Accepted Manuscript Absorption solar cooling systems using optimal driving temperatures Antonio Lecuona, Rubén Ventas, Ciro Vereda, Ricardo López PII:
S13594311(15)000162
DOI:
10.1016/j.applthermaleng.2014.10.097
Reference:
ATE 6280
To appear in:
Applied Thermal Engineering
Received Date: 24 June 2014 Revised Date:
22 September 2014
Accepted Date: 26 October 2014
Please cite this article as: A. Lecuona, R. Ventas, C. Vereda, R. López, Absorption solar cooling systems using optimal driving temperatures, Applied Thermal Engineering (2015), doi: 10.1016/ j.applthermaleng.2014.10.097. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Absorption solar cooling systems using optimal driving temperatures Antonio Lecuona*, Rubén Ventas, Ciro Vereda, Ricardo López. Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911 Leganés, Madrid, Spain. * Tel: (34) 916249475; Fax: (34) 91 624 9430; email:
[email protected]
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10 11 12 13 14
Abstract
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along a day. The chillers compared use single effect cycles working with NH3/LiNO3,
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either conventional or hybridised by incorporating a low pressure booster compressor.
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Their performances are compared with a H2O/LiBr single effect absorption chiller as
18
part of the same solar system. The results of a detailed thermodynamic cycle for the
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absorption chillers allow synthesizing them in a modified characteristic temperature
20
difference model. The day accumulated solar cold production is determined using this
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optimum temperature during two sunny days in midJuly and midSeptember, located in
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Madrid, Spain. The work shows the influences of operational variables and a striking
23
result: selection of a timeconstant temperature during all the day does not necessarily
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imply a substantial loss, being the temperature chosen a key parameter. The results
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indicate that the NH3/LiNO3 option with no boosting offers a smaller production above
26
zero Celsius degrees temperatures, but does not require higher hot water driving
27
temperatures than H2O/LiBr. The boosted cycle offers superior performance. Some
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operational details are discussed.
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The optimum instantaneous driving temperature of a solar cooling facility is determined
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Keywords: solar cooling, optimum hot water temperature, hybrid cycle, chillers,
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NH3/LiNO3, H2O/LiBr.
32
Nomenclature
33 a
Absorber; Constant
35
As
Collector area, m2
36
b
Constant
37
COP Coefficient of performance
38
COPe Electrical coefficient of performance
39 40 41
COPM Asymptotic value for COP when ∆∆t → ∞. c
Condenser
42
e
Evaporator
43
g
Generator
44
GT
Solar intensity, tilted, W/m2
45
h
Specific enthalpy, external fluid, J kg1
46
H
Specific enthalpy, internal fluid, J kg1
47
m&
Mass flow rate, external fluid, kg/s
48
M&
Mass flow rate, internal fluid, kg/s
49
P
50
pr
51
Q
52
Q&
53
SCOP Solar coefficient of performance
54
SE
Singleeffect
55
she
Solution heat exchanger
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Pressure, Pa
Pressure ratio of booster compressor
Daily solar cold production, J/m2
Heat power, W
2
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Averaged external fluid temperature between inlet and outlet, ºC
57
t’e
Equivalent external fluid temperature averaged between inlet and outlet, ºC
58
tg,op
Optimum external generator temperature averaged between inlet and outlet, ºC
59
tg,0
Activation external generator temperature averaged between inlet and outlet, ºC
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T
Averaged internal fluid temperature between inlet and outlet, ºC
61
T’e
Equivalent internal fluid temperature averaged between inlet and outlet, ºC
62
UA
Heat exchanger thermal conductivity, W/ºC
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Mechanical power to the booster compressor W
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64 Greek
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∆∆t
Characteristic temperature difference, ºC
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∆Tml
Mean logarithmic temperature difference, ºC
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ε
Efficiency of heat exchanger in the solar facility
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η
Isentropic efficiency of the compressor
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70 Subscripts
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a
Absorber
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ac
AbsorberCondenser
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atm
Atmospheric
75
c
Condenser
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e
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g
Generator
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i
Inlet
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o
Outlet
80
r
Solution or refrigerant, internal fluid of the absorption chiller
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Evaporator
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s
solution
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she
Solution heat exchanger, State at the outlet of the absorption pump
83
w
water, external fluid of the absorption chiller
84
x
Components of the absorption chiller: a, c, e, g
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85 1. Introduction
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The use of absorption chillers to produce cold by means of solar thermal energy has
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generated a high interest in the last decades; e. g. Zhai et al. [1] and Boophathi Raja and
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Shanmugam [2] among others, where the importance of the three temperatures of
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interchange of the absorption chiller is highlighted. The solar collectors produce hot
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water that drives the chiller. The synchronicity between heat production and cold
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demand makes this technology very attractive. The solar irradiance has a nonsteady
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behaviour during the day what makes necessary to actively control the system. The
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solar thermal collectors exhibit a continuously decaying efficiency for collecting heat
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with an increase of the temperature of the flowing water inside them. On the other hand
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the conversion efficiency of the collected heat into cold by the absorption machine
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(COP) typically exhibits a continuously increasing value when the hot water
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temperature increases within the reasonable operating range, e. g. FernándezSeara and
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Vázquez [3]. A further increase eventually leads to a slight decrease in COP that
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obviously is not of interest in this case; moreover some authors do not report this
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decrease, e. g. Sun [4]. Thus, a water temperature exists that results in maximum
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conversion of solar energy into cooling energy, quantified by SCOP, Eq. (14). Such
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optimum value depends on operating and environmental variables, and varies
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throughout the day. A suitable optimum driving temperature has been explored in the
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past with different aims and different methodologies. Albers [5] performs a theoretical
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ACCEPTED MANUSCRIPT and experimental study where both the driving and recooling (absorber and condenser)
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temperatures are controlled with the aim of minimizing the total cost of solar cooling.
