicª (formerly known as Electrolux in Europe), 2004. Available from: http://www.dometic.com. Grossman, G., DeVault, R.C., Creswick, F.A., 1995. Simulation and performance analysis of an ammonia-water absorption heat pump based on the generator-absorber heat exchange (GAX) cycle. ASHRAE Trans. 101 (1), 1313e1323. Gutie´rrez, F., 1988. Behaviour of a household a absorptiondiffusion refrigerator adapted to autonomous solar operation. Sol. Energy 40 (1), 17e23. Jakob, U., Eicker, U., Schneider, D., Taki, A.H., Cook, M.J., 2008. Simulation and experimental investigation into diffusion absorption cooling machines for air-conditioning applications. Appl. Therm. Eng. 28, 1138e1150. Keizer, C., 1979. Absorption Refrigeration Machine Driven by Solar Heat. Proceedings of the 15th IIR International Congress of Refrigeration, Venice, pp. 861e868. Kouremenos, D.A., Stegou-Sagia, A., 1988. Measuring the evaporation of NH3 in triple-fluid gas absorption units. Int. J. Refrigeration 11, 153e158. Maiya, M.P., 2003. Studies on Gas Circuit of Diffusion Absorption Refrigerator. Proceedings of the 21st IIR International Congress of Refrigeration August, Washington D.C. National Instruments, 2009. Labview v.8.6. http://www.ni.com/ labview/.
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Pa´tek, J., Klomfar, J., 1995. Simple function for fast calculations of selected thermodynamic properties of ammonia-water system. Int. J. Refrigeration 18 (4), 228e234. Reistad, B., 1968. Thermal conditions in heat driven refrigerating units for domestic use. Sa¨rtryck ur Kylteknisk Tidskrift 3. Srikhirin, P., Aphornratana, S., 2002. Investigation on a diffusion absorption refrigerator. Appl. Therm. Eng. 22, 1181e1193.
Von Platen, B.C., Munters, C.G., 1928. Refrigerator. U.S. Patent 1,685,764. Zohar, A., Jelinek, M., Levy, A., Borde, I., 2005. Numerical investigation of a diffusion absorption refrigerator cycle. Int. J. Refrigeration 28, 515e525. Zohar, A., Jelinek, M., Levy, A., Borde, I., 2009. Performance of diffusion absorption refrigeration cycle with organic working fluids. Int. J. Refrigeration 32 (6), 1241e1246.
Available online at www.sciencedirect.com
w w w . i i fi i r . o r g
journal homepage: www.elsevier.com/locate/ijrefrig
An advanced analytical model of the Diffusion Absorption Refrigerator cycle Giuseppe Starace*, Lorenzo De Pascalis Department of Engineering for Innovation, University of Salento, LECCE, Italy
article info
abstract
Article history:
The results about the performance of a new DAR’s thermodynamic model are compared
Received 7 March 2011
with the predictions of Zohar et al. (2009). The main difference is due to an accurate
Received in revised form
modeling of the refrigerant composition, assumed there as pure ammonia. A sensitivity
29 October 2011
analysis shows that, as the generator temperature increases, the rich solution mass
Accepted 6 November 2011
flowrate reduces more than that of the refrigerant one, and COP decreases. This happens as
Available online 15 November 2011
the absorption temperature increases as well, due to the lower absorption of ammonia in the weak solution. COP was found to increase when the ammonia concentration decreases.
Keywords:
In addition, for lower heat fluxes supplied to the generator, the heat dissipation toward
Adsorption
ambient dominates and COP becomes small; when the heat flux overtakes a threshold, the
Diffusion absorption refrigerator
evaporator reaches its maximum heat transfer, that remains constant for any further
Diffusion system
increase of heat supplied. COP presents its highest values over a limited range of the
Analytical model
generator’s operating conditions.
Refrigeration cycle
ª 2011 Elsevier Ltd and IIR. All rights reserved.
