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Theoretical analysis of a diffusion-absorption refrigerator
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
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Theoretical analysis of a diffusion-absorption refrigerator Ahmed Taieb*, Khalifa Mejbri, Ahmed Bellagi U. R. Thermique et Thermodynamique des Procedes Industriels, Ecole Nationale d'ingenieurs de Monastir (E.N.I.M.), University of Monastir, Tunisia
article info
abstract
Article history:
This paper proposes an elaborated simulation model for an ammonia/water diffusion-
Received 19 March 2016
absorption refrigerator, developed to describe and predict the behavior of the device
Received in revised form
under different operating conditions. This model describes the function of the different
1 June 2016
components of the system, namely condenser, evaporator, absorber, heat-exchangers,
Accepted 17 June 2016
bubble pump, boiler and rectifier. The coefficient of performance of the machine (COP) is
Available online xxx
calculated for different power supply to the refrigerant in the range 100e250 W. It is found that the COP of the machine under the standard operating conditions is about 0.128.
Keywords:
Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Diffusion-absorption refrigerator Model and simulation Water-ammonia-hydrogen Performance
Introduction The Diffusion Absorption Refrigerator (DAR) introduced by Platen and Munters in 1928 [1] has been recognized as an encouraging sustainable technology for the production of cold. The DAR operates at a uniform total pressure level and uses ammonia as refrigerant, water as absorbent and hydrogen as non-absorbable auxiliary inert gas. This inert gas is necessary to reduce the partial pressure of the refrigerant in the evaporator in order to allow the evaporation to occur in the uniform pressure device. A DAR has no moving parts, that is why it is both reliable and inaudible. The circulation of the aqueous ammonia solution is driven by a bubble-pump and that of the gas between absorber and evaporator by natural convection. The first refrigerator of this type was introduced to the market by Electrolux Company in Sweden (also known as Dometic) [2],
and since then, millions of refrigerators have been marketed and used mainly in domestic applications (mini-bar in hotel rooms, refrigerator in camping cars and caravans). The DAR is driven by thermal energy, so no mechanical or electric power is needed. This energy can be provided by fossil fuel combustion (gas, fuel, etc), and for temperatures varying between 90 and 200 C, by industrial waste heat or, even better, by solar energy from evacuated tube collectors. In recent decades the growing concerns about worldwide climate changes, depleting fossil energy sources and environmental sustainability have boosted the research in the environment friendly DAR field [3e12]. The DAR systems have been theoretically and experimentally investigated by various researchers. Chen et al. [13] designed a new generator including a heat-exchanger that re-uses the rejected heat. The new configuration of the cycle showed a slight improvement of the COP (5%). Srikhirin et al. [14] carried out an experimental study on an NH3eH2O DAR
* Corresponding author. Tel.: þ216 52 330 272. E-mail address: [email protected] (A. Taieb). http://dx.doi.org/10.1016/j.ijhydene.2016.06.180 0360-3199/Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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cycle using helium as auxiliary gas. They also developed a mathematical model to determine the optimal operating conditions for maximum performance, and observed that the mass transfer rates in evaporator and absorber affect largely the system performances [15]. The COP of the machine is found to vary in the range 0.09e0.15. Zohar et al. [16] studied two configurations of a DAR with and without sub-cooling the liquid refrigerant leaving the condenser. The results showed that the COP of the cycle without sub-cooling is better by approximately 14e20%. Further, the best performances are obtained when the mass fraction of ammonia in the rich solution varies in the range (0.25e0.40) [16]. In another paper, Zohar et al. [17] simulated the performances of a diffusioneabsorption refrigerator using five alternative refrigerants (R22; R32; R124; R125; R134a) in combination with an organic absorbent (DMAC DiMethylAcetAmide) and helium as inert gas. The obtained results were compared with those of a DAR operating with the system ammonia-water-hydrogen. Once again, helium was found preferable to hydrogen as inert gas. The COP can be higher by 40%. Ben Ezzine et al. [18,19] reported that the R124eDMAC DAR performs better and at lower driving temperatures in comparison to the standard working fluids; they also experimentally investigated a DAR using C4H10eC9H20 as working fluid mixture in combination with helium [13]. Benhmidene et al. [20] used the two-fluid model to investigate the influence of heat input to a uniformly heated bubble pump for different operating conditions. The optimum heat flux was correlated to the tube diameter and mass flow rate, and the minimum required heat flux for pumping to the tube diameter. The same bubble pump configuration was numerically investigated by Garma et al. [21] using the commercial CFD (Computational Fluid Dynamics) package FLUENT. It was found that the onset of boiling is reduced from 0.43 to 0.0016 m when the wall heat input is increased from 25 to 150 k Wm2. Mazouz et al. [22] investigated the cooling capacity of a 20 W commercial absorption diffusion machine in steady state and transient mode with heating powers ranging from 10 to 70 W and ambient temperatures between 20 and 30 C. The best performance of the refrigerator is obtained experimentally with a heat supply of 42 W by a generator temperature of 185 C. The COP of the machine is found equal to 0.12. In the present paper an advanced steady-state model for an ammonia-water-hydrogen diffusion-absorption refrigerator is developed. The cycle performances are theoretically analyzed and evaluated. In particular, a realistic model for the bubble pump is incorporated, and the effects of the heat supply to this machine component as well as those of the temperature of the driving heat and ambient temperature is analyzed. Further, for the estimation of the working fluid mixture the PC-SAFT equation of state is used. The performance of the absorber is evaluated basing on the McCabe and Thiele procedure.
Cycle description The investigated configuration is represented in Fig. 1. The machine is composed mainly of a generator (a thermal bubble pump and a boiler), a rectifier, a condenser, a gas heat-
exchanger (GHX), an expansion chamber, an evaporator, an absorber and a solution heat-exchanger (SHX). To explain the functioning of the machine one can start at the absorber. The weak liquid entering at the top of the absorber coil (15) comes out at the bottom as ammonia-rich liquid (11), after having dissolved the refrigerant from the gaseous mixture circulating counter-currently. The rich solution (11) is accumulated in the solution tank located at the bottom of the absorber. This rich solution moves thereafter to the bubble pump through the solution heat exchanger where it is preheated by the hot weak solution (14) on its way back to the absorber. At the bottom of the vertical tube of the bubble pump, thermal energy at a rate of Q_ P is supplied to the solution to onset its boiling. Small vapor bubbles are formed at the wall of the tube and coalesce during their upward motion to form larger bubbles occupying the entire tube section. During this process they lift-up liquid to the boiler (13). The liquid is pumped high enough to allow it to return to the top of the absorber by gravity. The liquid is further heated in the boiler by a supplementary heat flow Q_ B . Additional vapor is produced (16) this way. The resulting weak solution (14) falls in the absorber by gravity via the SHX. The combined vapor stream (13v þ 16) rises to the rectifier where almost all of the remaining water (17) is removed by partial condensation. The purified ammonia vapor (1) is condensed in the aircooled condenser by rejecting the heat Q_ C to the ambient. The condenser is situated higher than the evaporator, so condensed ammonia flows by gravity from one to the other. Before entering the evaporator in (4), the liquid (2) is precooled in the gas heat exchanger by the cold gas hydrogen/ ammonia gas mixture exiting the evaporator. The gasexchanger and the evaporator are formed by two coaxial tubes: in the central tube flows the rich hydrogen gas from the absorber and in the annular space the cool hydrogen/ ammonia leaving the evaporator. At the entrance of the evaporator, the liquid refrigerant (4) is injected into the inert gas. As a consequence and under appropriate conditions its partial pressure is so reduced that it begins to evaporate at a low temperature producing useful cold at the rate Q_ E . The liquid continues its evaporation as it moves to the evaporator exit. This provokes the cooling of the gaseous phase and the evaporator surroundings (9e10). On the other side, this vaporization process results in a progressive increase of the partial pressure of the ammonia/water system in the gas phase and consequently, a gradual increase of the evaporation temperature in the evaporator. At the evaporator outlet (6), most of the refrigerant liquid is evaporated and the temperature of the resulting liquidevapor mixture reached T6. In the GHX, the cold gas stream provides the sub-cooling of the refrigerant liquid (2) and the hydrogen gas (8). The evaporation of the liquid ammonia is completed in the GHX and enters the absorber (7) as ammonia rich gas mixture. Inside the absorber, the ammonia vapor (7) separates from the hydrogen through absorption by the aqueous ammonia solution (15). The lighter gas (8) returns back to the evaporator. This natural circulation of the gas loop is reinforced by the temperature gradient between absorber and evaporator: hydrogen warms to about 50 C when it passes through the
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Fig. 1 e Schematic diagram of the considered diffusion-absorption machine.
absorber and it cools down to 10 C when it goes through the evaporator.
