Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle - Ijieee
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982Volume-3, Issue-11, Nov.-2015THERMAL EXERGY OPTIMIZATION OF AN IRREVERSIBLECOGENERATION CYCLE1RUPINDER SINGH JOHAL, 2N. GAUTAM, 3H. CHANDRA1Research Scholar, Industrial Engineering Department, Singhania University, JhunJhunu , Rajasthan, India2,3Department of Mechanical Engineering, Vishwavidyalya Engineering College,Lakhanpur, Sarguja University Ambikapur (C.G.) – IndiaAbstract — This paper investigates the cogeneration system coupled with external heat reservoir of finite heat capacity andincluding both external irreversibility and internal irreversibility due to the finite-rate heat transfer between the working fluidand heat reservoirs and due to heat dissipation of working fluid respectively. The effect of operating inlet and outlettemperature, heat capacitance rate of external fluid, effectiveness of source/sink side heat exchanger and internalirreversibility parameter and temperature ranges of reservoir on the design parameter of cogeneration cycle has been included.The presence of both the irreversibility parameters shows that a cogeneration power plant with irreversibility delivers lessexergy output and has a lower efficiency as compared to reversible cycles. The model presented here is of more use whencompared to those obtained by earlier researchers. The effect of the heat consumer temperature parameter (Ψ) & extremetemperature ratio (Φ) on the maximum total exergy rate and the corresponding exergy efficiency are investigated. The resultsare plotted in graphs with considering various parameters.Index Terms — Cogeneration, Exergy, Endoreversible, Combined Heat And Power.on heat and work of processes operating at finite rates.One approach is to require processes to take place inan arbitrary but fix time interval. We then carry theanalysis further to determine the optimal interval inwhich a process should be carried out in order tooptimize power or any index of optimality.I. INTRODUCTIONCogeneration, simply, is generation of energy for theprocess from the excess energy supplied to anotherprocess. It is the production of electric power and otherforms of useful energy such as heat or process steamfrom the same facility. Cogeneration is thesimultaneous production of two forms of energy e.g.steam and electricity from a single power plant.Cogeneration is also known as, “In plant generation(IPG)”, “By product power”, “Total energy”,“Combined heat and power (CHP)”.Most machines,whether automobiles or steam turbines, are built toperform a particular function. It takes so much energyto get the unit to a level performance capable ofaccomplishing the function, but it takes less energy toactually perform the task. This is the main reasonbehind development of cogeneration plant. In realworld, the actual changes in enthalpy and free energyin a process rarely approach the ideal thermodynamicenthalpy and free energy changes for that process.Typically the actual expenditure of enthalpy and freeenergy as fuel and other inputs tends to be more thanthe ideal thermodynamic limit.It is important to usethe differences of actual and ideal requirements ofenergy, enthalpy, free energy or availability as anindex of how a process could be improved. Thisdiscussion is intended to meet the challenge byprovidinganextensionofconventionalthermodynamics that will give limits on processvariables carried out in limited or finite time intervals.This discipline is known as finite timethermodynamics or finite temperature differencethermodynamics. The goal of finite timethermodynamics is a means to evaluate the ideal limitsThe only fact the classical thermodynamics tells aboutreal process is that they always produce less work andmore entropy than the corresponding reversibleprocesses. Reversible processes are however, possiblein the limit of infinite time. But no one wants toproduce finite work in infinite time and/or to run themachine infinitely slowly. Thus the concept of finitetime thermodynamics came into existence, which notonly answer the above questions but also solve theproblems of heat transfer and energy conversionsystems. Finite time thermodynamics is concerned withthe finite temperature difference during external heattransfer between system and source/sink thermalreservoirs. Heat is a kind of energy, which can betransferred from one body to another because oftemperature difference between them, but finitetemperature difference makes the process irreversible.Therefore, the heat transfers process, approaches areversible one as the temperature difference betweenthe two bodies approaches to zero. However, transfer offinite amount of heat through infinitesimal temperaturedifference would take infinite time or infinite heattransfer area. From the heat transfer theory, the amountof heat (Q) transfer between two bodies is proportionalto the temperature difference, the contact area and thetime taken i.e.Q A T tOrQ U A T tThermal Exergy Optimization Of An Irreversible Cogeneration Cycle43