Mode`le analytique de pointe du cycle frigorifique a` absorption a` diffusion Mots cle´s : Adsorption ; Re´frige´rateur a` absorption a` diffusion ; Syste`me a` diffusion ; Mode`le analytique ; Cycle frigorifique
1.
Introduction
The Diffusion Absorption Refrigerator (DAR) cycle was introduced in 1928 by Von Platen and Munters (1928) and uses a binary mixture of ammonia (refrigerant) and water (absorbent) as working fluids in solution with either hydrogen or helium as auxiliary inert gas. The inert gas plays its role to reduce the partial pressure of the refrigerant in the evaporator according to Dalton’s law and to allow the fluid to evaporate
producing the cooling effect. The main characteristic of the DAR is of having no moving parts: a thermally driven pump (also referred to as the generator) acts to circulate the fluid in place of a mechanical device (this is the reason why it is both quiet and reliable). Nowadays, the refrigerator is commercially available only in a small cooling power range up to 100 W, where heat is supplied to the generator by electrical heating cartridges or a direct flame. These characteristics make the DAR small and simple to be built, but not really
* Corresponding author. Dipartimento di Ingegneria dell’Innovazione, Corpo O, via per Monteroni, snc e 73100 Lecce, Italy. Tel.: þ39 0832 297753; fax: þ39 0832 297777. E-mail address: [email protected] (G. Starace). 0140-7007/$ e see front matter ª 2011 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2011.11.007
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Nomenclature A COP cp C_ p;min h _ m p Q_ R T U x y DTmax
2
heat transfer area, m coefficient of performance specific heat at constant pressure, J kg1 K1 minimum heat capacity, J K1 s1 specific enthalpy, J kg1 mass flowrate, kg s1 pressure, Pa heat transfer, W gas constant, J kg1 K1 temperature, K global heat transfer coefficient, W m2 K1 molar concentration of ammonia in liquid solution molar concentration of ammonia in vapor solution maximum temperature difference between refrigerated air and refrigerant in the evaporator, K
efficient with very low COPs and, therefore, with high primary energy consumptions per unit of heat removed. Since the 1930s, the DAR cycle was studied and many authors have proposed papers on its performance and optimization. Up to now, a number of commercial DARs have been investigated. Results showed COPs of 0.2e0.3 and cooling powers between 16 W and 62 W at about 18 to 6 C obtained with temperatures of heat supplied to the generator in the range of 160 and 230 C (Keizer, 1979; Bourseau et al., 1987; Gutierrez, 1988; Jakob et al., 2008). Some methods to calculate graphically and/or numerically or to evaluate experimentally the properties of the working fluids circulating in the refrigerator were carried out by Reistad (1968), Kouremenos and Stegou-Sagia (1988), Chen et al. (1996), Srikhirin and Aphornratana (2002), Al-Shemmeri and Wang (2003) and Maiya (2003). Some of these works present models based on very limiting assumptions and their results frequently diverge from DAR real behavior. Actually when authors compare and fit analytical predictions with their experimental data in order to model the performance of the device, the results of their models can be only referred to those particular cases of DAR circuits. Zohar et al. (2005) proposed a complex thermodynamic model that explored the DAR performance. He and his coauthors found that the maximum COP values reachable with a DAR cycle can be obtained when the ammonia concentrations in rich and weak solutions are respectively 0.25e0.30 and 0.10, and that the generator’s temperature is approximately 200 C. The assumption was that the vapor exiting the rectifier is pure ammonia and no traces of water are present. This is rarely true, due to the not full efficiency of the rectifier in the process of separating the water from the ammonia. In addition to that, it must be pointed out that the temperature of the saturated liquid solution strongly depends on ammonia concentration. For instance, at 25 bar a reduction from 1.00 to 0.90 of the ammonia molar concentration in the liquid solution causes the effect of an increase of the liquid saturation
Subscripts 1.11 states of working solutions a absorption conditions air refrigerated air in evaporation chamber c condensation conditions e evaporation conditions H highest temperature in generator H,d heat dissipated at the highest temperature in the generator I,a intermediate temperature in the absorber I,c intermediate temperature in the condenser I,r intermediate temperature in the rectifier ig auxiliary inert gas l saturated liquid state L lowest temperature in evaporator L,max maximum evaporator heat transfer p weak solution r rich solution refr refrigerant v saturated vapor state
temperature from 57.95 to 63.17 C, of higher temperatures at the condenser and of a decrease of the DAR performance. The aim of the present study is to provide a thermodynamic model of the DAR cycle (shown in Fig. 1) with no pure
Fig. 1 e Schematic diagram of the DAR cycle, adapted from Dometic, 2004.
