researcharticle analysis of hybrid ejector absorption

Research ArticleAnalysis of Hybrid Ejector Absorption Cooling System

Doniazed Sioud and Ahmed Bellagi

Department of Energy Engineering, Ecole Nationale d’Ingenieurs de Monastir (ENIM), University of Monastir, Tunisia

Correspondence should be addressed to Doniazed Sioud; siouddoniazed@gmail.com

Received 17 July 2018; Revised 25 February 2019; Accepted 17 March 2019; Published 2 September 2019

Academic Editor: Oronzio Manca

Copyright © 2019 Doniazed Sioud and Ahmed Bellagi. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

In this paper, a hybrid ejector single-effect lithium-bromide water cycle is theoretically investigated. The system is a conventionalsingle-effect cycle activated by an external steam-ejector loop. Amathematicalmodel of the whole system is developed. Simulationsare carried out to study the effect of the major parameters of the hybrid cycle on its performances and in comparison with theconventional cycle. The ejector performance is also investigated. Results show that the entrainment ratio rises with steam pressureand condenser temperature, while it decreases with increasing generator temperature.The effect of the evaporator temperature onejector performance is negligible. It is shown also that the hybrid cycle exhibits better performances than the corresponding basiccycle. However, the performance improvement is limited to a specific range of the operating parameters. Outside this range, thehybrid system behaves similar to a conventional cycle. Inside this range, the𝐶𝑂𝑃 increases, reaches amaximum, and then decreasesand rejoins the behavior of the basic cycle.The maximum 𝐶𝑂𝑃, which can be as large as that of a conventional double-effect cycle,about 1, is obtained at lower temperatures than in the case of single-effect cycles.

1. Introduction

Cooling and air conditioning are essential for small scale andlarge industrial process applications. While systems applyingthe vapor-compression technique use environmental harmfulrefrigerants (FCC, FCHC, etc.), absorption technique forproduction of cold is based on environment friendly workingfluids, namely, aqueous lithium bromide solutions with wateras refrigerant or water-ammonia mixtures with ammonia asrefrigerant. This technique however suffers from low perfor-mances. That is the reason why new hybrid and combinedconfigurations are proposed, implying the integration of newcomponents, particularly ejectors, in order to enhance theperformances.

Various configurations incorporating ejectors were stud-ied. Exhaustive review of the literature on this subject canbe found in Besagni et al. [1, 2]. Elaborated CFD-models ofejectors developed to evaluate the ejector performances inboth on-design and off-design conditions have been also pub-lished [3]. Combined cycles were investigated with ejector setat the absorber inlet [4–9]. 𝐶𝑂𝑃 of such cycles are reportedto be higher by about 2–4% than that of conventional cycles.Principally, investigations indicate that 𝐶𝑂𝑃 of the combined

configuration are greater or equal to that of single-effectcycles, but reached at lower generator temperatures.

Other configurations are discussed where the ejector islocated at the condenser inlet of single-effect systems [10–14].Theoretical investigations confirm the improvement of theperformances in comparison with basic single-effect cycles.Experimental studies [15] show that this combined cycle is 30-60% more performant than conventional absorption cyclesand almost reaches the𝐶𝑂𝑃 of double-effect systems. Besidesmodifying configurations, adding a flash tank between ejec-tor and evaporator was also proposed [16, 17].

Ejector improved double-effect absorption system wasalso investigated [18–20].The𝐶𝑂𝑃 of the proposed refrigera-tion schemewas found to increasewith the temperature of theheat source until this temperature reaches 150∘C. Beyond thatvalue, the new cycle worked as a conventional double-effectcycle. Another configuration was studied with an ejector cou-pled to vapor generator [21–23]. This procedure is intendedto enhance the concentration process by compressing thevapor produced from the lithium bromide solution in orderto reheat the solution fromwhich it came. Results showed that𝐶𝑂𝑃 of the new cycle increases especially with the heat sourcetemperature.

HindawiJournal of EngineeringVolume 2019, Article ID 1862917, 13 pageshttps://doi.org/10.1155/2019/1862917

2 Journal of Engineering

Condenser

EvaporatorAbsorber

Generator Q CD

Evaporator

Generator

Absorber

SteamGenerator

Condenser

Q EVQAB

Figure 1: Single-effect absorption system: (a) conventional; (b) hybrid, ejector-enhanced.

In this paper, an ejector-activated single-effect LiBr-water cycle is proposed and theoretically investigated. Theobjective is to assess the feasibility and limits of performanceof this new cycle scheme. If the 𝐶𝑂𝑃 of the proposedsystem could reach that of a conventional double-effect cycle,this would mean obtaining high performance by avoidingthe configuration complexity of double-effect cycles. Weinvestigate the evolution of the 𝐶𝑂𝑃 of the hybrid cycle withthe steam generator temperature and the main factors of thecooling machine, i.e., desorber, condenser, and evaporatortemperature.The behavior of the entrainment ratio as ejectorperformance criterion is also investigated for various primaryand secondary flow pressure and backpressure.

