ARTICLE pubs.acs.org/IECR
Dynamic Simulation of an Ammoniawater Absorption Refrigeration System Weihua Cai,† Mihir Sen,* and Samuel Paolucci Department of Aerospace and Mechanical Engineering University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: A dynamic model of a single-effect absorption refrigeration cycle with realistic thermodynamics has been developed. The thermodynamic properties are obtained from the RedlichKwong equation of state for ammonia/water as the refrigerant/ absorbent mixture. The governing ordinary differential equations are derived from the mass, momentum and energy balances for the different components of the system. Lumped parameters are assumed, so that at any instant of time the generator, condenser, evaporator and absorber are each characterized by a single temperature, pressure and concentration. Friction factors are used to calculate pressure drops in the pipes. The transient response of the cycle to a step change in pressure rise across the pump is determined from numerical solutions of the governing equations. The dynamic responses of the mass flow rates, heat rates and the coefficient of performance are shown. The rise time seems to be about two loop circulation times.
1. INTRODUCTION A typical single-effect absorption refrigeration cycle consists of four basic components: an evaporator, an absorber, a generator, and a condenser, as shown in the schematic of Figure 1. The cooling cycle starts at the evaporator, where liquefied refrigerant boils and takes some heat away with it from the evaporator, which produces the “cold” desired in the refrigerated space. The refrigerant vapor releases its latent heat as it is absorbed by a liquid absorbent in the absorber. It is necessary to separate the refrigerant from the absorbent, and this is done in the generator. A pump drives the solution into the generator which is heated by a heat source (e.g., steam, hot water, direct firing, solar cell). The solution is heated and the refrigerant vapor driven out of it. Part of the solution is throttled back into the absorber. A solution heat exchanger, normally located between the absorber and the generator, makes the process more efficient without changing its basic operation. Subsequently, the condenser cools the refrigerant vapor back into the liquid state. The cycle continues after the refrigerant goes through an expansion valve. There have been some papers published on the steady-state and dynamic simulations of absorption refrigeration systems. A computer code ABSIM has been developed for steady-state simulation of absorption systems in a flexible and modular form.1 It has been employed by many users for performing cycle evaluations, testing control strategies, and preliminary design optimization. Detailed distributed models of absorption heat pumps using H2O/NH3 have been developed.2 Step change response of the system has been investigated. In an advanced energy storage system using H2O/LiBr as the working fluid,3,4 dynamic models of the operation have been developed, and the simulation results predicted the dynamic characteristics and performance of the system. An object-oriented dynamic modeling library named ABSML has been designed.5 Numerical simulation have been carried out to predict the transient operating characteristics and performance of an absorption heat pump using H2O/LiBr to recover waste heat.6 A single stage ammoniawater absorption chiller with complete r 2011 American Chemical Society
condensation has been recently studied.7 The simulation of absorption and refrigeration systems is very helpful for understanding and evaluating the system, as well as for system design, operation and control, and device design or selection in detail.814 Modeling the cycle performance requires thermodynamic properties, but equations of state are usually not utilized in the models. Yokozeki15 was the first to perform the steady-state modeling of an absorption-refrigeration cycle using equations of state to calculate thermodynamic properties. In the present work we develop, for the first time, a dynamical model for a single-stage absorption refrigeration cycle, where all thermodynamic properties have been consistently obtained from equations of state for mixtures. The aim of this work is to study the effects of thermodynamic properties on the steady-state performance and dynamic response of an absorption refrigeration cycle. The dynamic results will be of importance for transient conditions, such as start-up, which have not been modeled up to now. The modeling and calculations are carried out for an ammoniawater system for which good data are available.
2. DYNAMIC MODELING 2.1. Governing Equations. Figure 1 shows a schematic of the absorption refrigeration cycle. The principal components of a conventional absorption refrigeration system are generator, condenser, evaporator, and absorber. In the present study, some assumptions are made in developing the dynamic modeling. In the lumped-parameter approach, each component is characterized by a single temperature, pressure, and concentration. The flow in Special Issue: Nigam Issue Received: April 1, 2011 Accepted: June 2, 2011 Revised: June 2, 2011 Published: June 02, 2011 2070
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absorbent mass balances d ðMA CA Þ ¼ m_ 10 C10 m_ 5 C5 dt
ð2aÞ
d ðMG CG Þ ¼ m_ 7 C7 m_ 8 C8 dt
ð2bÞ
C5 ¼ C 6 ¼ C7 ¼ CA
ð2cÞ
C8 ¼ C9 ¼ C10 ¼ CG
ð2dÞ
The momentum equations between the components are given by
Figure 1. Schematic of absorption refrigeration cycle. C = condenser, A = absorber, E = evaporator, G = generator, V1,2 = valves, P = pump.