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This cost is the addition of fixed plus variable cost, including backup heat from a
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district heating network and recooling fan electric consumption. Minimization was
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performed with a specified cooling water temperature and cooling capacity (load). The
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optimization algorithm is based on a modified characteristic temperature difference
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method ∆∆t as the design variable, which will be explained in Section 2. It was
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enhanced by considering internal variable losses of the real absorption machine to better
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follow its performances, instead of constant values as in the original method. This
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modification requires additional internal data from the machine, what is an undesirable
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condition for commercial application. In [6] Li et al. perform a theoretical study of the
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dependence of SCOP on the hot water temperature, evaporator temperature and
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recooling temperature, for constant hot water flow rate and a simplified CPC collector
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efficiency equation. A numerically solved thermodynamic absorption cycle represents a
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generic double effect machine. From this study the optimum monthly average hot water
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temperature is deduced for a single specific subtropical location. More straightforward
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criteria for optimization seem desirable, especially for online control.
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The optimum driving temperature has been already analytically made explicit and
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applied to commercial H2O/LiBr absorption chillers, Lecuona et al. [7] using the
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concept of an empirical characteristic temperature difference ∆∆t [8], Kühn and Ziegler,
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defined in Eq. (1). The experimentally obtained ∆∆t serves to describe the cooling
127
power of the absorption chiller [8], and it is able to describe different commercial
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absorption chillers, in both the configuration of single and double effect, as it has been
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demonstrated by PuigArnavat et al. in [9], with advantages over other approximate
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[10] by GutiérrezUrueta et al. underlining the usefulness of the concept.
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The most common working pair used in absorption chillers for airconditioning is
133
H2O/LiBr. This working pair yields a good performance for airconditioning
134
temperatures but it risks of crystallizing and it cannot produce cold under 0 ºC
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temperatures. For temperatures under 0 ºC the common working fluid is NH3/H2O.
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There is an alternative working fluid, NH3/LiNO3. This pair does not need a
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rectification tower, reaches a higher efficiency in single effect cycles, e. g. Sun [11], and
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does not suffer from crystallization risk, so that a dry cooling tower is possible. In
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addition, the absence of water with this working fluid offers a low risk of corrosion.
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NH3 is a natural refrigerant and LiNO3 is an inorganic salt; neither of them does
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represent an environmental hazard when recycled at the end of their long operating life.
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Some experimental works show the good performance of this working solution [1215].
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In [12] Antonopoulus and Rogdakis show that LiNO3 is superior to other salts with
144
NH3. In [13] LlamasGuillén et al. show the feasibility for high recooling temperatures.
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New absorbing technologies for this working pair have been explored in [14] and [15]
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by Zacarías et al. for coping with the high viscosity of this fluid at low temperatures.
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They take advantage of the high pressure differential.
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In order to produce cold when the solar irradiance is not enough to satisfy the cold
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demand it is necessary to use additional chillers, generally consuming electricity. This
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independent backup system increases cost and complexity, difficulting the solar cooling
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implementation. Burning a fossil fuel for helping the absorption chiller drive means net
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direct and indirect CO2 emissions that can be higher than using mechanical compression
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cooling, at least for singleeffect absorption cycles, Fig 1 a. For a more widespread
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ACCEPTED MANUSCRIPT implementation of solar cooling it seems that an integrated approach is needed. To this
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end the hybridization of an absorption cycle with a mechanical compression cycle has
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been attempted, using a parallel configuration of a mechanical and a thermochemical
157
compressor, e. g. Morawetz [16], but with nonknown practical implementations up to
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now. The idea is simple, when the refrigerant production by the solar driven absorption
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cycle is not enough, extra cooling capacity can be produced in parallel by the
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electrically driven mechanical compressor, sharing the condenser and evaporator.
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Interactions between both cycles have not been much studied. The very large specific
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volume of H2O vapour at the usual working temperatures precludes basing the hybrid
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cycle on the H2O/LiBr working pair. On the other hand, the working pair NH3/LiNO3
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offers the possibility of hybridization as there is much experience on the suitable NH3
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compressors; the pressure levels are acceptable and oilless compressors and pumps are
166
available.
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Ventas et al. [17] showed another possibility of hybridization by pressure boosting a
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single effect absorption cycle, Fig 1 b. In this configuration the compressor is installed
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between the evaporator and the absorber keeping the same evaporation temperature (and
170
pressure) but forcing a higher absorption pressure, in favour of the absorption process.
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The resulting electrical COP (COPe) is high, e. g. [17]. Considering the same upper part
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of the cycle, the result is a wider concentration change in the absorber and consequently
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a higher cooling capacity for the same external temperatures. Modulating the booster
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compressor pressure ratio pr gives control of the refrigerant mass flow, thus allowing a
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control of the cooling capacity. From another perspective, the NH3/LiNO3 pair has been
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studied for this configuration allowing to reduce the driving temperature up of 24 ºC for
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pr = 2.0, maintaining the same COP and cooling capacity as the regular single effect
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ACCEPTED MANUSCRIPT cycle [17]. That reduction in temperature seems to be interesting for improving the
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overall efficiency of a solar cooling facility. If a reduction in driving temperature is not
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the scope of boosting, an increase in cooling capacity is observed for the same external
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temperatures. Thus, pressure boosting offers an additional controllable degree of
182
freedom for absorption machines for increasing capacity without wasting solar heat.
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Another cycle that has been studied with NH3/LiNO3 allowing increasing the pressure
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of the absorber is the use of an ejector within the cycle; only as a booster [18] or as a
185
simultaneous adiabatic absorber [19], both by Vereda et al.
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Within this framework, the aim of this work is to obtain and to discuss how the
187
optimum hot water temperature evolves during reference sunny days, in this case for
188
Madrid, central Spain, using the most common technology available: the combination of
189
high efficiency flat plate collectors and single effect machines. From these results the
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possible strategies of temperature control for obtaining the maximum cold production
191
are studied. Three types of absorption chillers are studied and the results are compared
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in order to know their behaviour for a common airconditioning purpose: 1) H2O/LiBr
193
single effect absorption chiller; 2) NH3/LiNO3 single effect absorption chiller; and 3)
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NH3/LiNO3 single effect absorption chiller hybridized with a low pressure compressor
195
booster [17]. To allow the same basis for comparison, the data needed are obtained in
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all cases from a detailed thermodynamic cycle and their behaviour is synthesized by
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means of the modified characteristic temperature difference ∆∆t so that a
198
straightforward calculation and optimization is allowed, even for the hybrid cycle. The
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outcome of this first study is of use to establish strategies for controlling the absorption
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machines in a solar cooling arrangement and gives the maximum production profile
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along the day. Also it will indicate whether the emerging NH3/LiNO3 working pair is
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203
efficiency and operating temperature for the solar collectors. Moreover, this paper
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quantifies the gain obtained by hybridizing this cycle with a low pressure compressor
205
booster.