2. System Description

Figures 1(a) and 1(b) are schematics of a conventional single-effect absorption cycle and an ejector-enhanced single-effectabsorption system. A conventional single-effect absorptionchiller (Figure 1(a)) is composed of evaporator, absorber,condenser, generator, solution expansion-valve, pump, solu-tion heat exchanger, and refrigerant expansion-valve. In ahybrid system (Figure 1(b)) a steam-generator-ejector loopis coupled to the conventional single-effect installation viathe machine generator. This extra circuit is constituted of anejector, a steam generator, a water pump, and an expansionvalve.

Journal of Engineering 3

Primaryfluid

Secondaryfluid

CONSTANT AREASECTION

NOZZLESECTION

DIFFUSER SECTION

zle ex

Figure 2: Ejector schematics.

The ejector loop is intended to improve the cycle per-formance by enhancing the concentration process in themachine generator. A high-pressure flow (18) coming fromthe external steam generator enters the primary nozzle ofthe ejector where its pressure drops while it is accelerated.At the nozzle exit section (𝑖) (Figure 2) its velocity becomessupersonic and high enough to entrain a secondary flow (19in Figure 1), part of the vapor (7) generated in the desorber.The two streams mix in the mixing chamber and the resultinggas, after undergoing a shockwave that reduces its velocityto subsonic, is compressed in the diffuser forming the lastsegment of the ejector. The exiting vapor (12) condenses inthe coil placed inside the solution generator, liberating thuscondensation heat used to concentrate the saline solution bydesorbing vapor from the water-rich solution (3) enteringthe generator. Part of the condensate flows, after appropriatepressure reduction, to the condenser, and the rest is pumpedback to the steam generator.

3. Chiller Model

Basing on mass and energy balances written for everymachine element a mathematical model of the installationis set up. For the numerical simulations, a computer code ofthemachinemodel is realized using the software EngineeringEquations Solver, EES [24].

Themodel is elaborated under the following assumptions:

(i) Steady state conditions

(ii) Negligible heat losses to the surroundings at genera-tor, condenser, absorber, and evaporator

(iii) Negligible pressure losses in pipes and components

(iv) Saturated refrigerant exiting condenser and evapora-tor

(v) Isenthalpic flow in solution and refrigerant valves

(vi) Phase equilibrium between solution entering refrig-erant generator and vapor leaving

(vii) Constant solution flow-rate leaving the absorber,specifically 2 kg/s

(viii) Heat exchanger effectiveness, 𝜀HX = 80%In the following major elements of the model are presented.

3.1. Ejector Loop. This loop includes steam generator, ejector,heating coil placed in solution generator, expansion valve,and water pump.

(i) Steam Generator

The mass and energy balances on steam generator write,respectively,

��17 = ��18 (1)

��𝑆𝐺 = ��17 (ℎ18 − ℎ17) (2)

The properties of exiting saturated vapor (18) are:𝑃𝑆𝐺 = 𝑃18 = 𝑃𝑊−𝑠𝑎𝑡 (𝑇18) (3)

ℎ18 = ℎ𝑊−𝑠𝑎𝑡 (𝑇18, 𝑋18 = 1) (4)

Further, 𝑃17 = 𝑃18 .Properties with index 𝑊 for water refer to pure water

properties as given in steam tables.

(ii) Ejector

The ejector performance depends on the backpressure𝑃𝑏𝑝—the pressure of the exiting (supposed saturated) steamflowing in the heating coil—, the primary pressure, 𝑃18 ,and the secondary pressure, 𝑃19. The relations between thedifferent pressures around the ejector are

𝑃𝑏𝑝 = 𝑃13 = 𝑃𝑊−𝑠𝑎𝑡 (𝑇13) (5)

𝑃19 = 𝑃7 = 𝑃8 (6)

The mass balance for the ejector writes

��12 = ��18 + ��19 = (1 + 𝜔) ��18 (7)

where 𝜔 stands for the entrainment ratio

𝜔 = ��19��18

The enthalpy of exiting flow (12) can be deduced from theenergy balance

ℎ12 = ℎ18 + 𝜔ℎ191 + 𝜔 (9)

(iii) Heating Coil

Assuming a difference of 5 K between the temperatures of theheat source and that of the refrigerant generator solution, weget

𝑇13 = 𝑇12 = 𝑇𝐺 + 5 = 𝑇4 + 5 (10)

ℎ13 = ℎ𝑊−𝑠𝑎𝑡 (𝑇13, 𝑋13 = 0) (11)

The mass balance writes

��12 = ��13 (12)

(iv) Water Pump

We suppose approximately isothermal pumping

𝑇17 = 𝑇16 = 𝑇13 = 𝑇14 (13)

The mass and energy balances write, successively,

��17 = ��16 (14)

ℎ17 = ℎ16 + (𝑃17 − 𝑃16)𝜌17 (15)

where the term [(𝑃17−𝑃16)/𝜌17] in the last equation representsthe specific pump work (kJ/kg), with (𝜌17 = 𝜌𝑊(𝑇17, 𝑃17)).

(v) Expansion Valve

The expansion is isenthalpic, i.e.,

ℎ14 = ℎ15 = ℎ13 (16)

��14 = ��15 (17)

3.2. Liquid Solution Loop. The absorber-generator loop com-prises absorber, solution valve, solution pump, solution heatexchanger, and refrigerant generator.

