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Parametric analysis and optimization for a combined power and refrigeration cycle
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APPLIED ENERGY Applied Energy 85 (2008) 1071–1085 www.elsevier.com/locate/apenergy
Parametric analysis and optimization for a combined power and refrigeration cycle Jiangfeng Wang *, Yiping Dai, Lin Gao Institute of Turbomachinery, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, PR China Received 25 December 2007; received in revised form 19 February 2008; accepted 21 February 2008 Available online 18 April 2008
Abstract A combined power and refrigeration cycle is proposed, which combines the Rankine cycle and the absorption refrigeration cycle. This combined cycle uses a binary ammonia–water mixture as the working fluid and produces both power output and refrigeration output simultaneously with only one heat source. A parametric analysis is conducted to evaluate the effects of thermodynamic parameters on the performance of the combined cycle. It is shown that heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration have significant effects on the net power output, refrigeration output and exergy efficiency of the combined cycle. A parameter optimization is achieved by means of genetic algorithm to reach the maximum exergy efficiency. The optimized exergy efficiency is 43.06% under the given condition. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Ammonia–water; Exergy efficiency; Combined cycle; Optimization
1. Introduction In recent years, there are a great deal of waste heats being released into environment, such as exhaust gas from turbines and engines, and waste heat from industrial plant, which lead to serious environmental pollution. In addition, there are also abundant geothermal resources and solar energy available in the world. Therefore, it is very important to focus on utilizing these waste heats and renewable energy for their potential in reducing fossil fuel consumption and alleviating environmental problems. Binary component mixtures exhibit variable boiling temperatures during the boiling process. This allows a small temperature difference for a good thermal match between the variable temperature heat sources and the working fluid, and consequently reduces irreversibility loss in the heat addition process. The ammonia–water mixture is a typical binary mixture, which not only has excellent thermo-physical properties, but also is an environmentally-friendly material. It is also the best substitute for the CFCs for solving global-warming prob-
*
Corresponding author. Tel./fax: +86 029 82668704. E-mail addresses: [email protected], [email protected] (J. Wang).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.02.014
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Nomenclature E G h m p Q s t T v W x
exergy (kJ/s) Gibbs free energy (kJ/kg) enthalpy (kJ/kg) mass flow rate (kg/s) pressure (MPa) heat addition (kJ/s) entropy (kJ/(kg K)) temperature (°C) temperature (K) specific volume (m3/kg) power (kW) mass fraction
Greek symbol g efficiency Subscripts a ammonia b bubble point d dew point eva refrigeration output eva,i evaporator inlet eva,o evaporator outlet g heat source i,j,k,l state points in inlet mix mixture net net w water 0 environment state 1 first law of thermodynamics 2 second law of thermodynamics Superscripts g vapor l liquid E excess
lem. Maloney and Robertson [1] first used an ammonia–water mixture as the working fluid in an absorption power cycle in the early 1950s. However, the condensation process took place at a variable temperature resulting in a higher turbine back pressure than that of the conventional steam Rankin cycle. Higher turbine back pressure was good to prevent air leakage into the system, but unfavorable to the power generation and cycle efficiency. Kalina [2] proposed a power cycle which employed an ammonia–water mixture as the bottoming cycle working fluid, and solved the problem of higher turbine back pressure by replacing the condensation process with an absorption process. A combined thermal power and refrigeration cycle was proposed by Goswami [3], and some further researches on the cycle performance were carried out [4–9]. It could provide power output as well as refrigeration and used an absorption condensation instead of the conventional condensation process. One of the char-
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acteristics of this cycle is that it can use low heat source temperatures bellow 200 °C in comparison with other dual-output concepts. Since this cycle employs the ammonia-rich vapor in the turbine to generate power, and then the turbine exhaust passes through a heat exchanger (cooler) transferring sensible heat to the chilled water, the refrigeration output is relatively small. In order to produce a larger refrigeration output, the fluid should go through a phase change in the cooler. Zheng et al. [10] proposed an absorption combined power/ cooling cycle based on the Kalina cycle. The flash tank in Kalina cycle was replaced by a rectifier which could obtain a higher concentration ammonia–water vapor for refrigeration. A condenser and an evaporator were introduced between the rectifier and the second absorber. The cycle was able to provide power and refrigeration