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ammonia as refrigerant assumptions. Several runs of the model were carried out to investigate its potential and to perform a sensitivity analysis to some input parameters.
2.
The DAR model
In the generator, heat (Q_ H in Fig. 1) is supplied to the rich solution to reach the state 2. The hot refrigerant and absorbent vapor mixture arises in the capillary and, at point 4, is separated from the remaining weak liquid solution that returns in the shell of the capillary (state 3). The vapor at state 5, goes through the rectifier and is cooled down to separate most of the absorbent fluid. The remaining near-pure ammonia vapor at state 6 moves toward the condenser where condenses (7). Then it flows to the evaporator entrance (9) after a cooling in the gas heat exchanger (gas HX). The uncondensed refrigerant flows to a reservoir through the gas bypass. At the evaporator entrance, the liquid refrigerant reduces its partial pressure as it mixes with the auxiliary inert gas arriving from the absorber through the gas HX. The resulting mixture leaves the evaporator and the following preheating in the gas HX allows the refrigerant to become a saturated vapor (state 10). Then, the gas-vapor mixture passes through the reservoir, entering the absorber coil from the bottom by flowing upward in a counter-current arrangement to the weak solution, which enters the absorber coil from the top (state 8) through the liquid solution heat exchanger (liquid HX). The refrigerant vapor is absorbed in the weak solution. The resulting rich solution flows to the reservoir. Then it leaves the reservoir (11) toward the generator. The inert gas is not absorbed and returns to the evaporator. Fig. 1 schematizes the DAR circuit. The weak solution (state 3 þ 5) is not reheated in the generator before entering the liquid HX because it passes through a separated pipe. Referring to the Fig. 1, the analytical thermodynamic model presented here is based on the following assumptions: pressure drops along the pipes are negligible; hydrostatic pressures are negligible; the liquid solution (state 3) and the vapor bubbles (state 4) exit the capillary and leave the generator at the same temperature (i.e., T3 ¼ T4 ); the generator is not completely thermally insulated, so a part Q_ H;d of the supplied heat, depending on a variable heat exchanger efficiency, dissipates toward the ambient; in the state 6 the whole refrigerant flowrate is condensed (i.e., no flow in the gas bypass) and becomes a saturated liquid (i.e., no sub-cooling in the condenser); the refrigerant and the rich solution leave respectively the condenser and the reservoir at the same temperature, as the cooling medium is ambient air (i.e., T7 ¼ T11 ); refrigerant and inert gas mixing at the entrance of the evaporator is adiabatic; the refrigerant leaves the gas HX in state 10 as saturated vapor; no absorption takes place inside the reservoir. To extend the model applicability to most of the real situations, no assumptions were made on the pureness of