206
2. ∆∆t model for the absorption chillers
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2.1. ∆∆t of 1) H2O/LiBr and 2) NH3/LiNO3 conventional single effect absorption chiller
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The cooling capacity of an absorption machine can be formulated as a linear
210
dependence on the characteristic temperature difference ∆∆t within the normal
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operating range. The characteristic temperature difference depends on the inlet to outlet
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averaged external temperatures of the absorption chiller heat exchangers. The ones
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corresponding to condenser and absorber are the same tac (thus in parallel balanced
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cooling circuits), being calculated as the averaged temperature of condenser and
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absorber tac =
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for the generator is tg. From its inception in Helman et al. [20] it is a linear function
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using two empirical constants, a and b:
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tc + t a , from now called for simplicity tc = tac. For the evaporator is te and 2
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∆∆t = t g − a tc + b te
(1)
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These constants have been obtained fitting the experimental data resulting from a steady
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state operating singleeffect absorption chiller (Fig. 1 a) of the H2O/LiBr type [8],
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corresponding the constant values = 2.5 and = 1.8.
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A thermodynamic model for H2O/LiBr has been carried out to determine whether the
223
driving power and cooling power (capacity) can be described with a linear
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ACCEPTED MANUSCRIPT dependence on ∆∆t. From a thermodynamic cycle model ∆∆t has been obtained in [9]
225
and compared to experimental results from commercial machines. The results showed
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that the characteristic temperature, with = 2.3031 and = 1.3034 , allowed
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describing with reasonable accuracy the performance of the commercial absorption
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chillers tested. This means that the values of those coefficients are no longer the original
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values proposed but, according to the modified method based on ∆∆t, [8] and [9] among
230
others, this meaning that ∆∆t can be < 0.
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The thermodynamic model is based on energy balances and heat transfer quasisteady
232
equations, constant overall UA and logarithmic temperature difference ∆Tlm, in every
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countercurrent heat exchanger of the absorption chiller: absorber, generator, solution
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heat exchanger, evaporator and condenser, thus involving the external temperatures.
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These equations are summarized as follows, denoting i and o respectively inlet and
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outlet:
237
Internal side:
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External side:
(2)
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= , ℎ − ℎ
(3)
Q& x = UAx ∆Tmlx
(4)
Heat transfer equation:
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x corresponds to every component, x = e (evaporator), x = c (condenser), x = a
244
(absorber), x = g (generator), x = she (solution heat exchanger). h is the specific
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ACCEPTED MANUSCRIPT enthalpy of the internal or external fluids, either solution or refrigerant. Variables are
246
marked with the subscript s for internal flow. For external water flow, they are marked
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with the subscript w.
248
The model has been described in detail in [17], but in this paper there is a small
249
modification; saturation state at the outlet of the evaporator, condenser, generator and
250
absorber has been imposed. The equation set is solved with the software EES® [21]. It
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incorporates the input values that have been selected from the simulation of a single
252
effect absorption chiller of NH3/LiNO3 [17]. Table 1 summarizes those values.
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For obtaining the performance of the selected absorption chiller, the external inlet
254
temperatures of the four plate heat exchangers have been varied. The absorber and
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condenser inlet temperatures, have been taken as ta,i = tc,i = 30  35 ºC, the evaporator
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inlet temperature te,i = 5  10  15 ºC and the generator inlet temperature from the
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specific activation temperature up to 30 ºC above that value, being the overall range of
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tg,i from 48 to 100 ºC. This absorption chiller has a capacity of 7.08 kW for tg,i = 84 ºC,
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te,i = 10 ºC and and tc,i = 30 ºC. The software EES® [21] gives the properties of
260
H2O/LiBr, using the formulation of the work [22] by Patek and Klomfar. This model
261
has been experimentally verified in Ventas et al. [23].
262
The values of the constants in the characteristic temperature difference have been
263
obtained by means of a multivariable linear regression to the results of the
264
thermodynamic cycle [23], resulting in:
265
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∆∆tH2O/ LiBr = tg − 2.322 tc + 1.342 te
(5)
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ACCEPTED MANUSCRIPT The constant values a and b obtained with the model are quite similar to those obtained
267
in [9], although, the values are different from the results given in [8], as already
268
commented. An absorption chiller working with solar heat should operate at relatively
269
low ∆∆t values [7] to avoid excessive collectors’ temperature. For this reason the
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cooling power and driving powers have been correlated with the thermodynamic model
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results with ∆∆ < 10 ºC. The output of this correlation is shown below, as
272
characteristic equations: 0.310 kW Q& e = ⋅ ∆∆t H 2O / LiBr + 1.530 kW ºC
274
0.326 kW Q& g = ⋅ ∆∆t H 2O / LiBr + 1.956 kW ºC
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(6)
(7)
These equations show an asymptotically increasing COP with tg, what is only valid for
276
the range of interest for solar cooling, as explained in the Introduction section. The
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cooling power is described with a linear dependence on ∆∆t with a smaller variance
278
than the driving power, as also observed in [8] and [9].
279
Now the model of the same singleeffect cycle is applied to the NH3/LiNO3 solution as
280
working fluid, keeping constant the input variables shown in Table 1, except that the
281
solution mass flow rate now is = 0.058 kg s1, according to the lower latent heat of
282
ammonia. The condenser and absorber inlet temperatures have been taken as ta,i = tc,i =
283
25  30  35 ºC. The evaporator inlet temperature taken are te,i = 5  10  15 ºC and the
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generator inlet temperature from the activation temperature to 60 ºC more than that
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value, being the range of tg,i from 42 to 122 ºC. This absorption chiller has a capacity of
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6.08 kW for tg,i = 84 ºC, te,i = 10 ºC and tc,i = 30 ºC. The solution properties used for the
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model are those given by Infante Ferreira [24].