2 1:69V_ V 0:136V_ V 0:316 V_ L ¼ 1:5 H h
Mathematical and thermodynamic property model Reliable prediction of working fluids properties is of vital importance for the simulation, design and sizing of absorption refrigeration machines [23]. Selection of the appropriate thermodynamic property model is then crucial. Various equations of state have been proposed for the binary system water/ammonia. The most accurate in the temperature and pressure range suitable for the absorption refrigeration is found to the PC-SAFT equation of state [23,24]. This model is then adopted in the present work. In the cold machine components (evaporator, absorber), the working fluid mixture is a ternary system, because of the presence of the inert gas hydrogen. This component is assumed to be immiscible in the liquid phase, this means it remains always in the gas phase. The gas phase is treated as an ideal mixture of real gases [23]. The individual thermodynamic properties of hydrogen are retrieved from the NIST data bank [25] and integrated in the binary mixture model using the equation of state of Younglove [26].
(1)
þ1
Fig. 2 shows the geometrical parameters of the bubble pump. Mass and energy balances for the bubble pump are formulated by Eqs. (2)e(4). n_13 ¼ n_13V þ n_13L ¼ n_12 a13 ¼
x12 x13 n_13V ¼ y13 x13 n_13
Q_ P ¼ n_13 ½a13 h13V þ ð1 a13 Þh13L n_12 h12
(2)
(3)
(4)
Bubble pump and boiler In order to evaluate the pumping capacity in the investigated DAR, the correlation developed by Behringer [27] for a tube diameter d ¼ 4 mm is adopted, relating the pumped liquid volume flow rate V_ L (cm3/s) to the vapor flow rate V_ V (cm3/s) produced and to the submergence ratio ðH=hÞ,
Fig. 2 e Bubble pump configuration.
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_ and Q_ representing respectively liquid and With x, y, a, n, vapor molar composition, vapor fraction in the liquidevapor mixture, molar flow (mol s1), and thermal flow (W). The liquidevapor equilibrium (VLE) is described by the chemical potential. mL;NH3 T80 ; P*80 ; x*80 ¼ mV;NH3 T80 ; P*80 ; y*80 mL;H2 O T80 ; P*80 ; x*80 ¼ mV;H2 O T80 ; P*80 ; y*80
(5) (6)
Absorber The air-cooled absorber is supposed to be at uniform tem~air þ DTAair , with DTAair the pinch between perature T8 ¼ T cooling medium and absorber temperature. The efficiency of the absorber is defined by Eq. (18). EABS ¼
p*7 p*8 yH2 ;8 yH2 ;7 ¼ p*7 p*8min yH2 ;8max yH2 ;7
(18)
The mass and energy balances of the absorber are:
mL and mV express the chemical potential in the liquid and vapor mixture. The mass and energy balances for the boiler are:
n_8 þ n_11 ¼ n_7 þ n_15 þ n_80
(19)
n_14 þ n_16 ¼ n_13L þ n_17
(7)
n_8 y8 þ n_11 x11 ¼ n_7 x7 þ n_15 x15 þ n_80 x80
(20)
n_14 x14 þ n_16 y16 ¼ n_13L x13 þ n_17 x17
(8)
Q_ A ¼ n_8 h8 þ n_11 h11 ðn_15 h15 þ n_7 h7 þ n_80 h80 Þ
(21)
Q_ B ¼ n_14 h14 þ n_16 h16 ðn_13L h13L þ n_17 h17 Þ
(9)
The VLE equations are also written for this machine element.
The VLE is described by two equations similar to Eqs. (5) and (6).
Evaporator and GHX
Solution heat exchanger
Mass and energy balances equations for the GHX and evaporator are the following:
The solution heat exchanger is characterized by its thermal efficiency defined as ESHX ¼ ðT14 T15 Þ=ðT14 T11 Þ. The mass and energy balances for this machine element are:
n_5V þ n_5L ¼ n_6V þ n_6L
(22)
n_5V y5 þ n_5V x5 ¼ n_6V y6 þ n_6L x6
(23)
n_6V yH2 ;6 ¼ n_5V yH2 ;5
(24)
n_6V þ n_6L ¼ n_7
(25)
n_6V y6 þ n_6L x6 ¼ n_7 y7
(26)
n_6V yH2 ;6 ¼ n_7 yH2 ;7
(27)
n_8 þ n_90 ¼ n_80 þ n_9
(28)
n_8 y8 þ n_90 x90 ¼ n_80 x80 þ n_9 y9
(29)
n_9 yH2 ;9 ¼ n_8 yH2 ;8
(30)
n_12 ¼ n_11
(10)
n_15 ¼ n_14
(11)
n_12 h12 þ n_15 h15 ðn_11 h11 þ n_14 h14 Þ ¼ 0
(12)
Rectifier The rectifier is required to purify the ammonia refrigerant vapor (1) up to a desired purity y1. The water rich condensate liquid (17) returning to the boiler is supposed to be saturated at a temperature T17 ¼ T16 5 C. Mass and energy balances of the rectifier are formulated by Eqs. (13)e(15) in association with the VLE condition. . r ¼ n_10 =n_1 ¼ yH2 ;7 yH2 ;10 yH2 ;7
(13)
n_9 y9 ¼ n_90 x90 þ n_10 y10
(31)
n_13V þ n_16 ¼ n_1 þ n_17
(14)
n_9 yH2 ;9 ¼ n_10 yH2 ;10
(32)
Q_ R ¼ n_1 h1 þ n_17 h17 n_13V h13V n_16 h16
(15)
Q_ E ¼ n_4 h4 þ n_6L h6L þ n_6V h6V þ n_90 h90 þ n_10 h10 n_3 h3 ðn_5L h5L þ n_5V h5V Þ n_9 h9
Condenser
(33)
The condenser is air-cooled. A pinch DTCair between the condensation temperature and the air temperature characterizes it. The refrigerant liquid at the outlet (2) is considered to be saturated. The mass and energy balances of the condenser are formulated in Eqs. (16) and (17). n_1 ¼ n_2 ; y1 ¼ x2
(16)
Q_ c ¼ n_2 h2 n_1 h1
(17)
Two VLE equations are added for evaporator and GHX in case of the presence of coexisting vapor and liquid phases.
Results and discussions For the simulation of the machine model a FORTRAN code is developed basing on the non-linear equation subroutine CONLES [28].