the pipes is assumed to be one-dimensional, and no diffusion of heat occurs in the flow direction. In addition, there is no heat loss from generator to the surroundings nor heat gain by the evaporator from the surroundings, except the heat transfer from the heat source or to the cooling space. The expansion process in the valve is assumed to occur at constant enthalpy. The coupled governing equations for the complete absorption refrigeration cycle are written by examining the balances of mass, energy, and momentum for the different components in the cycle. Mi(t) is taken to correspond to the mass within component i, and m_ i(t) to the mass flow rate between components, as labeled in Figure.1. Subsequently, the overall mass balances for each component are given by
dm_ 1 1 m_ 1 jm_ 1 j A1 + f1 ¼ ðPG PC Þ dt 2 F1 A1 D1 L1
ð3aÞ
dm_ 2 1 m_ 2 jm_ 2 j A2 + f2 ¼ ðPC PVi 1 Þ dt 2 F2 A2 D2 L2
ð3bÞ
1 1 ξ m_ 2 jm_ 2 j ¼ PVi 1 PVo 1 2 1 F2 A2V1
ð3cÞ
dm_ 3 1 m_ 3 jm_ 3 j A3 o + f3 ¼ ðP PE Þ dt 2 F3 A3 D3 L3 V1
ð3dÞ
dm_ 4 1 m_ 4 jm_ 4 j A4 + f4 ¼ ðPE PA Þ dt 2 F4 A4 D4 L4
ð3eÞ
dm_ 5 1 m_ 5 jm_ 5 j A5 + f5 ¼ ðPA PPi Þ dt 2 F5 A5 D5 L5
ð3f Þ
ΔP ¼ PPo PPi
ð3gÞ
dMC ¼ m_ 1 m_ 2 dt
ð1aÞ
dm_ 6 1 m_ 6 jm_ 6 j A6 o + f6 ¼ ðP PG Þ dt 2 F6 A6 D6 L6 P
ð3hÞ
dME ¼ m_ 3 m_ 4 dt
ð1bÞ
dm_ 9 1 m_ 9 jm_ 9 j A9 + f9 ¼ ðPG PVi 2 Þ dt 2 F9 A9 D9 L9
ð3iÞ
dMA ¼ m_ 4 + m_ 10 m_ 5 dt
ð1cÞ
1 1 ξ m_ 9 jm_ 9 j ¼ PVi 2 PVo 2 2 2 F9 A2V2
ð3jÞ
dMG ¼ m_ 7 m_ 8 m_ 1 dt
ð1dÞ
dm_ 10 1 m_ 10 jm_ 10 j A10 o + f10 ¼ ðP PA Þ 2 F10 A10 D10 dt L10 V2
ð3kÞ
m_ 2 ¼ m_ 3
ð1eÞ
m_ 5 ¼ m_ 6 ¼ m_ 7
ð1f Þ
m_ 8 ¼ m_ 9 ¼ m_ 10
ð1gÞ
where fi is the pipe friction factor (a single correlation relating pipe friction loss to Reynolds number and surface roughness for laminar, transitional, and turbulent flow alike is used16), ξi is the expansion valve friction factor, Li and Di are pipe length and diameter, respectively, Ai is the pipe crosssectional area, and AVi is the smallest cross-sectional area of the expansion valve, Fi is the density, and Pi is the pressure. The superscripts i and o stand for the inlet and outlet of a component, respectively.
