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Thermodynamic optimization of combined power and refrigeration cycle using binary organic working fluid
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Thermodynamic optimization of combined power and refrigeration cycle using binary organic working fluid H. Abed*, K. Atashkari, A. Niazmehr, A. Jamali Department of Mechanical Engineering, University of Guilan, PO Box 3756, Rasht, Iran
article info
abstract
Article history:
A combined cycle has been proposed for the production of power and refrigeration
Received 9 December 2012
simultaneously. The cycle can be driven by low grade heat sources such as solar,
Received in revised form
geothermal and waste heat sources. In the first part of this paper, a model has been
24 June 2013
developed to perform a parametric analysis to evaluate the effects of important parameters
Accepted 26 June 2013
on the performance of the cycle, which is a combination of Rankine and absorption
Available online 4 July 2013
refrigeration cycle. Propaneedecane has been used as an organic dual working fluid. In the second part, multi objective genetic algorithm is applied for Pareto approach optimization
Keywords:
of the cycle. There are three important conflicting objectives namely, turbine work (Wt),
Thermal power
cooling capacity (Qc) and thermal efficiency (hth) which have been selected to find the best
Cooling cycle
possible combination of these performance parameters. Optimization has been carried out
Organic working fluid
by varying turbine inlet pressure, superheated temperature and condenser temperature as
Multi-objective optimization
design variables. Among optimum design parameters, a trade-off point is selected. Turbine inlet pressure, superheated temperature and condenser temperature are assumed to be 29.5 bar, 410 K and 386.6 K respectively as the values assigned to this point. Furthermore, it has been shown that some interesting and important relationships can be discovered among optimal objective functions and decision variables involved, consequently. ª 2013 Elsevier Ltd and IIR. All rights reserved.
Optimisation thermodynamique du cycle de coge´ne´ration d’e´lectricite´ et de froid utilisant un fluide actif organique binaire Mots cle´s : Puissance thermique ; Cycle frigorifique ; Fluide actif organique ; Optimisation multi-objectifs
* Corresponding author. E-mail address: [email protected] (H. Abed). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2013.06.013
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1.
Introduction
Nowadays, the worldwide energy demand has been increasing steadily and is expected to increase continuously in the future. A greater effort in developing more efficient systems has been necessitated due to growing concerns about the rapid depletion of conventional fossil fuel resources. In recent years, substantial efforts have been made for using low grade heat sources such as geothermal, solar and waste heat energy. Utilization of low temperature sources and heat recovery is an active step in improving the overall energy conversion efficiency and decreasing the capital cost of energy per unit. An improvement in performance of cycles which use low grade sources can be achieved by using multi component zeotropic working fluids by decreasing the mismatch in temperature between working fluid and heat sources fluid during the heat addition. The most important characteristic of these fluids is their variable temperature during the boiling process (Maloney and Robertson, 1953). The idea of utilizing binary mixture was first proposed by Kalina in bottoming cycle of a combined power plant (Kalina, 1984). The study has shown that the overall efficiency of a combined cycle, which uses ammoniaewater power bottoming cycle, is 14.5%e23% higher than the efficiency of a combined system using the Rankine bottoming cycle for the same conditions. Several investigations have been performed on the Kalina cycle by using ammoniaewater under different operating conditions (Park and Sonntag, 1990; Ibrahim and Klein, 1996; Marston, 1990). The comparison of performances of Kalina and Rankine cycles has also been performed by Park and Sonntag (1990). They showed that the Kalina cycle bottoming systems have an advantage over the Rankine cycle systems in terms of first law and second law efficiencies. The ammoniaewater combined power/cooling cycle was proposed by Xu et al. (2000). This cycle utilizes a binary mixture, such as ammoniaewater, working fluid to produce both power and refrigeration simultaneously in the same loop and requires less equipment; simply an absorber, separator, boiler, heat recovery and refrigeration heat exchangers and a turbine. The cycle is a combination of Rankine cycle and an absorption refrigeration system. This cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or as an independent cycle using low temperature sources such as geothermal and solar energy, the investigation showed that the cycle could achieve high thermal efficiency for a low temperature heat source. Some further studies have been carried out in this context (Hasan et al., 2000; Goswami et al., 2004; Tamm et al., 2004; Yidal et al., 2006; Vijayaraghavan and Goswami, 2006; Martin and Goswami, 2006; Sadrameli and Goswami, 2007; Pouraghaie et al., 2010; Padilla et al., 2010). The main advantage of this cycle is that it can use low heat sources (below 250 C) in comparison to other systems (Goswami et al., 2004). A novel hybrid solar/gas system which is based on the combination of an ejector cycle heat pump with a turbine/generator has been presented in Oliveira et al. (2002). Colonna and Gabrielli worked on a combined system where a gas turbine or gas internal combustion engine drives an ammoniaewater absorption refrigeration plant through a heat recovery exchanger
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(Colonna and Gabrielli, 2003). A cogeneration system which is a combination of Rankine cycle and steam ejector refrigeration cycle has been investigated by Alexis (2007) to produce electrical power and refrigeration capacity. A trinary cycle using a gas turbine at the topping cycle, a steam Rankine cycle at the intermediate stage and an ammoniaewater cycle at the bottoming stage has been developed by Takeshita et al. (2005). The bottoming stage is a combination of Kalina power cycle and ammonia refrigeration cycle. A combined Power/Cooling cycle which replaces the flash tank in Kalina cycle by a rectifier to enhance the separation process and obtain a higher purity of ammonia for refrigeration has been proposed in Zheng et al. (2006). A novel ammoniaewater system has also been studied, for the cogeneration of refrigeration and power. The plant operates in a parallel combined cycle mode with an ammoniaewater Rankine cycle and an ammonia refrigeration cycle, interconnected by the absorption, separation, and heat transfer processes (Zhang and Lior, 2007). Recently extensive researches have been performed for the development and analysis of combined power and ejector-absorption refrigeration cycle for the waste heat utilization (Dai et al., 2009; Hong et al., 2011; Khaliq et al., 2012). Optimization in engineering design has always been of great importance and interest particularly in solving complex real-world design problems. Basically, the optimization process is defined as finding a set of values for a vector of design variables so that it leads to an optimum value of an objective or cost function. In such single objective optimization problems, there may or may not exist some constraint functions on the design variables and they are respectively referred to as constrained or unconstrained optimization problems. There are many calculus-based methods including gradient approaches to search for mostly local optimum solutions and