ammonia vapor in state 6 (i.e., the solution does contain water vapor). In order to determine the state of the working solutions at each point of the cycle, the relations among temperature, pressure, concentration and enthalpy described by Pa´tek and Klomfar (1995) were used. In Table 1 the state properties of the working fluids are resumed. The input parameters to the model are: the temperature of the rich solution entering the generator, T1 ; the temperature reached by the rich solution after heating, T2 ; the temperature of the weak solution and the vapor leaving the generator, T3 ¼ T4 ; the temperature of the refrigerant leaving the rectifier, T6 ; the temperature of the refrigerant leaving the condenser, T7 ;
Table 1 e State properties of working fluids. State 1
2 3
4
5
6
7
8
8,ig 9
10
10,ig
11
Property
Value
p h x p x p h x p h y p T h x p h x p h x p T x p h p T h x p h y p h
p 1 ¼ pc h1 ¼ hl ðT1 ; x1 Þ T1 ¼ Tðpa ; x1 Þ0x1 (by iterations) p 2 ¼ pc x2 ¼ x12 p 3 ¼ pc h3 ¼ hl ðT3 ; x3 Þ T3 ¼ Tðpc ; x3 Þ0x3 (by iterations) p 4 ¼ pc h4 ¼ hv ðT4 ; y4 Þ T4 ¼ Tðpc ; y4 Þ0y4 (by iterations) p 5 ¼ pc T5 ¼ Tðpc ; x5 Þ h5 ¼ hl ðT5 ; x5 Þ y4 ¼ yðpc ; x5 Þ0x5 (by iterations) p 6 ¼ pc h6 ¼ hv ðT6 ; y6 Þ T6 ¼ Tðpc ; y6 Þ0y6 (by iterations) p 7 ¼ pc h7 ¼ hl ðT7 ; x7 Þ x7 ¼ y6 T8 ¼ Tðp8 ; x8 Þ0p8 (by iterations) h8 ¼ hl ðT8 ; x8 Þ0T8 (by iterations) x8 ¼ x3 p8;ig ¼ pc h8;ig ¼ cp;ig ,T8;ig p 9 ¼ pe T9 ¼ Tðp9 ; x9 Þ h9 ¼ hl ðT9 ; x9 Þ x9 ¼ y6 T10 ¼ Tðp10 ; y10 Þ0p10 ¼ pe (by iterations) h10 ¼ hv ðT10 ; y10 Þ y10 ¼ y6 p10;ig ¼ pc pe h10;ig ¼ cp;ig ,T10;ig
p
pa ¼
h x
h11 ¼ hl ðT11 ; x11 Þ x11 ¼ x1
_ r ½xr RNH3 þ ð1 xr ÞRH2 O m p _ ig Rig þ m _ r ½xr RNH3 þ ð1 xr ÞRH2 O c m
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the temperature of the refrigerant and of the auxiliary gas leaving the gas HX, T10 ¼ T10;ig ; the operating pressure, pc ; the heat supplied to the generator, Q_ H ; the temperature of air in the refrigerated chamber, Tair ; _ air . the refrigerated air mass flowrate, m The condition T10 ¼ T10;ig allows to determine the temperature of the refrigerant (as saturated liquid) and the auxiliary gas in the evaporator, T9 ¼ T9;ig . A large number of input variables is necessary to describe the real working operations of the DAR cycle. Most of previous models use fewer input values and, despite the easiness of use, results remain affected by too many assumptions. A great number of input variables, on the contrary, allows to run the model here proposed according to the real DAR cycle operation and to perform better predictions. In Fig. 2, detailed schemes of the evaporator and of the gas HX are shown: hatched contours indicate the presence of thermal insulation. For all the heat exchangers shown in Fig. 1, considering positive the heat supplied to the working solution, and referring to the scheme of the evaporator of Fig. 2, total mass, ammonia mass and energy balances can be written as: 8 _3þm _4 _1¼m
x1 ¼ x2 ¼ x11 ¼ xr
(10)
x3 ¼ x8 ¼ xp
(11)
(2)
y6 ¼ x7 ¼ x9 ¼ y10 ¼ yrefr
(12)
(3)
pc pe yrefr RNH3 þ 1 yrefr RH3 O _ refr _ ig ¼ m m pe Rig
(1)
8 _7¼m _9¼m _ 10
8 _ 11 ¼ m _1
Fig. 2 e Scheme of the evaporator and of the gas HX.