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The variance of the configuration of the refrigerating machine shown in Fig. 1 is 31: that means 31 independent data are needed to completely determine its state. A basic set of values of this independent data is given in Table 1. As can be seen, the purity of ammonia in the outlet of the rectifier is assumed to be 99%, the temperature inside the cold space is set to 5 C, the ambient temperature is 26 C assuming that the space containing the refrigerator is air conditioned. The poor solution in the absorber dissolves 80% of the ammonia coming from the evaporator. The power input of the bubble pump and boiler are fixed respectively to 47 W and 128 W. The heat exchangers are characterized either by a thermal pinch or a thermal effectiveness. The submergence ratio is set to 3 [30], the uniform pressure in the DAR is 20.7 bar. The coefficient of performance, COP, is defined as COP ¼
Q_ E _ Q B þ Q_ P
(34)
Table 2 provides the most important simulation results for the considered base data set. The ammonia rich solution leaves the reservoir at a molar composition x11 ¼ 0.334 and a molar flow rate delivered by the thermal bubble pump of n_11 ¼ 0.0111 mol s1 equivalent to a mass flow of 0.196 g s1. In the SHX, the rich solution is preheated by the poor solution to a temperature T12 ¼ 116 C, close to its saturation temperature of 129.7 C. In the heating zone at the bottom of the bubble pump, the supplied heat Q_ P allows the boiling of 8.6% of the liquid solution, the generated vapor serving to pump the remainder of the liquid. The corresponding void fraction of the two-phase flow in the bubble pump tube is estimated by the CISE correlation [31] to about 0.283 [30]; this value corresponds to a slug flow in the bubble pump. At the top of the bubble pump, the saturated liquid and vapor phases at temperature T13 ¼ 140.8 C are separated; the liquid is further heated in the boiler to a temperature T14 ¼ 176.7 C. The vapor, with an average ammonia molar fraction of 0.634, is generated to 78.7% in the boiler and to 21.3% in the bubble pump. In the rectifier, the refrigerant vapor flow raten_1 ¼ 0.00257 mol s1 (0.0438 g s1) is purified up to ammonia molar composition of y1 ¼ 0.99. The water rich condensate (x17 ¼ 0.156) returns to the boiler at the rate of n_17 ¼ 0.0019 mol s1. The heat Q_ R ¼ 73.7 W is rejected to ambient air is of Q_ C ¼ 51 W. The liquid refrigerant at a temperature T4 ¼ 25 C is injected in the expansion chamber, where 34.3% of the liquid is evaporated reducing the hydrogen composition in the gas
Table 1 e Independent data basic values for the cycle simulation. Data
Basic values
y1 Tcf Tamb H/h DTGHX DT6cf DT510 DTABS DTcond DT4cf
0.99 5 C 26 C 3 12 C 10 C 5 C 20 C 25 C 10 C
Data SR3 εAbs εSHX _ Qchexp _ QGHX Q_ P Q_ B
T8 ¼ T80 T16 ¼ T14 T17 ¼ T16 - 5
Basic values 15 C 80% 70% 0 0 47 W 128 W
Table 2 e Base case simulation results. Variables
Values
Variables
Values
P (bar) T5 ( C) T7 ( C) T9 ( C) T12 ( C) T14 ( C) r n_ 5L (mol/s) n_ 6L (mol/s) n_ 6 (mol/s) n_ 8 (mol/s) n_ 80 (mol/s) n_ 9 (mol/s) n_ 90 (mol/s) n_ 10 (mol/s) n_ 13V (mol/s) n_ 13L (mol/s) n_ 14 (mol/s) n_ 16 (mol/s)
20.7 27.4 34 23.6 116 176.7 5.05 0.003 0.001 0.016 0.013 0.0007 0.012 6.10e6 0.012 0.001 0.010 0.013 0.004
n_ 17 (mol/s) x5 yHe5 x6 yHe6 x7 yHe7 y8 x 90 y9 yHe9 x10 yHe10 a5 Q_ R (W) Q_ C (W) Q_ E (W) Q_ A (W) COP (W)
0.0020 0.98666 0.9357 0.96872 0.83827 0.56373 0.8346 0.02394 0.00002 0.00058 0.99659 0.00005 0.99985 0.23749 73.7 51 22.2 74.5 0.128
phase to yH2 ;5 ¼ 0.9357. The two-phase flow is now at the very low temperature T5 ¼ 27.4 C.The expansion chamber is equivalent to an isenthalpic expansion in a vaporcompression refrigerator. The liquid refrigerant continues its evaporation into the inert gas in the annular space producing the useful cold Q_ E ¼ 22.2 W. The temperature at the outlet (6) of the evaporator reaches T6 ¼ 5 C: 9.7% of the refrigerant is still in liquid state. In the annular space of the GHX, the entire liquid refrigerant evaporates and the gas stream becomes superheated at a temperature T7 ¼ 34 C. The absorber coils are equivalent to 4 theoretical stages. The rich ammonia gas at the bottom of the absorber is characterized by a hydrogen molar composition yH2 ;7 ¼ 0.7809 and a molar flow rate n_7 ¼ 0.01545 mol s1. The weak liquid solution injected at the top with a molar composition x15 ¼ 0.1362, at temperature T15 ¼ 85.2 C and with a flow rate n_15 ¼ 0.00852 mol s1. Due to the gas absorption process heat is rejected at the rate Q_ A ¼ 74.5 W. The ammonia rich solution is stored in the reservoir at a molar composition x11 ¼ 0.334. The poor gas stream exits at the top of the absorber with a rate of n_8 ¼ 0.0136 mol s1 and at a temperature T8 ¼ 46 C. Its molar compositions in hydrogen, ammonia and water are, respectively, yH2 ;8 ¼ 0.9460, yNH3 ;8 ¼ 0.0317 and yH2 O;8 ¼ 0.0223. It is noted here that some water is transferred from the liquid phase to the gas phase during the absorption process. During the sub-cooling of the inert gas stream in the GHX central tube, its temperature is reduced to T9 ¼ 23.6 C and the major part of its ammonia and water contents is condensed (yH2 ;9 ¼ 0.99659) and rejoin the absorber at a molar rate of n_80 ¼ 0.00073 mol s1. The inert gas stream continues its subcooling in the evaporator central tube up to T10 ¼ 17.4 C. The gas flow at the expansion chamber inlet is composed of almost pure hydrogen (yH2 ;10 ¼ 0.99985). The circulation ratio of the inert gas and refrigerant in the gas loop is r ¼ 5.05. It should be noted that a significant quantity of cold is dissipated during the purification and sub-cooling of the inert gas in the GHX and evaporator (39.8 W). On the other side, and under the specified operating conditions, the degassing of
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30
0,130
QE (W) COP (W))
25
0,120
20
0,115
15
0,110 60
80
100
120
140
160
180
QE (W)
COP
0,125
10 200
QB (W) Fig. 3 e Variation of COP and Q_ E with Q_ B .
refrigerant in the generator is low and hence, the rich solution flow rate is large compared to that of the refrigerant (4.31 times). This means that the heat supplied to the generator is accordingly large compared to the cooling power. For all these reasons, the COP of a diffusion-absorption refrigerator is normally low, in the present case it is equal 0.126. It must be noted that all these model predicted temperatures are in good agreement with the experimental values measured on similar, but lower capacity refrigerator investigated in our research laboratory [18e22].
