researcharticle analysis of hybrid ejector absorption
TRANSCRIPT
Research ArticleAnalysis of Hybrid Ejector Absorption Cooling System
Doniazed Sioud and Ahmed Bellagi
Department of Energy Engineering, Ecole Nationale dโIngenieurs de Monastir (ENIM), University of Monastir, Tunisia
Correspondence should be addressed to Doniazed Sioud; [email protected]
Received 17 July 2018; Revised 25 February 2019; Accepted 17 March 2019; Published 2 September 2019
Academic Editor: Oronzio Manca
Copyright ยฉ 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, the๐ถ๐๐ increases, reaches amaximum, and then decreasesand rejoins the behavior of the basic cycle.The maximum ๐ถ๐๐, 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 [4โ9]. ๐ถ๐๐ of such cycles are reportedto be higher by about 2โ4% than that of conventional cycles.Principally, investigations indicate that ๐ถ๐๐ 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 [10โ14].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 the๐ถ๐๐ 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 [18โ20].The๐ถ๐๐ of the proposed refrigera-tion schemewas found to increasewith the temperature of theheat source until this temperature reaches 150โC. Beyond thatvalue, the new cycle worked as a conventional double-effectcycle. Another configuration was studied with an ejector cou-pled to vapor generator [21โ23]. 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 that๐ถ๐๐ 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
4
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QG
QAB
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Condenser
EvaporatorAbsorber
Generator Q CD
Q EV
(a)
Evaporator
Generator
Absorber
SteamGenerator
Condenser
Q EVQAB
QCD
QSG
11
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16
1719
18
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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 ๐ถ๐๐ 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 ๐ถ๐๐ 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
Back
-pre
ssur
e
Noz
zle ex
it pl
ane (
i)
Plan
e (j)
Plan
e (k)
18
19
12At
Ai Ac
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 (๐) (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, ๐HX = 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,
๏ฟฝ๏ฟฝ17 = ๏ฟฝ๏ฟฝ18 (1)
๏ฟฝ๏ฟฝ๐๐บ = ๏ฟฝ๏ฟฝ17 (โ18 โ โ17) (2)
The properties of exiting saturated vapor (18) are:๐๐๐บ = ๐18 = ๐๐โ๐ ๐๐ก (๐18) (3)
โ18 = โ๐โ๐ ๐๐ก (๐18, ๐18 = 1) (4)
Further, ๐17 = ๐18 .Properties with index ๐ for water refer to pure water
properties as given in steam tables.
(ii) Ejector
The ejector performance depends on the backpressure๐๐๐โthe pressure of the exiting (supposed saturated) steamflowing in the heating coilโ, the primary pressure, ๐18 ,and the secondary pressure, ๐19. The relations between thedifferent pressures around the ejector are
๐๐๐ = ๐13 = ๐๐โ๐ ๐๐ก (๐13) (5)
๐19 = ๐7 = ๐8 (6)
The mass balance for the ejector writes
๏ฟฝ๏ฟฝ12 = ๏ฟฝ๏ฟฝ18 + ๏ฟฝ๏ฟฝ19 = (1 + ๐) ๏ฟฝ๏ฟฝ18 (7)
4 Journal of Engineering
where ๐ stands for the entrainment ratio
๐ = ๏ฟฝ๏ฟฝ19๏ฟฝ๏ฟฝ18
(8)
The enthalpy of exiting flow (12) can be deduced from theenergy balance
โ12 = โ18 + ๐โ191 + ๐ (9)
(iii) Heating Coil
Assuming a difference of 5 K between the temperatures of theheat source and that of the refrigerant generator solution, weget
๐13 = ๐12 = ๐๐บ + 5 = ๐4 + 5 (10)
โ13 = โ๐โ๐ ๐๐ก (๐13, ๐13 = 0) (11)
The mass balance writes
๏ฟฝ๏ฟฝ12 = ๏ฟฝ๏ฟฝ13 (12)
(iv) Water Pump
We suppose approximately isothermal pumping
๐17 = ๐16 = ๐13 = ๐14 (13)
The mass and energy balances write, successively,
๏ฟฝ๏ฟฝ17 = ๏ฟฝ๏ฟฝ16 (14)
โ17 = โ16 + (๐17 โ ๐16)๐17 (15)
where the term [(๐17โ๐16)/๐17] in the last equation representsthe specific pump work (kJ/kg), with (๐17 = ๐๐(๐17, ๐17)).