if if
(5)
Q_ L Q_ L;max Q_ L > Q_ L;max
where:
(4)
_ 4 h4 jT4
_ _ 11 h11 m _ 10 h10 m _ 8 h8 þ m _ ig h8;ig m _ ig h10;ig Q I;a ¼ m _ 11 h11 m _ 10 h10 m _ 8 h8 þ m _ ig h8;ig m _ ig h10;ig þ Q_ L Q_ L;max Q_ I;a ¼ m
Absorber
if if
Q_ L Q_ L;max Q_ L > Q_ L;max
Q_ L;max ¼ C_ p;min ,DTmax
_1¼m _2¼m _ 11 ¼ m _r m
(7)
_8¼m _p m
(8)
_7¼m _9¼m _ 10 ¼ m _ refr _6¼m m
(9)
(13)
(14)
(6)
(15)
The terms hi jTj ¼Tk and hi jTj
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Table 2 e Differences between the assumptions of the present model and the Zohar’s one. Zohar model
Temperature of the gas mixture in the evaporator
Assumption of a fixed reduction in the fluid temperature along the tube Input value
Thermal insulation of the generator
No heat losses toward the ambient
Fluid composition at the output of the rectifier Weak solution entering the absorber (state 8)
Pure ammonia Equilibrium state
f¼
Q_ L Q_ H
_r m _ refr m
3.
Predictions
3.1.
Comparison with Zohar et al. (2009) model
The evaporator and the gas HX are treated as a single control volume (Fig. 1): the input value is T10 ¼ T10,ig Heat losses (Q_ H;d ) are taken into account with some assumptions of heat transfer toward the ambient Mixture of water and ammonia Not necessarily in the equilibrium state
Advantages Flexible and better description of the real operation of the cycle None
More realistic conditions
More realistic conditions More flexible model
(16)
The maximum differences in results between the Zohar et al. (2009) model and the one here presented are 8.5% in terms of xp , 6.1% of xr and 2.0% of COP. They are due to the pure ammonia as refrigerant (i.e., yrefr ¼ 1) assumption in the model of Zohar et al. (2009). The model here presented, actually, shows an ammonia molar concentration at the vapor refrigerant exit from the rectifier different from 1 (yrefr ¼ 0:985). Considering pure ammonia as refrigerant, therefore, leads to no significant errors when the generator temperatures are approximately up to 170 C; errors increase with T2 , due to a greater water evaporation rate in the generator.
(17)
3.2.
ambient in the generator using Eq. (14)) considers the temperature reduction of the working solution changing its state from 2 to 3 and 4. This is a measure of the imperfect insulation of the generator. In Eq. (15), _ air ,cp;air ; m _ refr ,cp;refr Þ is the minimum value C_ p;min ¼ minðm between heat capacities of the refrigerated air and the refrigerant in the evaporator, and DTmax ¼ Tair T9 is the maximum temperature difference. The performance of the DAR cycle can be calculated in terms of COP and mass flowrates ratio f: COP ¼
T2 and T3 ¼ T4 as input variables
The analytical model was set up with Labview v.8.6 (National Instruments, 2009). In order to test the model consistency, a comparison with results provided by Zohar et al. (2009) was performed. The differences between the assumptions of the model here developed and the Zohar’s one are reported in Table 2. To guarantee a correct comparison, the same operating conditions and working fluids have been adopted:
fluids: ammonia and water; auxiliary inert gas: hydrogen; operating pressure pc ¼ 15:5 bar; maximum evaporator cooling capacity Q_ L;max Q_ L ; temperature of the working solution leaving the generator T3 ¼ T4 ¼ T2 5 C; condensing temperature T7 ¼ 40 C; evaporator inlet temperature T9 ¼ 5 C. Comparisons between weak and rich solution concentrations are depicted in Fig. 3 as temperature T2 goes from 150 to 160 C; COP variations are shown in Fig. 4.