Ci(t) is the mass fraction of the absorbent coming out of a component. Subsequently, we have the following
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Table 1. Critical Parameters and EOS Constants of Pure Refrigerants and Absorbents compound Tc (K) Pc (bar)
β0
β1
β2
β3 103 reference
NH3
405.4 113.33 1.0018 0.46017 0.06185
1.68
15
H2O
647.1 220.64 1.0024 0.54254 0.08667
5.25
15
Letting hi(t) be the specific enthalpy, the energy balances for the components are given by d ðMC hC Þ ¼ m_ 1 h1 m_ 2 h2 QC dt
ð4bÞ
d ðMA hA Þ ¼ m_ 4 h4 + m10 h10 m_ 5 h5 QA dt
ð4cÞ
d ðMG hG Þ ¼ m_ 7 h7 m_ 8 h8 m_ 1 h1 + QG dt
ð4dÞ
Qx ¼ m_ 7 h7 m_ 6 h6 ¼ m_ 8 h8 m_ 9 h9
ð4eÞ
m_ 6 h6 ¼ m_ 5 h5 + WP
ð4f Þ
h2 ¼ h3
ð4gÞ
h9 ¼ h10
ð4hÞ
where Qi = FiUiΔTi, Fi is the total heat transfer area, Ui is the overall heat transfer coefficient, ΔTi = Ti Ti,¥, Ti is the temperature of the component, Ti,¥ is the temperature surrounding the component. The pump power is given by
l12
n12
c12
reference
NH3/H2O
0.316
0.013
0
15
where i = A or G. Note that
where F is the total density given by F¼
1 ½xM r + ð1 xÞM a V
ð8Þ
where M r and M a are the molecular masses of the refrigerant and absorbent respectively. Lastly, the mass fractions of the absorbent and refrigerant are given by ð1 xi ÞM i Ci ¼ xi M r + ð1 xi ÞM a
RT a V b V ðV + bÞ
P¼
ð11Þ
where R is the universal gas constant. For a pure species i, parameters ai and bi are given as R 2 Tci2 RTci θi , bi ¼ 0:08664 Pci Pci
ai ¼ 0:42748
ð12Þ
where Tci and Pci are the critical temperature and pressure, and 3 Tci T j θi ¼ βj ð13Þ T Tci j¼0
∑
The subscripts are 1 for NH3 and 2 for H2O. The critical parameters and EOS constants of the pure refrigerant and absorbent are shown in Table 1. For the mixture, the following rules are used15 pffiffiffiffiffiffiffi a¼ xi xj ai aj ½1 gij ðTÞkij ð14aÞ
∑i ∑j
b¼
∑i ∑j xi xj
bi + bj ð1 nij Þ 2
ð14bÞ
where gij ¼ 1 + cij T
ð15aÞ
cij ¼ cji , cii ¼ 0
ð15bÞ
ð6Þ
ð7Þ
ð10Þ
2.2. Equation of State. The theoretical performance of a vapor-absorption refrigeration cycle can be determined once the equation of state is given. A generic RedlichKwong (RK) EOS15 for the mixture is
where V = V/n is the molar volume, V is the total volume, x xr = nr/n is the mole fraction of the refrigerant, n = nr + na is the total number of moles, and nr and na are the number of moles of the refrigerant and absorbent respectively. In addition, it can be noted that the total mass M is given by M ¼ FV
ð1 CÞM i CM r + ð1 CÞM a
xi ¼
ð5Þ
Note that convective heat losses have been neglected in the above model. The above equations are complemented by an equation of state (EOS) P ¼ PðT, V , xÞ
binary system (1)/(2)
ð4aÞ
d ðME hE Þ ¼ m_ 3 h3 m_ 4 h4 + QE dt
WP ¼ m_ 5 ΔP=F5
Table 2. Binary Interaction Parameters of Refrigerant/ Absorbent Pairs Determined from Experimental Pressure, Temperature and Mole Fraction Data
lij lji ðxi + xj Þ , kii ¼ 0 lji xi + lij xj
kij ¼
ð15cÞ
and where cij = cji, lij = lji, and nij = nji are empirical interaction parameters given in Table 2. The enthalpy h is a thermodynamically derived variable given by Z C0pk xk dT Δh0 ð16Þ h¼
∑k
where 0
Z
Δh ¼ RT
ð9Þ 2072
V
2 ¥
∂Z ∂T
dV RTðZ 1Þ V V
ð17Þ
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Table 3. Coefficients for Ideal-Gas Heat Capacity (J mol1 K1) in eq 19a compound
C0
C1
C2
C3
Table 4. Parameters for Steady-State Simulation
reference
NH3
27.31 0.02383
1.707 105 1.185 108
18
H2O
32.24 1.924 103 1.055 105 3.596 109
18
a
Fitted coefficients are based on calculated ideal gas heat capacity from Paulechka et al.19
ð18Þ
¼ C0 + C1 T + C2 T + C3 T 2
3
ξ1
ξ2
AV1,2 (m2)
VC,E,A,G(m3)
0.0254
1
0.1
0.0532
3.142 107
1
F9 A29 D9 ðPG PVi 2 Þ f9 L9
F9 A2 ¼ 2 V2 ðPVi 2 PVo 2 Þ ξ2
is the compressibility. The ideal gas heat capacity at constant pressure for each component is modeled as a polynomial C0p
L1,...,10 (m)
m_ s m_ r ¼ 2
and Z ¼ PV =RT
D1,...,10 (m)
¼2
ð19Þ
F10 A210 D10 o ðPV2 PA Þ f10 L10
ð20mÞ
ð20nÞ ð20oÞ
where the coefficients are given in Table 3.