(v) Expansion Valve
The expansion is isenthalpic, i.e.,
โ14 = โ15 = โ13 (16)
๏ฟฝ๏ฟฝ14 = ๏ฟฝ๏ฟฝ15 (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 ๐ denoting the lithium bromide concentration in theliquid solution, the mass balances for this machine elementwrite
๏ฟฝ๏ฟฝ3 = ๏ฟฝ๏ฟฝ7 + ๏ฟฝ๏ฟฝ4 (18)
๏ฟฝ๏ฟฝ4๐4 = ๏ฟฝ๏ฟฝ3๐3 (19)
Solving for ๏ฟฝ๏ฟฝ7 yields
๏ฟฝ๏ฟฝ7 = ๏ฟฝ๏ฟฝ4
๐4 โ ๐3๐3 (20)
For the energy balance we get
๏ฟฝ๏ฟฝ4โ4 + ๏ฟฝ๏ฟฝ7โ7 = ๏ฟฝ๏ฟฝ3โ3 + ๏ฟฝ๏ฟฝ12 (โ12 โ โ13) (21)
from which we deduce
๏ฟฝ๏ฟฝ4 = ๏ฟฝ๏ฟฝ12 (โ12 โ โ13) โ (๏ฟฝ๏ฟฝ7โ7 โ ๏ฟฝ๏ฟฝ3โ3)โ4
(22)
The properties of water-weak solution (4) exiting the genera-tor are determined as follows:
๐๐บ = ๐๐ถ๐ท = ๐4 (23)
๐4 = ๐๐๐๐ฟโ๐ ๐๐ก (๐๐บ, ๐๐บ) (24)
โ4 = โ๐๐๐ฟโ๐ ๐๐ก (๐๐บ, ๐4) (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)
๐7 = ๐๐บ (26)
๐7 = ๐๐๐๐ฟโ๐ ๐๐ก (๐7, ๐3) (27)
โ7 = โ๐ (๐7, ๐7) (28)
(ii) Solution Heat Exchanger
Besides the trivial relations
๐5 = ๐4๐3 = ๐2
(29)
Mass and energy balance equations write
๐5 = ๐4๐3 = ๐2๏ฟฝ๏ฟฝ3 = ๏ฟฝ๏ฟฝ2๏ฟฝ๏ฟฝ5 = ๏ฟฝ๏ฟฝ4
(30)
โ3 = โ2 + ๏ฟฝ๏ฟฝ4๏ฟฝ๏ฟฝ2
(โ4 โ โ5) (31)
Considering the heat exchanger effectiveness, ๐๐ป๐, we havethe following further relations:
๐5 = ๐๐ป๐๐2 + (1 โ ๐๐ป๐) ๐4 (32)
โ5 = โ๐๐๐ฟโ๐ ๐๐ก (๐5, ๐5) (33)
Journal of Engineering 5
โ3 = โ๐๐๐ฟโ๐ ๐๐ก (๐3, ๐3) (34)
(iii) Solution Valve
Through the solution valve, the pressure is reduced fromcondenser to evaporator pressure. In addition to the usualmass balance-equations (๐6 = ๐5) and (๏ฟฝ๏ฟฝ6 = ๏ฟฝ๏ฟฝ5) we havethe relations
โ6 = โ5 (35)
๐6 = ๐๐๐๐ฟโ๐ ๐๐ก (๐4, โ6) (36)
(iv) Solution Pump
Again, we have the trivial mass balances ๏ฟฝ๏ฟฝ2 = ๏ฟฝ๏ฟฝ1and ๐2 =๐1. As for the water-pump, the pumping process is assumedisothermal (๐2 = ๐1). During pumping, the enthalpy of therefrigerant-rich solution from absorber is increased by [(๐2 โ๐1)/๐2], with [๐2 = ๐๐๐๐ฟโ๐ ๐๐ก(๐2, โ2)],
