Open Access is an initiative that aims to make scientific research freely available to all. To date our community has made over 100 million downloads. It’s based on principles of collaboration, unobstructed discovery, and, most importantly, scientific progression. As PhD students, we found it difficult to access the research we needed, so we decided to create a new Open Access publisher that levels the playing field for scientists across the world. How? By making research easy to access, and puts the academic needs of the researchers before the business interests of publishers.
We are a community of more than 103,000 authors and editors from 3,291 institutions spanning 160 countries, including Nobel Prize winners and some of the world’s most-cited researchers. Publishing on IntechOpen allows authors to earn citations and find new collaborators, meaning more people see your work not only from your own field of study, but from other related fields too.
To purchase hard copies of this book, please contact the representative in India:
CBS Publishers & Distributors Pvt. Ltd.
www.cbspd.com
|
customercare@cbspd.com
L2MSP, Department of Physics, University of Dschang, Dschang, Cameroon
Réné Tchinda
LISIE, University Institute of Technology Fotso Victor, University of Dschang, Bandjoun, Cameroon
*Address all correspondence to:
1. Introduction
In this chapter, the optimization analysis based on the new thermo-ecological criterion (ECOP) first performed by Ust et al. [1] for the heat engines is extended to an irreversible three-heat-source absorption refrigerator. The thermo-ecological objective function ECOP is optimized with respect to the temperatures of the working fluid. The maximum ECOP and the corresponding optimal temperatures of the working fluid, coefficient of performance, specific cooling load, specific entropy generation rate and heat-transfer surface areas in the exchangers are then derived analytically. Comparative analysis with the COP criterion is carried out to prove the utility of the ecological coefficient of performance criterion.
The main components of an absorption refrigeration system are a generator, an absorber, a condenser and an evaporator as shown schematically in Fig. 1 [2]. In the shown model, Q.His the rate of absorbed heat from the heat source at temperature TH to generator, Q.Cand Q.A are, respectively, the heat rejection rates from the condenser and absorber to the heat sinks at temperatures TC and TA and Q.L is the heat input rate from the cooling space at temperature TL to the evaporator. In absorption refrigeration systems, usually NH3/H2O and LiBr/H2O are used as the working substances, and these substances abide by ozone depletion regulations, since they do not consist of chlorofluorocarbons. In Fig. 1, the liquid rich solution at state 1 is pressurized to state 1’ with a pump. In the generator, the working fluid is concentrated to state 3 by evaporating the working medium by means of Q.H heat rate input. The weak solution at state 2 passes through the expansion valve into the absorber with a pressure reduction (2–2’). In the condenser, the working fluid at state 3 is condensed to state 4 by removing Q.C heat rate. The condensed working fluid at state 4 is then throttled by a valve and enters the evaporator at state 4’. The liquid working fluid is evaporated due to heat transfer rate Q.L from the cooling space to the working fluid (4’–5). Finally, the vaporized working fluid is absorbed by the weak solution in the absorber, and by means of Q.A heat rate release in the absorber, state 1 is reached.
Work input required by the solution pump in the system is negligible relative to the energy input to the generator and is often neglected for the purpose of analysis. Under such assumption, the equation for the first law of thermodynamics is written as:
Q.H+Q.L−Q.C−Q.A=0E1
Absorption refrigeration systems operate between three temperature levels, ifTA=TC, or four temperature levels whenTA≠TC. In this chapter, by takingTA=TC, the cycle of the working fluid consists of three irreversible isothermal and three irreversible adiabatic processes. The temperatures of the working fluid in the three isothermal processes are different from those of the external heat reservoirs so that heat is transferred under a finite temperature difference, as shown in Fig. 2 where
Q.O=Q.C+Q.AE2
T1and T2 are, respectively, the temperatures of the working fluid in the generator and evaporator. It is assumed that the working fluid in the condenser and absorber has the same temperature T3 [2]. Q.LCis the heat leak from the heat sink to the cooled space.
The heat exchanges between the working fluid and heat reservoirs obey a linear heat transfer law, so that the heat-transfer equations in the generator, evaporator, condenser and absorber are, respectively, expressed as follows:
Q.H=UHAH(TH−T1)E3
(
Q.L=ULAL(TL−T2)E4
Q.O=UO(AA+AC)(T3−TO)E5
whereAH, AL, ACand AA are, respectively, the heat-transfer areas of the generator, evaporator, condenser and absorber, UHand UL are, respectively, the overall heat-transfer coefficients of the generator and evaporator, and it is assumed that the condenser and absorber have the same overall heat-transfer coefficient UO [2].
Figure 1.
Schematic diagram of absorption refrigeration system [2]
Figure 2.
Considered irreversible absorption refrigeration model and its T–S diagram.