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∆∆t NH3 / LiNO3 = t g − 2.225 tc + 1.198 te The cooling power and the driving power as a function of ∆∆ are shown below:
291
0.3 kW Q& e = ⋅ ∆∆t NH 3 / LiNO3 + 1.695 kW ºC
292
0.383 kW Q& g = ⋅ ∆∆t NH 3 / LiNO3 + 2.732 kW ºC
(9)
(10)
2.2. ∆∆t of 3) NH3/LiNO3 single effect hybridized with a low pressure
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(8)
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The characteristic temperature difference obtained for NH3/LiNO3 as working fluid is:
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booster compressor
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In this section a new characteristic equation is determined for the hybrid cycle. The
296
difference between the hybrid cycle and the single effect conventional absorption chiller
297
is the use of a mechanical compressor between the evaporator and the absorber. This
298
cycle is in detail described and analysed in [17], Fig. 1 b.
299
The low pr mechanical compressor helps the thermochemical compressor reaching the
300
pressure increase needed by the solution. The thermochemical compressor is working as
301
if it being a part of a singleeffect absorption chiller but as having a higher evaporation
302
pressure Pe and, correspondingly, as it would work at a higher evaporation temperature.
303
This temperature would be the saturation temperature at the outlet pressure of the
304
mechanical compressor T’e instead of the real evaporation temperature Te. For
305
calculating how the equivalent saturation temperature changes with pressure, the
306
ammonia properties from the EES® software [21] have been used. The correlation
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obtained is for external evaporation temperatures from 5 to 10 ºC and pr = 11.21.4
308
1.61.82:
T 'e = pr 0.1054 Te
;
pr =
Pa Pe
(10)
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The evaporation absolute temperature of the evaporator Te [K] is an internal temperature
311
of the cycle but it is considered that a virtual external evaporator average temperature
312
follows the behaviour of the internal temperature. For this reason the external average
313
temperature of the evaporator for the characteristic equation t’e [ºC] is defined by means
314
of Eq. (2) using te:
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t 'e = (te + 273.16 ºC) pr 0.1054 − 273.16 ºC
315
(11)
Thus, the equivalent characteristic temperature for the hybrid cycle can now be written
317
in a new way, on the grounds of the method for single effect cycles [7] to [9] as:
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∆∆thybrid = t g − a tc + b t 'e
318
(12)
The values of the constants a and b selected are the same than those found for a single
320
effect absorption chiller, Eq. (8).
321
The same input variables, Table 1, than the singleeffect cycle with NH3/LiNO3 have
322
been used, but adding a compressor with an isentropic efficiency η = 0.7. The vapour
323
overheating because of the internal irreversibilities is considered on the thermodynamic
324
cycle.
325
It was checked that the same correlations for and for ∆∆ < 5 ºC, indicated in
326
Eqs. (9) and (10), can be used for the hybrid cycle, but using ∆∆thybrid,.
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328
capacity through Eq. (10). At the same time increases, according to Eq. (11). The
329
electric power of the booster compressor is given by the thermodynamic cycle and is
330
defined by the ratio of cooling power versus work power consumption of the
331
compressor Q& e / W&c that depends only on the pressure ratio, as demonstrated in [17].
332
The electrical COP of the booster compressor, COPe =∆Q&e / W&c , meaning this the
333
increase of capacity over the conventional nonboosted cycle, as defined in [17], is high
334
for low values of ∆∆t. For low
335
in [17] it is demonstrated that this ratio is constant for all the temperatures involved.
336
Actually, the lower is pr, the higher %&' is.
337
3. Solar cooling model
338
In [7] the conditions for maximizing the instantaneous cooling power for a prescribed
339
solar irradiance on the collectors, using a linear characteristic curve for the solar
340
collector efficiency and a ∆∆t model have been analytically obtained. No thermal inertia
341
is considered. This means maximizing the solar coefficient of performance SCOP:
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where the single effect cycle is not producing cold,
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SCOP = Q&e / ( GT As )
(14)
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343
SCOP is the product of the solar collector energy efficiency times the COP of the
344
absorption machine and times the hydronic facility energy efficiency, owing to heat
345
losses and the associated temperature drops in the thermal fluid. This model is of only
346
relative accuracy but offers a tool for discriminating general trends and offering guides
347
for further study.
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ACCEPTED MANUSCRIPT The model for the solar collectors and hydronic circuits uses the same values than in
349
[7], corresponding to high efficiency flat plate collectors of contemporary technology.
350
The application of this model to two real absorption machines versus time is offered in
351
[7].
352
In this paper, sunny days have been considered as representative of the maximum
353
possible. Madrid (Spain) has been selected as a continental Mediterranean climate with
354
dry summers. It is located at 687 m altitude. Day 196 (midJuly) has been selected as
355
representative of the cooling season with an average maximum tatm = 31.2 ºC and
356
minimum of 18.9 ºC, as can be seen in Figs. 2 and 3. A second day two month later
357
(midSeptember), with lower temperatures and solar irradiance, serves as an endof
358
season example. A Hottel correlation for solar irradiance along the day has been used,
359
[25] and elsewhere. This yields GT = 1,082.0 W m2 of maximum total irradiance on the
360
optimally tilted fixed position collector for the selected midJuly day at noon.
361
4. Results and discussion
362
Figs. 2 and 3 show: the optimum driving temperature tg,op versus solar time from sunrise
363
to sunset, the atmospheric temperature tatm and the minimum temperature for cold
364
production, namely the activation temperature tg,0. Fig. 2 shows the results for the mid
365
July day for the three cycles, 1) singleeffect H2O/LiBr, 2) singleeffect NH3/LiNO3 and
366
3) NH3/LiNO3 single effect hybridized with a low pressure compressor booster with pr
367
= 1.5. Fig. 3 depicts the same results but for the midSeptember day. These figures show
368
that the optimum temperature smoothly grows above the activation temperature from an
369
instant about an hour after sunrise toward the early afternoon, decreasing afterwards
370
toward about an hour before sunset when the machine stops once tg,op = tg,0. The results
371
for the H2O/LiBr cycle show slightly higher tg,op than the NH3/LiNO3 cycle, being both
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373
values occur mainly because of the lower ambient temperature. The NH3/LiNO3 single
374
effect chiller hybridized with a low pressure compressor booster with pr = 1.5, shows
375
tg,op about 16 ºC lower than for the other cycles, what implies a less thermally stressed
376
solar facility, being this temperature in the range of 33 to 72 ºC for midJuly and 2562
377
for midSeptember.
