Absorption solar cooling systems using optimal driving temperatures

Accepted Manuscript Absorption solar cooling systems using optimal driving temperatures Antonio Lecuona, Rubén Ventas, Ciro Vereda, Ricardo López PII:

S1359-4311(15)00016-2

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; e-mail: [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

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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

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difference model. The day accumulated solar cold production is determined using this

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optimum temperature during two sunny days in mid-July and mid-September, located in

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Madrid, Spain. The work shows the influences of operational variables and a striking

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result: selection of a time-constant 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-

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zero Celsius degrees temperatures, but does not require higher hot water driving

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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.

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Nomenclature

33 a

Absorber; Constant

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As

Collector area, m2

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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 kg-1

46

H

Specific enthalpy, internal fluid, J kg-1

47

m&

Mass flow rate, external fluid, kg/s

48

M&

Mass flow rate, internal fluid, kg/s

49

P

50

pr

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Q

52

Q&

53

SCOP Solar coefficient of performance

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SE

Single-effect

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she

Solution heat exchanger

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Pressure, Pa

Pressure ratio of booster compressor

Daily solar cold production, J/m2

Heat power, W

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ACCEPTED MANUSCRIPT t

Averaged external fluid temperature between inlet and outlet, ºC

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t’e

Equivalent external fluid temperature averaged between inlet and outlet, ºC

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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

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T’e

Equivalent internal fluid temperature averaged between inlet and outlet, ºC

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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

Absorber-Condenser

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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

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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

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w

water, external fluid of the absorption chiller

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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 non-steady

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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. Fernández-Seara 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 on-line 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

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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 Puig-Arnavat et al. in [9], with advantages over other approximate

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ACCEPTED MANUSCRIPT methods. This model has been extended to absorption chillers with adiabatic absorbers

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[10] by Gutiérrez-Urueta et al. underlining the usefulness of the concept.

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The most common working pair used in absorption chillers for air-conditioning is

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H2O/LiBr. This working pair yields a good performance for air-conditioning

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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 [12-15].

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In [12] Antonopoulus and Rogdakis show that LiNO3 is superior to other salts with

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NH3. In [13] Llamas-Guillén 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 single-effect 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

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compressor, e. g. Morawetz [16], but with non-known 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 oil-less compressors and pumps are

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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

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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

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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

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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

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optimum hot water temperature evolves during reference sunny days, in this case for

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Madrid, central Spain, using the most common technology available: the combination of

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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

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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 air-conditioning purpose: 1) H2O/LiBr

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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

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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

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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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ACCEPTED MANUSCRIPT competitive against the more usual H2O/LiBr for air conditioning, either in terms of

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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

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booster.

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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

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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 single-effect 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

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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]

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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

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others, this meaning that ∆∆t can be < 0.

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The thermodynamic model is based on energy balances and heat transfer quasi-steady

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equations, constant overall UA and logarithmic temperature difference ∆Tlm, in every

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counter-current 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:

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Internal side:

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 = , ℎ − ℎ 

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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

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(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

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marked with the subscript s for internal flow. For external water flow, they are marked

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with the subscript w.

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The model has been described in detail in [17], but in this paper there is a small

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modification; saturation state at the outlet of the evaporator, condenser, generator and

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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-

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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

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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

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H2O/LiBr, using the formulation of the work [22] by Patek and Klomfar. This model

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has been experimentally verified in Ventas et al. [23].

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The values of the constants in the characteristic temperature difference have been

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obtained by means of a multivariable linear regression to the results of the

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thermodynamic cycle [23], resulting in:

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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

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in [9], although, the values are different from the results given in [8], as already

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commented. An absorption chiller working with solar heat should operate at relatively

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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

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characteristic equations: 0.310 kW Q& e = ⋅ ∆∆t H 2O / LiBr + 1.530 kW ºC

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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

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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

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than the driving power, as also observed in [8] and [9].