โ2 = โ1 + ๐2 โ ๐1๐2 (37)
(v) Absorber
Per definition, (๐๐ด๐ต = ๐1) and (๐๐ด๐ต = ๐1). For the liquidsolution (1) exiting the absorber we get in addition to themass and energy balance equations
๏ฟฝ๏ฟฝ1 = ๏ฟฝ๏ฟฝ6 + ๏ฟฝ๏ฟฝ11๏ฟฝ๏ฟฝ1๐1 = ๏ฟฝ๏ฟฝ6๐6 (38)
๏ฟฝ๏ฟฝ๐ด๐ต = (๏ฟฝ๏ฟฝ11โ11 + ๏ฟฝ๏ฟฝ6โ6) โ ๏ฟฝ๏ฟฝ1โ1 (39)
The property relations are
๐1 = ๐๐๐๐ฟโ๐ ๐๐ (๐1, ๐1) (40)
โ1 = โ๐๐๐ฟโ๐ ๐๐ก (๐1, ๐1) (41)
3.3. Refrigerant Loop
(i) Condenser
Streams (8) and (15) flow in the condenser where theycondensate. Condensing temperature and pressure are ๐๐ถ๐ท =๐9 and ๐๐ถ๐ท = ๐9, respectively. The mass and energy balancesaround the condenser write
๏ฟฝ๏ฟฝ9 = ๏ฟฝ๏ฟฝ8 + ๏ฟฝ๏ฟฝ15 = ๏ฟฝ๏ฟฝ8 + ๏ฟฝ๏ฟฝ19 = ๏ฟฝ๏ฟฝ7 (42)
๏ฟฝ๏ฟฝ๐ถ๐ท = ๏ฟฝ๏ฟฝ9 (โ8 โ โ9) (43)
Knowing the condensation temperature ๐9, pressure ๐9 aswell as the enthalpy of exiting liquid can be deduced as
๐9 = ๐๐โ๐ ๐๐ก (๐9) (44)
โ9 = โ๐โ๐ ๐๐ก (๐9, ๐9 = 0) (45)
(ii) Refrigerant Expansion Valve
Liquid refrigerant (9) undergoes a pressure reduction beforeit enters the evaporator. Evaporation temperature and pres-sure are ๐๐ธ๐ = ๐11 = ๐10 and ๐๐ธ๐ = ๐10, respectively.
For fixed evaporator temperature ๐๐ธ๐ and assumingsaturated vapor at exit, we can write ๐๐ธ๐ = ๐๐โ๐ ๐๐ก (๐๐ธ๐).
The mass and energy balances for the valve write
โ10 = โ9 (46)
๏ฟฝ๏ฟฝ10 = ๏ฟฝ๏ฟฝ9 (47)
(iii) Evaporator
The evaporator equations are
๏ฟฝ๏ฟฝ๐ธ๐ = ๏ฟฝ๏ฟฝ11 (โ11 โ โ10) (48)
๏ฟฝ๏ฟฝ11 = ๏ฟฝ๏ฟฝ10
โ11 = โ๐โ๐ ๐๐ก (๐๐ธ๐, ๐11 = 1) (49)
The ๐ถ๐๐โ๐ฆ๐๐๐๐ of the proposed absorption system, whenneglecting all pump work, can be expressed as
๐ถ๐๐โ๐ฆ๐๐๐๐=๏ฟฝ๏ฟฝ๐ธ๐๏ฟฝ๏ฟฝ๐๐บ
(50)
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, (๐๐), in the mixing process of primary andsecondary flow in themixing chamber, (๐๐), and finally in thecompression process in the diffuser, (๐๐). For the numericalsimulations we set ๐๐ = 0.95, ๐๐ = 0.95, and ๐๐ = 1.