(i) Refrigerant Generator

With 𝜉 denoting the lithium bromide concentration in theliquid solution, the mass balances for this machine elementwrite

��3 = ��7 + ��4 (18)

��4𝜉4 = ��3𝜉3 (19)

Solving for ��7 yields

��7 = ��4

𝜉4 − 𝜉3𝜉3 (20)

For the energy balance we get

��4ℎ4 + ��7ℎ7 = ��3ℎ3 + ��12 (ℎ12 − ℎ13) (21)

from which we deduce

��4 = ��12 (ℎ12 − ℎ13) − (��7ℎ7 − ��3ℎ3)ℎ4

The properties of water-weak solution (4) exiting the genera-tor are determined as follows:

𝑃𝐺 = 𝑃𝐶𝐷 = 𝑃4 (23)

𝜉4 = 𝜉𝑆𝑂𝐿−𝑠𝑎𝑡 (𝑇𝐺, 𝑃𝐺) (24)

ℎ4 = ℎ𝑆𝑂𝐿−𝑠𝑎𝑡 (𝑇𝐺, 𝜉4) (25)

For known solution temperature and pressure, the saturationconcentration can be deduced from solution property rela-tions. Following equations fix the properties of exiting vaporat (7)

𝑃7 = 𝑃𝐺 (26)

𝑇7 = 𝑇𝑆𝑂𝐿−𝑠𝑎𝑡 (𝑃7, 𝜉3) (27)

ℎ7 = ℎ𝑊 (𝑇7, 𝑃7) (28)

(ii) Solution Heat Exchanger

Besides the trivial relations

𝑃5 = 𝑃4𝑃3 = 𝑃2

Mass and energy balance equations write

𝜉5 = 𝜉4𝜉3 = 𝜉2��3 = ��2��5 = ��4

ℎ3 = ℎ2 + ��4��2

(ℎ4 − ℎ5) (31)

Considering the heat exchanger effectiveness, 𝜀𝐻𝑋, we havethe following further relations:

𝑇5 = 𝜀𝐻𝑋𝑇2 + (1 − 𝜀𝐻𝑋) 𝑇4 (32)

ℎ5 = ℎ𝑆𝑂𝐿−𝑠𝑎𝑡 (𝑇5, 𝜉5) (33)

ℎ3 = ℎ𝑆𝑂𝐿−𝑠𝑎𝑡 (𝜉3, 𝑇3) (34)

(iii) Solution Valve

Through the solution valve, the pressure is reduced fromcondenser to evaporator pressure. In addition to the usualmass balance-equations (𝜉6 = 𝜉5) and (��6 = ��5) we havethe relations

ℎ6 = ℎ5 (35)

𝑇6 = 𝑇𝑆𝑂𝐿−𝑠𝑎𝑡 (𝜉4, ℎ6) (36)

(iv) Solution Pump

Again, we have the trivial mass balances ��2 = ��1and 𝜉2 =𝜉1. As for the water-pump, the pumping process is assumedisothermal (𝑇2 = 𝑇1). During pumping, the enthalpy of therefrigerant-rich solution from absorber is increased by [(𝑃2 −𝑃1)/𝜌2], with [𝜌2 = 𝜌𝑆𝑂𝐿−𝑠𝑎𝑡(𝜉2, ℎ2)],

ℎ2 = ℎ1 + 𝑃2 − 𝑃1𝜌2 (37)

(v) Absorber

Per definition, (𝑇𝐴𝐵 = 𝑇1) and (𝑃𝐴𝐵 = 𝑃1). For the liquidsolution (1) exiting the absorber we get in addition to themass and energy balance equations

��1 = ��6 + ��11��1𝜉1 = ��6𝜉6 (38)

��𝐴𝐵 = (��11ℎ11 + ��6ℎ6) − ��1ℎ1 (39)

The property relations are

𝜉1 = 𝜉𝑆𝑂𝐿−𝑠𝑜𝑙 (𝑃1, 𝑇1) (40)

ℎ1 = ℎ𝑆𝑂𝐿−𝑠𝑎𝑡 (𝑇1, 𝑃1) (41)

3.3. Refrigerant Loop

(i) Condenser

Streams (8) and (15) flow in the condenser where theycondensate. Condensing temperature and pressure are 𝑇𝐶𝐷 =𝑇9 and 𝑃𝐶𝐷 = 𝑃9, respectively. The mass and energy balancesaround the condenser write

��9 = ��8 + ��15 = ��8 + ��19 = ��7 (42)

��𝐶𝐷 = ��9 (ℎ8 − ℎ9) (43)

Knowing the condensation temperature 𝑇9, pressure 𝑃9 aswell as the enthalpy of exiting liquid can be deduced as

𝑃9 = 𝑃𝑊−𝑠𝑎𝑡 (𝑇9) (44)

ℎ9 = ℎ𝑊−𝑠𝑎𝑡 (𝑇9, 𝑋9 = 0) (45)

(ii) Refrigerant Expansion Valve

Liquid refrigerant (9) undergoes a pressure reduction beforeit enters the evaporator. Evaporation temperature and pres-sure are 𝑇𝐸𝑉 = 𝑇11 = 𝑇10 and 𝑃𝐸𝑉 = 𝑃10, respectively.