Parametric study In Fig. 3, the COP is calculated under the basic conditions listed in Table 1 but by varying the power supply to the boiler Q_ B . It shows that the variation of the COP with Q_ B presents a
maximum, but the refrigerating power Q_ E increases steadily in the operating range. When Q_ B is low, the molar flow of the refrigerant (point 1), n_1 , is relatively small. As Q_ B increases, n_1 also increases. Thus the quantity of ammonia which will evaporate in the evaporator is more important, and hence, Q_ E increases. Thus the COP rapidly gets larger in the area on the left maximum point Q_ B ¼ 128 W and T14 ¼ 174.5 C. With Q_ B becoming larger, the driving temperature T14 also increases provoking the evaporation of additional water with ammonia. Evaporated water is condensed in the rectifier and falls back in the boiler. Thus, part of the heat provided to the boiler is rejected to the atmosphere as condensation heat. Consequently the COP decreases gradually. Q_ E increases since the quantity of ammonia evaporated (1) is more important. 23
0.14
P 22
COP 0.13
21
20
0.11
19
0.10
Psys (bar)
COP
0.12
18
0.09
0.08 18
20
22
24
26
28
17 30
Tair(°C) Fig. 4 e Variation of COP and Psys with Tamb. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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0.14
22 Q (W) COP
0.13 20
18 0.11
0.10
QE (W)
COP
0.12
16
0.09
65
70
75
80
85
Eff
90
95
14 100
(%)
Fig. 5 e Variation of COP and QE with absorber efficiency.
The variation of the COP and the pressure of the system according to the temperature of the cooling medium of the condenser and the absorber, Tamb, are illustrated in Fig. 4. As presented on Fig. 4 the operating pressure of the machine increases quickly with Tamb. When the temperature of the cooling medium increases from 19 to 29 C the pressure increases from 17.2 to 22.3 bar. Indeed, when the Tamb increases, the condensation temperature increases too, necessitating an augmentation of the system pressure. It is clear that the COP always decrease when the temperature of the cooling medium increases. This evolution is due mainly to the variation of the composition of the rich solution obtained at the bottom of the absorber and which strongly depends on the cooling temperature of the absorber. The
simulation results show that when the temperature of the cooling medium increases from 19 to 29 C, the composition of the rich solution decreases from 36% to 33% and the driving temperature rises from 155 to 179 C. Fig. 5 shows the evolution of the coefficient of performance and the cooling capacity with the absorber efficiency. It can be noted that for constant driving heat rate the COP increases first to a maximum value of 0.13 with increasing absorber efficiency and then becomes constant. This rise of the COP is essentially due to augmented circulation of the gas between absorber and evaporator. From an efficiency of the absorber in the range of 83% on, the amount of the absorbed refrigerant becomes constant. On the other hand, the performance of the machine is largely affected by the absorber efficiency: it
0.14 24
COP 0.13
Q (W) 22
0.12 20
18
0.10
QE (W)
COP
0.11
16
0.09
14
0.08
12
0.07 -10
-8
-6
-4
-2
0
2
4
6
T (°C) Fig. 6 e Variation of COP and Q_ E with heat source temperature. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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0,35
xrich, xpoor
0,30
xrich xpoor
0,25
0,20
0,15
0,10 156
159
162
165
168
171
174
177
180
183
T14(°C) Fig. 7 e Ammonia concentration in liquid solution at inlet and outlet of absorber vs. driving temperature.
sharply diminishes when this efficiency gets lower. The cooling capacity increases first to a maximum value of 21 W with the absorber efficiency and then it stagnates. Fig. 6 makes clear that the variation of the COP with evaporation temperature Tcf presents a maximum of 0.134 for Tcf of approximately 5 C. When Tcf is high, the thermal pinch is at the hot end of the GHX. While Tcf decreases, Q_ E almost does not change because the fraction of water increases in flow 9, consequently, part of Q_ E will be used to separate the water which will turn back to the absorber. For this reason, the COP slightly changes to the right part of the maximum point. With Tcf decreasing, the thermal pinch shifts to the cold end of the GHX. The rapid decline of x6 and H6 results in the decline from Q_ E . Consequently, the COP sharply decreases in the left part from the maximum point. Fig. 7 shows the variation of rich and poor solutions concentration with driving temperature T14. As the generator temperature rises, the poor solution concentration sharply changes and that of the rich solution decreases slowly. Further, as the generator temperature increases, more refrigerant desorbs from the rich solution.
Conclusion In this paper an air-cooled diffusion-absorption refrigerating machine operating with ammonia/water/hydrogen as working fluid is theoretically investigated. A simulation model of the machine incorporating a simplified model of the bubble pump is developed to explore the effect of the operating conditions on the machine performances. The COP presents a maximum of 0.128 when heat is supplied to the boiler at the rate of 128 W and to the bubble pump at the rate of 47 W. It is also observed that the COP decreases rapidly with ambient air temperature; its loses 40% of its value when the air temperature increases from 20 to 29 C. This leads to an increase of the system pressure from 17.5 bar to 22.5 bar. The performance of the absorber affects largely the COP of the machine,
particularly in the low range (65e85%). For absorber efficiency higher than 85% the COP is only moderately affected by the absorber performance.
references
[1] Von Platen BC, Munters CG. Refrigerator, US Patent 1, 685,764, 1928. [2] www.dometic.com; 2004. [3] Borg SP, Kelly NJ. The development and calibration of a generic dynamic absorption chiller model. Energy Build 2012;55:533e44. [4] Bouaziz N. Energy and exergy investigation of a novel double effect hybrid absorption refrigeration system for solar cooling. Int J Hydrogen Energy 2015;40:13849e56. mono-pression pour [5] Mazzouz S. Fonctionnement des cycles a tude the orique et expe rimentale d'un pilote le froid solaire : e [PhD thesis]. Tunisia: ENIM-University of Monastir; 2014. absorption a [6] Garma R. Machines frigorifiques a bulle [PhD Thesis]. monopression : Etude de la pompe a Tunisia: ENIM-University of Monastir; 2015. tude [7] Ben Jemaa R. Cycle de Platen et Munters : e rimentale et the orique d’un pilote et analyse en expe dynamique de l’installation [PhD Thesis]. Tunisia: ENIMUniversity of Monastir; 2014. [8] Emre Yuksel Y, Ozturk Mt. Thermodynamic and thermoeconomic analyses of a geothermal energy based integrated system for hydrogen. Int J Hydrogen Energy May 2016. [9] Castello D, Fiori L. Supercritical water gasification of biomass: a stoichiometric thermodynamic model. Int J Hydrogen Energy 2015;40:6771e81. [10] Lima da Silva A, Cezar Heck N. Oxide incorporation into Nibased solid oxide fuel cell anodes for enhanced sulfur tolerance during operation on hydrogen or biogas fuels: a comprehensive thermodynamic study. Int J Hydrogen Energy 2015;40:2334e53. [11] Thanomjit C, Patcharavorachot Y, Ponpesh P, Arpornwichanop A. Thermodynamic analysis of solid oxide fuel cell system using different ethanol reforming processes. Int J Hydrogen Energy 2015;40:6950e8.