with these modifications. Liu and Zhang [11] proposed a novel ammonia–water cycle for the cogeneration of power and refrigeration. They introduced a splitting/absorption unit into the combined power and refrigeration system. Zhang et al. [12,13] proposed a new ammonia–water system for the cogeneration of refrigeration and power. The plant operated in a parallel combined cycle mode with an ammonia–water Rankine cycle and an ammonia refrigeration cycle, interconnected by absorption, separation and heat transfer processes. They investigated the influences of the key thermodynamic parameters on both energy and exergy efficiencies. Zhang et al. [14] proposed several novel combined refrigeration and power systems using ammonia–water as working fluid, and summarized some guidelines for integration of refrigeration and power systems to produce higher energy and exergy efficiencies. Although these cycles showed higher energy and exergy efficiency, the systems were relatively complicated, resulting in higher capital investment. In this study, a combined power and refrigeration cycle is proposed, which is a marginal variation of the cycle in Ref. [12]. The most significant difference between this proposed cycle and the one in Ref. [12] is that the pump and the condenser before and after the turbine are eliminated. It is enough to increase the turbine inlet pressure by the pump which is used to send basic fluid to rectifier, because the turbine inlet pressure which is too high can result in reduction of the degree of dryness in the last stage of the turbine, that would influence turbine’s safe operation. In addition, the turbine exhaust with pressure which is higher than environment pressure can be condensed in the absorber. Thus, it is not necessary to add a feed pump to increase the turbine inlet pressure and add a condenser to condense the turbine exhaust. The advantage of the proposed cycle compared to the cycle in Ref. [12] is that the system is relatively simple, resulting in reduction of cost for investment. This cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or an independent cycle using low temperature sources such as geothermal and solar energy or waste heat. In this study, the parametric analysis for this cycle is performed, and the effects of thermodynamic parameters on the cycle performance are examined. In addition, parameter optimization is conducted with exergy efficiency as the objective function by means of genetic algorithm under the given condition. 2. Cycle description and assumptions 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 ammonia–water mixtures as a working fluid, which reduces the heat transfer irreversibility, especially for low temperature heat sources such as solar energy and geothermal heat. As shown in Fig. 1, the basic concentration saturated solution which leaves the absorber is pumped to a high pressure. After being heated in a heat exchanger, it is sent to the rectifier, where the basic solution is separated into ammonia-rich vapor and a weak solution. The bottom of the rectifier is boiler, where weak solution absorbs heat and becomes saturated vapor. The weak saturated solution is superheated through the superheater and then expanded through the turbine to produce power. The ammonia-rich vapor is condensed to liquid in the condenser. The liquid ammonia passes through a valve, and is throttled to a low pressure. This stream which is almost pure ammonia, evaporates completely to vapor in the evaporator for refrigeration. It is then absorbed by the weak solution which is brought to absorber after expansion through the turbine, to form the basic ammonia–water saturated liquid solution to complete the cycle. The heat source passes through superheater firstly, and then flows into boiler, and finally exhausts into environment through heat exchanger. It was assumed that the system reached a steady state, and the pressure drops and heat losses in pipe lines were neglected. Assuming the ammonia-rich solution at the evaporator outlet was saturated vapor. The low pressure was determined by absorber outlet temperature. The basic solution concentration was determined by
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10 condenser
11
rectifier
1
6 12 13
7
16
boiler 15
Throttle valve
turbine
8 14 superheater
heatex changer
5
Generator
2
9
17
evaporator
pump
3 absorber
4 Fig. 1. Schematic diagram of the combined power and refrigeration cycle.
the absorber outlet temperature and pressure. The absorber outlet temperature (pump inlet) was assumed to be approximately 5 °C higher than the assumed environment temperature. The ammonia-rich vapor separated from rectifier was saturated vapor, and the weak solution separated from rectifier was saturated liquid. The condenser outlet state was saturated liquid, and its temperature was assumed to be approximately 5 °C higher than the environment temperature. The main assumptions were shown in Table 1. 3. Mathematical model and performance criteria The cycle consists of some relatively simple units, such as the turbine, pump, heat exchanger, valve, combined with other relatively complex components, such as the absorber and rectifier. Each component can be treated as a control volume with inlet and outlet streams, heat transfer and work interactions. The basic models for all of the components involve mass and energy balance equations Table 1 Main assumptions for the combined power and refrigeration cycle Environment temperature (°C) Environment pressure (MPa) Turbine inlet pressure (MPa) Turbine inlet temperature (°C) Turbine isentropic efficiency (%) Minimum degree of dryness of turbine exhaust Refrigeration temperature (°C) Heat source temperature (°C) Heat source mass rate (kg/s) Ammonia mass fraction of basic solution Pump isentropic efficiency (%) Pinch point temperature difference (°C)