6 Journal of Engineering
4.1. Primary Nozzle. In the nozzle, the primary vapor (18)expands and accelerates. The Mach number ๐18๐ of the fluidat nozzle outlet plane (๐), deduced fromenergy balance, writes
๐18๐ = โ 2๐๐๐พ โ 1 ((๐18๐๐
)(๐พโ1)/๐พ โ 1) (51)
In this equation, ๐๐ is the isentropic nozzle efficiency,defined as the ratio between actual enthalpy change andenthalpy change undergone during an isentropic process.
The expression for (๐ด ๐/๐ด ๐ก) the area ratio at nozzle throatand outlet is
๐ด ๐๐ด ๐ก
= โ 1๐218๐
( 2๐พ + 1 (1 + ๐พ โ 12 ๐218๐))(๐พ+1)/(๐พโ1)
(52)
4.2. Suction Chamber. Because ๐๐ < ๐19, the secondary fluid(19) expands in the suction chamber and is entrained bythe high-speed primary flow. The Mach number ๐19๐ of theentrained fluid at nozzle exit plane writes
๐19๐ = โ 2๐พ โ 1 ((๐19๐๐
)(๐พโ1)/๐พ โ 1) (53)
4.3.MixingChamber. Here, primary and secondary fluids aremixed.Theproperties of the resulting streamat section (๐) arededuced from continuity, momentum, and energy equationsand expressed as function of the critical Mach number๐โ
๐ ,
๐โ๐ = ๐๐ ๐โ
18๐ + ๐๐โ19๐โ๐โ(1 + ๐๐) (1 + ๐) (54)
As can be noticed, themixture๐โ๐ is written as a combination
of critical Mach numbers of the original streams, ๐โ18๐ and๐โ
19๐. ๐ in this equation stands for the temperature ratio ofincoming streams (19) and (18):
๐ = ๐19๐18
(55)
The relationship between ๐ and ๐โ at any point of theejector is given by the equation
๐ = โ 2๐โ2
(๐พ + 1) โ (๐พ โ 1)๐โ2(56)
By the end of the mixing chamber, a shock wave occurs atsection (๐). 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
๐๐ = โ 2/ (๐พ โ 1) +๐2๐(2๐พ/ (๐พ โ 1))๐2
๐ โ 1 (57)
The corresponding pressure increase writes
๐๐๐๐
= ๐๐๐๐
โ 1 + (1/2)๐2๐ (๐พ โ 1)1 + (1/2)๐2๐(๐พ โ 1) (58)
4.4. Diffuser. Theexpression of the pressure lift in the diffuseris
๐12๐๐
= (1 + 12๐๐๐2๐ (๐พ โ 1))๐พ/(๐พโ1)
(59)
The ejector area ratio (๐ด ๐ก/๐ด๐), i.e., the ratio of nozzlethroat area and diffuser constant area section, writes
๐ด ๐ก๐ด๐
= ๐12๐18
( ๐๐๐12
)1/๐พ
โ โ1 โ ( ๐๐๐12
)(๐พโ1)/๐พโ 1(1 + ๐๐) (1 + ๐)โ โ(๐พ + 1) / (๐พ โ 1)(2/ (๐พ + 1))1/(๐พโ1)
(60)
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 ๐๐บ is set to 4โC, condensertemperature ๐๐ถ๐ท to 37โC, and absorber temperature ๐๐ด๐ต to(๐๐ถ๐ทโ2). 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,1.3โC; condenser andabsorber temperatures at 40.2โC and 32.7โC, 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
Journal of Engineering 7
Table 1: Simulation input data.
Parameter Value Variation rangeSteam generator pressure, ๐๐๐บ, bar 15 10โ15Generator temperature,๐๐บ,
โC 80 65โ90Evaporator temperature,๐๐ธ๐,
โC 4 2โ12Condensation temperature,๐๐ถ๐ท,
โC 37 28โ37Absorber temperature,๐๐ด๐ต,
โC ๐๐ถ๐ท โ 2Table 2: Program and machine model validation.