378
Fig. 4 shows the resulting timevarying optimal SCOP, and also with timeconstant tg of
379
70 ºC, 80 ºC and 90 ºC along the whole sunshine hours for the singleeffect NH3/LiNO3
380
cycle, producing cold only when they are higher than tg,0. There is some loss in SCOP
381
along time when they are different to tg,op, demonstrating the advantage of operating at
382
the instantaneous tg,op. This loss is more evident for tg < tg,op than for tg > tg,op owing to
383
the steep decrease of COP for lower hot water temperatures [7]. The figure also shows
384
that either pumping half the nominal mass flow rate through the solar collectors at tg,op,
385
a possible loss in SCOP is the result. For the case of pumping the double of the nominal
386
mass flow rate there are hardly any losses and for this reason it is not shown in the
387
figure. This paper does not include the possibility of operating at variable mass flow
388
rate neither at variable evaporation temperature te as part of a multivariable
389
optimization. But they can change along time in a prescribed way and the methodology
390
is still valid if the corresponding parameters are available.
391
Fig. 5 shows the resulting SCOP along solar time for the three cycles operating at tg,op,
392
exhibiting maximum values around 0.4 – 0.5. All the cycles show a similar time
393
evolution of the instantaneous maximum SCOP in spite of the higher COP curve of the
394
H2O/LiBr machine. This is a consequence of the combination of a) a lower ∆∆t for
395
activation, namely ∆∆t0, of the NH3/LiNO3 cycle, 5.65 ºC in front of 4.94 ºC for
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ACCEPTED MANUSCRIPT H2O/LiBr, giving a plus for the former, and b) a slightly lower sensitivity of COP to
397
∆∆t of the NH3/LiNO3 cycle, giving a minus, as Eqs. (6) and (9) show.
398
For the H2O/LiBr machine modelled in this work, Eq. (6), the solar field dimensions
399
would be 9.95 m2 to produce 5.45 kW at midday. This result has been obtained with the
400
optimum ∆∆t and the SCOP shown in Fig. 5. For the NH3/LiNO3 single effect machine
401
shown in Eq. (9) the solar field dimensions would be 10.54 m2 to produce 4.72 kW at
402
midday. Other values can be embraced by just escalation.
403
The resulting SCOP for the H2O/LiBr singleeffect machine is higher than for the
404
NH3/LiNO3 singleeffect machine. This is attributed to a higher raising COP curve for
405
the H2O/LiBr machine when tg increases, Eqs. (6) and (7). On the other hand the hybrid
406
cycle starts to produce cold sooner and stops later than the other two cycles. The
407
maximum SCOP is lower for the hybrid cycle than for the H2O/LiBr single effect cycle,
408
but the same than the NH3/LiNO3 single effect cycle. The main difference is that the
409
hybrid cycle maintains a flatter behaviour of SCOP near the maximum. The averaged
410
SCOP from 6:00 h and 18:00 h solar time of every cycle, obtained from Fig. 5, is 0.411
411
for the H2O/LiBr single effect cycle, 0.336 for the NH3/LiNO3 single effect cycle and
412
0.381 for the hybrid cycle with pr = 1.5.
413
Figure 6 show the day accumulated cold production per collector one meter surface
414
[J/m2] versus an imposed timeconstant driving temperature
415
day. This figure shows the results for the three cycles shown before: singleeffect
416
H2O/LiBr, singleeffect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5. This figure
417
incorporates a new curve showing the results of the hybrid cycle with pr = 2.0. The first key
418
result is that the SCOP curve around maximum is quite smooth, indicating that the
419
inaccuracies of the model parameters or in the control system are not crucial. One can
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also for the midJuly
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ACCEPTED MANUSCRIPT observe that too high tg stems into an almost linear SCOP decay caused by an almost
421
constant COP and linearly decreasing collector efficiency. On the other hand, a too low
422
tg derives into a fast decreasing SCOP.
423
The figure also show that there is an optimum timeconstant temperature maximizing
424
the cold production, depending on the solar and ambient conditions. This is evident
425
when comparing with the curve for the midSeptember day, Fig. 7. Moreover, operating
426
at a too high constant tg there is less risk to obtain a lower cold production than
427
operating at a too low constant tg. This seems to explain the current practice of operating
428
at somehow elevated hot water temperatures.
429
Figs. 6 and 7 also show that operating with the timevariable tg,op a higher production is
430
obtained. But the gain is modest within our constraints. This suggests that operating at a
431
specific constant driving temperature is an option, simplifying the control system, but
432
this temperature must of the appropriate value for the climate, the solar irradiance and
433
te. Another more elaborate option could be approaching the curve of tg,op with morning
434
and evening smooth ramps and setting a constant value for the middle of the assumed
435
sunny day. The ∆∆t model yields the clues on how to operate with a combination of the
436
influencing temperatures.
