THERMAL EXERGY OPTIMIZATION OF AN IRREVERSIBLE ...pep.ijieee.org.in/journal_pdf/11-203-144896259443-49.pdf · Thermal Exergy Optimization Of An Irreversible ... Thermal Exergy Optimization

International Journal of Industrial Electronics and Electrical Engineering, ISSN: 2347-6982 Volume-3, Issue-11, Nov.-2015

Thermal Exergy Optimization Of An Irreversible Cogeneration Cycle

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THERMAL EXERGY OPTIMIZATION OF AN IRREVERSIBLE COGENERATION CYCLE

1RUPINDER SINGH JOHAL, 2N. GAUTAM, 3H. CHANDRA

1Research Scholar, Industrial Engineering Department, Singhania University, JhunJhunu , Rajasthan, India 2,3Department of Mechanical Engineering, Vishwavidyalya Engineering College,

Lakhanpur, Sarguja University Ambikapur (C.G.) – India Abstract — This paper investigates the cogeneration system coupled with external heat reservoir of finite heat capacity and including both external irreversibility and internal irreversibility due to the finite-rate heat transfer between the working fluid and heat reservoirs and due to heat dissipation of working fluid respectively. The effect of operating inlet and outlet temperature, heat capacitance rate of external fluid, effectiveness of source/sink side heat exchanger and internal irreversibility 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 less exergy output and has a lower efficiency as compared to reversible cycles. The model presented here is of more use when compared to those obtained by earlier researchers. The effect of the heat consumer temperature parameter (Ψ) & extreme temperature ratio (Φ) on the maximum total exergy rate and the corresponding exergy efficiency are investigated. The results are plotted in graphs with considering various parameters.

Index Terms — Cogeneration, Exergy, Endoreversible, Combined Heat And Power. I. INTRODUCTION Cogeneration, simply, is generation of energy for the process from the excess energy supplied to another process. It is the production of electric power and other forms of useful energy such as heat or process steam from the same facility. Cogeneration is the simultaneous 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 to perform a particular function. It takes so much energy to get the unit to a level performance capable of accomplishing the function, but it takes less energy to actually perform the task. This is the main reason behind development of cogeneration plant. In real world, the actual changes in enthalpy and free energy in a process rarely approach the ideal thermodynamic enthalpy and free energy changes for that process. Typically the actual expenditure of enthalpy and free energy as fuel and other inputs tends to be more than the ideal thermodynamic limit.It is important to use the differences of actual and ideal requirements of energy, enthalpy, free energy or availability as an index of how a process could be improved. This discussion is intended to meet the challenge by providing an extension of conventional thermodynamics that will give limits on process variables carried out in limited or finite time intervals. This discipline is known as finite time thermodynamics or finite temperature difference thermodynamics. The goal of finite time thermodynamics is a means to evaluate the ideal limits

on heat and work of processes operating at finite rates. One approach is to require processes to take place in an arbitrary but fix time interval. We then carry the analysis further to determine the optimal interval in which a process should be carried out in order to optimize power or any index of optimality. The only fact the classical thermodynamics tells about real process is that they always produce less work and more entropy than the corresponding reversible processes. Reversible processes are however, possible in the limit of infinite time. But no one wants to produce finite work in infinite time and/or to run the machine infinitely slowly. Thus the concept of finite time thermodynamics came into existence, which not only answer the above questions but also solve the problems of heat transfer and energy conversion systems. Finite time thermodynamics is concerned with the finite temperature difference during external heat transfer between system and source/sink thermal reservoirs. Heat is a kind of energy, which can be transferred from one body to another because of temperature difference between them, but finite temperature difference makes the process irreversible. Therefore, the heat transfers process, approaches a reversible one as the temperature difference between the two bodies approaches to zero. However, transfer of finite amount of heat through infinitesimal temperature difference would take infinite time or infinite heat transfer area. From the heat transfer theory, the amount of heat (Q) transfer between two bodies is proportional to the temperature difference, the contact area and the time taken i.e. Q A T t Or Q = U A T t



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Where U is the overall heat transfer coefficient, A is the heat transfer area, ∆T is the temperature difference between the bodies and t is the time taken in the process. For infinitesimal temperature difference [i.e. ∆T → 0], either A →∞ or t→∞or U→∞.But the materials have the finite conductivity so U will be finite; thus the only possibility is that A→∞ or t →∞. If A→∞ means the heat exchanger area is infinite, the heat transfer unit becomes economically unviable, since as the heat exchanger units are quite expansive. If t→∞ means it takes infinite time to produce the finite

amount of work, then the power {which is work per unit time i.e. P = W/t →0 as t →0) will be zero. This means we need finite heat transfer in finite time, which produces irreversibility. In real world, every machine has some power, which means finite work in finite time. This requires that there should be a finite temperature difference between the working fluid and the external reservoirs. Thus, irreversible heat transfer due to finite temperature difference is known as “Finite Time Thermodynamics”.

Fig. 1 Conventional versus Cogeneration power plant.