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[12] Sun X, Chen M, Hojgaard Jensen S, Dalgaard Ebbesen S, Graves Ch, Mogensen M. Thermodynamic analysis of synthetic hydrocarbon fuel production in pressurized solid oxide electrolysis cells. Int J Hydrogen Energy 2012;37:17101e10. [13] Chen J, Kim KJ, Herold KE. Performance enhancement of a diffusioneabsorption refrigerator. Int J Refrig 1996;19:208e18. [14] Srikhirin P, Aphornratana S. Investigation of a diffusion absorption refrigerator. Appl Therm Eng 2002;22:1181e93. [15] Wilson LS, Carlos AC, Ednildo AT, Jacques CS, Evania CM. Exergoeconomic analysis of a single pressure absorption refrigeration cycle. In: 20th International Congress of Mechanical Engineering, Brazil; 2009. [16] Zohar A, Jelinek M, Levy A, Borde I. The influence of diffusion absorption refrigeration cycle configuration on the performance. Appl Therm Eng 2007;27:2213e9. [17] Zohar A, Jelinek M, Levy A, Borde I. Performance of diffusion absorption refrigeration cycle with organic working fluids. Int J Refrig 2009;32:1241e6. [18] Ben Ezzine N, Garma R, Bellagi A. A numerical investigation of a diffusioneabsorption refrigeration cycle based on R124eDMAC mixture for solar cooling. Energy 2010;35:1874e83. [19] Ben Ezzine N, Garma R, Bourouis M, Bellagi A. Experimental studies on bubble pump operated diffusion absorption machine based on light hydrocarbons for solar cooling. Renew Energy 2010;35:464e70. [20] Benhmidene A, Chaouachi B, Bourouis M, Gabsi S. Effect of operating conditions on the performance of the bubble pump of absorption-diffusion refrigeration cycles. Therm Sci 2011;15:793e806.
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[21] Garma R, Stiriba Y, Bourouis M, Bellagi A. Numerical investigations of the heating distribution effect on the boiling flow in bubble pumps. Int J Hydrogen Energy 2014;39:15256e60. [22] Mazzouz S, Mansouri R, Bellagi A. Experimental and thermodynamic investigation of an ammonia/water diffusion absorption machine. Int J Refrig 2014;45:83e91. [23] Mejbri Kh, Bellagi A. Modelling of the thermodynamic properties of the watereammonia mixture by three different approaches. Int J Refrig 2006;29:211e8. [24] Mejbri Kh, Taieb A, Bellagi A. Phase equilibria calculation of binary and ternary mixtures of associating fluids applying PC-SAFT equation of state. J Supercrit Fluids 2015;104:132e44. [25] Boggs PT, Byrd RH, Rogersand JE, Shnabel RB. User's guide for ODRPACK version 2.01 software for weighted orthogonal distance regression. 1992. NIST, Interagency Report 4834. [26] Younglove BA. Thermophysical properties of fluids. I. Argon, ethylene, parahydrogen, nitrogen, nitrogen trifluoride, and oxygen. J Phys Chem Ref Data 1982;11:1e11. [27] Carl Almen G. Gas absorption refrigerator technology. ABS reftec. 2003. http://www.absreftec.com/index.html [accessed 13.09.12]. [28] Shacham M. Numerical solution of constrained non-linear algebraic equations. Int J Num Methods Eng 1986;23:1455e81. [30] Hewitt GF. Multiphase fluid flow and pressure drop. In: Heat exchanger design handbook. Washington: Hemisphere Publishing Corporation; 1983. 2.3.2e13. [31] Hanafizadeh P, Moezzi M, Saidi MH. Simulation of gas-liquid two phase flow in upriser pipe of gas-lift systems. Energy Equip Syst 2014;2:25e41.
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Theoretical analysis of a diffusion-absorption refrigerator Ahmed Taieb*, Khalifa Mejbri, Ahmed Bellagi U. R. Thermique et Thermodynamique des Procedes Industriels, Ecole Nationale d'ingenieurs de Monastir (E.N.I.M.), University of Monastir, Tunisia
article info
abstract
Article history:
This paper proposes an elaborated simulation model for an ammonia/water diffusion-
Received 19 March 2016
absorption refrigerator, developed to describe and predict the behavior of the device
Received in revised form
under different operating conditions. This model describes the function of the different
1 June 2016
components of the system, namely condenser, evaporator, absorber, heat-exchangers,
Accepted 17 June 2016
bubble pump, boiler and rectifier. The coefficient of performance of the machine (COP) is
Available online xxx
calculated for different power supply to the refrigerant in the range 100e250 W. It is found that the COP of the machine under the standard operating conditions is about 0.128.
Keywords:
Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Diffusion-absorption refrigerator Model and simulation Water-ammonia-hydrogen Performance
Introduction The Diffusion Absorption Refrigerator (DAR) introduced by Platen and Munters in 1928 [1] has been recognized as an encouraging sustainable technology for the production of cold. The DAR operates at a uniform total pressure level and uses ammonia as refrigerant, water as absorbent and hydrogen as non-absorbable auxiliary inert gas. This inert gas is necessary to reduce the partial pressure of the refrigerant in the evaporator in order to allow the evaporation to occur in the uniform pressure device. A DAR has no moving parts, that is why it is both reliable and inaudible. The circulation of the aqueous ammonia solution is driven by a bubble-pump and that of the gas between absorber and evaporator by natural convection. The first refrigerator of this type was introduced to the market by Electrolux Company in Sweden (also known as Dometic) [2],
and since then, millions of refrigerators have been marketed and used mainly in domestic applications (mini-bar in hotel rooms, refrigerator in camping cars and caravans). The DAR is driven by thermal energy, so no mechanical or electric power is needed. This energy can be provided by fossil fuel combustion (gas, fuel, etc), and for temperatures varying between 90 and 200 C, by industrial waste heat or, even better, by solar energy from evacuated tube collectors. In recent decades the growing concerns about worldwide climate changes, depleting fossil energy sources and environmental sustainability have boosted the research in the environment friendly DAR field [3e12]. The DAR systems have been theoretically and experimentally investigated by various researchers. Chen et al. [13] designed a new generator including a heat-exchanger that re-uses the rejected heat. The new configuration of the cycle showed a slight improvement of the COP (5%). Srikhirin et al. [14] carried out an experimental study on an NH3eH2O DAR
* Corresponding author. Tel.: þ216 52 330 272. E-mail address: [email protected] (A. Taieb). http://dx.doi.org/10.1016/j.ijhydene.2016.06.180 0360-3199/Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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cycle using helium as auxiliary gas. They also developed a mathematical model to determine the optimal operating conditions for maximum performance, and observed that the mass transfer rates in evaporator and absorber affect largely the system performances [15]. The COP of the machine is found to vary in the range 0.09e0.15. Zohar et al. [16] studied two configurations of a DAR with and without sub-cooling the liquid refrigerant leaving the condenser. The results showed that the COP of the cycle without sub-cooling is better by approximately 14e20%. Further, the best performances are obtained when the mass fraction of ammonia in the rich solution varies in the range (0.25e0.40) [16]. In another paper, Zohar et al. [17] simulated the performances of a diffusioneabsorption refrigerator using five alternative refrigerants (R22; R32; R124; R125; R134a) in combination with an organic absorbent (DMAC DiMethylAcetAmide) and helium as inert gas. The obtained results were compared with those of a DAR operating with the system ammonia-water-hydrogen. Once again, helium was found preferable to hydrogen as inert gas. The COP can be higher by 40%. Ben Ezzine et al. [18,19] reported that the R124eDMAC DAR performs better and at lower driving temperatures in comparison to the standard working fluids; they also experimentally investigated a DAR using C4H10eC9H20 as working fluid mixture in combination with helium [13]. Benhmidene et al. [20] used the two-fluid model to investigate the influence of heat input to a uniformly heated bubble pump for different operating conditions. The optimum heat flux was correlated to the tube diameter and mass flow rate, and the minimum required heat flux for pumping to the tube diameter. The same bubble pump configuration was numerically investigated by Garma et al. [21] using the commercial CFD (Computational Fluid Dynamics) package FLUENT. It was found that the onset of boiling is reduced from 0.43 to 0.0016 m when the wall heat input is increased from 25 to 150 k Wm2. Mazouz et al. [22] investigated the cooling capacity of a 20 W commercial absorption diffusion machine in steady state and transient mode with heating powers ranging from 10 to 70 W and ambient temperatures between 20 and 30 C. The best performance of the refrigerator is obtained experimentally with a heat supply of 42 W by a generator temperature of 185 C. The COP of the machine is found equal to 0.12. In the present paper an advanced steady-state model for an ammonia-water-hydrogen diffusion-absorption refrigerator is developed. The cycle performances are theoretically analyzed and evaluated. In particular, a realistic model for the bubble pump is incorporated, and the effects of the heat supply to this machine component as well as those of the temperature of the driving heat and ambient temperature is analyzed. Further, for the estimation of the working fluid mixture the PC-SAFT equation of state is used. The performance of the absorber is evaluated basing on the McCabe and Thiele procedure.