Data 1 [27] Present work Data 2 [28] Present work Data 3[28] Present work
๐๐บ,โC 90 101.6 83๐๐ธ๐,โC 1.3 5 12.3๐๐ถ๐ท,โC 40.2 43 42๐๐ด๐ต,โC 32.7 38.3 39๏ฟฝ๏ฟฝ๐บ, kW 14.95 15.00 1150 1143 1100 1105๏ฟฝ๏ฟฝ๐ธ๐, kW 10.77 10.80 843 842.5 842.7 842.5๐ถ๐๐ 0.73 0.72 0.73 0.74 0.76 0.76๐4, % 62.6 62 65.5 65.8 57.2 58.5๐3, % 57.4 56.3 56.5 57.4 53.1 53.4
0.8 0.9 1.0 1.1 1.20.8
0.9
1.0
1.1
1.2
COPhybrid (exp)
COP h
ybrid
(theo
)
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 (๐ โ โ)โdiagram 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 6โ8, the coefficient of performanceof the hybrid cycle is in all cases larger than the ๐ถ๐๐ 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 temperature๐๐บ the๐ถ๐๐โcurve of thehybrid cycle first exceeds that of the basic cycle, reaches amaximum than decreases gradually, and resumes the curveof the conventional cycle ๐ถ๐๐. It is also worth noticingthat the ๐ถ๐๐ of the hybrid cycle under optimal conditionsapproaches the ๐ถ๐๐ of double-effect conventional cycle.
Figures 7 and 8 depict the evolution of the ๐ถ๐๐ ofboth cycles with condenser and evaporator temperature,respectively, for (๐18 = 15 bar; ๐18 โ 200โC). Note that ๐18
is the steam generator temperature, not the chiller desorbertemperature, the abscissa in Figures 6โ14. Both ๐ถ๐๐ areexpectably decreasing in the first case and increasing in thesecond. ๐ถ๐๐โ๐ฆ๐๐๐๐ is always larger than ๐ถ๐๐ of conventionalcycle because the constant maintained desorber-temperatureis set to 80โC, i.e., in the favourable interval 70โCโ90โC.In conclusion of this section we notice that an ejectorincorporated in the hybrid cycle (i) improves the cycleperformances and (ii) the maximal ๐ถ๐๐ 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
8 Journal of Engineering
50 10 15 20 25 30 40 45 50 55 60 65 70 75 80 85 90 100
105
110
11595 12035
50
10
5432
1
0.5
P [kPa]
Evaporatorpressure
Condenser pressure
Des
orbe
r tem
pera
ture
Con
dens
er te
mpe
ratu
re
Abso
rber
tem
pera
ture
11
9
1
4
6
Pure water,
=0
Aqueous LiBr solution,
=45
%
=50
%
=55
%
=60
%
=65%
T [โC]
Figure 4: Chiller cycle representation in the Oldham-diagram (๐๐๐บ โ 200โC; ๐๐บ = 85โC; ๐๐ธ๐ = 4โC; ๐๐ถ๐ท = 37โC).
0 200
104
103
102
101
100
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
13
159
10 11
17 18
19
12
P (kPa)
h (kJ/kg)i
Figure 5: Chiller cycle representation in the water (๐ โ โ)โdiagram (๐๐๐บ โ 200โC; ๐๐บ = 85โC; ๐๐ธ๐ = 4โC; ๐๐ถ๐ท = 37โC).