For fixed evaporator temperature 𝑇𝐸𝑉 and assumingsaturated vapor at exit, we can write 𝑃𝐸𝑉 = 𝑃𝑊−𝑠𝑎𝑡 (𝑇𝐸𝑉).

The mass and energy balances for the valve write

ℎ10 = ℎ9 (46)

��10 = ��9 (47)

(iii) Evaporator

The evaporator equations are

��𝐸𝑉 = ��11 (ℎ11 − ℎ10) (48)

��11 = ��10

ℎ11 = ℎ𝑊−𝑠𝑎𝑡 (𝑇𝐸𝑉, 𝑋11 = 1) (49)

The 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 of the proposed absorption system, whenneglecting all pump work, can be expressed as

𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑=��𝐸𝑉��𝑆𝐺

4. Ejector 1D Model and Analysis

Because the performances of the proposed cycle dependlargely on ejector performances, a reliable ejector model isnecessary for the cycle simulations. In this paper, the ejectoris modelled basing on the 1D analyses in [25, 26].

In this type of model, it is assumed that

(i) primary fluid expands isentropically in nozzle, andthe exiting flow compresses isentropically in diffuser

(ii) inlet velocities of primary and entrained fluids areinsignificant

(iii) velocity of the compressed mixture at ejector outlet isneglected

(iv) mixing of primary and secondary fluids in the suctionchamber occurs at constant pressure

(v) flow in ejector is adiabatic

Isentropic efficiencies are introduced in the model to accountfor eventual irreversibility in the expansion process in pri-mary nozzle, (𝜂𝑛), in the mixing process of primary andsecondary flow in themixing chamber, (𝜂𝑚), and finally in thecompression process in the diffuser, (𝜂𝑑). For the numericalsimulations we set 𝜂𝑛 = 0.95, 𝜂𝑑 = 0.95, and 𝜂𝑚 = 1.

4.1. Primary Nozzle. In the nozzle, the primary vapor (18)expands and accelerates. The Mach number 𝑀18𝑖 of the fluidat nozzle outlet plane (𝑖), deduced fromenergy balance, writes

𝑀18𝑖 = √ 2𝜂𝑛𝛾 − 1 ((𝑃18𝑃𝑖

)(𝛾−1)/𝛾 − 1) (51)

In this equation, 𝜂𝑛 is the isentropic nozzle efficiency,defined as the ratio between actual enthalpy change andenthalpy change undergone during an isentropic process.

The expression for (𝐴 𝑖/𝐴 𝑡) the area ratio at nozzle throatand outlet is

𝐴 𝑖𝐴 𝑡

= √ 1𝑀218𝑖

( 2𝛾 + 1 (1 + 𝛾 − 12 𝑀218𝑖))(𝛾+1)/(𝛾−1)

4.2. Suction Chamber. Because 𝑃𝑖 < 𝑃19, the secondary fluid(19) expands in the suction chamber and is entrained bythe high-speed primary flow. The Mach number 𝑀19𝑖 of theentrained fluid at nozzle exit plane writes

𝑀19𝑖 = √ 2𝛾 − 1 ((𝑃19𝑃𝑖

)(𝛾−1)/𝛾 − 1) (53)

4.3.MixingChamber. Here, primary and secondary fluids aremixed.Theproperties of the resulting streamat section (𝑗) arededuced from continuity, momentum, and energy equationsand expressed as function of the critical Mach number𝑀∗

𝑗 ,

𝑀∗𝑗 = 𝜂𝑚 𝑀∗

18𝑖 + 𝜔𝑀∗19𝑖√𝜏√(1 + 𝜔𝜏) (1 + 𝜔) (54)

As can be noticed, themixture𝑀∗𝑗 is written as a combination

of critical Mach numbers of the original streams, 𝑀∗18𝑖 and𝑀∗

19𝑖. 𝜏 in this equation stands for the temperature ratio ofincoming streams (19) and (18):

𝜏 = 𝑇19𝑇18

The relationship between 𝑀 and 𝑀∗ at any point of theejector is given by the equation

𝑀 = √ 2𝑀∗2

(𝛾 + 1) − (𝛾 − 1)𝑀∗2(56)

By the end of the mixing chamber, a shock wave occurs atsection (𝑘). The flow changes from supersonic to subsonicconditions, producing simultaneously a sudden rise in thestatic pressure. The relation between the Mach numberupstream and downstream of the shock wave is given by

𝑀𝑘 = √ 2/ (𝛾 − 1) +𝑀2𝑗(2𝛾/ (𝛾 − 1))𝑀2

𝑗 − 1 (57)

The corresponding pressure increase writes

𝑃𝑘𝑃𝑗

= 𝑀𝑗𝑀𝑘

√ 1 + (1/2)𝑀2𝑗 (𝛾 − 1)1 + (1/2)𝑀2𝑘(𝛾 − 1) (58)

4.4. Diffuser. Theexpression of the pressure lift in the diffuseris

𝑃12𝑃𝑘

= (1 + 12𝜂𝑑𝑀2𝑘 (𝛾 − 1))𝛾/(𝛾−1)