Cycle description The investigated configuration is represented in Fig. 1. The machine is composed mainly of a generator (a thermal bubble pump and a boiler), a rectifier, a condenser, a gas heat-
exchanger (GHX), an expansion chamber, an evaporator, an absorber and a solution heat-exchanger (SHX). To explain the functioning of the machine one can start at the absorber. The weak liquid entering at the top of the absorber coil (15) comes out at the bottom as ammonia-rich liquid (11), after having dissolved the refrigerant from the gaseous mixture circulating counter-currently. The rich solution (11) is accumulated in the solution tank located at the bottom of the absorber. This rich solution moves thereafter to the bubble pump through the solution heat exchanger where it is preheated by the hot weak solution (14) on its way back to the absorber. At the bottom of the vertical tube of the bubble pump, thermal energy at a rate of Q_ P is supplied to the solution to onset its boiling. Small vapor bubbles are formed at the wall of the tube and coalesce during their upward motion to form larger bubbles occupying the entire tube section. During this process they lift-up liquid to the boiler (13). The liquid is pumped high enough to allow it to return to the top of the absorber by gravity. The liquid is further heated in the boiler by a supplementary heat flow Q_ B . Additional vapor is produced (16) this way. The resulting weak solution (14) falls in the absorber by gravity via the SHX. The combined vapor stream (13v þ 16) rises to the rectifier where almost all of the remaining water (17) is removed by partial condensation. The purified ammonia vapor (1) is condensed in the aircooled condenser by rejecting the heat Q_ C to the ambient. The condenser is situated higher than the evaporator, so condensed ammonia flows by gravity from one to the other. Before entering the evaporator in (4), the liquid (2) is precooled in the gas heat exchanger by the cold gas hydrogen/ ammonia gas mixture exiting the evaporator. The gasexchanger and the evaporator are formed by two coaxial tubes: in the central tube flows the rich hydrogen gas from the absorber and in the annular space the cool hydrogen/ ammonia leaving the evaporator. At the entrance of the evaporator, the liquid refrigerant (4) is injected into the inert gas. As a consequence and under appropriate conditions its partial pressure is so reduced that it begins to evaporate at a low temperature producing useful cold at the rate Q_ E . The liquid continues its evaporation as it moves to the evaporator exit. This provokes the cooling of the gaseous phase and the evaporator surroundings (9e10). On the other side, this vaporization process results in a progressive increase of the partial pressure of the ammonia/water system in the gas phase and consequently, a gradual increase of the evaporation temperature in the evaporator. At the evaporator outlet (6), most of the refrigerant liquid is evaporated and the temperature of the resulting liquidevapor mixture reached T6. In the GHX, the cold gas stream provides the sub-cooling of the refrigerant liquid (2) and the hydrogen gas (8). The evaporation of the liquid ammonia is completed in the GHX and enters the absorber (7) as ammonia rich gas mixture. Inside the absorber, the ammonia vapor (7) separates from the hydrogen through absorption by the aqueous ammonia solution (15). The lighter gas (8) returns back to the evaporator. This natural circulation of the gas loop is reinforced by the temperature gradient between absorber and evaporator: hydrogen warms to about 50 C when it passes through the
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
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Fig. 1 e Schematic diagram of the considered diffusion-absorption machine.
absorber and it cools down to 10 C when it goes through the evaporator.
2 1:69V_ V 0:136V_ V 0:316 V_ L ¼ 1:5 H h
Mathematical and thermodynamic property model Reliable prediction of working fluids properties is of vital importance for the simulation, design and sizing of absorption refrigeration machines [23]. Selection of the appropriate thermodynamic property model is then crucial. Various equations of state have been proposed for the binary system water/ammonia. The most accurate in the temperature and pressure range suitable for the absorption refrigeration is found to the PC-SAFT equation of state [23,24]. This model is then adopted in the present work. In the cold machine components (evaporator, absorber), the working fluid mixture is a ternary system, because of the presence of the inert gas hydrogen. This component is assumed to be immiscible in the liquid phase, this means it remains always in the gas phase. The gas phase is treated as an ideal mixture of real gases [23]. The individual thermodynamic properties of hydrogen are retrieved from the NIST data bank [25] and integrated in the binary mixture model using the equation of state of Younglove [26].
(1)
þ1
Fig. 2 shows the geometrical parameters of the bubble pump. Mass and energy balances for the bubble pump are formulated by Eqs. (2)e(4). n_13 ¼ n_13V þ n_13L ¼ n_12 a13 ¼
x12 x13 n_13V ¼ y13 x13 n_13
Q_ P ¼ n_13 ½a13 h13V þ ð1 a13 Þh13L n_12 h12
(2)
(3)
(4)
Bubble pump and boiler In order to evaluate the pumping capacity in the investigated DAR, the correlation developed by Behringer [27] for a tube diameter d ¼ 4 mm is adopted, relating the pumped liquid volume flow rate V_ L (cm3/s) to the vapor flow rate V_ V (cm3/s) produced and to the submergence ratio ðH=hÞ,
Fig. 2 e Bubble pump configuration.
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_ and Q_ representing respectively liquid and With x, y, a, n, vapor molar composition, vapor fraction in the liquidevapor mixture, molar flow (mol s1), and thermal flow (W). The liquidevapor equilibrium (VLE) is described by the chemical potential. mL;NH3 T80 ; P*80 ; x*80 ¼ mV;NH3 T80 ; P*80 ; y*80 mL;H2 O T80 ; P*80 ; x*80 ¼ mV;H2 O T80 ; P*80 ; y*80
(5) (6)
Absorber The air-cooled absorber is supposed to be at uniform tem~air þ DTAair , with DTAair the pinch between perature T8 ¼ T cooling medium and absorber temperature. The efficiency of the absorber is defined by Eq. (18). EABS ¼
p*7 p*8 yH2 ;8 yH2 ;7 ¼ p*7 p*8min yH2 ;8max yH2 ;7
(18)
The mass and energy balances of the absorber are:
mL and mV express the chemical potential in the liquid and vapor mixture. The mass and energy balances for the boiler are:
n_8 þ n_11 ¼ n_7 þ n_15 þ n_80
(19)
n_14 þ n_16 ¼ n_13L þ n_17
(7)
n_8 y8 þ n_11 x11 ¼ n_7 x7 þ n_15 x15 þ n_80 x80
(20)
n_14 x14 þ n_16 y16 ¼ n_13L x13 þ n_17 x17
(8)
Q_ A ¼ n_8 h8 þ n_11 h11 ðn_15 h15 þ n_7 h7 þ n_80 h80 Þ
(21)
Q_ B ¼ n_14 h14 þ n_16 h16 ðn_13L h13L þ n_17 h17 Þ
(9)
The VLE equations are also written for this machine element.
The VLE is described by two equations similar to Eqs. (5) and (6).