70 75 80 85 90 95
basic cyclehybrid cycle
0.4
0.5
0.6
0.7
0.8
0.9
1.0
COP
๏ผ๏ผ ๏ผ = 4โC๏ผ๏ผ๏ผ = 37โC
Generator Temperature (โC)
Figure 6: ๐ถ๐๐ of hybrid and conventional cycle vs. machinegenerator temperature,๐๐บ(๐18 = 15 bar; ๐18 โ 200โC).
compartment of the machine) depends on the primary flowpressure ๐๐๐บ = ๐18 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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
COP
basic cyclehybrid cycle
Condenser Temperature (โC)
๏ผ๏ผ ๏ผ = 4โC๏ผ๏ผ = 80โC
Figure 7: ๐ถ๐๐ of hybrid and conventional cycle vs. condensertemperature,๐๐ถ๐ท.
(and consequently temperature), the larger the machine-generator temperature range where the cycle performanceis improved, and the higher the maximum ๐ถ๐๐ that could
Journal of Engineering 9
basic cyclehybrid cycle
๏ผ๏ผ๏ผ = 37โC๏ผ๏ผ = 80โC
2 4 6 8 10 12 140Evaporator Temperature (โC)
0.4
0.5
0.6
0.7
0.8
0.9
1.0CO
P
Figure 8: ๐ถ๐๐ of hybrid and conventional cycle vs. evaporatortemperature,๐๐ธ๐.
๏ผ๏ผ๏ผ = 37โC๏ผ๏ผ ๏ผ = 4โC
0.2
0.4
0.6
0.8
1.0
COP h
ybrid
75 80 85 90 9570Generator Temperature (โC)
๏ผ๏ผ๏ผ = 10bar๏ผ๏ผ๏ผ = 12bar๏ผ๏ผ๏ผ = 13bar
๏ผ๏ผ๏ผ = 14bar๏ผ๏ผ๏ผ = 15bar
Figure 9: ๐ถ๐๐โ๐ฆ๐๐๐๐ vs. ๐๐บ for various steam-generator tempera-tures, ๐๐๐บ.
be reached inside this interval. On the opposite, when thesteamgenerator pressure๐๐๐บ is decreased to 10 bar, practicallyno improvement more of the cycle performance is observedunder the prevailing conditions.
Figure 10 depicts the evolution of ๐ถ๐๐โ๐ฆ๐๐๐๐ with ๐๐บ
by varying the condenser temperature, ๐๐ถ๐ท. 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 ๐ถ๐๐ and enlarged favorable temperature interval,where the cycle performance is improved.
๏ผ๏ผ๏ผ = 15bar๏ผ๏ผ ๏ผ = 4โC
๏ผ๏ผ๏ผ = 32โC๏ผ๏ผ๏ผ = 34โC๏ผ๏ผ๏ผ = 36โC
0.2
0.4
0.6
0.8
1.0
1.2
COP h
ybrid
65 70 75 80 85 90 9560Generator Temperature (โC)
Figure 10: ๐ถ๐๐โ๐ฆ๐๐๐๐ vs. ๐๐บ for varying condenser temperature,๐๐ถ๐ท.
๏ผ๏ผ๏ผ = 15bar๏ผ๏ผ๏ผ = 37โC
๏ผ๏ผ ๏ผ = 4โC๏ผ๏ผ ๏ผ = 6โC
๏ผ๏ผ ๏ผ = 8โC๏ผ๏ผ ๏ผ = 10โC
65 70 75 80 85 90 9560Generator Temperature (โC)
0.2
0.4
0.6
0.8
1.0
1.2
COP h
ybrid
Figure 11: ๐ถ๐๐โ๐ฆ๐๐๐๐ vs. ๐๐บ for varying evaporator temperature,๐๐ธ๐.
Similar effects are observed in Figure 11 depicting the evo-lution of ๐ถ๐๐โ๐ฆ๐๐๐๐ with ๐๐บ by varying evaporator tempera-ture. Here, the typical COPโimproved portion of the curve isshifted to lower๐๐บโvalues when the evaporator temperatureis increased, a thermodynamically more favourable situation.The ๐ถ๐๐ of the hybrid cycle rises from 0.85 to 1.12 forgenerator temperature decreasing from 78โC to 67โC whenthe evaporator temperature increases from 4โC to 12โC.