these are well documented in Arora (1989). However, some basic difficulties in the gradient methods such as their strong dependence on the initial guess can cause them to find a local optimum rather than a global one. This has led to other heuristic optimization methods, particularly genetic algorithms (GAs) being used extensively during the last decade. Such nature-inspired evolutionary algorithms (Goldberg, 1989) differ from other traditional calculus based techniques. The main difference is that GAs work with a population of candidate solutions not a single point in search space. This helps significantly to avoid being trapped in local optima as long as the diversity of the population is well preserved. In multiobjective optimization problems, there are several objective of cost functions (a vector of objectives) to be optimized simultaneously. These objectives often conflict with each other so when one objective function improves, another deteriorates. Therefore, there is no single optimal solution that is best with respect to all of the objective functions. Instead, there is a set of optimal solutions, well known as Pareto optimal solutions (Srinivas and Deb, 1994), which distinguish significantly the inherent natures between single-objective and multi-objective optimization problems. The concept of a Pareto front in the space of objective functions in multiobjective optimization problems stand for a set of solutions that are non-dominated to each other but are superior to the rest of the solutions in the search space. Evidently, changing the vector of design variables in such Pareto optimal solutions,
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which distinguish significantly the inherent natures between single-objective and multi-objective optimization problems. The concept of a Pareto front in the space of objective functions in multi-objective optimization problems stand for a set of solutions that are non-dominated to each other but are superior to the rest of solutions in the search space. Evidently, changing the vector of design variables in such Pareto optimal solutions consisting of these non-dominated solutions would not lead to the improvement of all objectives simultaneously. Consequently, such a change leads to a deterioration of at least one objective to an inferior one. Thus, each solution of the Pareto set includes at least one objective inferior to that of another solution in that Pareto set, although both are superior to others in the rest of search space. The inherent parallelism in evolutionary algorithms makes this suitably eligible for solving multi-objective optimization problems. In thermal systems, like many real world engineering design problems, there are many complex optimization design problems which can also be multi-objective in nature. The objectives in thermal systems are usually conflicting and non-commensurable, and thus Pareto solutions provide more insights into the competing objectives. Recently, there has been a growing interest in evolutionary Pareto optimization in thermal systems. A thermo-economic analysis has been performed by Toffolo and Lazzaretto (2002) in which two exergic and economic issues in a cogeneration power plant have been considered as conflicting objectives. A monetary multiobjective optimization of a combined cycle power system has been studied by Roosen et al. (2003). The aim of the present investigation is to study the performance of a combined cooling and power cycle, proposed by Xu et al. (2000) for the Pareto approach optimization. In this evaluation, propaneedecane is used as organic binary working fluid. The thermodynamic model of the cycle has been developed, based on this model, multi-objective optimization has been performed by genetic algorithm. Three design variables namely, turbine inlet pressure, superheater temperature and condenser temperature have been used for this purpose. In this way, diversity preserving algorithm called ε-elimination diversity algorithm is used to enhance the performance of NSGA-II (Non-dominated Sorting Genetic Algorithm) in terms of diversity of population and Pareto fronts.
2.
System description and modeling
The proposed cycle combines the Rankine cycle and the absorption refrigeration cycle, which can produce both power and refrigeration simultaneously with only one heat source. This cycle uses propaneedecane as a working fluid, which reduces the heat transfer irreversibility, especially for low temperature heat sources such as solar energy and geothermal heat. The detailed analysis of the cycle is given by Xu et al. (2000); however, a brief description is covered in this section. A glance at Fig. 1, the basic concentration of binary fluid mixture (propaneedecane) which leaves the absorber as saturated solution (state 1) is pumped to a high pressure (state 2). After being heated from the returning weak solution in a heat exchanger, it is then sent to the boiler. The boiler
Fig. 1 e Combined cycle with propaneedecane.
operates between the bubble and dew point of binary working fluid at the system pressure. The basic solution is partially boiled to produce a two-phase mixture, a liquid (state 10), which is relatively weak in propane, and a vapor (state 4) with a high concentration of propane. This two-phase mixture is separated, and the weak liquid transfers the heat to the high concentration stream before it is throttled to the system in low pressure and sprayed into the absorber. The rectifier cools the saturated propane vapor (state 6) to condense out any remaining decane. Heat can be added in the superheater as the vapor (state 7) proceeds to the expander. The expander extracts energy from the high-pressure vapor as it is expanded to the system’s low-pressure (state 8). The vapor temperature exiting the expander can be significantly below ambient condition which provides cooling in the cooler. The use of a working fluid mixture, propaneedecane, is the key to this process. At constant pressure, the condensing temperature of a propane rich vapor can be below the saturation temperature of a lower concentration liquid. The vapor (state 9) rejoins the weak liquid in the absorber, where with heat rejection the basic solution is regenerated. Absorption condensation is used to regenerate the working fluid, which allows the expander exhaust temperature to be significantly below the temperature at which absorption is taking place. This process differs from pure working fluid Rankine cycle operation, where the limiting expander exhaust temperature is the vapor condensation temperature. The thermodynamic properties of the working fluid were calculated using a theoretical model based on Helmholtz free energy formulation used in Reference Fluid Thermodynamic and Transport properties data base (REFPROP) developed by the National Institute of Standards and Technology of the United States (NIST) (McLinden et al.). REFPROP has been used for calculation of the properties. The pump and turbine isentropic efficiency is 85% (hp ¼ ht ¼ 85%). Applying simple thermodynamic relations to
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the system components, the outputs can be evaluated as below. The amount of net output work produced by the cycle can be determined as: Wn ¼ m7 ðh7 h8 Þ m1 ðh2 h1 Þ
(1)
The amount of heat added to the system is equal to the difference between inlet and outlet enthalpy of the boiler: Q boiler ¼ m4 h4 þ m10 h10 m3 h3 m5 h5
(2)
The amount of heat added in superheater can be calculated as: Q superheater ¼ m6 ðh7 h6 Þ
Fig. 3 e Effect of turbine inlet pressure on cooling capacity.
(3)
For the cooler: Q c ¼ m8 ðh9 h8 Þ
(4)
Finally, thermal efficiency can be evaluated as: hth
3.
Wn þ Q c ¼ Q superheater þ Q boiler
performance, are selected as the objective functions for parameter optimization of the cycle.