Sensitivity analysis
In Fig. 5, a decrease of mass flowrates ratio f with T2 is shown. This happens as a more intense reduction of the rich solution mass flowrate than that of the refrigerant mass flowrate is present; at higher temperatures this yields to a higher quantity of refrigerant produced per mass of rich solution. Anyway,
xp , xr
Generator’s capillary
Present model
Solution concentrations,
Issue
0.6 0.5 0.4 0.3 0.2 0.1 0.0
xp (Proposed model) xr (Proposed model) xp (Zohar et al.) xr (Zoharet al.)
148 150 152 154 156 158 160 162 Generator temperature,T2 [°C] Fig. 3 e Comparison between the present and the Zohar et al. (2009) models in terms of solution concentrations vs. T2 at constant heat power supplied to the generator.
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0.35
COP
0.33
COP (Proposed model) COP (Zohar et al.)
0.31 0.29 0.27 0.25 148 150 152 154 156 158 160 162 Generator temperature,T2 [°C]
Fig. 4 e Comparison between the present and the Zohar et al. (2009) models in terms of COP vs. T2 at constant heat power supplied to the generator.
the reduction of the refrigerant mass flowrate leads to the COP decrease shown in Fig. 6 for different temperatures of the refrigerant leaving the rectifier. As expected, increasing T6 leads to a reduction of the purity of ammonia in the refrigerant and COP increases as a consequence. Thus, a raise in the rectifier temperature causes an increase in COP, an increase in the water content of the refrigerant, a decrease of the evaporation pressure and an increase of the temperature glide in the evaporator (see also Grossman et al., 1995). This happens because the latent heat of water is higher than that of ammonia. The DAR cycle performance is influenced by the absorption temperature T11 as well. Assuming a fixed geometry of the absorber, T11 results strongly influenced by the ambient temperature (Fig. 7): higher ambient temperatures lead to lower absorption rates of the refrigerant in the absorbent. This, in turn, leads to a decrease of the ammonia concentration in the rich solution entering the generator and, therefore, to a decrease of the refrigerant mass separating from the liquid solution that produces a cooling effect at the evaporator. COP values decrease as well. The heat Q_ H supplied to the generator, as well as the generator and absorption temperatures, influences the DAR
_ r, m _ refr Fig. 5 e Mass flowrates ratio f and mass flowrates m as functions of the generator temperature T2 .
Fig. 6 e COP as a function of the generator temperature T2 for different ammonia concentrations in refrigerant.
cycle performance. COP actually depends on Q_ H for three reasons: 1. the thermal insulation of the generator is not perfect (a part of Q_ H is dissipated toward the ambient); 2. a minimum value of Q_ H is needed to realize the two-phase flow regime in the capillary of the generator, i.e. bubbles begin to form at the inner surface of the tube walls only when a certain value of heat supplied is reached (Jakob et al., 2008); 3. the dimensional and geometrical characteristics limit the maximum evaporator heat transfer. Reasons no. 1 and 2 imply that the working solutions in the generator need a minimum value of heat Q_ H;d supplied to start the cycle. The reason 3 implies that the physical configuration of the evaporator allows the refrigerant to exchange up to a Q_ L;max . Therefore, when this limit is reached, an increase Q_ H þ DQ_ H of heat supplied to generator will not correspond to an increase of energy stored in the fluid; the exceeding power DQ_ H will be dissipated toward the ambient through the absorber. The COP, then, begins to decrease. In Fig. 8, COP and Q_ L are depicted as functions of Q_ H . The heat Q_ L is calculated up to Q_ L;max using Eq. (4). The left field of the graph represents the operation of DAR dominated by the
Fig. 7 e Coefficient of performance COP as a function of the absorption temperature T11 .