The ejector area ratio (𝐴 𝑡/𝐴𝑐), i.e., the ratio of nozzlethroat area and diffuser constant area section, writes

𝐴 𝑡𝐴𝑐

= 𝑃12𝑃18

( 𝑃𝑘𝑃12

)1/𝛾

⋅ √1 − ( 𝑃𝑘𝑃12

)(𝛾−1)/𝛾√ 1(1 + 𝜔𝜏) (1 + 𝜔)⋅ √(𝛾 + 1) / (𝛾 − 1)(2/ (𝛾 + 1))1/(𝛾−1)

5. Results and Discussion

The EES machine model program is run to thermodynam-ically analyze the proposed hybrid single-effect absorptionrefrigeration system. The thermophysical properties of LiBr-H2O solution are estimated using the software property data-and model-bank.

The simulations are performed for the conditions given inTable 1. Evaporator temperature 𝑇𝐺 is set to 4∘C, condensertemperature 𝑇𝐶𝐷 to 37∘C, and absorber temperature 𝑇𝐴𝐵 to(𝑇𝐶𝐷−2). Condenser and absorber are both supposed water-cooled. The cooling medium is processed thereafter in acooling tower.

5.1. Program and Machine Model Validation. The simulationprogram is first validated by comparing our simulationresults for a conventional single-effect cycle with the resultspublished by Somers (2009) [27] for the same operatingconditions: evaporator temperature,1.3∘C; condenser andabsorber temperatures at 40.2∘C and 32.7∘C, respectively;effectiveness of solution heat exchanger, 0.5; mass flow rateof solution leaving absorber, 1 kg/s. As can be noticed whencomparing the results in columns 2 and 3 of Table 2, both setsof data are in very good agreement. Therefore, we can nowproceed to the simulations of the proposed hybrid cycle withsome confidence.

The next step was to validate the adequacy of theconventional model by comparing the predicted, calculatedperformance with experimental data reported in [28] con-cerning a large capacity LiBr-chiller. Two different sets ofoperating conditions are considered. As can be observedwhen studying columns 4 to 7 in Table 2, the calculated datais for both tests very close to the reported data in [28]. Finally,the proposed ejector configuration model is validated using

Table 1: Simulation input data.

Parameter Value Variation rangeSteam generator pressure, 𝑃𝑆𝐺, bar 15 10–15Generator temperature,𝑇𝐺,

∘C 80 65–90Evaporator temperature,𝑇𝐸𝑉,

∘C 4 2–12Condensation temperature,𝑇𝐶𝐷,

∘C 37 28–37Absorber temperature,𝑇𝐴𝐵,

∘C 𝑇𝐶𝐷 − 2Table 2: Program and machine model validation.

Data 1 [27] Present work Data 2 [28] Present work Data 3[28] Present work

𝑇𝐺,∘C 90 101.6 83𝑇𝐸𝑉,∘C 1.3 5 12.3𝑇𝐶𝐷,∘C 40.2 43 42𝑇𝐴𝐵,∘C 32.7 38.3 39��𝐺, kW 14.95 15.00 1150 1143 1100 1105��𝐸𝑉, kW 10.77 10.80 843 842.5 842.7 842.5𝐶𝑂𝑃 0.73 0.72 0.73 0.74 0.76 0.76𝜉4, % 62.6 62 65.5 65.8 57.2 58.5𝜉3, % 57.4 56.3 56.5 57.4 53.1 53.4

0.8 0.9 1.0 1.1 1.20.8

COPhybrid (exp)

Figure 3: Hybrid cycle model validation basing on experimentaldata of ref. [29].

the only available experimental data found in the literature[29]. As represented in Figure 3, a fair agreement betweencalculated and reported data is noticed. Discrepancy mayhave its source in inaccuracy of experimental and/or toosimple ejector model (ideal gas behavior).

5.2. Comparison of Hybrid and Conventional Cycle Per-formances. For purpose of illustration, the chiller cycle isrepresented in Figure 4 in the usual Oldham-diagram and inthe water (𝑃 − ℎ)−diagram in Figure 5.

We now proceed to the comparison of the performancesof the proposed cycle and the conventional basic cycle

(without ejector) for varying machine generator called alsodesorber-temperature (Figure 6), condenser temperature(Figure 7), and evaporator temperature (Figure 8).

As depicted in Figures 6–8, the coefficient of performanceof the hybrid cycle is in all cases larger than the 𝐶𝑂𝑃 of theconventional cycle for the same operating conditions.

However, this performance enhancement is restrictedto a specific interval of machine-generator temperature, asFigure 6 clearly shows. Outside this temperature interval,both cycles are practically equivalent. Figure 6 shows also thatwith growing desorber temperature𝑇𝐺 the𝐶𝑂𝑃−curve of thehybrid cycle first exceeds that of the basic cycle, reaches amaximum than decreases gradually, and resumes the curveof the conventional cycle 𝐶𝑂𝑃. It is also worth noticingthat the 𝐶𝑂𝑃 of the hybrid cycle under optimal conditionsapproaches the 𝐶𝑂𝑃 of double-effect conventional cycle.

