Post on 05-Jun-2022
Research ArticleAnalysis of Hybrid Ejector Absorption Cooling System
Doniazed Sioud and Ahmed Bellagi
Department of Energy Engineering, Ecole Nationale dâIngenieurs 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, theð¶ðð increases, reaches amaximum, and then decreasesand rejoins the behavior of the basic cycle.The maximum ð¶ðð, 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 [4â9]. ð¶ðð of such cycles are reportedto be higher by about 2â4% than that of conventional cycles.Principally, investigations indicate that ð¶ðð 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 [10â14].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 theð¶ðð 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 [18â20].Theð¶ðð of the proposed refrigera-tion schemewas found to increasewith the temperature of theheat source until this temperature reaches 150âC. Beyond thatvalue, the new cycle worked as a conventional double-effectcycle. Another configuration was studied with an ejector cou-pled to vapor generator [21â23]. 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 thatð¶ðð 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
5
611
QG
QAB
3
7
1
2
9
10
Condenser
EvaporatorAbsorber
Generator Q CD
Q EV
(a)
Evaporator
Generator
Absorber
SteamGenerator
Condenser
Q EVQAB
QCD
QSG
11
8
16
1719
18
7
9
10
13 14
4
5
6
3
1
2
15
12
(b)
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 ð¶ðð 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 ð¶ðð 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 (ð) (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, ðHX = 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,
ᅵᅵ17 = ᅵᅵ18 (1)
ᅵᅵððº = ᅵᅵ17 (â18 â â17) (2)
The properties of exiting saturated vapor (18) are:ðððº = ð18 = ððâð ðð¡ (ð18) (3)
â18 = âðâð ðð¡ (ð18, ð18 = 1) (4)
Further, ð17 = ð18 .Properties with index ð for water refer to pure water
properties as given in steam tables.
(ii) Ejector
The ejector performance depends on the backpressureðððâthe pressure of the exiting (supposed saturated) steamflowing in the heating coilâ, the primary pressure, ð18 ,and the secondary pressure, ð19. The relations between thedifferent pressures around the ejector are
ððð = ð13 = ððâð ðð¡ (ð13) (5)
ð19 = ð7 = ð8 (6)
The mass balance for the ejector writes
ᅵᅵ12 = ᅵᅵ18 + ᅵᅵ19 = (1 + ð) ᅵᅵ18 (7)
4 Journal of Engineering
where ð stands for the entrainment ratio
ð = ᅵᅵ19ᅵᅵ18
(8)
The enthalpy of exiting flow (12) can be deduced from theenergy balance
â12 = â18 + ðâ191 + ð (9)
(iii) Heating Coil
Assuming a difference of 5 K between the temperatures of theheat source and that of the refrigerant generator solution, weget
ð13 = ð12 = ððº + 5 = ð4 + 5 (10)
â13 = âðâð ðð¡ (ð13, ð13 = 0) (11)
The mass balance writes
ᅵᅵ12 = ᅵᅵ13 (12)
(iv) Water Pump
We suppose approximately isothermal pumping
ð17 = ð16 = ð13 = ð14 (13)
The mass and energy balances write, successively,
ᅵᅵ17 = ᅵᅵ16 (14)
â17 = â16 + (ð17 â ð16)ð17 (15)
where the term [(ð17âð16)/ð17] in the last equation representsthe specific pump work (kJ/kg), with (ð17 = ðð(ð17, ð17)).