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982Where U is the overall heat transfer coefficient, A is theheat transfer area, T is the temperature differencebetween the bodies and t is the time taken in theprocess. For infinitesimal temperature difference [i.e. T 0], either A or t or U .But thematerials have the finite conductivity so U will befinite; thus the only possibility is that A or t . IfA means the heat exchanger area is infinite, theheat transfer unit becomes economically unviable,since as the heat exchanger units are quite expansive. Ift means it takes infinite time to produce the finiteVolume-3, Issue-11, Nov.-2015amount of work, then the power {which is work per unittime i.e. P W/t 0 as t 0) will be zero. This meanswe need finite heat transfer in finite time, whichproduces irreversibility. In real world, every machinehas some power, which means finite work in finitetime. This requires that there should be a finitetemperature difference between the working fluid andthe external reservoirs. Thus, irreversible heat transferdue to finite temperature difference is known as “FiniteTime Thermodynamics”.Fig. 1 Conventional versus Cogeneration power plant.Fig. 2 Comparison between Conventional and CHPFrom time to time over last three decades, we haveheard about energy crisis. The term has widely used intechnical as well as non-technical circle. Yet the termenergy crisis is itself quite ambiguous and confusing. InApril 1977 energy message, President Carter coined anew word-“Cogeneration”. “Cogeneration is thesimultaneous production of two forms of energy e.g.steam and electricity from a single power plant” Or “the coincident generation of necessary heat and power–electrical or mechanical-or the recovery of low levelheat for power generation” investigated by Ingersoll etal. [1]. Cogeneration is also known as, “In plantgeneration (IPG)”, “By product power”, “Totalenergy”, “Combined heat and power (CHP)” by HallThermal Exergy Optimization Of An Irreversible Cogeneration Cycle44
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982[2].Cogeneration is the production of more than oneuseful form of energy (such as process heat and electricpower) from the same energy source. Cogenerationsystems often capture otherwise wasted thermal energy,usually from an electricity producing device like a ngine), and use it for space and water heating,industrial process heating, or as a thermal energysource for another system component. The principletechnical advantage of cogeneration systems is theirability to improve the efficiency of fuel use in theproduction of electrical and thermal energy. Less fuel isrequired to produce a given amount of electrical andthermal energy in a single cogeneration unit than isneeded to generate the same quantities of both types ofenergy with separate, conventional technologies (e.g.,turbine-generator sets and steam boilers). The technicaladvantages of cogeneration lead to significantenvironmental advantages. That is, the increase inefficiency and corresponding decrease in fuel use by acogeneration system, compared to other conventionalprocesses for thermal and electrical energy production,normally yield large reductions in greenhouse gasemissions. These reductions can be as large as 50% insome situations, while the same thermal and electricalservices are provided by Mehmet Kanoglu et al [3].The optimal design of heat engines and refrigeratorsystems is a major objective of engineeringthermodynamics. In classical thermodynamics, it iswell known that the most efficient cycles are reversiblecycles. The Carnot heat engine cycle, which iscomposed of four reversible processes, is the bestknown reversible cycle observed by Chambadal P. etal. [4]. But in reality reversible processes require aninfinite process time and/or an infinite system