3.1. (5)
The performance of cycle
For practical operation, the cycle has many parameters that are varied together, presenting a multi-dimensional surface on which an optimum can be found. These parameters have an effect on the cycle performance. In the present study, in order to investigate the effect of different input parameters on the performance of a combined cooling/power cycle, a parametric study of the cycle is necessary. The input parameters are inlet and outlet turbine pressure, propane mass fraction in pump output, boiler temperature, superheater temperature, condenser temperature and outlet absorber temperature. Since the purpose of this study is to investigate the effect of organic dual working fluid on the operation of cycle and compare it with ammoniaewater, so the parameters and their values have been selected according to Ref (Pouraghaie et al., 2010). The effects of turbine inlet pressure (Ph), condenser temperature (Tcondenser) and a superheater temperature (Tsuperheater) on the performance are examined. For cycle performance simulation, some input parameters are assumed as, Tboiler ¼ 400K, Tab ¼ 280K (state 1), PL ¼ 2 bar, x ¼ 0.47e0.53 The thermal efficiency (h), turbine work (Wt) and cooling capacity (Q c) which can evaluate the cycle
Fig. 2 e Effect of turbine inlet pressure on turbine work.
Effect of turbine inlet pressure
Figs. 2e4 show the effect of turbine inlet pressure on the turbine work (Wt), cooling capacity (Q c) and thermal efficiency (hth) for different basic solution of propane concentrations (state 2). Condenser and superheater temperatures have been selected as 360K and 410K, respectively. Due to vapor production decreasing at high turbine inlet pressure, the turbine work goes almost linearly down as the pressure increases as seen in Fig. 2. Figs. 3 and 4 show the variation of the cooling capacity and turbine exit temperature with respect to the change in turbine inlet pressure. It is found that the turbine outlet temperature decreases with the increase in pressure. Decreasing in turbine exit temperature leads to increase in cooling capacity. Also the slope of cooling capacity variation increases with the propane mass fraction in the basic solution. In spite of reduction in turbine work output, the thermal efficiency goes up first and then decreases (Fig. 5).
3.2.
Effect of superheater temperature
The effect of superheater temperature on the outputs of the system is shown in Figs. 6e8 for proposed turbine inlet pressure and condenser temperature at 25 bar and 360 K respectively. It is found that as the superheater temperature increases, the cooling capacity and thermal efficiency decreases and as may be expected, the turbine work goes up. The
Fig. 4 e Effect of turbine inlet pressure on turbine exit temperature.
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Fig. 5 e Effect of turbine inlet pressure on thermal efficiency.
reason for this is that the exit turbine temperature increases as the turbine inlet temperature increases for a fixed pressure ratio. There is no cooling capacity available when the superheater is greater than 420 K (Fig. 8).
Fig. 7 e The effect of superheater temperature on thermal efficiency.
Thermodynamic properties differences between ammoniaewater and organic working fluid such as boiling temperature, enthalpy and entropy, caused the differences in results.
4. 3.3.
Effect of condenser temperature
As clearly illustrated Figs. 9e11 show the effect of condenser temperature on the turbine work, cooling capacity and thermal efficiency. Turbine inlet pressure and superheater temperature are fixed at 25 bar and 410 K for different basic solution propane concentration. Lower condenser temperature generates drier propane vapor and controls its concentration. The advantage is that the very high propane vapor concentration can provide lower temperature for refrigeration production. It can be seen that cooling capacity decreases with the increasing condenser temperature. There is no cooling available when the condenser temperature is greater than 382 K in the present case. The turbine work increases as condenser temperature goes down. Changes in thermal efficiency are led by the combined effects of turbine work and cooling capacity that are shown in Fig. 11. It is interesting to compare the results of the present investigation with those using ammoniaewater effects on this cycle which have been studied by Xu et al. (2000). Figs. 12e14 lucidly demonstrate thermal efficiencies improve in all cases while cooling capacity and turbine work decrease when using organic working fluid at identical concentration (x ¼ 0.50).
Fig. 6 e The effect of superheater temperature on turbine work.
Multi-objective Pareto optimization
Multi-objective optimization which is also called multicriteria optimization or vector optimization has been defined as finding a vector of decision variables satisfying constraints to give optimal values to all objective functions. In general, it can be mathematically defined as: Find the vector X ¼ ½x1 ; x2 ; .; xn T to optimize T FðXÞ ¼ f1 ðXÞ; f2 ðXÞ; .; fk ðXÞ
(6)
Subject to m inequality constraints li ðXÞ 0; i ¼ 1 to m
(7)
And p equality constraints hj ðXÞ ¼ 0; j ¼ 1 to p A vector U ¼ ½u1 ; u2 ; .; uk ˛
Fig. 8 e The effect of superheater temperature on cooling capacity.
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Fig. 9 e The effect of condenser temperature on turbine work.
{1,2,.,k}, cX˛U{X*}fi(X*) fi(X )^dj{1,2,.,k}: fi(X*)fi(X ). It means that the solution X* is said to be Pareto optimal (minimal) if no other solutions can be found to dominate X* using the definition of Pareto dominance. Evolutionary algorithms have been widely used for multiobjective optimization because of their natural properties suited for these types of problems. This is mostly because of their parallel or population-based search approach. Therefore, most difficulties and deficiencies within the classical methods in solving multi-objective optimization problems are eliminated. For example, there is no need for either several runs to find the Pareto front or quantification of the importance of each objective using numerical weights. It is very important in evolutionary algorithms that the genetic diversity within the population be preserved sufficiently. This main issue in multiobjective problems has been addressed by much related research work (Toffolo and Benini, 2003). Consequently, the premature convergence of multi-objective evolutionary algorithms is prevented and the solutions are directed and distributed along the true Pareto front if such genetic diversity is well provided. The Pareto-based approach of NSGA-II (Deb et al., 2002) has been recently used in a wide range of engineering multi-objective problems because of its simple yet efficient non-dominance ranking procedure in yielding different levels of Pareto frontiers. However, the crowding approach in such a state-of the-art multi-objective evolutionary algorithm works efficiently for two-objective optimization problems as a diversity-preserving operator which is not the case for problems with more than two objective
Fig. 10 e The effect of condenser temperature on cooling capacity.
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Fig. 11 e The effect of condenser temperature on thermal efficiency.
functions. The reason is that the sorting procedure of individuals based on each objective in this algorithm will cause different enclosing hyper-boxes. It must be noted that, in a two-objective Pareto optimization, if the solutions of a Pareto front are sorted in a decreasing order of importance to one objective, these solutions are then automatically ordered in an increasing order of importance to the second objective. Thus, the hyper-boxes surrounding an individual solution remain unchanged in the objective-wise sorting procedure of the crowding distance of NSGA-II in the two-objective Pareto optimization problem. However, in multi-objective Pareto optimization problem with more than two objectives, such sorting procedure of individuals based on each objective in this algorithm will cause different enclosing hyper-boxes. Thus, the overall crowding distance of an individual computed in this way may not exactly reflect the true measure of diversity or crowding property for the multi-objective Pareto optimization problems with more than two objectives. In this work, a new method called ε-elimination diversity algorithm is deployed to modify NSGA-II so that it can safely be used for any number of objective functions (particularly for more than two objectives) in multi-objective optimization problems.