(v) Expansion Valve
The expansion is isenthalpic, i.e.,
â14 = â15 = â13 (16)
ᅵᅵ14 = ᅵᅵ15 (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 ð denoting the lithium bromide concentration in theliquid solution, the mass balances for this machine elementwrite
ᅵᅵ3 = ᅵᅵ7 + ᅵᅵ4 (18)
ᅵᅵ4ð4 = ᅵᅵ3ð3 (19)
Solving for ᅵᅵ7 yields
ᅵᅵ7 = ᅵᅵ4
ð4 â ð3ð3 (20)
For the energy balance we get
ᅵᅵ4â4 + ᅵᅵ7â7 = ᅵᅵ3â3 + ᅵᅵ12 (â12 â â13) (21)
from which we deduce
ᅵᅵ4 = ᅵᅵ12 (â12 â â13) â (ᅵᅵ7â7 â ᅵᅵ3â3)â4
(22)
The properties of water-weak solution (4) exiting the genera-tor are determined as follows:
ððº = ðð¶ð· = ð4 (23)
ð4 = ðððð¿âð ðð¡ (ððº, ððº) (24)
â4 = âððð¿âð ðð¡ (ððº, ð4) (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)
ð7 = ððº (26)
ð7 = ðððð¿âð ðð¡ (ð7, ð3) (27)
â7 = âð (ð7, ð7) (28)
(ii) Solution Heat Exchanger
Besides the trivial relations
ð5 = ð4ð3 = ð2
(29)
Mass and energy balance equations write
ð5 = ð4ð3 = ð2ᅵᅵ3 = ᅵᅵ2ᅵᅵ5 = ᅵᅵ4
(30)
â3 = â2 + ᅵᅵ4ᅵᅵ2
(â4 â â5) (31)
Considering the heat exchanger effectiveness, ðð»ð, we havethe following further relations:
ð5 = ðð»ðð2 + (1 â ðð»ð) ð4 (32)
â5 = âððð¿âð ðð¡ (ð5, ð5) (33)
Journal of Engineering 5
â3 = âððð¿âð ðð¡ (ð3, ð3) (34)
(iii) Solution Valve
Through the solution valve, the pressure is reduced fromcondenser to evaporator pressure. In addition to the usualmass balance-equations (ð6 = ð5) and (ᅵᅵ6 = ᅵᅵ5) we havethe relations
â6 = â5 (35)
ð6 = ðððð¿âð ðð¡ (ð4, â6) (36)
(iv) Solution Pump
Again, we have the trivial mass balances ᅵᅵ2 = ᅵᅵ1and ð2 =ð1. As for the water-pump, the pumping process is assumedisothermal (ð2 = ð1). During pumping, the enthalpy of therefrigerant-rich solution from absorber is increased by [(ð2 âð1)/ð2], with [ð2 = ðððð¿âð ðð¡(ð2, â2)],
â2 = â1 + ð2 â ð1ð2 (37)
(v) Absorber
Per definition, (ððŽðµ = ð1) and (ððŽðµ = ð1). For the liquidsolution (1) exiting the absorber we get in addition to themass and energy balance equations
ᅵᅵ1 = ᅵᅵ6 + ᅵᅵ11ᅵᅵ1ð1 = ᅵᅵ6ð6 (38)
ᅵᅵðŽðµ = (ᅵᅵ11â11 + ᅵᅵ6â6) â ᅵᅵ1â1 (39)
The property relations are
ð1 = ðððð¿âð ðð (ð1, ð1) (40)
â1 = âððð¿âð ðð¡ (ð1, ð1) (41)
3.3. Refrigerant Loop
(i) Condenser
Streams (8) and (15) flow in the condenser where theycondensate. Condensing temperature and pressure are ðð¶ð· =ð9 and ðð¶ð· = ð9, respectively. The mass and energy balancesaround the condenser write
ᅵᅵ9 = ᅵᅵ8 + ᅵᅵ15 = ᅵᅵ8 + ᅵᅵ19 = ᅵᅵ7 (42)
ᅵᅵð¶ð· = ᅵᅵ9 (â8 â â9) (43)
Knowing the condensation temperature ð9, pressure ð9 aswell as the enthalpy of exiting liquid can be deduced as
ð9 = ððâð ðð¡ (ð9) (44)
â9 = âðâð ðð¡ (ð9, ð9 = 0) (45)
(ii) Refrigerant Expansion Valve
Liquid refrigerant (9) undergoes a pressure reduction beforeit enters the evaporator. Evaporation temperature and pres-sure are ððžð = ð11 = ð10 and ððžð = ð10, respectively.
For fixed evaporator temperature ððžð and assumingsaturated vapor at exit, we can write ððžð = ððâð ðð¡ (ððžð).