Evaporator and GHX
Solution heat exchanger
Mass and energy balances equations for the GHX and evaporator are the following:
The solution heat exchanger is characterized by its thermal efficiency defined as ESHX ¼ ðT14 T15 Þ=ðT14 T11 Þ. The mass and energy balances for this machine element are:
n_5V þ n_5L ¼ n_6V þ n_6L
(22)
n_5V y5 þ n_5V x5 ¼ n_6V y6 þ n_6L x6
(23)
n_6V yH2 ;6 ¼ n_5V yH2 ;5
(24)
n_6V þ n_6L ¼ n_7
(25)
n_6V y6 þ n_6L x6 ¼ n_7 y7
(26)
n_6V yH2 ;6 ¼ n_7 yH2 ;7
(27)
n_8 þ n_90 ¼ n_80 þ n_9
(28)
n_8 y8 þ n_90 x90 ¼ n_80 x80 þ n_9 y9
(29)
n_9 yH2 ;9 ¼ n_8 yH2 ;8
(30)
n_12 ¼ n_11
(10)
n_15 ¼ n_14
(11)
n_12 h12 þ n_15 h15 ðn_11 h11 þ n_14 h14 Þ ¼ 0
(12)
Rectifier The rectifier is required to purify the ammonia refrigerant vapor (1) up to a desired purity y1. The water rich condensate liquid (17) returning to the boiler is supposed to be saturated at a temperature T17 ¼ T16 5 C. Mass and energy balances of the rectifier are formulated by Eqs. (13)e(15) in association with the VLE condition. . r ¼ n_10 =n_1 ¼ yH2 ;7 yH2 ;10 yH2 ;7
(13)
n_9 y9 ¼ n_90 x90 þ n_10 y10
(31)
n_13V þ n_16 ¼ n_1 þ n_17
(14)
n_9 yH2 ;9 ¼ n_10 yH2 ;10
(32)
Q_ R ¼ n_1 h1 þ n_17 h17 n_13V h13V n_16 h16
(15)
Q_ E ¼ n_4 h4 þ n_6L h6L þ n_6V h6V þ n_90 h90 þ n_10 h10 n_3 h3 ðn_5L h5L þ n_5V h5V Þ n_9 h9
Condenser
(33)
The condenser is air-cooled. A pinch DTCair between the condensation temperature and the air temperature characterizes it. The refrigerant liquid at the outlet (2) is considered to be saturated. The mass and energy balances of the condenser are formulated in Eqs. (16) and (17). n_1 ¼ n_2 ; y1 ¼ x2
(16)
Q_ c ¼ n_2 h2 n_1 h1
(17)
Two VLE equations are added for evaporator and GHX in case of the presence of coexisting vapor and liquid phases.
Results and discussions For the simulation of the machine model a FORTRAN code is developed basing on the non-linear equation subroutine CONLES [28].
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The variance of the configuration of the refrigerating machine shown in Fig. 1 is 31: that means 31 independent data are needed to completely determine its state. A basic set of values of this independent data is given in Table 1. As can be seen, the purity of ammonia in the outlet of the rectifier is assumed to be 99%, the temperature inside the cold space is set to 5 C, the ambient temperature is 26 C assuming that the space containing the refrigerator is air conditioned. The poor solution in the absorber dissolves 80% of the ammonia coming from the evaporator. The power input of the bubble pump and boiler are fixed respectively to 47 W and 128 W. The heat exchangers are characterized either by a thermal pinch or a thermal effectiveness. The submergence ratio is set to 3 [30], the uniform pressure in the DAR is 20.7 bar. The coefficient of performance, COP, is defined as COP ¼
Q_ E _ Q B þ Q_ P
(34)
Table 2 provides the most important simulation results for the considered base data set. The ammonia rich solution leaves the reservoir at a molar composition x11 ¼ 0.334 and a molar flow rate delivered by the thermal bubble pump of n_11 ¼ 0.0111 mol s1 equivalent to a mass flow of 0.196 g s1. In the SHX, the rich solution is preheated by the poor solution to a temperature T12 ¼ 116 C, close to its saturation temperature of 129.7 C. In the heating zone at the bottom of the bubble pump, the supplied heat Q_ P allows the boiling of 8.6% of the liquid solution, the generated vapor serving to pump the remainder of the liquid. The corresponding void fraction of the two-phase flow in the bubble pump tube is estimated by the CISE correlation [31] to about 0.283 [30]; this value corresponds to a slug flow in the bubble pump. At the top of the bubble pump, the saturated liquid and vapor phases at temperature T13 ¼ 140.8 C are separated; the liquid is further heated in the boiler to a temperature T14 ¼ 176.7 C. The vapor, with an average ammonia molar fraction of 0.634, is generated to 78.7% in the boiler and to 21.3% in the bubble pump. In the rectifier, the refrigerant vapor flow raten_1 ¼ 0.00257 mol s1 (0.0438 g s1) is purified up to ammonia molar composition of y1 ¼ 0.99. The water rich condensate (x17 ¼ 0.156) returns to the boiler at the rate of n_17 ¼ 0.0019 mol s1. The heat Q_ R ¼ 73.7 W is rejected to ambient air is of Q_ C ¼ 51 W. The liquid refrigerant at a temperature T4 ¼ 25 C is injected in the expansion chamber, where 34.3% of the liquid is evaporated reducing the hydrogen composition in the gas
Table 1 e Independent data basic values for the cycle simulation. Data
Basic values
y1 Tcf Tamb H/h DTGHX DT6cf DT510 DTABS DTcond DT4cf
0.99 5 C 26 C 3 12 C 10 C 5 C 20 C 25 C 10 C
Data SR3 εAbs εSHX _ Qchexp _ QGHX Q_ P Q_ B
T8 ¼ T80 T16 ¼ T14 T17 ¼ T16 - 5
Basic values 15 C 80% 70% 0 0 47 W 128 W
Table 2 e Base case simulation results. Variables
Values
Variables
Values
P (bar) T5 ( C) T7 ( C) T9 ( C) T12 ( C) T14 ( C) r n_ 5L (mol/s) n_ 6L (mol/s) n_ 6 (mol/s) n_ 8 (mol/s) n_ 80 (mol/s) n_ 9 (mol/s) n_ 90 (mol/s) n_ 10 (mol/s) n_ 13V (mol/s) n_ 13L (mol/s) n_ 14 (mol/s) n_ 16 (mol/s)
20.7 27.4 34 23.6 116 176.7 5.05 0.003 0.001 0.016 0.013 0.0007 0.012 6.10e6 0.012 0.001 0.010 0.013 0.004
n_ 17 (mol/s) x5 yHe5 x6 yHe6 x7 yHe7 y8 x 90 y9 yHe9 x10 yHe10 a5 Q_ R (W) Q_ C (W) Q_ E (W) Q_ A (W) COP (W)
0.0020 0.98666 0.9357 0.96872 0.83827 0.56373 0.8346 0.02394 0.00002 0.00058 0.99659 0.00005 0.99985 0.23749 73.7 51 22.2 74.5 0.128
phase to yH2 ;5 ¼ 0.9357. The two-phase flow is now at the very low temperature T5 ¼ 27.4 C.The expansion chamber is equivalent to an isenthalpic expansion in a vaporcompression refrigerator. The liquid refrigerant continues its evaporation into the inert gas in the annular space producing the useful cold Q_ E ¼ 22.2 W. The temperature at the outlet (6) of the evaporator reaches T6 ¼ 5 C: 9.7% of the refrigerant is still in liquid state. In the annular space of the GHX, the entire liquid refrigerant evaporates and the gas stream becomes superheated at a temperature T7 ¼ 34 C. The absorber coils are equivalent to 4 theoretical stages. The rich ammonia gas at the bottom of the absorber is characterized by a hydrogen molar composition yH2 ;7 ¼ 0.7809 and a molar flow rate n_7 ¼ 0.01545 mol s1. The weak liquid solution injected at the top with a molar composition x15 ¼ 0.1362, at temperature T15 ¼ 85.2 C and with a flow rate n_15 ¼ 0.00852 mol s1. Due to the gas absorption process heat is rejected at the rate Q_ A ¼ 74.5 W. The ammonia rich solution is stored in the reservoir at a molar composition x11 ¼ 0.334. The poor gas stream exits at the top of the absorber with a rate of n_8 ¼ 0.0136 mol s1 and at a temperature T8 ¼ 46 C. Its molar compositions in hydrogen, ammonia and water are, respectively, yH2 ;8 ¼ 0.9460, yNH3 ;8 ¼ 0.0317 and yH2 O;8 ¼ 0.0223. It is noted here that some water is transferred from the liquid phase to the gas phase during the absorption process. During the sub-cooling of the inert gas stream in the GHX central tube, its temperature is reduced to T9 ¼ 23.6 C and the major part of its ammonia and water contents is condensed (yH2 ;9 ¼ 0.99659) and rejoin the absorber at a molar rate of n_80 ¼ 0.00073 mol s1. The inert gas stream continues its subcooling in the evaporator central tube up to T10 ¼ 17.4 C. The gas flow at the expansion chamber inlet is composed of almost pure hydrogen (yH2 ;10 ¼ 0.99985). The circulation ratio of the inert gas and refrigerant in the gas loop is r ¼ 5.05. It should be noted that a significant quantity of cold is dissipated during the purification and sub-cooling of the inert gas in the GHX and evaporator (39.8 W). On the other side, and under the specified operating conditions, the degassing of
Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
30
0,130
QE (W) COP (W))
25
0,120
20
0,115
15
0,110 60
80
100
120
140
160
180
QE (W)
COP
0,125
10 200
QB (W) Fig. 3 e Variation of COP and Q_ E with Q_ B .