4.1. Multi-objective optimization of combined cycle using organic working fluid Some predicted results of thermal efficiency, turbine work and cooling capacity have been produced applying the
Fig. 12 e The effect of condenser temperature on thermal efficiency and Turbine work by using propaneedecane and ammoniaewater.
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Fig. 16 e Pareto front of cooling capacity and turbine work. Fig. 13 e The effect of superheater on thermal efficiency and turbine work by using propaneedecane and ammoniaewater.
Fig. 17 e Non-dominated individuals in the plane of turbine cooling capacityethermal efficiency.
Fig. 14 e The effect of turbine inlet pressure on thermal efficiency and turbine work by using propaneedecane and ammoniaewater.
simulation procedure. As clearly shown in previous figures, there is a conflict between the values of three outputs of the system. Three output parameters, namely Wt, hth and Qc are considered as objective functions of cycle. Evidently, it is expected that all objective functions to be optimized (maximized in this case) simultaneously. The design variable vector is d ¼ [Ph, Tsuperheater, Tcondenser], which has to be optimally determined based on the multi-objective Pareto approach. Changing these parameters according to the type of related equipment is easier than others and also has behavior diversity on objective functions. The evolutionary process of optimum selection of the design variables vector to obtain the
Fig. 15 e Pareto front of thermal efficiency and turbine work.
Pareto front of those objective functions is accomplished with a population the size of 100 with crossover probability, Pc, and mutation probability, Pm, of 0.9 and 0.1 respectively, using the modified NSGA-II (Atashkari et al., 2005). According to thermodynamic analysis and using previous study (Pouraghaie et al., 2010), the range of variations for Ph, TSuperheater and Tcondenser are assumed to be 25e34 bar, 410e500 K and 360e400 K, respectively. Fig. 14 depicts the non-dominated individuals in two objective optimization in the plane of (Wthth). As can be seen, there exists conflict between thermal efficiency and turbine work output of the cycle. In other words, improving one of the objective functions leads to the deterioration of the other output. Such non-dominated individuals have alternatively been shown in the plane of (WtQc) and (Qchth) as laid out in Figs. 16 and 17 respectively. Fig. 17 points out clearly; there exists no conflict between thermal efficiency cooling capacity
Fig. 18 e Relationships of turbine work and cooling capacity with turbine inlet pressure.
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of the cycle. In other words, improving one of the objective functions leads to the improvement of the other output. Points A and B, as depicted in Fig. 16, represent the highest cooling capacity and highest turbine work respectively. The values of the objective functions in these optimal points are very close to those obtained by single-objective optimization. These agreements confirm the accuracy of multi-objective optimization. The values assigned to A are d ¼ [33.9 bar, 410 K, 386.6 K], and to B are d ¼ [25.4 bar, 414.9 K, 361.7 K]. However, optimum design point C demonstrates a trade-off design point in terms of the three selected objective functions which is located almost on all Figs. 15 through 17. This can be simply achieved by mapping of the values of objective functions of all non-dominated points into interval 0 and 100. Using the sum of these values for each non-dominated points, the design point C simply represents the maximum of those values. The values assigned to this point are d ¼ [29.5 bar, 410 K, 386.6 K]. Fig. 18 furthermore demonstrates the behaviors of cooling capacity and turbine work with respect to Ph. It can be readily seen that the optimal values of these objective functions have a polynomial relation with Ph approximately, that is Wt ¼ 2:93Ph þ 144
(8)
Qc ¼ 0:666Ph 16:5
(9)
The optimal values of turbine work and cooling capacity can be determined at a given turbine inlet pressure.
5.
Conclusions
Parametric analysis and optimization of combined power and refrigeration cycle have been presented. propaneedecane mixture has been used as the working fluid. The thermodynamic properties of the working fluid have been evaluated using REFPROP developed by the National Institute of Standards and Technology of the United States. Parametric analysis of the cycle revealed that varying each of the three selected design variables, namely turbine inlet pressure, superheater temperature and condenser temperature, shows conflict among performance parameters. A multi-objective genetic algorithm (non-dominated sorting genetic algorithms, NSGA II) was successfully applied with Pareto approach for optimization of the proposed cycle. Applying the first law of thermodynamics, three objective functions, namely, turbine work, thermal efficiency and cooling capacity were determined in terms of three design variables. Optimization led to the discovering of important relationships and useful optimal design principles in thermodynamic optimization of the proposed cycle both in the space of objective functions and decision variables. The results of multiobjective optimization of the three functions revealed that there is no conflict between cooling capacity and thermal efficiency. The evolutionary multi-objective optimization process has helped to discover important relationships with relatively few efforts of modeling preparation that would otherwise have required at least a very thorough mathematical analysis.
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Nomenclature
h m P Q T x X* F(X ) h CT ST
specific enthalpy [kj kg1] mass flow rate [kg s1] pressure [bar] heat [kW kg1] temperature [K] propane mass concentration vector of optimal design vector of objective function efficiency Condenser Temperature Superheater Temperature
Subscripts t turbine c cooling n net h high pressure ab ambient p pump th thermal L lower pressure
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Sadrameli, S.M., Goswami, D.Y., 2007. Optimum operating conditions for a combined power and cooling thermodynamic cycle. Appl. Energy 84, 254e265. Srinivas, N., Deb, K., 1994. Multi-objective optimization using non-dominated sorting in genetic algorithms. Evol. Comput. 3 (2), 221e248. Takeshita, K., Amano, Y., Hashizume, T., 2005. Experimental study of advanced cogeneration system with ammoniaewater mixture cycles at bottoming. Energy 30, 247e260. Tamm, G., Goswami, D.Y., Lu, S., Hasan, A.A., 2004. Theoretical and experimental investigation of an ammoniaewater power and refrigeration thermodynamic cycle. Solar Energy 76, 217e228. Toffolo, A., Benini, E., 2003. Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol. Comput. 2 (11), 151e167. Toffolo, A., Lazzaretto, A., 2002. Evolutionary algorithms for multi-objective energetic and economic optimization in thermal system design. Energy 27, 549e567. Vijayaraghavan, S., Goswami, D.Y., 2006. A combined power and cooling cycle modified to improve resource utilization efficiency using a distillation stage. Energy 31, 1177e1196. Xu, F., Goswami, D.Y., Bhagwat, S.S., 2000. A combined power/ cooling cycle. Energy 3, 233e246. Yidal, A., Best, R., Rivero, R., Cervantes, J., 2006. Analysis of a combined power and refrigeration cycle by the exergy method. Energy 31, 3401e3414. Zhang, N., Lior, N., 2007. Development of a novel combined absorption cycle for power generation and refrigeration. J. Energy Resour. Technol. 129, 254e265. Zheng, D., Chen, B., Qi, Y., Jin, H., 2006. Thermodynamic analysis of a novel absorption power/cooling combined-cycle. Appl. Energy 83 (4), 311e323.