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Now the model of the same single-effect cycle is applied to the NH3/LiNO3 solution as

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working fluid, keeping constant the input variables shown in Table 1, except that the

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solution mass flow rate now is  = 0.058 kg s-1, according to the lower latent heat of

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ammonia. The condenser and absorber inlet temperatures have been taken as ta,i = tc,i =

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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:

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0.3 kW Q& e = ⋅ ∆∆t NH 3 / LiNO3 + 1.695 kW ºC

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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

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difference between the hybrid cycle and the single effect conventional absorption chiller

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is the use of a mechanical compressor between the evaporator and the absorber. This

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cycle is in detail described and analysed in [17], Fig. 1 b.

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The low pr mechanical compressor helps the thermochemical compressor reaching the

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pressure increase needed by the solution. The thermochemical compressor is working as

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if it being a part of a single-effect absorption chiller but as having a higher evaporation

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pressure Pe and, correspondingly, as it would work at a higher evaporation temperature.

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This temperature would be the saturation temperature at the outlet pressure of the

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mechanical compressor T’e instead of the real evaporation temperature Te. For

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calculating how the equivalent saturation temperature changes with pressure, the

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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 = 1-1.2-1.4-

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1.6-1.8-2:

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

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of the cycle but it is considered that a virtual external evaporator average temperature

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follows the behaviour of the internal temperature. For this reason the external average

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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

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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

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(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).

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The same input variables, Table 1, than the single-effect cycle with NH3/LiNO3 have

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been used, but adding a compressor with an isentropic efficiency η = 0.7. The vapour

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overheating because of the internal irreversibilities is considered on the thermodynamic

324

cycle.

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It was checked that the same correlations for  and  for ∆∆ < 5 ºC, indicated in

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Eqs. (9) and (10), can be used for the hybrid cycle, but using ∆∆thybrid,.

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ACCEPTED MANUSCRIPT Eq. (11) indicates that increasing pr increases ∆∆thybrid, thus increasing the cooling

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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].

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The electrical COP of the booster compressor, COPe =∆Q&e / W&c , meaning this the

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increase of capacity over the conventional non-boosted 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.

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Actually, the lower is pr, the higher %&' is.

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3. Solar cooling model

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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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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

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[7].

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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 (mid-July) has been selected as

355

representative of the cooling season with an average maximum tatm = 31.2 ºC and

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minimum of 18.9 ºC, as can be seen in Figs. 2 and 3. A second day two month later

357

(mid-September), with lower temperatures and solar irradiance, serves as an end-of-

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 m-2 of maximum total irradiance on the

360

optimally tilted fixed position collector for the selected mid-July day at noon.

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4. Results and discussion

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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) single-effect H2O/LiBr, 2) single-effect 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 mid-September 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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ACCEPTED MANUSCRIPT in the range of 49 – 86 ºC for mid-July and 41-76 for mid-September; these lower

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 mid-July and 25-62

377

for mid-September.

378

Fig. 4 shows the resulting time-varying optimal SCOP, and also with time-constant tg of

379

70 ºC, 80 ºC and 90 ºC along the whole sunshine hours for the single-effect 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 multi-variable

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 single-effect machine is higher than for the

404

NH3/LiNO3 single-effect 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 time-constant driving temperature

415

day. This figure shows the results for the three cycles shown before: single-effect

416

H2O/LiBr, single-effect 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 mid-July

18

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 time-constant temperature maximizing

424

the cold production, depending on the solar and ambient conditions. This is evident

425

when comparing with the curve for the mid-September 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 time-variable 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 m-2 of cold for the mid-July day and 9.2 MJ m-2 for the mid-September

439

day. Meanwhile the H2O/LiBr cycle produces 12.8 MJ m-2 for the mid-July day and

440

11.2 MJ m-2 for the mid-September 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 mid-July day of 11.9 MJ

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ACCEPTED MANUSCRIPT m-2 for pr = 1.5 and 12.9 MJ m-2 for pr = 2.0, for the same day, this is respectively 8 %

445

lower and 0.6 % higher than using the single-effect H2O/LiBr cycle; for this reason only