Fig. 2 Comparison between Conventional and CHP

From time to time over last three decades, we have heard about energy crisis. The term has widely used in technical as well as non-technical circle. Yet the term energy crisis is itself quite ambiguous and confusing. In April 1977 energy message, President Carter coined a new word-“Cogeneration”. “Cogeneration is the simultaneous 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 level heat for power generation” investigated by Ingersoll et al. [1]. Cogeneration is also known as, “In plant generation (IPG)”, “By product power”, “Total energy”, “Combined heat and power (CHP)” by Hall



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[2].Cogeneration is the production of more than one useful form of energy (such as process heat and electric power) from the same energy source. Cogeneration systems often capture otherwise wasted thermal energy, usually from an electricity producing device like a heat engine (e.g., steam-turbine, gas-turbine, diesel-engine), and use it for space and water heating, industrial process heating, or as a thermal energy source for another system component. The principle technical advantage of cogeneration systems is their ability to improve the efficiency of fuel use in the production of electrical and thermal energy. Less fuel is required to produce a given amount of electrical and thermal energy in a single cogeneration unit than is needed to generate the same quantities of both types of energy with separate, conventional technologies (e.g., turbine-generator sets and steam boilers). The technical advantages of cogeneration lead to significant environmental advantages. That is, the increase in efficiency and corresponding decrease in fuel use by a cogeneration system, compared to other conventional processes for thermal and electrical energy production, normally yield large reductions in greenhouse gas emissions. These reductions can be as large as 50% in some situations, while the same thermal and electrical services are provided by Mehmet Kanoglu et al [3]. The optimal design of heat engines and refrigerator systems is a major objective of engineering thermodynamics. In classical thermodynamics, it is well known that the most efficient cycles are reversible cycles. The Carnot heat engine cycle, which is composed of four reversible processes, is the best known reversible cycle observed by Chambadal P. et al. [4]. But in reality reversible processes require an infinite process time and/or an infinite system area which is not the case in practice. However, reversible cycles provide the upper bounds for the performance criteria and hence are considered as models for the actual systems by Bejan A. et al. [7]. Chambadal P. et al [4, 5, and 6] used the concept of finite-time thermodynamics to optimize the power outputof a Carnot engine. Nowadays cogeneration power plants (in which heat and power are produced together) are widely used to minimize the transmission and distribution losses by Chandra H. et al [8]. According to Chandra, Hall and Wilson, [8, 4 and 9] cogeneration power plants are also known as ìn-plant generation (IPG)', `combined heat and power (CHP)', and `by-product power'. These cogeneration power plants are more advantageous in terms of energy and exergy efficiencies than plants, which produce heat and power separately by Sahin et al. [10]. Sahin and Kodal [10] carried out the exergy optimization for an endo reversible cogeneration cycle based on finite-time thermodynamic having infinite heat capacity and determined the optimum values for design parameters of the cogeneration cycle at maximum exergy output.

The exergy optimization of irreversible cogeneration cycle based on finite time thermodynamics which consider the internal irreversibility caused due to entropy generation during the internal process for more accurate determination of optimum vale of design parameter Chandra H. et al. [11]. However, the limitation with their model was that they considered the cogeneration plant is coupled with thermal reservoir of infinite heat capacity and the design parameter are very much affected by irreversibility of finite-rate heat transfer. II THERMODYNAMIC FORMULATION OF THE PROBLEM With the fast pace of modernization and industrialization, Energy crisis is the greatest burning issue of any country. With unending research made on non-conventional research, energy output is still largely dependent on conventional research The threat of decreasing level of non-renewable resource with the growing demands of developing countries has made the mankind to think for the future generations. We can’t go for blindly feeding on such resource, nor can we think of shutting the power plants which are the pillars of the nation. Such situations have led to price hikes and energy starvations: Also unlimited usage of commercial resources have added to the serious problems like pollution and global warming.

The model of the irreversible cogeneration cycle (in which both external and internal irreversibility’s are considered) and its T-S diagram is shown in fig. 3 and 4respectively. There are three heat sources, QH, QL and QK between which the cogeneration cycle operates. The temperatures of the working fluids exchanging heat with this heat sources at QH, QK and QL are TH, TK and TL respectively. The model of the cogeneration cycle shown in fig. 1 and 2 represents cogeneration plants that have a pass-out condensing steam turbine. In these plants, some steam is extracted from the turbine at an intermediate pressure and transferred to a heat consumer for process heating. The condensate is then returned to the steam plant/boiler. In the irreversible Cogeneration cycle:-

(a) QH is the rate of heat transfer from heat

source at TmH to the warm working fluid at the constant temperature TH in process 2’-3

(b) QK is the rate of heat transfer from the working fluid at constant TK to the heat consuming device at TmK in process 4’-5

(c) QL is the rate of heat transfer from the cold working fluid at constant TL to the heat source at TmL in process 6’-1

1



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Fig. 3 Schematic model of irreversible cogeneration cycle coupled with

finite heat capacity heat exchanger

Fig.4 T-S diagram of irreversible cogeneration cycle coupled

with finite capacity heatexchanger.