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Thermodynamic optimization of combined power and refrigeration cycle using binary organic working fluid H. Abed*, K. Atashkari, A. Niazmehr, A. Jamali Department of Mechanical Engineering, University of Guilan, PO Box 3756, Rasht, Iran
article info
abstract
Article history:
A combined cycle has been proposed for the production of power and refrigeration
Received 9 December 2012
simultaneously. The cycle can be driven by low grade heat sources such as solar,
Received in revised form
geothermal and waste heat sources. In the first part of this paper, a model has been
24 June 2013
developed to perform a parametric analysis to evaluate the effects of important parameters
Accepted 26 June 2013
on the performance of the cycle, which is a combination of Rankine and absorption
Available online 4 July 2013
refrigeration cycle. Propaneedecane has been used as an organic dual working fluid. In the second part, multi objective genetic algorithm is applied for Pareto approach optimization
Keywords:
of the cycle. There are three important conflicting objectives namely, turbine work (Wt),
Thermal power
cooling capacity (Qc) and thermal efficiency (hth) which have been selected to find the best
Cooling cycle
possible combination of these performance parameters. Optimization has been carried out
Organic working fluid
by varying turbine inlet pressure, superheated temperature and condenser temperature as
Multi-objective optimization
design variables. Among optimum design parameters, a trade-off point is selected. Turbine inlet pressure, superheated temperature and condenser temperature are assumed to be 29.5 bar, 410 K and 386.6 K respectively as the values assigned to this point. Furthermore, it has been shown that some interesting and important relationships can be discovered among optimal objective functions and decision variables involved, consequently. ª 2013 Elsevier Ltd and IIR. All rights reserved.
Optimisation thermodynamique du cycle de coge´ne´ration d’e´lectricite´ et de froid utilisant un fluide actif organique binaire Mots cle´s : Puissance thermique ; Cycle frigorifique ; Fluide actif organique ; Optimisation multi-objectifs
* Corresponding author. E-mail address: [email protected] (H. Abed). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2013.06.013
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1.
Introduction
Nowadays, the worldwide energy demand has been increasing steadily and is expected to increase continuously in the future. A greater effort in developing more efficient systems has been necessitated due to growing concerns about the rapid depletion of conventional fossil fuel resources. In recent years, substantial efforts have been made for using low grade heat sources such as geothermal, solar and waste heat energy. Utilization of low temperature sources and heat recovery is an active step in improving the overall energy conversion efficiency and decreasing the capital cost of energy per unit. An improvement in performance of cycles which use low grade sources can be achieved by using multi component zeotropic working fluids by decreasing the mismatch in temperature between working fluid and heat sources fluid during the heat addition. The most important characteristic of these fluids is their variable temperature during the boiling process (Maloney and Robertson, 1953). The idea of utilizing binary mixture was first proposed by Kalina in bottoming cycle of a combined power plant (Kalina, 1984). The study has shown that the overall efficiency of a combined cycle, which uses ammoniaewater power bottoming cycle, is 14.5%e23% higher than the efficiency of a combined system using the Rankine bottoming cycle for the same conditions. Several investigations have been performed on the Kalina cycle by using ammoniaewater under different operating conditions (Park and Sonntag, 1990; Ibrahim and Klein, 1996; Marston, 1990). The comparison of performances of Kalina and Rankine cycles has also been performed by Park and Sonntag (1990). They showed that the Kalina cycle bottoming systems have an advantage over the Rankine cycle systems in terms of first law and second law efficiencies. The ammoniaewater combined power/cooling cycle was proposed by Xu et al. (2000). This cycle utilizes a binary mixture, such as ammoniaewater, working fluid to produce both power and refrigeration simultaneously in the same loop and requires less equipment; simply an absorber, separator, boiler, heat recovery and refrigeration heat exchangers and a turbine. The cycle is a combination of Rankine cycle and an absorption refrigeration system. This cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or as an independent cycle using low temperature sources such as geothermal and solar energy, the investigation showed that the cycle could achieve high thermal efficiency for a low temperature heat source. Some further studies have been carried out in this context (Hasan et al., 2000; Goswami et al., 2004; Tamm et al., 2004; Yidal et al., 2006; Vijayaraghavan and Goswami, 2006; Martin and Goswami, 2006; Sadrameli and Goswami, 2007; Pouraghaie et al., 2010; Padilla et al., 2010). The main advantage of this cycle is that it can use low heat sources (below 250 C) in comparison to other systems (Goswami et al., 2004). A novel hybrid solar/gas system which is based on the combination of an ejector cycle heat pump with a turbine/generator has been presented in Oliveira et al. (2002). Colonna and Gabrielli worked on a combined system where a gas turbine or gas internal combustion engine drives an ammoniaewater absorption refrigeration plant through a heat recovery exchanger
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(Colonna and Gabrielli, 2003). A cogeneration system which is a combination of Rankine cycle and steam ejector refrigeration cycle has been investigated by Alexis (2007) to produce electrical power and refrigeration capacity. A trinary cycle using a gas turbine at the topping cycle, a steam Rankine cycle at the intermediate stage and an ammoniaewater cycle at the bottoming stage has been developed by Takeshita et al. (2005). The bottoming stage is a combination of Kalina power cycle and ammonia refrigeration cycle. A combined Power/Cooling cycle which replaces the flash tank in Kalina cycle by a rectifier to enhance the separation process and obtain a higher purity of ammonia for refrigeration has been proposed in Zheng et al. (2006). A novel ammoniaewater system has also been studied, for the cogeneration of refrigeration and power. The plant operates in a parallel combined cycle mode with an ammoniaewater Rankine cycle and an ammonia refrigeration cycle, interconnected by the absorption, separation, and heat transfer processes (Zhang and Lior, 2007). Recently extensive researches have been performed for the development and analysis of combined power and ejector-absorption refrigeration cycle for the waste heat utilization (Dai et al., 2009; Hong et al., 2011; Khaliq et al., 2012). Optimization in engineering design has always been of great importance and interest particularly in solving complex real-world design problems. Basically, the optimization process is defined as finding a set of values for a vector of design variables so that it leads to an optimum value of an objective or cost function. In such single objective optimization problems, there may or may not exist some constraint functions on the design variables and they are respectively referred to as constrained or unconstrained optimization problems. There are many calculus-based methods including gradient approaches to search for