The absorption refrigeration system does not exchange heat with other external reservoirs except for the three heat reservoirs at temperaturesTH, TLandTO, so the total heat-transfer area between the cycle system and the external heat reservoirs is given by the relationships:
A=AH+AL+AOE6
where
AO=AC+AA.E7
The rate of heat leakage Q.LC from the heat sink at temperature TO to the cold reservoir at temperature TL was first provided by Bejan [3] and it is given as:
Q.LC=KLC(TO−TL)E8
where KLC is the heat leak coefficient.
Real absorption refrigerators are complex devices and suffer from a series of irreversibilities. Besides the irreversibility of finite rate heat transfer which is considered in the endoreversible cycle models and the heat leak from the heat sink to the cooled space, there also exist other sources of irreversibility. The internal irreversibilities that result from friction, mass transfer and other working fluid dissipations are an another main source of irreversibility, which can decrease the coefficient of performance and the cooling load of absorption refrigerators. The total effect of the internal irreversibilities on the working fluid can be characterized in terms of entropy production. An irreversibility factor is introduced to describe these internal irreversibilities:
I=ΔS3ΔS1+ΔS2E9
On the basis of the second law of thermodynamics, ΔS3>ΔS1+ΔS2for an internally irreversible cycle, so thatI>1. If the internal irreversibility is neglected, the cycle is endoreversible and soI=1. The second law of thermodynamics for an irreversible three-heat-source cycle requires that:
Combining Eqs. (1) and (11), the following ratios are derived:
Q.LQ.H=T2(T1−IT3)T1(IT3−T2)E15
Q.OQ.L=IT3(T1−T2)(T1−IT3)T2E16
The first is the coefficient of performance of the irreversible three-heat-source absorption refrigeration cycle without heat leak losses.
Substituting Eqs. (15) and (16) into Eq. (14), the heat-transfer area of the evaporator is expressed as a function ofT1, T2and T3 for a given total heat-transfer areas :
Combining Eqs. (8), (12), (15) and (20), the coefficient of performance of the irreversible three-heat-source refrigerator as a function of the temperaturesT1, T2and T3 of the working fluid in the generator, evaporator, condenser and absorber is obtained:
is the coefficient of performance for reversible three-heat-source refrigerator.
According to the definition of the general thermo-ecological criterion function for different heat engine models [4-9], a two-heat-source refrigerator [10, 11] and three-heat-source absorption refrigerator [2], the new thermo-ecological objective function called ecological coefficient of performance (ECOP) of an absorption refrigerator is defined as:
When Eq. (21) is put in Eq. (30), the ecological coefficient of performance of the irreversible three-heat-source absorption refrigerator as a function ofT1, T2and T3 is derived as :
3. Performance optimization for a three-heat-source irreversible absorption refrigerator based on ECOP criterion
The ECOP function given in Eq. (31) is plotted with respect to the working fluid temperatures (T1, T2andT3) for different internal irreversibility parameters as shown in Fig. 3(a), (b) and (c). As it can be seen from the figure, there exists a specificT1, T2and T3 that maximize the ECOP function for given I and ξ values. Therefore, Eq. (31) can be maximized (or optimized) with respect toT1, T2andT3. The optimization is carried out analytically.
Figure 3.
Variation of the ECOP objective function with respect to T1 (a), T2(b) and T3 (c) for different I values (TG=403K, TL=273K, TO=303K, Tenv=290K, UG=1163W/m2K, UE=2326W/m2K, UO=4650W/m2K, KL=1082W/K, A=1100m2)
Using Eqs. (49), (52) and (53) with Eqs.(32)-(34), the corresponding optimal temperatures of the working fluid in the three isothermal processes when the ecological coefficient of performance is a maximum, are, respectively, determined by:
T1*=THD+b2(1+b1)(D+B)E56
T2*=TLD+b2D(1+b2)E57
T3*=TOD+b21+b2E58
Substituting Eqs. (56)-(58) into Eqs. (21), (23), (27) and (31) the maximum ECOP function and the corresponding optimal coefficient of performance, optimal specific cooling load and optimal specific entropy generation rate are derived, respectively, as:
From Eqs. (17)-(19) and (56)-(58), it is found that, when the three-heat-source absorption refrigerator is operated in the state of maximum ecological coefficient of performance, the relations between the heat-transfer areas of the heat exchangers and the total heat-transfer area are determined by:
In Fig.4, the variation of the normalized ECOP (ECOP¯=ECOPECOPmax), normalized COP (COP¯=COPCOPmax) and the specific cooling load (r) with respect to the specific entropy generation rate (s) are demonstrated. One interesting observation from this figure is that maximum of the ECOP and COP coincides although their functional forms are different: the coefficient of performance gives information about the necessary heat rate input in order to produce certain amount of cooling load and the ecological coefficient of performance gives information about the entropy generation rate or loss rate of availability in order to produce certain amount of cooling load. The maximum ECOP and COP conditions give the same amount of cooling load and entropy generation rate. It is also seen analytically that the performance parametersT1*, T2*, T3*, A1*, A2*, A3*, r*, s*and COP*=COPmax at the maximum ECOP and maximum COP are same. Getting the same performance at maximum ECOP and COP conditions is an expected and logical result. Since, for a certain cooling load the maximum COP results from minimum heat consumption so that minimum environmental pollution. The minimum environmental pollution is also achieved by maximizing theECOP. Although the optimal performance conditions ECOP and COP criteria are same, their impact on the system design performance is different. The coefficient of performance is used to evaluate the performance and the efficiency of systems. This method only takes into account the first law of thermodynamics which is concerned only with the conversion of energy, and therefore, can not show how or where irreversibilities in a system or process occur. Also, when different sources and forms of energy are involved within a system, the COP criterion of a system doesn’t describe its performance from the view point of the energy quality involved. This factor is taken into account by the second law of thermodynamics characterized by the entropy production which appears in the ecological coefficient of performance criterion (ECOP). This aspect is of major importance today since that with the requirement of a rigorous management of our energy resources, one should have brought to be interested more and more in the second principle of thermodynamics, because degradations of energy, in other words the entropy productions, are equivalent to consumption of energy resources. For this important reason, the ECOP criterion can enhance the system performance of the absorption refrigerators by reducing the irreversible losses in the system. A better understanding of the second law of thermodynamics reveals that the ecological coefficient of performance optimization is an important technique in achieving better operating conditions.