The mass and energy balances for the valve write
â10 = â9 (46)
ᅵᅵ10 = ᅵᅵ9 (47)
(iii) Evaporator
The evaporator equations are
ᅵᅵðžð = ᅵᅵ11 (â11 â â10) (48)
ᅵᅵ11 = ᅵᅵ10
â11 = âðâð ðð¡ (ððžð, ð11 = 1) (49)
The ð¶ððâðŠðððð of the proposed absorption system, whenneglecting all pump work, can be expressed as
ð¶ððâðŠðððð=ᅵᅵðžðᅵᅵððº
(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, (ðð), in the mixing process of primary andsecondary flow in themixing chamber, (ðð), and finally in thecompression process in the diffuser, (ðð). For the numericalsimulations we set ðð = 0.95, ðð = 0.95, and ðð = 1.
6 Journal of Engineering
4.1. Primary Nozzle. In the nozzle, the primary vapor (18)expands and accelerates. The Mach number ð18ð of the fluidat nozzle outlet plane (ð), deduced fromenergy balance, writes
ð18ð = â 2ðððŸ â 1 ((ð18ðð
)(ðŸâ1)/ðŸ â 1) (51)
In this equation, ðð is the isentropic nozzle efficiency,defined as the ratio between actual enthalpy change andenthalpy change undergone during an isentropic process.
The expression for (ðŽ ð/ðŽ ð¡) the area ratio at nozzle throatand outlet is
ðŽ ððŽ ð¡
= â 1ð218ð
( 2ðŸ + 1 (1 + ðŸ â 12 ð218ð))(ðŸ+1)/(ðŸâ1)
(52)
4.2. Suction Chamber. Because ðð < ð19, the secondary fluid(19) expands in the suction chamber and is entrained bythe high-speed primary flow. The Mach number ð19ð of theentrained fluid at nozzle exit plane writes
ð19ð = â 2ðŸ â 1 ((ð19ðð
)(ðŸâ1)/ðŸ â 1) (53)
4.3.MixingChamber. Here, primary and secondary fluids aremixed.Theproperties of the resulting streamat section (ð) arededuced from continuity, momentum, and energy equationsand expressed as function of the critical Mach numberðâ
ð ,
ðâð = ðð ðâ
18ð + ððâ19ðâðâ(1 + ðð) (1 + ð) (54)
As can be noticed, themixtureðâð is written as a combination
of critical Mach numbers of the original streams, ðâ18ð andðâ
19ð. ð in this equation stands for the temperature ratio ofincoming streams (19) and (18):
ð = ð19ð18
(55)
The relationship between ð and ðâ at any point of theejector is given by the equation
ð = â 2ðâ2
(ðŸ + 1) â (ðŸ â 1)ðâ2(56)
By the end of the mixing chamber, a shock wave occurs atsection (ð). 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
ðð = â 2/ (ðŸ â 1) +ð2ð(2ðŸ/ (ðŸ â 1))ð2
ð â 1 (57)
The corresponding pressure increase writes
ðððð
= ðððð
â 1 + (1/2)ð2ð (ðŸ â 1)1 + (1/2)ð2ð(ðŸ â 1) (58)
4.4. Diffuser. Theexpression of the pressure lift in the diffuseris
ð12ðð
= (1 + 12ððð2ð (ðŸ â 1))ðŸ/(ðŸâ1)
(59)
The ejector area ratio (ðŽ ð¡/ðŽð), i.e., the ratio of nozzlethroat area and diffuser constant area section, writes
ðŽ ð¡ðŽð
= ð12ð18
( ððð12
)1/ðŸ
â â1 â ( ððð12
)(ðŸâ1)/ðŸâ 1(1 + ðð) (1 + ð)â â(ðŸ + 1) / (ðŸ â 1)(2/ (ðŸ + 1))1/(ðŸâ1)
(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 ððº is set to 4âC, condensertemperature ðð¶ð· to 37âC, and absorber temperature ððŽðµ to(ðð¶ð·â2). 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,1.3âC; condenser andabsorber temperatures at 40.2âC and 32.7âC, 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, ðððº, bar 15 10â15Generator temperature,ððº,
âC 80 65â90Evaporator temperature,ððžð,
âC 4 2â12Condensation temperature,ðð¶ð·,
âC 37 28â37Absorber temperature,ððŽðµ,
âC ðð¶ð· â 2Table 2: Program and machine model validation.