mostly local optimum solutions and these are well documented in Arora (1989). However, some basic difficulties in the gradient methods such as their strong dependence on the initial guess can cause them to find a local optimum rather than a global one. This has led to other heuristic optimization methods, particularly genetic algorithms (GAs) being used extensively during the last decade. Such nature-inspired evolutionary algorithms (Goldberg, 1989) differ from other traditional calculus based techniques. The main difference is that GAs work with a population of candidate solutions not a single point in search space. This helps significantly to avoid being trapped in local optima as long as the diversity of the population is well preserved. In multiobjective optimization problems, there are several objective of cost functions (a vector of objectives) to be optimized simultaneously. These objectives often conflict with each other so when one objective function improves, another deteriorates. Therefore, there is no single optimal solution that is best with respect to all of the objective functions. Instead, there is a set of optimal solutions, well known as Pareto optimal solutions (Srinivas and Deb, 1994), which distinguish significantly the inherent natures between single-objective and multi-objective optimization problems. The concept of a Pareto front in the space of objective functions in multiobjective optimization problems stand for a set of solutions that are non-dominated to each other but are superior to the rest of the solutions in the search space. Evidently, changing the vector of design variables in such Pareto optimal solutions,
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which distinguish significantly the inherent natures between single-objective and multi-objective optimization problems. The concept of a Pareto front in the space of objective functions in multi-objective optimization problems stand for a set of solutions that are non-dominated to each other but are superior to the rest of solutions in the search space. Evidently, changing the vector of design variables in such Pareto optimal solutions consisting of these non-dominated solutions would not lead to the improvement of all objectives simultaneously. Consequently, such a change leads to a deterioration of at least one objective to an inferior one. Thus, each solution of the Pareto set includes at least one objective inferior to that of another solution in that Pareto set, although both are superior to others in the rest of search space. The inherent parallelism in evolutionary algorithms makes this suitably eligible for solving multi-objective optimization problems. In thermal systems, like many real world engineering design problems, there are many complex optimization design problems which can also be multi-objective in nature. The objectives in thermal systems are usually conflicting and non-commensurable, and thus Pareto solutions provide more insights into the competing objectives. Recently, there has been a growing interest in evolutionary Pareto optimization in thermal systems. A thermo-economic analysis has been performed by Toffolo and Lazzaretto (2002) in which two exergic and economic issues in a cogeneration power plant have been considered as conflicting objectives. A monetary multiobjective optimization of a combined cycle power system has been studied by Roosen et al. (2003). The aim of the present investigation is to study the performance of a combined cooling and power cycle, proposed by Xu et al. (2000) for the Pareto approach optimization. In this evaluation, propaneedecane is used as organic binary working fluid. The thermodynamic model of the cycle has been developed, based on this model, multi-objective optimization has been performed by genetic algorithm. Three design variables namely, turbine inlet pressure, superheater temperature and condenser temperature have been used for this purpose. In this way, diversity preserving algorithm called ε-elimination diversity algorithm is used to enhance the performance of NSGA-II (Non-dominated Sorting Genetic Algorithm) in terms of diversity of population and Pareto fronts.
2.
System description and modeling
The proposed cycle combines the Rankine cycle and the absorption refrigeration cycle, which can produce both power and refrigeration simultaneously with only one heat source. This cycle uses propaneedecane as a working fluid, which reduces the heat transfer irreversibility, especially for low temperature heat sources such as solar energy and geothermal heat. The detailed analysis of the cycle is given by Xu et al. (2000); however, a brief description is covered in this section. A glance at Fig. 1, the basic concentration of binary fluid mixture (propaneedecane) which leaves the absorber as saturated solution (state 1) is pumped to a high pressure (state 2). After being heated from the returning weak solution in a heat exchanger, it is then sent to the boiler. The boiler
Fig. 1 e Combined cycle with propaneedecane.
operates between the bubble and dew point of binary working fluid at the system pressure. The basic solution is partially boiled to produce a two-phase mixture, a liquid (state 10), which is relatively weak in propane, and a vapor (state 4) with a high concentration of propane. This two-phase mixture is separated, and the weak liquid transfers the heat to the high concentration stream before it is throttled to the system in low pressure and sprayed into the absorber. The rectifier cools the saturated propane vapor (state 6) to condense out any remaining decane. Heat can be added in the superheater as the vapor (state 7) proceeds to the expander. The expander extracts energy from the high-pressure vapor as it is expanded to the system’s low-pressure (state 8). The vapor temperature exiting the expander can be significantly below ambient condition which provides cooling in the cooler. The use of a working fluid mixture, propaneedecane, is the key to this process. At constant pressure, the condensing temperature of a propane rich vapor can be below the saturation temperature of a lower concentration liquid. The vapor (state 9) rejoins the weak liquid in the absorber, where with heat rejection the basic solution is regenerated. Absorption condensation is used to regenerate the working fluid, which allows the expander exhaust temperature to be significantly below the temperature at which absorption is taking place. This process differs from pure working fluid Rankine cycle operation, where the limiting expander exhaust temperature is the vapor condensation temperature. The thermodynamic properties of the working fluid were calculated using a theoretical model based on Helmholtz free energy formulation used in Reference Fluid Thermodynamic and Transport properties data base (REFPROP) developed by the National Institute of Standards and Technology of the United States (NIST) (McLinden et al.). REFPROP has been used for calculation of the properties. The pump and turbine isentropic efficiency is 85% (hp ¼ ht ¼ 85%). Applying simple thermodynamic relations to
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the system components, the outputs can be evaluated as below. The amount of net output work produced by the cycle can be determined as: Wn ¼ m7 ðh7 h8 Þ m1 ðh2 h1 Þ
(1)
The amount of heat added to the system is equal to the difference between inlet and outlet enthalpy of the boiler: Q boiler ¼ m4 h4 þ m10 h10 m3 h3 m5 h5
(2)
The amount of heat added in superheater can be calculated as: Q superheater ¼ m6 ðh7 h6 Þ
Fig. 3 e Effect of turbine inlet pressure on cooling capacity.