437
Comparing the three cycles a conclusion can be drawn. The NH3/LiNO3 cycle produces
438
at tg,op 10.5 MJ m2 of cold for the midJuly day and 9.2 MJ m2 for the midSeptember
439
day. Meanwhile the H2O/LiBr cycle produces 12.8 MJ m2 for the midJuly day and
440
11.2 MJ m2 for the midSeptember day, 22 % and 23 % more than the NH3/LiNO3
441
cycle respectively. Hybridizing the NH3/LiNO3 cycle with a booster compressor this
442
loss can be reduced or even overcome, not deteriorating the efficiency of the absorption
443
cycle [11]. This hybrid cycle totalizes a cold production for the midJuly day of 11.9 MJ
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ACCEPTED MANUSCRIPT m2 for pr = 1.5 and 12.9 MJ m2 for pr = 2.0, for the same day, this is respectively 8 %
445
lower and 0.6 % higher than using the singleeffect H2O/LiBr cycle; for this reason only
446
one line is represented in Fig. 6 for the hybrid cycle with pr = 2 and singleeffect
447
H2O/LiBr cycle. This improvement has been achieved thanks to the electricity
448
consumption of the compressor. It is necessary to evaluate the quantity of energy
449
consumed for that in a day. For the case of pr = 1.5 the ratio of cooling power versus
450
power consumption results to be constant, being in this case Q& e / W&c = 14.5 and being
451
of identical value of COPe = 14.5, so that the hybrid cycle was working at tg lower than
452
the activation temperature of the conventional singleeffect absorption cycle [17]. The
453
Q& e / W&c result has been obtained by means of the thermodynamic model. The work
454
consumption is 0.819 MJ m2 in July and 0.721 MJ m2 in September. For the case of pr
455
= 2.0, Q& e / W&c is also kept constant, being in this case Q& e / W&c = 8.07 and, as well as for
456
pr = 1.5. This ratio sensibly coincides with the electrical coefficient of performance
457
COPe = 8.07, being the work consumption of the compressor 1.45 MJ/m2 in July and
458
1.29 MJ/m2 in September. The resulting high COPe guarantees CO2 reductions over a
459
system solely based on mechanical compression cooling consuming electricity from the
460
grid.
461
The hybrid cycle curves show a shift towards even lower constant tg for which the cold
462
production losses are minimum with respect the optimum driving temperature. This is
463
the result of the higher pr, so that the maximum production appears at tg = 58 ºC for
464
July and 47 ºC for September for pr = 2.0. For the conventional single effect cycles this
465
signifies 25 ºC lower with H2O/LiBr and 24 ºC lower with NH3/LiNO3.
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ACCEPTED MANUSCRIPT Running the model for other days, the results indicate that when the date separates from
467
about the summer solstice the optimum constant temperature tg decreases. They also
468
indicate a stronger convenience to increase pr to increase the capacity over solar alone.
469
This reveals that the hybrid cycle incorporates solar heat in an effective way combining
470
it with work to fulfil the user needs. For the conventional nonboosted cycle it could be
471
less and less possible to profit from solar cold. This singular advantage of boosting
472
using the hybrid cycle is a consequence of higher collector efficiencies caused by the
473
lower tg.
474
The thermodynamic model used in Section 2 for each cycle is now used to show the
475
cooling power obtained instantaneously for the optimum temperature determined. The
476
results are compared to the cooling power given for the approximate ∆∆t model along
477
the midJuly day in order to explore the accuracy of the ∆∆t model. Fig. 8 a shows the
478
results of e for the midJuly day with respect the solar angle, for H2O/LiBr, and for
479
both cases: the thermodynamic model and the ∆∆t model. The total energy obtained
480
along the day is 3.6 % lower for the case of the thermodynamic model than the ∆∆t
481
model. For the NH3/LiNO3 single effect cycle the total energy obtained is
482
underestimated a 5.8 % by the ∆∆t model compared to the thermodynamic model. On
483
the other hand, for the NH3/LiNO3 single effect cycle hybridized with a low pressure
484
compressor booster with pr = 1.5 the ∆∆t model underestimates a 7.6 % of the total
485
energy obtained, Fig. 8 b. For the case of the NH3/LiNO3 single effect absorption cycle
486
hybridized with low pressure compressor booster with pr = 2.0 the ∆∆t model
487
underestimates by 14.9 % the total energy. It can be said that the accuracy of the ∆∆t
488
model is quite high for the single effect cycles but its accuracy decreases for the hybrid
489
cycle when the pressure ratio of the hybrid cycle increases.
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ACCEPTED MANUSCRIPT Correcting the ∆∆t model results with the thermodynamic model for the July cases
491
shown in Fig. 6, the total energy obtained would be 11.07 MJ m2 for the NH3/LiNO3
492
singleeffect cycle, 12.35 MJ m2 for the H2O/LiBr singleeffect cycle, 12.76 MJ m2 for
493
the hybrid with pr = 1.5 cycle and 14.81 MJ m2for the hybrid with pr = 2.0 cycle. With
494
the corrected results the hybridization cycle for pr = 2.0 produces a 15.6 % more cold
495
than the singleeffect H2O/LiBr cycle. In order to obtain this improvement a work
496
consumption is needed, being 1.67 MJ m2 for the pr = 2.0 case in July.
497
5. Conclusions
498
This paper offers the results of modelling the instantaneous solar cold production during
499
two sunny summer days using: 1) a H2O/LiBr single effect cycle, 2) a NH3/LiNO3
500
single effect cycle, and 3) a NH3/LiNO3 single effect cycle hybridized with a low
501
pressure compressor booster. The resulting cooling capacity and driving heat power are
502
fitted with a simple empirical model based on the modified ∆∆t concept instead of the
503
thermodynamic cycle, signifying an extension of the concept for hybrid booster cycles.
504
This allows an analytical maximization of cold production. The low side is that some
505
accuracy is lost, but fortunately the optimized variables show a smooth hill around
506
maximum, so that the error seems acceptable in front of the optimization capability
507
obtained. The reasons for the accuracy loss when pr increases have not been
508
investigated in detail, but one reason could be the vapor temperature increase through
509
the compressor as a result of its irreversibility; this loss was not considered in the
510
original ∆∆t method.
511
The results indicate that:
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•
Maximum solar cold production requires a time varying temperature tg,op for driving the absorption machine that requires finely controlling the working of
514
the system. During a sunny day it grows towards an instant some hours after
515
noon. The resulting COP and SCOP evolves in the same manner. The
516
instantaneous cold capacity shows a more peaky behaviour. Primary circuit flow
517
rate variation seems customary for reaching tg,op. •
Using a fixed tg, implies a loss in the daily production that is not substantial if
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the temperature is chosen as suitable for the day. This simplifies the chiller
520
control and partially reduces the thermal inertia effects. The optimum fixed
521
temperature has to be determined at the beginning of the day depending on the
522
meteorological forecast. It could be corrected along the day using online
523
meteorological information. •
Cooling power under optimum solar driving temperature is significantly lower
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than the usual nominal power of absorption chillers, which corresponds to
526
higher values of ∆∆t than the one corresponding to tg,op. This seems relevant for
527
dimensioning.