areawhich is not the case in practice. However, reversiblecycles provide the upper bounds for the performancecriteria and hence are considered as models for theactual systems by Bejan A. et al. [7]. Chambadal P. etal [4, 5, and 6] used the concept of finite-timethermodynamics to optimize the power outputof aCarnot engine. Nowadays cogeneration power plants(in which heat and power are produced together) arewidely used to minimize the transmission anddistribution losses by Chandra H. et al [8]. Accordingto Chandra, Hall and Wilson, [8, 4 and 9]cogeneration power plants are also known as in-plantgeneration (IPG)', combined heat and power (CHP)',and by-product power'. These cogeneration powerplants are more advantageous in terms of energy andexergy efficiencies than plants, which produce heatand power separately by Sahin et al. [10]. Sahin andKodal [10] carried out the exergy optimization for anendo reversible cogeneration cycle based onfinite-time thermodynamic having infinite heatcapacity and determined the optimum values fordesign parameters of the cogeneration cycle atmaximum exergy output.The exergy optimization of irreversible cogenerationcycle based on finite time thermodynamics whichconsider the internal irreversibility caused due toentropy generation during the internal process formore accurate determination of optimum vale ofdesign parameter Chandra H. et al. [11]. However, thelimitation with their model was that they consideredthe cogeneration plant is coupled with thermalreservoir of infinite heat capacity and the designparameter are very much affected by irreversibility offinite-rate heat transfer.II THERMODYNAMIC FORMULATION OFTHE PROBLEMWith the fast pace of modernization andindustrialization, Energy crisis is the greatest burningissue of any country. With unending research made onnon-conventional research, energy output is stilllargely dependent on conventional research The threatof decreasing level of non-renewable resource with thegrowing demands of developing countries has madethe mankind to think for the future generations. Wecan’t go for blindly feeding on such resource, nor canwe think of shutting the power plants which are thepillars of the nation. Such situations have led to pricehikes and energy starvations: Also unlimited usage ofcommercial resources have added to the seriousproblems like pollution and global warming.The model of the irreversible cogenerationcycle (in which both external and internalirreversibility’s are considered) and its T-S diagram isshown in fig. 3 and 4respectively. There are three heatsources, QH, QL and QK between which thecogeneration cycle operates. The temperatures of theworking fluids exchanging heat with this heat sourcesat QH, QK and QL are TH, TK and TL respectively. Themodel of the cogeneration cycle shown in fig. 1 and 2represents cogeneration plants that have a pass-outcondensing steam turbine. In these plants, some steamis extracted from the turbine at an intermediatepressure and transferred to a heat consumer forprocess heating. The condensate is then returned tothe steam plant/boiler. In the irreversibleCogeneration cycle:(a) QH is the rate of heat transfer from heatsource at TmH to the warm working fluid 1at the constant temperature TH in process2’-3(b) QK is the rate of heat transfer from the workingfluid at constant TK to the heat consumingdevice at TmK in process 4’-5(c) QL is the rate of heat transfer from the coldworking fluid at constant TL to the heatsource at TmL in process 6’-1Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle45Volume-3, Issue-11, Nov.-2015
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982Volume-3, Issue-11, Nov.-2015Power to process heat ratio is given by,Thus theLagrangian function is given by,SinceFig. 3 Schematic model of irreversible cogeneration cycle coupled withfinite heat capacity heat exchangerAfter simplifying the above equation, we getFig.4 T-S diagram of irreversible cogeneration cycle coupledwith finite capacity heatexchanger.And further solving, we getThe rate of heat input from high temperature heatsource to the cogeneration cycle is given byWhere(1)Now from equation (6),(2)Put the value of equation (13) in equation (5), we getIn order to achieve optimal thermal conductance,which are measures of heat-exchangersizes, weassume that the total thermal conductance is fixed(3)(4)Define the thermal conductance allocation ratios x, y,and z for the heat-source,heat-sink and heat-consumersides respectively, as:(5)(15)Total exergy is given by,Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle46