(3)
For the cooler: Q c ¼ m8 ðh9 h8 Þ
(4)
Finally, thermal efficiency can be evaluated as: hth
3.
Wn þ Q c ¼ Q superheater þ Q boiler
performance, are selected as the objective functions for parameter optimization of the cycle.
3.1. (5)
The performance of cycle
For practical operation, the cycle has many parameters that are varied together, presenting a multi-dimensional surface on which an optimum can be found. These parameters have an effect on the cycle performance. In the present study, in order to investigate the effect of different input parameters on the performance of a combined cooling/power cycle, a parametric study of the cycle is necessary. The input parameters are inlet and outlet turbine pressure, propane mass fraction in pump output, boiler temperature, superheater temperature, condenser temperature and outlet absorber temperature. Since the purpose of this study is to investigate the effect of organic dual working fluid on the operation of cycle and compare it with ammoniaewater, so the parameters and their values have been selected according to Ref (Pouraghaie et al., 2010). The effects of turbine inlet pressure (Ph), condenser temperature (Tcondenser) and a superheater temperature (Tsuperheater) on the performance are examined. For cycle performance simulation, some input parameters are assumed as, Tboiler ¼ 400K, Tab ¼ 280K (state 1), PL ¼ 2 bar, x ¼ 0.47e0.53 The thermal efficiency (h), turbine work (Wt) and cooling capacity (Q c) which can evaluate the cycle
Fig. 2 e Effect of turbine inlet pressure on turbine work.
Effect of turbine inlet pressure
Figs. 2e4 show the effect of turbine inlet pressure on the turbine work (Wt), cooling capacity (Q c) and thermal efficiency (hth) for different basic solution of propane concentrations (state 2). Condenser and superheater temperatures have been selected as 360K and 410K, respectively. Due to vapor production decreasing at high turbine inlet pressure, the turbine work goes almost linearly down as the pressure increases as seen in Fig. 2. Figs. 3 and 4 show the variation of the cooling capacity and turbine exit temperature with respect to the change in turbine inlet pressure. It is found that the turbine outlet temperature decreases with the increase in pressure. Decreasing in turbine exit temperature leads to increase in cooling capacity. Also the slope of cooling capacity variation increases with the propane mass fraction in the basic solution. In spite of reduction in turbine work output, the thermal efficiency goes up first and then decreases (Fig. 5).
3.2.
Effect of superheater temperature
The effect of superheater temperature on the outputs of the system is shown in Figs. 6e8 for proposed turbine inlet pressure and condenser temperature at 25 bar and 360 K respectively. It is found that as the superheater temperature increases, the cooling capacity and thermal efficiency decreases and as may be expected, the turbine work goes up. The
Fig. 4 e Effect of turbine inlet pressure on turbine exit temperature.
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Fig. 5 e Effect of turbine inlet pressure on thermal efficiency.
reason for this is that the exit turbine temperature increases as the turbine inlet temperature increases for a fixed pressure ratio. There is no cooling capacity available when the superheater is greater than 420 K (Fig. 8).
Fig. 7 e The effect of superheater temperature on thermal efficiency.
Thermodynamic properties differences between ammoniaewater and organic working fluid such as boiling temperature, enthalpy and entropy, caused the differences in results.
4. 3.3.
Effect of condenser temperature
As clearly illustrated Figs. 9e11 show the effect of condenser temperature on the turbine work, cooling capacity and thermal efficiency. Turbine inlet pressure and superheater temperature are fixed at 25 bar and 410 K for different basic solution propane concentration. Lower condenser temperature generates drier propane vapor and controls its concentration. The advantage is that the very high propane vapor concentration can provide lower temperature for refrigeration production. It can be seen that cooling capacity decreases with the increasing condenser temperature. There is no cooling available when the condenser temperature is greater than 382 K in the present case. The turbine work increases as condenser temperature goes down. Changes in thermal efficiency are led by the combined effects of turbine work and cooling capacity that are shown in Fig. 11. It is interesting to compare the results of the present investigation with those using ammoniaewater effects on this cycle which have been studied by Xu et al. (2000). Figs. 12e14 lucidly demonstrate thermal efficiencies improve in all cases while cooling capacity and turbine work decrease when using organic working fluid at identical concentration (x ¼ 0.50).
Fig. 6 e The effect of superheater temperature on turbine work.
Multi-objective Pareto optimization
Multi-objective optimization which is also called multicriteria optimization or vector optimization has been defined as finding a vector of decision variables satisfying constraints to give optimal values to all objective functions. In general, it can be mathematically defined as: Find the vector X ¼ ½x1 ; x2 ; .; xn T to optimize T FðXÞ ¼ f1 ðXÞ; f2 ðXÞ; .; fk ðXÞ
(6)
Subject to m inequality constraints li ðXÞ 0; i ¼ 1 to m
(7)
And p equality constraints hj ðXÞ ¼ 0; j ¼ 1 to p A vector U ¼ ½u1 ; u2 ; .; uk ˛
Fig. 8 e The effect of superheater temperature on cooling capacity.
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Fig. 9 e The effect of condenser temperature on turbine work.
{1,2,.,k}, cX˛U{X*}fi(X*) fi(X )^dj{1,2,.,k}: fi(X*)fi(X ). It means that the solution X* is said to be Pareto optimal (minimal) if no other solutions can be found to dominate X* using the definition of Pareto dominance. Evolutionary algorithms have been widely used for multiobjective optimization because of their natural properties suited for these types of problems. This is mostly because of their parallel or population-based search approach. Therefore, most difficulties and deficiencies within the classical methods in solving multi-objective optimization problems are eliminated. For example, there is no need for either several runs to find the Pareto front or quantification of the importance of each objective using numerical weights. It is very important in evolutionary algorithms that the genetic diversity within the population be preserved sufficiently. This main issue in multiobjective problems has been addressed by much related research work (Toffolo and Benini, 2003). Consequently, the premature convergence of multi-objective evolutionary algorithms is prevented and the solutions are directed and distributed along the true Pareto front if such genetic diversity is well provided. The Pareto-based approach of NSGA-II (Deb et al., 2002) has been recently used in a wide range of engineering multi-objective problems because of its simple yet efficient non-dominance ranking procedure in yielding different levels of Pareto frontiers. However, the crowding approach in such a state-of the-art multi-objective evolutionary algorithm works efficiently for two-objective optimization problems as a diversity-preserving operator which is not the case for problems with more than two objective
Fig. 10 e The effect of condenser temperature on cooling capacity.