Data 1 [27] Present work Data 2 [28] Present work Data 3[28] Present work
ððº,âC 90 101.6 83ððžð,âC 1.3 5 12.3ðð¶ð·,âC 40.2 43 42ððŽðµ,âC 32.7 38.3 39ᅵᅵðº, kW 14.95 15.00 1150 1143 1100 1105ᅵᅵðžð, kW 10.77 10.80 843 842.5 842.7 842.5ð¶ðð 0.73 0.72 0.73 0.74 0.76 0.76ð4, % 62.6 62 65.5 65.8 57.2 58.5ð3, % 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 (ð â â)âdiagram 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 6â8, the coefficient of performanceof the hybrid cycle is in all cases larger than the ð¶ðð 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 temperatureððº theð¶ððâcurve of thehybrid cycle first exceeds that of the basic cycle, reaches amaximum than decreases gradually, and resumes the curveof the conventional cycle ð¶ðð. It is also worth noticingthat the ð¶ðð of the hybrid cycle under optimal conditionsapproaches the ð¶ðð of double-effect conventional cycle.
Figures 7 and 8 depict the evolution of the ð¶ðð ofboth cycles with condenser and evaporator temperature,respectively, for (ð18 = 15 bar; ð18 â 200âC). Note that ð18
is the steam generator temperature, not the chiller desorbertemperature, the abscissa in Figures 6â14. Both ð¶ðð areexpectably decreasing in the first case and increasing in thesecond. ð¶ððâðŠðððð is always larger than ð¶ðð of conventionalcycle because the constant maintained desorber-temperatureis set to 80âC, i.e., in the favourable interval 70âCâ90âC.In conclusion of this section we notice that an ejectorincorporated in the hybrid cycle (i) improves the cycleperformances and (ii) the maximal ð¶ðð 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 [âC]
Figure 4: Chiller cycle representation in the Oldham-diagram (ðððº â 200âC; ððº = 85âC; ððžð = 4âC; ðð¶ð· = 37âC).
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 (ð â â)âdiagram (ðððº â 200âC; ððº = 85âC; ððžð = 4âC; ðð¶ð· = 37âC).
70 75 80 85 90 95
basic cyclehybrid cycle
0.4
0.5
0.6
0.7
0.8
0.9
1.0
COP
ïŒïŒ ïŒ = 4âCïŒïŒïŒ = 37âC
Generator Temperature (âC)
Figure 6: ð¶ðð of hybrid and conventional cycle vs. machinegenerator temperature,ððº(ð18 = 15 bar; ð18 â 200âC).
compartment of the machine) depends on the primary flowpressure ðððº = ð18 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 (âC)
ïŒïŒ ïŒ = 4âCïŒïŒ = 80âC
Figure 7: ð¶ðð of hybrid and conventional cycle vs. condensertemperature,ðð¶ð·.
(and consequently temperature), the larger the machine-generator temperature range where the cycle performanceis improved, and the higher the maximum ð¶ðð that could
Journal of Engineering 9
basic cyclehybrid cycle
ïŒïŒïŒ = 37âCïŒïŒ = 80âC
2 4 6 8 10 12 140Evaporator Temperature (âC)
0.4
0.5
0.6
0.7
0.8
0.9
1.0CO
P
Figure 8: ð¶ðð of hybrid and conventional cycle vs. evaporatortemperature,ððžð.
ïŒïŒïŒ = 37âCïŒïŒ ïŒ = 4âC
0.2
0.4
0.6
0.8
1.0
COP h
ybrid
75 80 85 90 9570Generator Temperature (âC)
ïŒïŒïŒ = 10barïŒïŒïŒ = 12barïŒïŒïŒ = 13bar
ïŒïŒïŒ = 14barïŒïŒïŒ = 15bar
Figure 9: ð¶ððâðŠðððð vs. ððº for various steam-generator tempera-tures, ðððº.
be reached inside this interval. On the opposite, when thesteamgenerator pressureðððº is decreased to 10 bar, practicallyno improvement more of the cycle performance is observedunder the prevailing conditions.