446

one line is represented in Fig. 6 for the hybrid cycle with pr = 2 and single-effect

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 single-effect 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 m-2 in July and 0.721 MJ m-2 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/m-2 in July and

458

1.29 MJ/m-2 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 non-boosted 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 mid-July day in order to explore the accuracy of the ∆∆t model. Fig. 8 a shows the

478

results of  e for the mid-July 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 m-2 for the NH3/LiNO3

492

single-effect cycle, 12.35 MJ m-2 for the H2O/LiBr single-effect cycle, 12.76 MJ m-2 for

493

the hybrid with pr = 1.5 cycle and 14.81 MJ m-2for 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 single-effect H2O/LiBr cycle. In order to obtain this improvement a work

496

consumption is needed, being 1.67 MJ m-2 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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ACCEPTED MANUSCRIPT 512

•

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 on-line

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 single-effect 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 ENE2009-11097 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)

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4416–4423.

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[2] Boopathi Raja V., Shanmugam V. A review and new approach to minimize the

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cost of solar assisted absorption cooling system. Renew and Sustainable Energy

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Rev 16 (2012) 6725–6731.

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[3] Fernández-Seara J. A., Vázquez M.. Study and control of the optimal generation

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temperature in NH3/H2O absorption refrigeration systems. Appl Therm Eng, 21

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(2001) 343-357.

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[4] Sun, D. Comparison of the performances of NH3-H20, NH3-LiNO3 and NH3-

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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) 48-56

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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) 19-28.

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[7] Lecuona, A., Ventas, R., Venegas, M, Zacarías, A., Salgado, R. Optimum hot water for absorption solar cooling, Sol Energy 83 (2009) 1806-1814.

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[8] Kühn, A., Ziegler, F. Operational results of a 10 kW absorption chiller and

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adaptation of the characteristic equation. International Conference of Solar-Air

563

Conditioning, 70-74, 6-7 October 2005, Kloster Banz, Germany.

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[9] Puig-Arnavat, M., López-Villada, J., Bruno, J.C., Coronas, A. Analysis and

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parameter identification for characteristic equation of single- and double-effect

566

absorption chillers by means of multivariable regression. Int J of Refrig 33 (2010)

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70-78.

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[10] Gutierrez-Urueta, Rodríguez, P., Ziegler, F., Lecuona, A., Rodriguez-Hidalgo,

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M.C. Extension of the characteristic equation to absorption chillers with adiabatic

570

absorbers. Int J of Refrig, 35 (2012) 709-718.

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[11] D. W. Sun. Comparison of the performance of NH3-H2O, NH3-LiNO3 and NH3-

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NaSCN absorption refrigeration systems. Energy Convers Manag 39 (5/6) (1998)

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357-368.

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[12] Antonopoulos, K. A., Rogdakis, D. E. Performance of solar driven ammonia-

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lithium nitrate and ammonia-sodium thiocyanate absorption systems operating as

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coolers or heat pumps in Athens. Appl Therm Eng, 16 (1996) 127-147.

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[13] Llamas Guillén, S.U., Cuevas, R., Best, R., Gómez, V. H. Experimental results of

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direct air-cooled ammonia-lithium nitrate absorption refrigeration system, Appl

579

Therm Eng 64 (2014) 362-369.

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[14] Zacarías, A., Venegas, M., Ventas, R., Lecuona, A. Experimental assessment of

581

ammonia adiabatic absorption into ammonia-lithium nitrate solution using a flat

582

fan nozzle, Appl Therm Eng. 31 (2011) 781-790.

583

[15] Zacarías, A.,Venegas, M., Lecuona, A., Ventas, R. Experimental evaluation of ammonia adiabatic absorption into ammonia-lithium nitrate solution using a fog

585

jet nozzle, Appl Therm Eng 50 (2013) 3569-3579.

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[16] Morawetz, M., 1989. Sorption-compression heat pumps. Int J of Energy Res, 13 (1989) 83-102.