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Fig. 11 e The effect of condenser temperature on thermal efficiency.
functions. The reason is that the sorting procedure of individuals based on each objective in this algorithm will cause different enclosing hyper-boxes. It must be noted that, in a two-objective Pareto optimization, if the solutions of a Pareto front are sorted in a decreasing order of importance to one objective, these solutions are then automatically ordered in an increasing order of importance to the second objective. Thus, the hyper-boxes surrounding an individual solution remain unchanged in the objective-wise sorting procedure of the crowding distance of NSGA-II in the two-objective Pareto optimization problem. However, in multi-objective Pareto optimization problem with more than two objectives, such sorting procedure of individuals based on each objective in this algorithm will cause different enclosing hyper-boxes. Thus, the overall crowding distance of an individual computed in this way may not exactly reflect the true measure of diversity or crowding property for the multi-objective Pareto optimization problems with more than two objectives. In this work, a new method called ε-elimination diversity algorithm is deployed to modify NSGA-II so that it can safely be used for any number of objective functions (particularly for more than two objectives) in multi-objective optimization problems.
4.1. Multi-objective optimization of combined cycle using organic working fluid Some predicted results of thermal efficiency, turbine work and cooling capacity have been produced applying the
Fig. 12 e The effect of condenser temperature on thermal efficiency and Turbine work by using propaneedecane and ammoniaewater.
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Fig. 16 e Pareto front of cooling capacity and turbine work. Fig. 13 e The effect of superheater on thermal efficiency and turbine work by using propaneedecane and ammoniaewater.
Fig. 17 e Non-dominated individuals in the plane of turbine cooling capacityethermal efficiency.
Fig. 14 e The effect of turbine inlet pressure on thermal efficiency and turbine work by using propaneedecane and ammoniaewater.
simulation procedure. As clearly shown in previous figures, there is a conflict between the values of three outputs of the system. Three output parameters, namely Wt, hth and Qc are considered as objective functions of cycle. Evidently, it is expected that all objective functions to be optimized (maximized in this case) simultaneously. The design variable vector is d ¼ [Ph, Tsuperheater, Tcondenser], which has to be optimally determined based on the multi-objective Pareto approach. Changing these parameters according to the type of related equipment is easier than others and also has behavior diversity on objective functions. The evolutionary process of optimum selection of the design variables vector to obtain the
Fig. 15 e Pareto front of thermal efficiency and turbine work.
Pareto front of those objective functions is accomplished with a population the size of 100 with crossover probability, Pc, and mutation probability, Pm, of 0.9 and 0.1 respectively, using the modified NSGA-II (Atashkari et al., 2005). According to thermodynamic analysis and using previous study (Pouraghaie et al., 2010), the range of variations for Ph, TSuperheater and Tcondenser are assumed to be 25e34 bar, 410e500 K and 360e400 K, respectively. Fig. 14 depicts the non-dominated individuals in two objective optimization in the plane of (Wthth). As can be seen, there exists conflict between thermal efficiency and turbine work output of the cycle. In other words, improving one of the objective functions leads to the deterioration of the other output. Such non-dominated individuals have alternatively been shown in the plane of (WtQc) and (Qchth) as laid out in Figs. 16 and 17 respectively. Fig. 17 points out clearly; there exists no conflict between thermal efficiency cooling capacity
Fig. 18 e Relationships of turbine work and cooling capacity with turbine inlet pressure.
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of the cycle. In other words, improving one of the objective functions leads to the improvement of the other output. Points A and B, as depicted in Fig. 16, represent the highest cooling capacity and highest turbine work respectively. The values of the objective functions in these optimal points are very close to those obtained by single-objective optimization. These agreements confirm the accuracy of multi-objective optimization. The values assigned to A are d ¼ [33.9 bar, 410 K, 386.6 K], and to B are d ¼ [25.4 bar, 414.9 K, 361.7 K]. However, optimum design point C demonstrates a trade-off design point in terms of the three selected objective functions which is located almost on all Figs. 15 through 17. This can be simply achieved by mapping of the values of objective functions of all non-dominated points into interval 0 and 100. Using the sum of these values for each non-dominated points, the design point C simply represents the maximum of those values. The values assigned to this point are d ¼ [29.5 bar, 410 K, 386.6 K]. Fig. 18 furthermore demonstrates the behaviors of cooling capacity and turbine work with respect to Ph. It can be readily seen that the optimal values of these objective functions have a polynomial relation with Ph approximately, that is Wt ¼ 2:93Ph þ 144
(8)
Qc ¼ 0:666Ph 16:5
(9)
The optimal values of turbine work and cooling capacity can be determined at a given turbine inlet pressure.
5.
Conclusions
Parametric analysis and optimization of combined power and refrigeration cycle have been presented. propaneedecane mixture has been used as the working fluid. The thermodynamic properties of the working fluid have been evaluated using REFPROP developed by the National Institute of Standards and Technology of the United States. Parametric analysis of the cycle revealed that varying each of the three selected design variables, namely turbine inlet pressure, superheater temperature and condenser temperature, shows conflict among performance parameters. A multi-objective genetic algorithm (non-dominated sorting genetic algorithms, NSGA II) was successfully applied with Pareto approach for optimization of the proposed cycle. Applying the first law of thermodynamics, three objective functions, namely, turbine work, thermal efficiency and cooling capacity were determined in terms of three design variables. Optimization led to the discovering of important relationships and useful optimal design principles in thermodynamic optimization of the proposed cycle both in the space of objective functions and decision variables. The results of multiobjective optimization of the three functions revealed that there is no conflict between cooling capacity and thermal efficiency. The evolutionary multi-objective optimization process has helped to discover important relationships with relatively few efforts of modeling preparation that would otherwise have required at least a very thorough mathematical analysis.
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Nomenclature
h m P Q T x X* F(X ) h CT ST
specific enthalpy [kj kg1] mass flow rate [kg s1] pressure [bar] heat [kW kg1] temperature [K] propane mass concentration vector of optimal design vector of objective function efficiency Condenser Temperature Superheater Temperature
Subscripts t turbine c cooling n net h high pressure ab ambient p pump th thermal L lower pressure
references
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i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 2 1 6 0 e2 1 6 8
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