QC =m_ r ¼ ðh1 h2 Þ
ð20pÞ
3. RESULTS AND DISCUSSION
QE =m_ r ¼ ðh4 h3 Þ
ð20qÞ
QA =m_ r ¼ h4 + ðr 1Þh10 rh5
ð20rÞ
QG =m_ r ¼ h1 rh7 + ðr 1Þh8
ð20sÞ
3.1. Steady State. In the steady-state calculation, the pipe and valve parameters are shown in Table 4. Let m_ r denote the refrigerant mass flow rate, m_ s the solution mass flow rate, and r the mass flow rate recirculation factor. After a sufficiently long time the system relaxes to the following steady state:
m_ 1 ¼ m_ 2 ¼ m_ 3 ¼ m_ 4 ¼ m_ r
ð20aÞ
m_ 5 ¼ m_ 6 ¼ m_ 7 ¼ m_ s
ð20bÞ
m_ 8 ¼ m_ 9 ¼ m_ 10 ¼ m_ s m_ r
ð20cÞ
r
m_ s CG ¼ m_ r CG CA
ð20dÞ ð20eÞ
F2 A22 D2 ðPC PVi 1 Þ f2 L2
ð20f Þ
F2 A2V1 i ðPV1 PVo 1 Þ ξ1
ð20gÞ
F3 A23 D3 o ðPV1 PE Þ f3 L3
ð20hÞ
F A2 D4 ¼ 2 4 4 ðPE PA Þ f4 L 4
ð20iÞ
F5 A25 D5 ðPA PPi Þ f5 L5
ð20jÞ
F A2 D6 ¼ 2 6 6 ðPPo PG Þ f6 L6
ð20kÞ
ΔP ¼ PPo PPi
ð20lÞ
¼2
¼2
m_ s jm_ s j ¼ 2
ð20tÞ
WP =m_ r ¼ rðh6 h5 Þ
ð20uÞ
h2 ¼ h3
ð20vÞ
h9 ¼ h10
ð20wÞ
Substituting eqs 20t and 20u into eq 20s gives QG =m_ r ¼ h1 + ðr 1Þh10 rh5 WP =m_ r
F A 2 D1 m_ r jm_ r j ¼ 2 1 1 ðPG PC Þ f1 L1 ¼2
Qx =m_ r ¼ rðh7 h6 Þ ¼ ðr 1Þðh8 h9 Þ
ð21Þ
To calculate the COP, the following assumptions are made: (1) the condition at Point 4 in Figure 1 (exit of evaporator) is a pure refrigerant dew point with T = TE ; (2) the condition at Point 2 is a refrigerant bubble point and there is no subcooled (saturated) liquid; (3) the condition at Point 1 (inlet to condenser) is a superheated state of a pure refrigerant with T = TG ; (4) the condition at Point 10 (solution inlet to the absorber) is a bubble point for the solution specified with the absorber pressure PA and a solution concentration of the generator CG. These simplifying assumptions are fairly similar to what would be found in a real system. The first step is to obtain PC and PE as saturated vapor pressures of a pure refrigerant at given temperatures of TC and TE. Then, given the pipe geometry and expansion valve specifics, the refrigerant flow rate m_ r is obtained from eqs 20f20h. The pressures PG and PA are obtained from eqs 20e and 20i. Using a suitable method, such as flash calculation,15,17 xG, xA, V G and V A are obtained at the given temperatures TG and TA and pressures PG and PA. Given PC and PE and pipe geometry and expansion valve and flow properties, m_ r is first calculated from eqs 20f20h, and then the mass circulation ratio r can be calculated from eq 9, and therefore m_ s. Then, given PG, PA, m_ s and the piping geometry and flow properties of the strong solution, the pump pressure rise ΔP can be obtained. The thermodynamic properties at point 10 are determined using the bubble-point T-method.15,17 2073
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Table 5. Theoretical Cycle Performancea
a
binary system
PC,G (bar)
PA,E (bar)
r
CG (mass%)
CA (mass%)
QE (kW)
COP
reference
NH3/H2O
15.48
6.15
2.54
59.3
35.5
1111.4
0.645
15
NH3/H2O
15.64
6.19
2.51
59.2
35.7
1109.9
0.642
this work
TG = 100 C, TC = 40 C, TA = 30 C, TE = 10 C, and m_ r = 1 kg/s. Ideal gas heat capacity coefficients taken from Shiflett and Yokozeki.20
Figure 2. COP vs generator temperature.