The rate of heat input from high temperature heat source to the cogeneration cycle is given by

(1)

(2)

(3)

(4) Total exergy is given by,

(5)

Power to process heat ratio is given by,

Thus theLagrangian function is given by,

Since

After simplifying the above equation, we get

And further solving, we get

Where

Now from equation (6),

Put the value of equation (13) in equation (5), we get

In order to achieve optimal thermal conductance, which are measures of heat-exchangersizes, we assume that the total thermal conductance is fixed

Define the thermal conductance allocation ratios x, y, and z for the heat-source,heat-sink and heat-consumer sides respectively, as:

(15)



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Where z=1-x-y. Therefore the maximum total exergy rate given inEquation (14) can be optimized with respect 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 are

(19)

(20)

III. RESULTS& DISCUSSION In this paper, the effect of the heat-consumer temperature parameter (Ψ) and extreme temperature ratio (Φ) on the maximum total exergy rate and the corresponding exergy efficiency are analyzed. 1) Effect of heat-consumer temperature parameter The effect of the heat-consumer temperature parameter on the maximum total exergy rate and the corresponding exergy efficiency, with the ratio of power output to process heat R is given in Figures 5 and 6 respectively. The values of Φ and I are taken as 4 and 1.12, while the value of (Ψ) is varied from 1.2 to 1.8 and the value of R is varied from 0 to 20. It has been observed in this curve that for a particular value of heat-consumer temperature parameter (Ψ), exergy rate and corresponding efficiency varies inversely with respect to power to heat ratio. With increasing

value of (Ψ), slope of the curve increases. Initially up to R=6, the value of exergy rate and corresponding efficiency decrease and then with higher values of R, exergy rate and corresponding efficiency become constant. The reason for these decreases is that the temperature T*

K at maximum total exergy increases for increasing TminK, which is the heat-consumer temperature. The increase in T*

K causes the isentropic expansion work of the heat engine and thus causes the exergetic performance of the irreversible cogeneration system to decrease.The value of the maximum total exergy rate and exergy efficiency at maximum total exergy for the irreversible cogeneration cycle are lower than that for the endoreversible cogeneration cycle due to the presence of cycle irreversibility parameter in the irreversible cogeneration cycle, which is less than unity. The effect of external irreversibility on the exergy&exergy efficiency is on the lower side as compared to the previous papers i.e. exergy optimization for endoreversible cogeneration cycle by Sahin and Kodal&Thermal exergy optimization for an irreversible cogeneration power plant by Chandra and Kaushik due to in cooperation of external irreversibility. 2) Effects of extreme temperature ratio(Φ) The effect of the extreme temperature ratio (Φ) for various values of R on ETmax and are shown in Figures 6 and 7 respectively. The values of Ψ and I are taken as 1.33 and 1.11, while the value of Φ is varied from 2 to 7 and the value of R is varied from 0 to infinity. Although both ETmax and increase for increasing Φ and decreasing R, the increase in ETmaxis more rapid than . It is also observed that the value of ETmaxand for the irreversible cogeneration cycle is less than that for the endoreversible cogeneration cycle due to the presence of the cycle irreversibilities.

Fig. 5 Variation of maximum total energy rate with respect to R

for various Ψ, Φ 4,



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Fig. 6 Variation of exergy efficiency at maximum total energy

with respect to R for Various Ψ , Φ 4,

Fig.7 Effects of Φ and R on total exergy rate for Ψ=1.33

CONCLUSIONS The thermal exergy optimization for an irreversible cogeneration cycle has been carried out by introducing the cycle irreversibility parameter as a modified criterion. From this study it is clear that the endoreversible cogeneration cycle is a special case of the irreversible cogeneration cycle. The exergetic performance of the irreversible cogeneration cycle for different design parameters has been analyzed and the performance is always less than that for the endoreversible cogeneration cycle case, due to the presence of the cycle irreversibility parameter. In order to get the high exergetic performance of the irreversible cogeneration system the heat-consumer temperature should be as low as possible. The value of the optimum conductance-allocation ratio on heat-source side remains approximately constant near 0.5, and for the heat-sink and heat-consumer sides, depend R,Ψ & Φ In our continuing search for a realistic theoretical upper limit for the exergetic performance, the new equations with cycle irreversibility represent a further insight over the

exergetic performance of the endoreversible cogeneration cycle. To obtain a high exergetic performance from the cogeneration system the heat-consumer temperature must be kept low to decrease T*

K.The results obtained are quite useful for analyzing the scope of cogeneration power plants. Future work can be finite time exergy based ecological optimization of cogeneration cycle considering irreversibility between the heat source/sink and the irreversibility within the cycle. This consists of maximizing a function representing the compromise between the power output and entropy production rate of the cogeneration cycle. REFERENCES

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THERMAL EXERGY OPTIMIZATION OF AN IRREVERSIBLE ...pep.ijieee.org.in/journal_pdf/11-203-144896259443-49.pdf · Thermal Exergy Optimization Of An Irreversible ... Thermal Exergy Optimization