refrigerant in the generator is low and hence, the rich solution flow rate is large compared to that of the refrigerant (4.31 times). This means that the heat supplied to the generator is accordingly large compared to the cooling power. For all these reasons, the COP of a diffusion-absorption refrigerator is normally low, in the present case it is equal 0.126. It must be noted that all these model predicted temperatures are in good agreement with the experimental values measured on similar, but lower capacity refrigerator investigated in our research laboratory [18e22].
Parametric study In Fig. 3, the COP is calculated under the basic conditions listed in Table 1 but by varying the power supply to the boiler Q_ B . It shows that the variation of the COP with Q_ B presents a
maximum, but the refrigerating power Q_ E increases steadily in the operating range. When Q_ B is low, the molar flow of the refrigerant (point 1), n_1 , is relatively small. As Q_ B increases, n_1 also increases. Thus the quantity of ammonia which will evaporate in the evaporator is more important, and hence, Q_ E increases. Thus the COP rapidly gets larger in the area on the left maximum point Q_ B ¼ 128 W and T14 ¼ 174.5 C. With Q_ B becoming larger, the driving temperature T14 also increases provoking the evaporation of additional water with ammonia. Evaporated water is condensed in the rectifier and falls back in the boiler. Thus, part of the heat provided to the boiler is rejected to the atmosphere as condensation heat. Consequently the COP decreases gradually. Q_ E increases since the quantity of ammonia evaporated (1) is more important. 23
0.14
P 22
COP 0.13
21
20
0.11
19
0.10
Psys (bar)
COP
0.12
18
0.09
0.08 18
20
22
24
26
28
17 30
Tair(°C) Fig. 4 e Variation of COP and Psys with Tamb. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
0.14
22 Q (W) COP
0.13 20
18 0.11
0.10
QE (W)
COP
0.12
16
0.09
65
70
75
80
85
Eff
90
95
14 100
(%)
Fig. 5 e Variation of COP and QE with absorber efficiency.
The variation of the COP and the pressure of the system according to the temperature of the cooling medium of the condenser and the absorber, Tamb, are illustrated in Fig. 4. As presented on Fig. 4 the operating pressure of the machine increases quickly with Tamb. When the temperature of the cooling medium increases from 19 to 29 C the pressure increases from 17.2 to 22.3 bar. Indeed, when the Tamb increases, the condensation temperature increases too, necessitating an augmentation of the system pressure. It is clear that the COP always decrease when the temperature of the cooling medium increases. This evolution is due mainly to the variation of the composition of the rich solution obtained at the bottom of the absorber and which strongly depends on the cooling temperature of the absorber. The
simulation results show that when the temperature of the cooling medium increases from 19 to 29 C, the composition of the rich solution decreases from 36% to 33% and the driving temperature rises from 155 to 179 C. Fig. 5 shows the evolution of the coefficient of performance and the cooling capacity with the absorber efficiency. It can be noted that for constant driving heat rate the COP increases first to a maximum value of 0.13 with increasing absorber efficiency and then becomes constant. This rise of the COP is essentially due to augmented circulation of the gas between absorber and evaporator. From an efficiency of the absorber in the range of 83% on, the amount of the absorbed refrigerant becomes constant. On the other hand, the performance of the machine is largely affected by the absorber efficiency: it
0.14 24
COP 0.13
Q (W) 22
0.12 20
18
0.10
QE (W)
COP
0.11
16
0.09
14
0.08
12
0.07 -10
-8
-6
-4
-2
0
2
4
6
T (°C) Fig. 6 e Variation of COP and Q_ E with heat source temperature. Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e9
0,35
xrich, xpoor
0,30
xrich xpoor
0,25
0,20
0,15
0,10 156
159
162
165
168
171
174
177
180
183
T14(°C) Fig. 7 e Ammonia concentration in liquid solution at inlet and outlet of absorber vs. driving temperature.
sharply diminishes when this efficiency gets lower. The cooling capacity increases first to a maximum value of 21 W with the absorber efficiency and then it stagnates. Fig. 6 makes clear that the variation of the COP with evaporation temperature Tcf presents a maximum of 0.134 for Tcf of approximately 5 C. When Tcf is high, the thermal pinch is at the hot end of the GHX. While Tcf decreases, Q_ E almost does not change because the fraction of water increases in flow 9, consequently, part of Q_ E will be used to separate the water which will turn back to the absorber. For this reason, the COP slightly changes to the right part of the maximum point. With Tcf decreasing, the thermal pinch shifts to the cold end of the GHX. The rapid decline of x6 and H6 results in the decline from Q_ E . Consequently, the COP sharply decreases in the left part from the maximum point. Fig. 7 shows the variation of rich and poor solutions concentration with driving temperature T14. As the generator temperature rises, the poor solution concentration sharply changes and that of the rich solution decreases slowly. Further, as the generator temperature increases, more refrigerant desorbs from the rich solution.
Conclusion In this paper an air-cooled diffusion-absorption refrigerating machine operating with ammonia/water/hydrogen as working fluid is theoretically investigated. A simulation model of the machine incorporating a simplified model of the bubble pump is developed to explore the effect of the operating conditions on the machine performances. The COP presents a maximum of 0.128 when heat is supplied to the boiler at the rate of 128 W and to the bubble pump at the rate of 47 W. It is also observed that the COP decreases rapidly with ambient air temperature; its loses 40% of its value when the air temperature increases from 20 to 29 C. This leads to an increase of the system pressure from 17.5 bar to 22.5 bar. The performance of the absorber affects largely the COP of the machine,
particularly in the low range (65e85%). For absorber efficiency higher than 85% the COP is only moderately affected by the absorber performance.
references
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Please cite this article in press as: Taieb A, et al., Theoretical analysis of a diffusion-absorption refrigerator, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.06.180