5.4. Ejector Performance. The ejector model presented inSection 4 will help us interpret the represented simulationresults in Figures 7โ11 and assess the beneficial effectโand
10 Journal of Engineering
๏ผ๏ผ๏ผ = 37โC๏ผ๏ผ ๏ผ = 4โC
๏ผ๏ผ๏ผ = 10bar๏ผ๏ผ๏ผ = 12bar๏ผ๏ผ๏ผ = 13bar
๏ผ๏ผ๏ผ = 14bar๏ผ๏ผ๏ผ = 15bar
70 80 90 10060Generator Temperature (โC)
0.0
0.1
0.2
0.3
0.4
0.5En
trai
nmen
t rat
io
Figure 12: ๐ vs. ๐๐บ for various primary pressure ๐๐๐บ.
limitsโof 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 ๐, and significant absorption machineparameters, namely, desorber temperature ๐๐บ, evaporatortemperature ๐๐ธ๐, and condenser temperature ๐๐ถ๐ท. Figure 12depicts the evolution of ๐ with ๐๐บ. For a given primarypressure ๐๐๐บ, the entrainment ratio decreases monotonouslywith ๐๐บ 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 ๐ vs. ๐๐บ
is noticed if the steam pressure ๐๐๐บ is increased. However,in this case the curve is shifted upwards to larger values of๐; i.e., more secondary vapour is sucked in the ejector for agiven temperature ๐๐บ, and the limit value of ๐๐บ 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 ๐ vs. ๐๐บ for the various condenser temperatures allconverge to the same point on the temperature-axis where๐ 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 fixed๐๐๐บ and ๐๐ถ๐ท, as all ๐ vs. ๐๐บ for the various tested ๐๐ธ๐ 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., ๐ =๐(๐ด ๐/๐ด ๐ก, ๐18, ๐18, ๐19, ๐19, ๐12). The results presented in the
๏ผ๏ผ๏ผ = 15bar
๏ผ๏ผ๏ผ = 28โC๏ผ๏ผ๏ผ = 30โC๏ผ๏ผ๏ผ = 32โC
๏ผ๏ผ๏ผ = 34โC๏ผ๏ผ๏ผ = 36โC
๏ผ๏ผ ๏ผ = 4โC
70 80 90 10060Generator Temperature (โC)
0.0
0.1
0.2
0.3
0.4
0.5
Entr
ainm
ent r
atio
Figure 13: ๐ vs. ๐๐บ for various condenser temperature ๐๐ถ๐ท.
๏ผ๏ผ๏ผ = 15bar๏ผ๏ผ๏ผ = 37โC
๏ผ๏ผ ๏ผ = 4โC๏ผ๏ผ ๏ผ = 6โC๏ผ๏ผ ๏ผ = 8โC
๏ผ๏ผ ๏ผ = 10โC๏ผ๏ผ ๏ผ = 12โC
70 80 90 10060Generator Temperature (โC)
0.0
0.1
0.2
0.3
0.4
0.5
Entr
ainm
ent r
atio
Figure 14: ๐ vs. ๐๐บ for various evaporator temperature๐๐ธ๐.
foregoing sections are obtained for simulations with thespecific conditions: (i) constant ejector nozzle ratio set to(๐ด ๐/๐ด ๐ก) = 17.3; (ii) saturated ejector-driving steam; i.e., ๐18
and ๐18 are then no more both independent; (iii) pressureof secondary flow ๐19 equals condenser pressure, an inde-pendent parameter; (iv) temperature ๐19 of flow ๐19 is notan independent variable. It depends on the processes takingplace in rest of the absorption chiller and in particular on thebackpressure,๐12, which is considered here as an independentparameter.
Journal of Engineering 11
0.4
0.2
0.0
5
10
15P18 [bar]
1.0
0.5P12 [bar]
Figure 15: Entrainment ratio vs. primary pressure, ๐18, and back-pressure, ๐12, for fixed nozzle area ratio, (๐ด ๐/๐ด ๐ก) = 17.3, andsecondary pressure, ๐19 = 0.0628 bar.