Figure 10 depicts the evolution of ð¶ððâðŠðððð with ððº
by varying the condenser temperature, ðð¶ð·. 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 ð¶ðð and enlarged favorable temperature interval,where the cycle performance is improved.
ïŒïŒïŒ = 15barïŒïŒ ïŒ = 4âC
ïŒïŒïŒ = 32âCïŒïŒïŒ = 34âCïŒïŒïŒ = 36âC
0.2
0.4
0.6
0.8
1.0
1.2
COP h
ybrid
65 70 75 80 85 90 9560Generator Temperature (âC)
Figure 10: ð¶ððâðŠðððð vs. ððº for varying condenser temperature,ðð¶ð·.
ïŒïŒïŒ = 15barïŒïŒïŒ = 37âC
ïŒïŒ ïŒ = 4âCïŒïŒ ïŒ = 6âC
ïŒïŒ ïŒ = 8âCïŒïŒ ïŒ = 10âC
65 70 75 80 85 90 9560Generator Temperature (âC)
0.2
0.4
0.6
0.8
1.0
1.2
COP h
ybrid
Figure 11: ð¶ððâðŠðððð vs. ððº for varying evaporator temperature,ððžð.
Similar effects are observed in Figure 11 depicting the evo-lution of ð¶ððâðŠðððð with ððº by varying evaporator tempera-ture. Here, the typical COPâimproved portion of the curve isshifted to lowerððºâvalues when the evaporator temperatureis increased, a thermodynamically more favourable situation.The ð¶ðð of the hybrid cycle rises from 0.85 to 1.12 forgenerator temperature decreasing from 78âC to 67âC whenthe evaporator temperature increases from 4âC to 12âC.
5.4. Ejector Performance. The ejector model presented inSection 4 will help us interpret the represented simulationresults in Figures 7â11 and assess the beneficial effectâand
10 Journal of Engineering
ïŒïŒïŒ = 37âCïŒïŒ ïŒ = 4âC
ïŒïŒïŒ = 10barïŒïŒïŒ = 12barïŒïŒïŒ = 13bar
ïŒïŒïŒ = 14barïŒïŒïŒ = 15bar
70 80 90 10060Generator Temperature (âC)
0.0
0.1
0.2
0.3
0.4
0.5En
trai
nmen
t rat
io
Figure 12: ð vs. ððº for various primary pressure ðððº.
limitsâof 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 ð, and significant absorption machineparameters, namely, desorber temperature ððº, evaporatortemperature ððžð, and condenser temperature ðð¶ð·. Figure 12depicts the evolution of ð with ððº. For a given primarypressure ðððº, the entrainment ratio decreases monotonouslywith ððº 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 ð vs. ððº
is noticed if the steam pressure ðððº is increased. However,in this case the curve is shifted upwards to larger values ofð; i.e., more secondary vapour is sucked in the ejector for agiven temperature ððº, and the limit value of ððº 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 ð vs. ððº for the various condenser temperatures allconverge to the same point on the temperature-axis whereð 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 fixedðððº and ðð¶ð·, as all ð vs. ððº for the various tested ððžð 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., ð =ð(ðŽ ð/ðŽ ð¡, ð18, ð18, ð19, ð19, ð12). The results presented in the
ïŒïŒïŒ = 15bar
ïŒïŒïŒ = 28âCïŒïŒïŒ = 30âCïŒïŒïŒ = 32âC
ïŒïŒïŒ = 34âCïŒïŒïŒ = 36âC
ïŒïŒ ïŒ = 4âC
70 80 90 10060Generator Temperature (âC)
0.0
0.1
0.2
0.3
0.4
0.5
Entr
ainm
ent r
atio
Figure 13: ð vs. ððº for various condenser temperature ðð¶ð·.