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Fig. 8 e COP and Q_ L as functions of the heat Q_ H supplied to the generator.
heat dissipation and flow regime behaviors; the right field that dominated by the evaporator heat transfer limit. These behaviors are important for the design of a DAR cycle. The designer has to carefully take into account the influence of the heat supplied to the generator and the physical configuration of the evaporator. Consequences will be evident for the DAR performance.
4.
Conclusions
An advanced thermodynamic analytical model of the Diffusion Absorption Refrigerator was developed with no assumptions made on the composition of the refrigerant leaving the rectifier. The model was compared with the one by Zohar et al. (2009). The differences between the predictions of the two models vary in the range from 2.0% to 8.5% and are certainly due to the main difference in the assumption concerning the ammonia content in the refrigerant flow. This was assumed as 1 by the Zohar et al. (2009) and, in the present model, comes out form calculations (for the case here reported the value is 0.985). Differences are much less consistent when the generator temperatures are low; mismatches in results increase with T2 due to a greater water evaporation rate in the generator. Compared with the other models in literature (Reistad, 1968; Kouremenos and Stegou-Sagia, 1988; Chen et al., 1996; Srikhirin and Aphornratana, 2002; Al-Shemmeri and Wang, 2003; Maiya, 2003; Zohar et al., 2005,2009), the one presented here uses a higher number of inputs and this lets to describe more real working operations in a wide range of the DAR cycles. The high number of input values leads to an increase of model’s accuracy but, on the other hand, to an higher complexity in use. Some efforts will be done in the future by the authors to reduce the computation complexity, even referring, for real cases, to the results of simulations (to be performed with CFD codes) or to experimentals of heat transfer in real devices. The model was also used to carry out a sensitivity analysis of the DAR cycle performance. The results showed that, as the
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generator temperature increases, the rich solution mass flowrate decreases more than the refrigerant one. This leads to a decrease of the mass flowrates ratio and to a reduction in COP. The pureness of ammonia in refrigerant is another leading parameter that influences the DAR cycle performance: a higher water content in refrigerant causes a higher COP value. Some problems, on the other hand, could occur in the circuit with water freezing in the evaporator, when a too low evaporation pressure is reached. On the contrary, the COP decreases as the absorption temperature increases, because of the reduction in the absorption rate of the ammonia in the weak solution. The DAR performance is influenced as well by the heat flux supplied to generator: for a small heat power, the heat dissipation toward the ambient and the reduced fluid mass flowrates in the generator dominate and COP values become very small. Vice versa, if Q_ H exceeds the value that allows the evaporator to exchange its maximum power, Q_ L remains constant and COP begins to reduce. As a result, the COP shows its maximum values over a limited range of the heat power supplied to the generator. In the next future an experimental validation campaign will be performed on an instrumented DAR commercial refrigerator.
references
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Pa´tek, J., Klomfar, J., 1995. Simple function for fast calculations of selected thermodynamic properties of ammonia-water system. Int. J. Refrigeration 18 (4), 228e234. Reistad, B., 1968. Thermal conditions in heat driven refrigerating units for domestic use. Sa¨rtryck ur Kylteknisk Tidskrift 3. Srikhirin, P., Aphornratana, S., 2002. Investigation on a diffusion absorption refrigerator. Appl. Therm. Eng. 22, 1181e1193.
Von Platen, B.C., Munters, C.G., 1928. Refrigerator. U.S. Patent 1,685,764. Zohar, A., Jelinek, M., Levy, A., Borde, I., 2005. Numerical investigation of a diffusion absorption refrigerator cycle. Int. J. Refrigeration 28, 515e525. Zohar, A., Jelinek, M., Levy, A., Borde, I., 2009. Performance of diffusion absorption refrigeration cycle with organic working fluids. Int. J. Refrigeration 32 (6), 1241e1246.