[17] Ventas, A., Lecuona, A., R., Zacarías, Venegas, M,. Ammonia-lithium nitrate

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absorption chiller with an integrated low-pressure compression booster cycle for

590

low driving temperatures. Appl Therm Eng 30 (2010) 1351-1359.

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[18] Vereda, C., Ventas, R., Lecuona, A., Venegas, M. Study of an ejector-absorption

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refrigeration cycle with an adaptable ejector nozzle for different working

593

conditions, Appl Energy 97 (2012) 305-312.

[19] Vereda, C, Ventas, R., Lecuona, A., Lopez, R. Single-effect absorption cycle

595

boosted with an ejector-adiabatic absorber using a single solution pump 38 (2014)

596

22-29.

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[20] Helman, H.M., Schweigler, C., Ziegler, F. A simple method for modelling the

598

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. 6-7 July 1998, 219-226.

[21] Klein, S. A., Alvarado, F. Engineering Equation Solver, v. 8.186-3D, F-Chart 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 LiBr-H2O solutions from 273 to 500 K over full

605

composition range. Int J of Ref 29 (2006) 566-578.

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[23] Ventas, R., Vereda, C., Lecuona, A., Venegas, M. Experimental study of a

607

thermochemical compressor for an absorption/compression hybrid cycle. Appl

608

Energy 97 (2012) 297-304. [24] C.A. Infante Ferreira, Thermodynamic and physical property data equations for

610

ammonia-lithium nitrate and ammonia-sodium thiocyanate solutions. Sol Energy 2

611

(1984) 231-236.

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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 s-1

UAc

3.0 kW K-1

,

0.40 kg s-1

UAe

2.5 kW K-1

,

0.17 kg s-1

UAg

1.8 kW K-1



0.028 kg s-1

UAshx

1.4 kW K-1

UAa

2.25 kW K-1

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,( = ,

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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 mid-July day and for the three cycles: single-effect H2O/LiBr, single-effect 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

16

17

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Figure 3. tg,op , tg,0 and tatm [ºC] versus solar time [h] for the mid-September day and for the three cycles: single-effect H2O/LiBr, single-effect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5.

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627 628 629 630 631

tg,op SE H2O/LiBr tatm September

0

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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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SCOP with tg,op and half nominal mass flow rate

15

16

17

18

Figure 4. Solar coefficient of performance SCOP [-] versus solar time for the mid-July

634

day, single-effect 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

8

9

10

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12

solar time (h)

13

14

15

16

17

18

Figure 5. Solar coefficient of performance SCOP [-] using tg,op versus solar time for the

640

mid-July day and for the three cycles: single-effect H2O/LiBr, single-effect 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 hybrid pr = 2 4.00E+09

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 m-2] versus time-constant tg (curves) and tg,op

645

(horizontal lines) for the mid-July day and for the three cycles: single-effect H2O/LiBr,

646

single-effect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5 and pr = 2.0.

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ACCEPTED MANUSCRIPT 1.20E+10

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 SE H2O/LiBr Qe with tg,op SE NH3/LiNO3 2.00E+09

Qe with tg,op hybrid pr =1.5 Qe with tg,op hybrid pr = 2

0.00E+00 40

45

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55

60

65

70

tg (ºC)

75

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Figure 7. Daily solar cold production [J m-2] versus time-constant tg (curves) and tg,op

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(horizontal lines) for the mid-September day and for the three cycles: single-effect

651

H2O/LiBr, single-effect NH3/LiNO3, and NH3/LiNO3 hybrid cycle with pr = 1.5 and pr = 2.0.

M AN U

649

652

EP AC C

654

TE D

653

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500

500 400

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Qe (W/m2)

Qe (W/m2)

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Characteristic temperature model

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16

18

6

8

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16

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solar time (h)

solar time (h)

a-)

b-)

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TE D

M AN U

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Figure 8. Instantaneous cooling power  [W m-2] 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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Thermodynamic model

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Characteristic temperature model

0

655 656

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Thermodynamic model

RI PT

200

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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.

AC C

EP

TE D

M AN U

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RI PT

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