529 530 531
•
Solar cooling using the NH3/LiNO3 working pair inside a hybrid booster cycle is
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feasible, promising and convenient, as it operates efficiently with low cost flat plate collectors. This setup is capable of covering a wide range of cooling demands, even in the case of no solar irradiance. Its produces 15.6 % more cold
532
than the singleeffect H2O/LiBr cycle for air conditioning, using a moderate
533
pressure ratio of 2.0.
23
ACCEPTED MANUSCRIPT 534
As a main conclusion solar cooling using the NH3/LiNO3 working pair is feasible and
535
attractive using just the simplest solar setup.
536
Acknowledgements
538
The financial support of this study by the Spanish Ministry of Education and Science
539
research grant ENE200911097 is greatly appreciated.
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References
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[1] Zhai X.Q., Qu M., Li Y., Wang R.Z. A review for research and new design options
543
of solar absorption cooling systems. Renew and Sustainable Energy Rev 15 (2011)
544
4416–4423.
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SC
541
[2] Boopathi Raja V., Shanmugam V. A review and new approach to minimize the
546
cost of solar assisted absorption cooling system. Renew and Sustainable Energy
547
Rev 16 (2012) 6725–6731.
TE D
545
[3] FernándezSeara J. A., Vázquez M.. Study and control of the optimal generation
549
temperature in NH3/H2O absorption refrigeration systems. Appl Therm Eng, 21
550
(2001) 343357.
552 553 554 555
[4] Sun, D. Comparison of the performances of NH3H20, NH3LiNO3 and NH3
AC C
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EP
548
NaSCN absorption refrigeration systems. Energy Convers. Mgmt (1998), 39 (5/6), 357–368.
[5] Albers J. New absorption chiller and control strategy for the solar assisted cooling system at the German federal environment agency Int J of Refrig 39 (2014) 4856
24
ACCEPTED MANUSCRIPT 556
[6] Li Z., Ye X., Liu J. Optimal temperature of collector for solar double effect
557
LiBr/H2O absorption cooling system in subtropical city based on a year round
558
meteorological data. Appl Therm Eng, 69 (2014) 1928.
560
[7] Lecuona, A., Ventas, R., Venegas, M, Zacarías, A., Salgado, R. Optimum hot water for absorption solar cooling, Sol Energy 83 (2009) 18061814.
RI PT
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[8] Kühn, A., Ziegler, F. Operational results of a 10 kW absorption chiller and
562
adaptation of the characteristic equation. International Conference of SolarAir
563
Conditioning, 7074, 67 October 2005, Kloster Banz, Germany.
SC
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[9] PuigArnavat, M., LópezVillada, J., Bruno, J.C., Coronas, A. Analysis and
565
parameter identification for characteristic equation of single and doubleeffect
566
absorption chillers by means of multivariable regression. Int J of Refrig 33 (2010)
567
7078.
M AN U
564
[10] GutierrezUrueta, Rodríguez, P., Ziegler, F., Lecuona, A., RodriguezHidalgo,
569
M.C. Extension of the characteristic equation to absorption chillers with adiabatic
570
absorbers. Int J of Refrig, 35 (2012) 709718.
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[11] D. W. Sun. Comparison of the performance of NH3H2O, NH3LiNO3 and NH3
572
NaSCN absorption refrigeration systems. Energy Convers Manag 39 (5/6) (1998)
573
357368.
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[12] Antonopoulos, K. A., Rogdakis, D. E. Performance of solar driven ammonia
575
lithium nitrate and ammoniasodium thiocyanate absorption systems operating as
576
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coolers or heat pumps in Athens. Appl Therm Eng, 16 (1996) 127147.
577
[13] Llamas Guillén, S.U., Cuevas, R., Best, R., Gómez, V. H. Experimental results of
578
direct aircooled ammonialithium nitrate absorption refrigeration system, Appl
579
Therm Eng 64 (2014) 362369.
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[14] Zacarías, A., Venegas, M., Ventas, R., Lecuona, A. Experimental assessment of
581
ammonia adiabatic absorption into ammonialithium nitrate solution using a flat
582
fan nozzle, Appl Therm Eng. 31 (2011) 781790.
583
[15] Zacarías, A.,Venegas, M., Lecuona, A., Ventas, R. Experimental evaluation of ammonia adiabatic absorption into ammonialithium nitrate solution using a fog
585
jet nozzle, Appl Therm Eng 50 (2013) 35693579.
586 587
RI PT
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[16] Morawetz, M., 1989. Sorptioncompression heat pumps. Int J of Energy Res, 13 (1989) 83102.
[17] Ventas, A., Lecuona, A., R., Zacarías, Venegas, M,. Ammonialithium nitrate
589
absorption chiller with an integrated lowpressure compression booster cycle for
590
low driving temperatures. Appl Therm Eng 30 (2010) 13511359.
M AN U
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588
591
[18] Vereda, C., Ventas, R., Lecuona, A., Venegas, M. Study of an ejectorabsorption
592
refrigeration cycle with an adaptable ejector nozzle for different working
593
conditions, Appl Energy 97 (2012) 305312.
[19] Vereda, C, Ventas, R., Lecuona, A., Lopez, R. Singleeffect absorption cycle
595
boosted with an ejectoradiabatic absorber using a single solution pump 38 (2014)
596
2229.
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[20] Helman, H.M., Schweigler, C., Ziegler, F. A simple method for modelling the
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operating characteristics of absorption chillers. Seminar Eurotherm nº 59,
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Thermodynamics, heat and mass transfer of refrigeration machines and heat
601 602
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pumps. 67 July 1998, 219226.
[21] Klein, S. A., Alvarado, F. Engineering Equation Solver, v. 8.1863D, FChart Software, Middleton, WI, USA, 1999.