Figures 7 and 8 depict the evolution of the 𝐶𝑂𝑃 ofboth cycles with condenser and evaporator temperature,respectively, for (𝑃18 = 15 bar; 𝑇18 ≈ 200∘C). Note that 𝑇18

is the steam generator temperature, not the chiller desorbertemperature, the abscissa in Figures 6–14. Both 𝐶𝑂𝑃 areexpectably decreasing in the first case and increasing in thesecond. 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 is always larger than 𝐶𝑂𝑃 of conventionalcycle because the constant maintained desorber-temperatureis set to 80∘C, i.e., in the favourable interval 70∘C–90∘C.In conclusion of this section we notice that an ejectorincorporated in the hybrid cycle (i) improves the cycleperformances and (ii) the maximal 𝐶𝑂𝑃 is reached at lowermachine generator temperature.

5.3. Performances of the Hybrid Cycle. The effect observedpreviously in Figure 6 (enhancement of the cycle perfor-mance due to the incorporation of ejector in the driving

50 10 15 20 25 30 40 45 50 55 60 65 70 75 80 85 90 100

11595 12035

P [kPa]

Evaporatorpressure

Condenser pressure

Pure water,

Aqueous LiBr solution,

T [∘C]

Figure 4: Chiller cycle representation in the Oldham-diagram (𝑇𝑆𝐺 ≈ 200∘C; 𝑇𝐺 = 85∘C; 𝑇𝐸𝑉 = 4∘C; 𝑇𝐶𝐷 = 37∘C).

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

P (kPa)

h (kJ/kg)i

Figure 5: Chiller cycle representation in the water (𝑃 − ℎ)−diagram (𝑇𝑆𝐺 ≈ 200∘C; 𝑇𝐺 = 85∘C; 𝑇𝐸𝑉 = 4∘C; 𝑇𝐶𝐷 = 37∘C).

70 75 80 85 90 95

basic cyclehybrid cycle

４％６ = 4∘C４＃＄ = 37∘C

Generator Temperature (∘C)

Figure 6: 𝐶𝑂𝑃 of hybrid and conventional cycle vs. machinegenerator temperature,𝑇𝐺(𝑃18 = 15 bar; 𝑇18 ≈ 200∘C).

compartment of the machine) depends on the primary flowpressure 𝑃𝑆𝐺 = 𝑃18 used to activate the ejector. Increasingthis pressure expands this effect in magnitude and amplitudeas Figure 9 shows: the higher the steam-generator pressure

28 30 32 34 36 38 40 42

Condenser Temperature (∘C)

４％６ = 4∘C４＇ = 80∘C

Figure 7: 𝐶𝑂𝑃 of hybrid and conventional cycle vs. condensertemperature,𝑇𝐶𝐷.

(and consequently temperature), the larger the machine-generator temperature range where the cycle performanceis improved, and the higher the maximum 𝐶𝑂𝑃 that could

４＃＄ = 37∘C４＇ = 80∘C

2 4 6 8 10 12 140Evaporator Temperature (∘C)

Figure 8: 𝐶𝑂𝑃 of hybrid and conventional cycle vs. evaporatortemperature,𝑇𝐸𝑉.

４＃＄ = 37∘C４％６ = 4∘C

75 80 85 90 9570Generator Temperature (∘C)

０３＇ = 10bar０３＇ = 12bar０３＇ = 13bar

０３＇ = 14bar０３＇ = 15bar

Figure 9: 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 vs. 𝑇𝐺 for various steam-generator tempera-tures, 𝑇𝑆𝐺.

be reached inside this interval. On the opposite, when thesteamgenerator pressure𝑃𝑆𝐺 is decreased to 10 bar, practicallyno improvement more of the cycle performance is observedunder the prevailing conditions.

Figure 10 depicts the evolution of 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 with 𝑇𝐺

by varying the condenser temperature, 𝑇𝐶𝐷. It is observedthat the typical pink curve of Figure 6 is expectedly shiftedto lower machine-generator temperatures (with lower con-denser temperature, less high desorber temperature is neededto activate the cycle) with however concomitantly increasedmaximal 𝐶𝑂𝑃 and enlarged favorable temperature interval,where the cycle performance is improved.

０３＇ = 15bar４％６ = 4∘C

４＃＄ = 32∘C４＃＄ = 34∘C４＃＄ = 36∘C

65 70 75 80 85 90 9560Generator Temperature (∘C)

Figure 10: 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 vs. 𝑇𝐺 for varying condenser temperature,𝑇𝐶𝐷.

０３＇ = 15bar４＃＄ = 37∘C

４％６ = 4∘C４％６ = 6∘C

４％６ = 8∘C４％６ = 10∘C

65 70 75 80 85 90 9560Generator Temperature (∘C)

Figure 11: 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 vs. 𝑇𝐺 for varying evaporator temperature,𝑇𝐸𝑉.