ïŒïŒïŒ = 15barïŒïŒïŒ = 37âC
ïŒïŒ ïŒ = 4âCïŒïŒ ïŒ = 6âCïŒïŒ ïŒ = 8âC
ïŒïŒ ïŒ = 10âCïŒïŒ ïŒ = 12âC
70 80 90 10060Generator Temperature (âC)
0.0
0.1
0.2
0.3
0.4
0.5
Entr
ainm
ent r
atio
Figure 14: ð vs. ððº for various evaporator temperatureððžð.
foregoing sections are obtained for simulations with thespecific conditions: (i) constant ejector nozzle ratio set to(ðŽ ð/ðŽ ð¡) = 17.3; (ii) saturated ejector-driving steam; i.e., ð18
and ð18 are then no more both independent; (iii) pressureof secondary flow ð19 equals condenser pressure, an inde-pendent parameter; (iv) temperature ð19 of flow ð19 is notan independent variable. It depends on the processes takingplace in rest of the absorption chiller and in particular on thebackpressure,ð12, 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, ð18, and back-pressure, ð12, for fixed nozzle area ratio, (ðŽ ð/ðŽ ð¡) = 17.3, andsecondary pressure, ð19 = 0.0628 bar.
In summary, the entrainment ratio depends then on justthree parameters
ð = ð (ð18, ð19, ð12) (61)
Figure 15 illustrates this dependency for a fixed secondarypressure, ð19 = 0.0628 bar, as it is the case for the datadepicted in Figures 6, 7, and 12. For a constant driving-steampressure ð18, ð 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 ð is the larger; i.e., thegreater the ð¶ðð-improvement, the higher the ð18 . Further,when ð18 becomes larger, the interval of backpressure ð12
(and hence, the range of ð12 as well as the range of desorbertemperature,ð4) where a chiller performance enhancement isexpected, expands. The pressure difference (ð18 â ð12) drivesthe ejector, and the difference (ð19 â ðð), where ðð is thepressure at nozzle exit, drives the entrainment process (Eq.(36)). With increasing primary pressure, ðð rises and comescloser to the secondary flow pressure ð19 . The suction of thesecondary flow into the mixing chamber declines graduallyand eventually vanishes for ðð = ð19. Consequently, at thislimit reached for ð18 = 18 bar, ð falls to zero. The verticalisobar-plane ð18 = 18 bar sets a geometrical limit to the usednozzle design.
The ð = 0 plane limits also the 3D surface of Figure 15.The calculations show that the Mach number ðð of themixed stream is there equal to ð18ð, 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 (ðŽ ð¡/ðŽð), which comes thenvery close to the nozzle area ratio, (ðŽ ð¡/ðŽ ð). The maximumvalue ofð is found for minimal values of backpressure. At thelimit, the Mach number of mixed gas ðð is the lowest andequals that of the entrained secondary flowð19ð.
The ð¶ðð curves represented in Figures 6â9 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 ð¶ðð tends first to increase as it does for a conventionalcycle. The entrainment ratio however is decreasing. Theresulting outcome is then first an increase of ð¶ðð 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, theð¶ðð 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 ð¶ðð 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 ð¶ðð 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
ðŽ: AreaðŽððŽð¡: Nozzle area ratio (ðŽ ð/ðŽ ð¡)ðŽððŽð¡: Ejector area ratio (ðŽð/ðŽ ð¡)ð¶ðð: Coefficient of performanceâ: Specific enthalpy (kJ/kg)ᅵᅵ: Mass flow rate (kg/s)ð: Mach numberðâ: Critical Mach numberð: Pressure (bar)ᅵᅵ: Heat transfer rate (kW)ð : Universal gas constant (kJ/(kg K))ð: Temperature (âC)ᅵᅵ: Work transfer rate (kW)ð: Steam quality
Greek Symbols
ðŸ: Ratio of steam specific heats (ð¶ð/ð¶V)ðHX: Heat exchanger effectivenessð: Nozzle, mixing, and diffuser efficiency
12 Journal of Engineering
ð: LiBr concentration in solution (mass. %)ð: Density (kg/m3)ð: ð19/ð18ð: Entrainment ratio (ᅵᅵ19/ᅵᅵ18).Subscripts
ðŽðµ: Absorberðð: Backpressureð: Constant section area (ejector)ð¶ð·: Condenserð: Diffuser (ejector)ðžð: Evaporatorðº: Generatorð: Nozzle exit plane (ejector)ð: Plane in mixing chamber (ejector)ð: Shockwave planeð: Mixing chamber (ejector)ð: Nozzle (ejector)ð ðð¡: Saturationððð¿: Solutionððº: Steam generatorð: Water1â19: 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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