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[22] Patek, J., Klomfar, J. A computationally effective formulation of the
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thermodynamics properties of LiBrH2O solutions from 273 to 500 K over full
605
composition range. Int J of Ref 29 (2006) 566578.
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[23] Ventas, R., Vereda, C., Lecuona, A., Venegas, M. Experimental study of a
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thermochemical compressor for an absorption/compression hybrid cycle. Appl
608
Energy 97 (2012) 297304. [24] C.A. Infante Ferreira, Thermodynamic and physical property data equations for
610
ammonialithium nitrate and ammoniasodium thiocyanate solutions. Sol Energy 2
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(1984) 231236.
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[25] Duffie J. A., Beckmann W. A. Solar Engineering of Thermal Processes (1980), John Wiley & Sons. Hoboken, New Jersey, USA.
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ACCEPTED MANUSCRIPT Table 1. Data for the thermodynamic cycle. Input Variable Value Input Variable
Value
0.35 kg s1
UAc
3.0 kW K1
,
0.40 kg s1
UAe
2.5 kW K1
,
0.17 kg s1
UAg
1.8 kW K1
0.028 kg s1
UAshx
1.4 kW K1
UAa
2.25 kW K1
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ACCEPTED MANUSCRIPT
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Figure 1 Pressure versus temperature diagram of a) single effect absorption cycle b)
620
single effect absorption cycle hybridized with low pressure compressor booster.
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ACCEPTED MANUSCRIPT 100 90 80 70 60
t (ºC) 50 40
20
tg,op SE H2O/LiBr
tg,op SE NH3/LiNO3
tg,op hybrid pr = 1.5
10
tg,0 SE H2O/LiBr
tg,0 SE NH3/LiNO3
tg,0 hybrid pr =1.5
tatm July
0 6
7
8
9
10
11
12
solar time (h)
13
14
15
16
17
18
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Figure 2. tg,op , tg,0 and tatm [ºC] versus solar time [h] for the midJuly day and for the three cycles: singleeffect H2O/LiBr, singleeffect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5.
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ACCEPTED MANUSCRIPT 90 80 70 60 50
t (ºC) 40
20 10 6
tg,op SE NH3/LiNO3
tg,op hybrid pr = 1.5
tg,0 SE H2O/ LiBr
tg,0 SE NH3/LiNO3
tg,0 hybrid pr =1.5
7
8
9
10
11
12
solar time (h)
13
14
15
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Figure 3. tg,op , tg,0 and tatm [ºC] versus solar time [h] for the midSeptember day and for the three cycles: singleeffect H2O/LiBr, singleeffect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5.
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tg,op SE H2O/LiBr tatm September
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ACCEPTED MANUSCRIPT 0.5
0.4
0.3
SCOP SCOP with tg,op
0.2
SCOP with tg = 70 º C
0.1
SCOP with tg = 80 ºC SCOP with tg = 90 ºC 0.0 6
7
8
9
10
11
12
solar time (h)
13
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15
16
17
18
Figure 4. Solar coefficient of performance SCOP [] versus solar time for the midJuly
634
day, singleeffect NH3/LiNO3 cycle. 5 different operation possibilities: tg,op, tg,op using half
635
nominal mass flow rate of the solar collectors, constant driving temperatures of tg = 70 ºC, tg =
636
80 ºC and tg = 90 ºC.
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ACCEPTED MANUSCRIPT 0.6 0.5 0.4
SCOP
0.3
SCOP with tg,op SE H2O/LiBr
0.1
SCOP with tg,op SE NH3/LiNO3
SCOP with tg,op hybrid pr = 1.5 0.0 6
7
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12
solar time (h)
13
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Figure 5. Solar coefficient of performance SCOP [] using tg,op versus solar time for the
640
midJuly day and for the three cycles: singleeffect H2O/LiBr, singleeffect NH3/LiNO3, and
641
NH3/LiNO3 hybrid cycle with pr = 1.5.
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ACCEPTED MANUSCRIPT 1.40E+10 1.20E+10 1.00E+10 Qe SE H2O/LiBr 8.00E+09
Qe SE NH3/LiNO3
Qe (J/m2)
Qe hybrid pr = 1.5
6.00E+09
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Qe with tg,op (SE H2O/LiBr and hybrid pr =2) Qe with tg,op SE NH3/LiNO3
2.00E+09
Qe with tg,op hybrid pr =1.5
0.00E+00 40
45
50
55
60
65
70
tg (ºC)
75
80
85
90
95
100
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Figure 6. Daily solar cold production [J m2] versus timeconstant tg (curves) and tg,op
645
(horizontal lines) for the midJuly day and for the three cycles: singleeffect H2O/LiBr,
646
singleeffect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5 and pr = 2.0.
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1.00E+10
8.00E+09 Qe SE H2O/LiBr Qe SE NH3/LiNO3
6.00E+09
Qe hybrid pr = 1.5
Qe (J/m2)
Qe hybrid pr = 2 4.00E+09
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Qe with tg,op hybrid pr =1.5 Qe with tg,op hybrid pr = 2
0.00E+00 40
45
50
55
60
65
70
tg (ºC)
75
80
85
90
95
100
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Figure 7. Daily solar cold production [J m2] versus timeconstant tg (curves) and tg,op
650
(horizontal lines) for the midSeptember day and for the three cycles: singleeffect
651
H2O/LiBr, singleeffect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5 and pr = 2.0.
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400
Qe (W/m2)
Qe (W/m2)
300
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6
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12
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Characteristic temperature model
0
16
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6
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solar time (h)
solar time (h)
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b)
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Figure 8. Instantaneous cooling power [W m2] with tg,op versus solar time in midJuly day. a) H2O/LiBr, b) NH3/LiNO3 for the hybrid cycle with pr = 1.5.
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657 658 659
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Characteristic temperature model
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655 656
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ACCEPTED MANUSCRIPT
Highlights: Instantaneous optimum driving temperature tg,op for solar cooling in Madrid. 3 absorption cycles tested: H2O/LiBr and NH3/LiNO3 single effect and hybrid. The tg,op of the hybrid cycle is 16 ºC lower than both single effect cycles. The best fixed driving temperature can reach almost the same behavior than tg,op.
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