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982Volume-3, Issue-11, Nov.-2015value of (Ψ), slope of the curve increases. Initially upto R 6, the value of exergy rate and correspondingefficiency decrease and then with higher values of R,exergy rate and corresponding efficiency becomeconstant.The reason for these decreases is that the temperatureT*K at maximum total exergy increases for increasingTminK, which is the heat-consumer temperature. Theincrease in T*K causes the isentropic expansion workof the heat engine and thus causes the exergeticperformance of the irreversible cogeneration system todecrease.The value of the maximum total exergy rateand exergy efficiency at maximum total exergy for theirreversible cogeneration cycle are lower than that forthe endoreversible cogeneration cycle due to thepresence of cycle irreversibility parameter in theirreversible cogeneration cycle, which is less thanunity. The effect of external irreversibility on theexergy&exergy efficiency is on the lower side ascompared to the previous papers i.e. exergyoptimization for endoreversible cogeneration cycle bySahin and Kodal&Thermal exergy optimization for anirreversible cogeneration power plant by Chandra andKaushik due to in cooperation of externalirreversibility.Where z 1-x-y. Therefore the maximum total exergyrate given inEquation (14) can be optimized withrespect to x and y by using equation (15) in equations(08)-(13). Then Equation (14) becomes (16)(16)(17)And the parameters D, E, F and G are2) Effects of extreme temperature ratio(Φ)The effect of the extreme temperature ratio (Φ) forvarious values of R on ETmax andare shown inFigures 6 and 7 respectively. The values of Ψ and I aretaken as 1.33 and 1.11, while the value of Φ is variedfrom 2 to 7 and the value of R is varied from 0 toinfinity. Although both ETmax andincrease forincreasing Φ and decreasing R, the increase in ETmaxismore rapid than . It is also observed that the value ofETmaxandfor the irreversible cogeneration cycle isless than that for the endoreversible cogenerationcycle due to the presence of the cycle irreversibilities.(19)(20)III. RESULTS& DISCUSSIONIn this paper, the effect of the heat-consumertemperature parameter (Ψ) and extreme temperatureratio (Φ) on the maximum total exergy rate and thecorresponding exergy efficiency are analyzed.1) Effect of heat-consumer temperature parameterThe effect of the heat-consumer temperatureparameter on the maximum total exergy rate and thecorresponding exergy efficiency, with the ratio ofpower output to process heat R is given in Figures 5and 6 respectively. The values of Φ and I are taken as4 and 1.12, while the value of (Ψ) is varied from 1.2 to1.8 and the value of R is varied from 0 to 20. It hasbeen observed in this curve that for a particular valueof heat-consumer temperature parameter (Ψ), exergyrate and corresponding efficiency varies inverselywith respect to power to heat ratio. With increasingFig. 5 Variation of maximum total energy rate with respect to Rfor various Ψ, Φ 4,Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle47
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982Volume-3, Issue-11, Nov.-2015exergetic performance of the endoreversiblecogeneration cycle. To obtain a high exergeticperformance from the cogeneration system theheat-consumer temperature must be kept low todecrease T*K.The results obtained are quite useful foranalyzing the scope of cogeneration power plants.Future work can be finite time exergy based ecologicaloptimization of cogeneration cycle consideringirreversibility between the heat source/sink and theirreversibility within the cycle. This consists ofmaximizing a function representing the compromisebetween the power output and entropy production rateof the cogeneration cycle.REFERENCESFig. 