Figure 4. Mass flow rate ratio versus generator temperature.
Figure 3. COP vs absorber temperature.
Figure 5. Mass flow rate ratio versus absorber temperature.
Enthalpies at other points are obtained from the equation of state with known T, P, V , and x. Now it can be readily shown that the COP for the steady-state cycle operation is given by COP ¼
QE h4 h3 ¼ QG + W P h1 + ðr 1Þh10 rh5
ð22Þ
Taking TG = 100 C, TC = 40 C, TA = 30 C, TE = 10 C, and assuming m_ r = 1 kg/s without loss of generality, the performance of the absorption refrigeration cycle is shown in Table 5. For the NH3/H2O pair, the calculated performance agrees with that of Yokozeki.15 Keeping other temperatures constant, the COP decreases nearly linearly as the temperature of the generator or absorber increases, as shown in Figures 2 and 3. The decrease in COP means that, in the present example, the generator heatinput increases while the evaporator heat (at a fixed temperature) is constant. The mass-flow-rate ratio r behaves in a highly nonlinear fashion but differently due to generator and absorber temperature, as shown in Figures 4 and 5. The steep increase in r at low TG or high TA can be easily understood. The decrease of
temperature difference between TG and TA results in a smaller solubility difference between xG and xA. As a result, the mass flow rate ratio r increases steeply, which can be seen in eq 20d. 3.2. Dynamic Response under Step Change. Next the dynamics of the NH3/H2O pair will be studied. An implicit Euler method with variable step size is implemented for numerical integration. Initially, the absorption refrigeration cycle is at steady state with TG = 100 C, TC = 40 C, TA = 30 C, TE = 10 C. The bulk concentration and temperature of a mixture determine its pressure. A step change is introduced by increasing the pressure rise ΔP across the pump by 5%. As a result, the mass flow rate m_ 5 quickly increases, as shown in Figure 6. It is seen that the system quickly reaches a new steady state. But as the flow rate increases, the frictional loss also increases. The combined result of pressure force and friction results in an overshoot of the flow rate. When more solution flows into the generator, more heat is gained from the high-temperature source, which explains the evolution of QG in Figure 7. As more solution flows into the generator, more refrigerant m_ 4 is generated, as shown in Figure 8. When more refrigerant is generated, more heat is gained from the 2074
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Figure 6. Response of mass flow rate of weak solution for step change.
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Figure 9. Heat transfer rate at evaporator for step change.
Figure 10. Coefficient of performance for step change. Figure 7. Heat transfer rate at generator for step change.
refrigerated space, which explains the increase of QE in Figure 9. The evolution of the COP is shown in Figure 10. This can be explained by the evolution of QE and QG. Both QE and QG increase while more heat goes into the evaporator. Figures 610 all show a similar rise time. Since the refrigerant velocity is about m_ r/FA ≈ 1 m/s, and the time to complete a loop is about 4s, the rise time seems to be about two loop circulation times.
Figure 8. Response of mass flow rate of refrigerant for step change. Dashed line m_ 1; solid line m_ 4.
4. CONCLUSIONS A lumped-parameter dynamic model has been developed for an absorption refrigeration cycle. All thermodynamic properties have been consistently calculated based on an equation of state for mixtures. The usefulness of the EOS model for the absorption refrigeration cycle process has been successfully demonstrated. It is shown that the coefficient of performance of the cycle increases when either generator or absorber temperature decreases. The dynamical response to a step change is also investigated. The system quickly reaches a steady state given the operating parameters for this specific example. The increase of pump 2075
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Caterpillar, Peoria, Illinois 61629, United States.