Figure 4.
Variation of the normalizedECOP, normalized COP and the specific cooling load with respect to the specific entropy generation rate (TG=403K,TL=273K ,TO=303K ,Tenv=290K , UG=1163W/m2K, UE=2326W/m2K, UO=4650W/m2K, KL=1082W/K, A=1100m2)
This chapter presented an analytical method developed to achieve the performance optimization of irreversible three-heat-source absorption refrigeration models having finite-rate of heat transfer, heat leakage and internal irreversibility based on an objective function named ecological coefficient of performance (ECOP). The optimization procedure consists in defining the objective function ECOP in term of the temperatures of the working fluid in the generator, evaporator, condenser and absorber and using extremal conditions to determine analytically the maximum ECOP and the corresponding optimal design parameters. It also established comparative analyses with the COP criterion and shown that the performance parameters at the maximum ECOP and maximum COP are same. The three-heat-source absorption refrigerator cycles are the simplified models of the absorption refrigerators, but the four-heat-source absorption refrigerators cycles are closer to the real absorption refrigerators.
References
1.Ust, Y.: Ecological performance analysis and optimization of power-generation systems, Ph.D.Thesis Progress Report, Yildiz Technical University, Istanbul. (2004
2.NgouateuWouagfack. P. A.TchindaR.Performanceoptimization.ofthree-heat-source.irreversiblerefrigerator.basedon. a.newthermo-ecological.criterionInternational Journal of Refrigeration1008 EOF1015 EOF2011
3.Bejan, A.: Theory of heat transfer-irreversible refrigeration plant.International Journal of Heat Transfer. 32, 1631 EOF1639 EOF1989
4.UstY.SahinB.SogutO. S.Performanceanalysis.optimizationof.anirreversible.Dualcycle.basedon.ecologicalcoefficient.ofperformance. . E. C. O. P.criterionApplied Energy. 82 (1), 23-39 (2005
5.Ust, Y., Sahin, Kodal, A.: Ecological coefficient of performance (ECOP) optimization for generalized irreversible Carnot heat engines.Journal of the Energy Institute. 78 (3), 145-151 (2005
6.Ust, Y., Sahin,B., Kodal, A.: Performance analysis of an irreversible Brayton heat engine based on ecological coefficient of performance criterion.International Journal of Thermal Science. 45 (1), 94-101 (2006
7.UstY.SogutO. S.SahinB.DurmayazA.Ecologicalcoefficient.ofperformance. . E. C. O. P.optimizationfor.anirreversible.Braytonheat.enginewith.variable-temperaturethermal.reservoirsJournal of the Energy Institute. 79 (1), 47-52 (2006
9.SogutO. S.UstY.SahinB.Theeffects.ofintercooling.regenerationon.thethermo-ecological.performanceanalysis.ofan.irreversible-closedBrayton.heatengine.withvariable-temperature.thermalreservoirs.Journal of Physics D: Applied Physics. 39, 4713-4721 (2006
10.Ust, Y., Sahin, B.: Performance optimization of irreversible refrigerators based on a new thermo-ecological criterion.International Journal of Refrigeration. 30, 527 EOF2007
11.Ust, Y.: Performance analysis and optimization of irreversible air refrigeration cycles based on ecological coefficient of performance criterion.Applied Thermal Engineering. 29, 47-55 (2009
Written By
Paiguy Armand Ngouateu Wouagfack and Réné Tchinda
Submitted: 05 December 2011Published: 03 October 2012