6 Variation of exergy efficiency at maximum total energywith respect to R forVarious Ψ , Φ 4,[1][2][3][4][5][6][7][8][9]Fig.7 Effects of Φ and R on total exergy rate for Ψ 1.33[10]CONCLUSIONS[11]The thermal exergy optimization for an irreversiblecogeneration cycle has been carried out by introducingthe cycle irreversibility parameter as a modifiedcriterion. From this study it is clear that theendoreversible cogeneration cycle is a special case ofthe irreversible cogeneration cycle. The exergeticperformance of the irreversible cogeneration cycle fordifferent design parameters has been analyzed and theperformance is always less than that for theendoreversible cogeneration cycle case, due to thepresence of the cycle irreversibility parameter. Inorder to get the high exergetic performance of theirreversible cogeneration system the heat-consumertemperature should be as low as possible. The value ofthe optimum conductance-allocation ratio onheat-source side remains approximately constant near0.5, and for the heat-sink and heat-consumer sides,depend R,Ψ & Φ In our continuing search for arealistic theoretical upper limit for the exergeticperformance, the new equations with cycleirreversibility represent a further insight over the[12][13][14][15][16][17][18][19]Ingersoll, John G., 1991, Energy storage systems, the energysource book, American Institute of Physics.Hall, M. (1981) Cogeneration: the promise is now', MechanicalEngineering, pp.22-23.Mehmet Kanoglu, Ibrahim Dincer(2009), ‘Performanceassessment of cogeneration plants’. Journal of EnergyConversion and Management. Vol. 50, pp.76-81.Chambadal, P. (1957) Les CentralessNuclearies, Paris: ArmandColin, pp.41-58.Curzon, F.L. and Ahlborn, B. (1975) Efficiency of a Carnotengine at maximum power output', American Journal of Physics,Vol. 43, pp.22-24.Novikov, I.I. (1958) The efficiency of atomic power stations',Journal of Nuclear Energy II, Vol. 17, pp.125-128.Bejan, A. (1996) Entropy generation minimization: the newthermodynamics of finite-size devices and finite-time processes',Journal of Applied Physics, Vol. 79, No. 3, pp.1191-1218.Chandra, H., Kaushik, S.C., (2005) ‘Thermal exergyoptimization for an irreversible cogeneration power plant’,International journal of Vol. 2, No. 3, pp.260-273.Wilson, W.B. (1979) Conserving energy via cogeneration',Mechanical Engineering, Vol. 101, pp.20-27.Sahin, B., Kodal, A., Ekmekci, I. and Yilmaz, T. (1997) Exergyoptimisation for an endoreversible cogeneration cycle',Energy, Vol. 22, No. 5, pp.551-557.Chandra, H., Chandra, A. and Kaushik, S.C. (2003) Cogeneration: environmentally sound energy efficienttechnology', National Seminar on Clean Coal Technologies forSustainable Power Development, Power System TrainingInstitute (PSTI) Bangalore, India, pp.7.1-7.14Bhardwaj, P.K., Kaushik. S. C. and Jain, Sanjeev, (2003) ‘Finitetime optimization of an endoreversible and irreversible vaporabsorption refrigeration system’. Energy Conversion andManagement Volume 44, Issue 7, Pages 1131-1144.Blanchard, C.H. (1989) Coefficient of performance for a finitespeed heat pump', Journal of Applied Physics, Vol. 51 No. 5,pp.2471-2472.Chih, Wu. & William H. Schulden.( 1995)Maximum obtainablespecific power of high temperature waste heat engine’. HeatRecover Systems & CHP Vol. 15, No. I, pp. 13-17.Chih,Wu and Robert L. Kiang.(1992) ‘finite timethermodynamics of Carnot engine with internal irreversibility’,Journal of Energy Vol. 17, No. 12, pp.1173-1178.Khaliq, Abdul (2004), ‘Finite-time heat-transfer analysis andgeneralized power-optimization of an endoreversible Rankineheat-engine’, Journal of Applied Energy Vol. 79, pp.27–40.Lingen Chen, Fengrui Sun, and Chih Wu (2006) ‘Optimalconfiguration of a two-heat-reservoir heat-engine with heat-leakand finite thermal-capacity’ Journal of Applied Energy.Vol. 83,pp. 71–81.Nag, P.K (2007) Engineering Thermodynamics third edition,Tata Mcgraw-Hill publishing company limited, New Delhi.Power, (2009), Business and technology global generationindustry Vol.151, No. 9, pp1-4.Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle48
International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982[20] Valentina A. Mironova and Anatolii M. Tsirlin. ‘Finite-timethermodynamics: Exergy and optimization of time-constrainedprocesses’ (1994) Journal Applied Phys. Vol. 76 (2),pp.629-636.[21] Vibhuti, Hate.(2006) South Asia monitor, Center for Strategicand International Studies (CSIS) Washington .D.C.[22] Xiaoli.Hao, Guoqiang.Zhang, ‘Maximum useful energy-rateanalysis of anendoreversible Joule–Brayton cogenerationVolume-3, Issue-11, Nov.-2015cycle’.(2007) Journal of Applied Energy Vol. 84,pp.1092-1101.[23] Yuehong, Bi. Lingen, Chen. andFengrui, Sun. (2009) ‘Exergybased ecological optimization variable temperature heatreservoir air heat pump cycle’, Rev. Mex. Fis. Vol. 55(2),pp.112-119. Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle49
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