Similar effects are observed in Figure 11 depicting the evo-lution of 𝐶𝑂𝑃ℎ𝑦𝑏𝑟𝑖𝑑 with 𝑇𝐺 by varying evaporator tempera-ture. Here, the typical COP—improved portion of the curve isshifted to lower𝑇𝐺—values when the evaporator temperatureis increased, a thermodynamically more favourable situation.The 𝐶𝑂𝑃 of the hybrid cycle rises from 0.85 to 1.12 forgenerator temperature decreasing from 78∘C to 67∘C whenthe evaporator temperature increases from 4∘C to 12∘C.

5.4. Ejector Performance. The ejector model presented inSection 4 will help us interpret the represented simulationresults in Figures 7–11 and assess the beneficial effect—and

４＃＄ = 37∘C４％６ = 4∘C

０３＇ = 10bar０３＇ = 12bar０３＇ = 13bar

０３＇ = 14bar０３＇ = 15bar

70 80 90 10060Generator Temperature (∘C)

Figure 12: 𝜔 vs. 𝑇𝐺 for various primary pressure 𝑃𝑆𝐺.

limits—of integration of an external ejector loop to a con-ventional absorption cycle. We first investigate the relationbetween the performance of the incorporated ejector, i.e.,its entrainment ratio 𝜔, and significant absorption machineparameters, namely, desorber temperature 𝑇𝐺, evaporatortemperature 𝑇𝐸𝑉, and condenser temperature 𝑇𝐶𝐷. Figure 12depicts the evolution of 𝜔 with 𝑇𝐺. For a given primarypressure 𝑃𝑆𝐺, the entrainment ratio decreases monotonouslywith 𝑇𝐺 and finally vanishes for a maximal value of thedesorber temperature; i.e., secondary flow (19) is no moreentrained inside the ejector.The ejector is then off-design andits geometry should be changed. Same behaviour of 𝜔 vs. 𝑇𝐺

is noticed if the steam pressure 𝑃𝑆𝐺 is increased. However,in this case the curve is shifted upwards to larger values of𝜔; i.e., more secondary vapour is sucked in the ejector for agiven temperature 𝑇𝐺, and the limit value of 𝑇𝐺 where theentrainment ration vanishes is pushed farther away.

Similar behaviour is observed in Figure 13, when forfixed primary pressure the condenser temperature (sec-ondary pressure) is varied. If the condensation temperatureis reduced (or alternatively enlarged), the entrainment ratiois also decreased (or increased, respectively). However, thecurves 𝜔 vs. 𝑇𝐺 for the various condenser temperatures allconverge to the same point on the temperature-axis where𝜔 vanishes. This temperature depends solely on the primarysteam pressure.

Finally, Figure 14 shows that the evaporator temperaturehas practically no effect on the ejector performance by fixed𝑃𝑆𝐺 and 𝑇𝐶𝐷, as all 𝜔 vs. 𝑇𝐺 for the various tested 𝑇𝐸𝑉 aresuperimposed.

According to the ejector model presented in Section 3of the present paper, the entrainment ratio depends on sixindependent parameters: nozzle area ratio, primary flowand secondary flow properties, and backpressure, i.e., 𝜔 =𝑓(𝐴 𝑖/𝐴 𝑡, 𝑃18, 𝑇18, 𝑃19, 𝑇19, 𝑃12). The results presented in the

０３＇ = 15bar

４＃＄ = 28∘C４＃＄ = 30∘C４＃＄ = 32∘C

４＃＄ = 34∘C４＃＄ = 36∘C

４％６ = 4∘C

Figure 13: 𝜔 vs. 𝑇𝐺 for various condenser temperature 𝑇𝐶𝐷.

０３＇ = 15bar４＃＄ = 37∘C

４％６ = 4∘C４％６ = 6∘C４％６ = 8∘C

４％６ = 10∘C４％６ = 12∘C

Figure 14: 𝜔 vs. 𝑇𝐺 for various evaporator temperature𝑇𝐸𝑉.

foregoing sections are obtained for simulations with thespecific conditions: (i) constant ejector nozzle ratio set to(𝐴 𝑖/𝐴 𝑡) = 17.3; (ii) saturated ejector-driving steam; i.e., 𝑇18

and 𝑃18 are then no more both independent; (iii) pressureof secondary flow 𝑃19 equals condenser pressure, an inde-pendent parameter; (iv) temperature 𝑇19 of flow 𝑃19 is notan independent variable. It depends on the processes takingplace in rest of the absorption chiller and in particular on thebackpressure,𝑃12, which is considered here as an independentparameter.

15P18 [bar]

0.5P12 [bar]

Figure 15: Entrainment ratio vs. primary pressure, 𝑃18, and back-pressure, 𝑃12, for fixed nozzle area ratio, (𝐴 𝑖/𝐴 𝑡) = 17.3, andsecondary pressure, 𝑃19 = 0.0628 bar.