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(14) Yang, W.-J.; Guo, K. H. Solar-assisted lithium-bromide absorption cooling systems. Proc. NATO Adv. Study Inst. 1987, 409–423. (15) Yokozeki, A. Theoretical performances of various refrigerantabsorbent pairs in a vapor-absorption refrigeration cycle by the use of equations of state. Appl. Energy 2005, 80, 83. (16) Churchill, S. W. Friction-factor equation spans all fluid-flow regimes. Chem. Eng. 1977, 84, 91. (17) Van Ness, H. C.; Abbott, M. M. Classical Thermodynamics of Non-Electrolyte Solutions with Applications to Phase Equilibria; McGrawHill: New York, 1982. (18) Reid, R. C.; Prausnitz, J.; Poling, B. E. The Properties of Gases & Liquids. McGraw-Hill, New York, 4 ed., 1987. (19) Paulechka, Y. U.; Kabo, G. J.; Blokhin, A. V.; Vydrov, O. A.; Magee, J. W.; Frenkel, M. Thermodynamic properties of 1-butyl-3methylimidazolium hexafluorophosphate in the ideal gas state. J. Chem. Eng. Data 2003, 48, 457. (20) Shiflett, M. B.; Yokozeki, A. Absorption cycle utilizing ionic liquid as working fluid, U.S. Patent 20060197053A1, 2006.
’ ACKNOWLEDGMENT Wes thank the U.S. Department of Energy under Contract No. DOE FG02-05CH11294 for support of this work, and Mr. G. Puliti and Drs. J. F. Brennecke, E. J. Maginn, and M. Stadtherr for discussions. ’ REFERENCES (1) Grossman, G.; Zaltash, A. ABSIM—Modular simulation of advanced absorption systems. Int. J. Refrig. 2001, 24, 531. (2) Butz, D. Dynamic behaviour of an absorption heat pump. Int. J. Refrig. 1989, 12, 204. (3) Xu, S. M.; Zhang, L.; Xu, C. H.; Liang, J.; Du, R. Numerical simulation of an advanced energy storage system using H2O-LiBr as working fluid, Part 2: System simulation and analysis. Int. J. Refrig. 2007, 30, 364. (4) Xu, S. M.; Zhang, L.; Xu, C. H.; Liang, J.; Du, R. Numerical simulation of an advanced energy storage system using H2O-LiBr as working fluid, Part 1: System design and modeling. Int. J. Refrig. 2007, 30, 354. (5) Fu, D. G.; Poncia, G.; Lu, Z. Implementation of an objectoriented dynamic modeling library for absorption refrigeration systems. Appl. Therm. Eng. 2006, 26, 217. (6) Jeong, S.; Kang, B. H.; Karng, S. W. Dynamic simulation of an absorption heat pump for recovering low grade waste heat. Appl. Therm. Eng. 1998, 18, 1. (7) Kong, D.; Liu, J.; Zhang, L.; He, H.; Fang, Z. Thermodynamic and experimental analysis of an ammonia-water absorption chiller. Energy Power Eng. 2010, 2, 298. (8) De Lucas, A.; Donate, M.; Rodriguez, J. F. Absorption of water vapor into new working fluids for absorption refrigeration systems. Ind. Eng. Chem. Res. 2007, 46, 345. (9) Sohel, M. I.; Dawoud, B. Dynamic modelling and simulation of a gravity-assisted solution pump of a novel ammonia-water absorption refrigeration unit. Appl. Therm. Eng. 2006, 26, 688. (10) Donate, M.; Rodriguez, L.; De Lucas, A.; Rodriguez, J. F. Thermodynamic evaluation of new absorbent mixtures of lithium bromide and organic salts for absorption refrigeration machines. Int. J. Refrig. 2006, 29, 30. (11) De Lucas, A.; Donate, M.; Molero, C.; Villasenor, J.; Rodriguez, J. F. Performance evaluation and simulation of a new absorbent for an absorption refrigeration system. Int. J. Refrig. 2004, 27, 324. (12) Atmaca, I.; Yigit, A.; Kilic, M. The effect of input temperatures on the absorber parameters. Int. Commun. Heat Mass Transfer 2002, 29, 1177. (13) Vargas, J. V. C.; Horuz, I.; Callander, T. M. S.; Fleming, J. S.; Parise, J. A. R. Simulation of the transient response of heat driven refrigerators with continuous temperature control. Int. J. Refrig. 1998, 21, 48. 2076
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