In summary, the entrainment ratio depends then on justthree parameters
๐ = ๐ (๐18, ๐19, ๐12) (61)
Figure 15 illustrates this dependency for a fixed secondarypressure, ๐19 = 0.0628 bar, as it is the case for the datadepicted in Figures 6, 7, and 12. For a constant driving-steampressure ๐18, ๐ 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 ๐ is the larger; i.e., thegreater the ๐ถ๐๐-improvement, the higher the ๐18 . Further,when ๐18 becomes larger, the interval of backpressure ๐12
(and hence, the range of ๐12 as well as the range of desorbertemperature,๐4) where a chiller performance enhancement isexpected, expands. The pressure difference (๐18 โ ๐12) drivesthe ejector, and the difference (๐19 โ ๐๐), where ๐๐ is thepressure at nozzle exit, drives the entrainment process (Eq.(36)). With increasing primary pressure, ๐๐ rises and comescloser to the secondary flow pressure ๐19 . The suction of thesecondary flow into the mixing chamber declines graduallyand eventually vanishes for ๐๐ = ๐19. Consequently, at thislimit reached for ๐18 = 18 bar, ๐ falls to zero. The verticalisobar-plane ๐18 = 18 bar sets a geometrical limit to the usednozzle design.
The ๐ = 0 plane limits also the 3D surface of Figure 15.The calculations show that the Mach number ๐๐ of themixed stream is there equal to ๐18๐, 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 (๐ด ๐ก/๐ด๐), which comes thenvery close to the nozzle area ratio, (๐ด ๐ก/๐ด ๐). The maximumvalue of๐ is found for minimal values of backpressure. At thelimit, the Mach number of mixed gas ๐๐ is the lowest andequals that of the entrained secondary flow๐19๐.
The ๐ถ๐๐ curves represented in Figures 6โ9 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 ๐ถ๐๐ tends first to increase as it does for a conventionalcycle. The entrainment ratio however is decreasing. Theresulting outcome is then first an increase of ๐ถ๐๐ 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, the๐ถ๐๐ 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 ๐ถ๐๐ 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 ๐ถ๐๐ 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
๐ด: Area๐ด๐๐ด๐ก: Nozzle area ratio (๐ด ๐/๐ด ๐ก)๐ด๐๐ด๐ก: Ejector area ratio (๐ด๐/๐ด ๐ก)๐ถ๐๐: Coefficient of performanceโ: Specific enthalpy (kJ/kg)๏ฟฝ๏ฟฝ: Mass flow rate (kg/s)๐: Mach number๐โ: Critical Mach number๐: Pressure (bar)๏ฟฝ๏ฟฝ: Heat transfer rate (kW)๐ : Universal gas constant (kJ/(kg K))๐: Temperature (โC)๏ฟฝ๏ฟฝ: Work transfer rate (kW)๐: Steam quality
Greek Symbols
๐พ: Ratio of steam specific heats (๐ถ๐/๐ถV)๐HX: Heat exchanger effectiveness๐: Nozzle, mixing, and diffuser efficiency
12 Journal of Engineering
๐: LiBr concentration in solution (mass. %)๐: Density (kg/m3)๐: ๐19/๐18๐: Entrainment ratio (๏ฟฝ๏ฟฝ19/๏ฟฝ๏ฟฝ18).Subscripts
๐ด๐ต: Absorber๐๐: Backpressure๐: Constant section area (ejector)๐ถ๐ท: Condenser๐: Diffuser (ejector)๐ธ๐: Evaporator๐บ: Generator๐: Nozzle exit plane (ejector)๐: Plane in mixing chamber (ejector)๐: Shockwave plane๐: Mixing chamber (ejector)๐: Nozzle (ejector)๐ ๐๐ก: Saturation๐๐๐ฟ: Solution๐๐บ: Steam generator๐: Water1โ19: 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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