In summary, the entrainment ratio depends then on justthree parameters

𝜔 = 𝑓 (𝑃18, 𝑃19, 𝑃12) (61)

Figure 15 illustrates this dependency for a fixed secondarypressure, 𝑃19 = 0.0628 bar, as it is the case for the datadepicted in Figures 6, 7, and 12. For a constant driving-steampressure 𝑃18, 𝜔 increases with falling backpressure, becomesa maximum, and decreases thereafter abruptly to zero. Moregenerally, on increasing the ejector backpressure by fixedejector geometry, a gradual reduction in entrainment ratiois induced. The maximal value of 𝜔 is the larger; i.e., thegreater the 𝐶𝑂𝑃-improvement, the higher the 𝑃18 . Further,when 𝑃18 becomes larger, the interval of backpressure 𝑃12

(and hence, the range of 𝑇12 as well as the range of desorbertemperature,𝑇4) where a chiller performance enhancement isexpected, expands. The pressure difference (𝑃18 − 𝑃12) drivesthe ejector, and the difference (𝑃19 − 𝑃𝑖), where 𝑃𝑖 is thepressure at nozzle exit, drives the entrainment process (Eq.(36)). With increasing primary pressure, 𝑃𝑖 rises and comescloser to the secondary flow pressure 𝑃19 . The suction of thesecondary flow into the mixing chamber declines graduallyand eventually vanishes for 𝑃𝑖 = 𝑃19. Consequently, at thislimit reached for 𝑃18 = 18 bar, 𝜔 falls to zero. The verticalisobar-plane 𝑃18 = 18 bar sets a geometrical limit to the usednozzle design.

The 𝜔 = 0 plane limits also the 3D surface of Figure 15.The calculations show that the Mach number 𝑀𝑗 of themixed stream is there equal to 𝑀18𝑖, the Mach number ofthe primary flow at nozzle exit; i.e., the mixed gas mass flowrate reduces to that of the primary flow and practically nosecondary gas is entrained. This constitutes a higher limit forthe design of the ejector area ratio (𝐴 𝑡/𝐴𝑐), which comes thenvery close to the nozzle area ratio, (𝐴 𝑡/𝐴 𝑖). The maximumvalue of𝜔 is found for minimal values of backpressure. At thelimit, the Mach number of mixed gas 𝑀𝑗 is the lowest andequals that of the entrained secondary flow𝑀19𝑖.

The 𝐶𝑂𝑃 curves represented in Figures 6–9 depict itsevolution when the effects of both the ejector and the single-effect absorption chiller are combined. By increasing thebackpressure and, consequently, the desorber temperature,the 𝐶𝑂𝑃 tends first to increase as it does for a conventionalcycle. The entrainment ratio however is decreasing. Theresulting outcome is then first an increase of 𝐶𝑂𝑃 and thena decrease after passing a maximum where opposed effectscancel each other.

6. Conclusion

A hybrid single-effect cycle with water lithium-bromide asworking fluid and activated by a steam-ejector loop is pro-posed and theoretically investigated. Mathematical models ofthe hybrid cycle and the ejector are detailed. Results showthat entrainment ratio of the ejector depends on activating-steam pressure, on condenser temperature, and only slightlyon evaporator temperature. For a fixed steam pressure, the𝐶𝑂𝑃 of the hybrid cycle first surpasses that of the corre-sponding conventional cycle when the desorber temperatureis increased, passes by a maximum, and then resumes theperformance of the basic cycle. The maximum 𝐶𝑂𝑃 of anejector-activated cycle is obtained at lower temperaturesthan that of a conventional system and can reach that of adouble-effect basic scheme. The span of machine generatortemperature where the 𝐶𝑂𝑃 is enhanced depends on theprimary ejector pressure: it is larger for higher pressure. Theentrainment ratio of the ejector is found to increase withthe steam pressure and to decrease with rising backpressure.However, the performance of the ejector is confined to a spe-cific region of the parameter-surface. Outside this domain,the entrainment ratio vanishes and the ejector is off-design.

Nomenclature

𝐴: Area𝐴𝑖𝐴𝑡: Nozzle area ratio (𝐴 𝑖/𝐴 𝑡)𝐴𝑐𝐴𝑡: Ejector area ratio (𝐴𝑐/𝐴 𝑡)𝐶𝑂𝑃: Coefficient of performanceℎ: Specific enthalpy (kJ/kg)��: Mass flow rate (kg/s)𝑀: Mach number𝑀∗: Critical Mach number𝑃: Pressure (bar)��: Heat transfer rate (kW)𝑅: Universal gas constant (kJ/(kg K))𝑇: Temperature (∘C)��: Work transfer rate (kW)𝑋: Steam quality

Greek Symbols

𝛾: Ratio of steam specific heats (𝐶𝑝/𝐶V)𝜀HX: Heat exchanger effectiveness𝜂: Nozzle, mixing, and diffuser efficiency

𝜉: LiBr concentration in solution (mass. %)𝜌: Density (kg/m3)𝜏: 𝑇19/𝑇18𝜔: Entrainment ratio (��19/��18).Subscripts

𝐴𝐵: Absorber𝑏𝑝: Backpressure𝑐: Constant section area (ejector)𝐶𝐷: Condenser𝑑: Diffuser (ejector)𝐸𝑉: Evaporator𝐺: Generator𝑖: Nozzle exit plane (ejector)𝑗: Plane in mixing chamber (ejector)𝑘: Shockwave plane𝑚: Mixing chamber (ejector)𝑛: Nozzle (ejector)𝑠𝑎𝑡: Saturation𝑆𝑂𝐿: Solution𝑆𝐺: Steam generator𝑊: Water1–19: Referred state points.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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