20 0.10135 2.5 285.0 85 0.88 5.0 300 20.0 0.34 70 15.0
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
Din out
X
! mi
¼0
i
Din out
X
1075
! mi hi
i
þ Din out
ð1Þ X
! Qj
j
þ Din out
X
! Wk
¼0
ð2Þ
k
In addition, the rectifier and absorber involve ammonia mass balance equation ! X in xl m l ¼ 0 Dout
ð3Þ
l
In this study, the thermal efficiency and exergy efficiency are adopted for the cycle performance evaluation. The first law or thermal efficiency is defined as the useful energy output divided by the total energy input, given by g1 ¼
W net þ Qeva Qin
ð4Þ
where W net is the power output from the turbine, reduced by the power input to the pump, Qeva is the refrigeration output and Qin is the total heat added to the cycle from the heat source in both the boiler and superheater. From the viewpoint of the first law of thermodynamics and energy conservation used to determine the overall thermal efficiency, work and heat are equivalent. On the other hand, exergy, based on the second law of thermodynamics, quantifies the difference between work and heat in terms of irreversibility, or change in energy quality. Therefore, the exergy efficiency is chosen to be the criterion for the cycle performance evaluation. Exergy is defined as the maximum reversible work a substance can do during the process of reaching equilibrium with its environment. Exergy efficiency is defined as the exergy output divided by the exergy input to the cycle [15]. The exergy input is taken as the available energy change of the heat source. The exergy output is the exergy of the net work and the exergy of the refrigeration. g2 ¼
W net þ Eeva Ein
ð5Þ
where Ein is the exergy of the heat source fluid, which is given as Ein ¼ mg ½ðhg h0 Þ T 0 ðsg s0 Þ
ð6Þ
Since the heat source fluid is finally exhausted into the environment, the calculation of the exergy input is based on the difference between its initial state and the environment state. Eeva is the exergy associated with the refrigeration output, which is calculated as the working fluid exergy difference across the evaporator. Eeva ¼ meva ½ðheva;i heva;o Þ T 0 ðseva;i seva;o Þ
ð7Þ
4. Thermodynamic property data of ammonia–water mixture The study of the combined power and refrigeration cycle requires the thermodynamic properties of an ammonia–water mixture. El-sayed and Tribus [16] developed correlations to represent the phase behavior of ammonia–water mixture system. Ziegler and Trepp [17] developed equations of state for ammonia–water mixture, which represented the Gibbs free energy of the mixture as a function of pressure, temperature and mixture composition. In the two phase region, the vapor–liquid fractions are always different and their fractions change continuously at constant pressure between the bubble point and dew point with the variation of mixture composition. To specify a pure substance, two degrees of freedom (i.e. pressure and temperature) are sufficient. But for a binary mixture, a third degree of freedom (i.e. concentration) is needed to specify the equilibrium state. In the equilibrium state, Eqs. (8) and (9), developed in [16], can be used to calculate the bubble and dew point
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temperatures, respectively. This avoids the complicated method of calculating the fugacity coefficient of a component in a mixture to determine the bubble and dew point temperatures. ! 7 10 X X i j Tb ¼ Tc ci þ cij x ½lnðpc =pÞ ð8Þ ij
i¼1
and Td ¼ Tc
6 X
( ai þ
i¼1
4 X
) Aij ½lnð1:0001 xÞ
j
i
½lnðpc =pÞ
ð9Þ
j¼1
where T c ¼ T cw
4 X
ai xi
ð10Þ
i¼1
pc ¼ pcw exp
8 X
! bi x
i
ð11Þ
i¼1
The thermodynamic property of mixture is the sum of analogous properties of pure components weighted with their fractional composition and the property change during mixing process. In the vapor phase, assuming that it is as an ideal solution, the property change during mixing process is neglected. The enthalpy, entropy, and volume of the vapor mixture are given as follows [17]: hgmix ¼ xhga þ ð1 xÞhgw sgmix vgmix
¼ ¼
xsga þ ð1 xÞsgw xvga þ ð1 xÞvgw
ð12Þ R½x ln x ð1 xÞ lnð1 xÞ
ð13Þ ð14Þ
where hga , sga and vga are the enthalpy, entropy and volume of pure ammonia vapor, and hgw , sgw and vgw are the enthalpy, entropy and volume of pure water vapor. The molar specific enthalpy, entropy, and volume of pure ammonia or water are related to Gibbs free energy by o ðG=T Þ h ¼ T ð15Þ oT p oG s¼ ð16Þ oT p oG v¼ ð17Þ op T where G is the Gibbs free energy and their values of the pure component in both vapor and liquid phases are taken from Ziegler and Trepp [17]. In the liquid phase, ammonia–water mixture deviates from ideal solution behavior, thus we must consider the Gibbs excess energy which influences liquid mixture. The enthalpy, entropy, and volume of the liquid mixture are given as: hlmix ¼ xhla þ ð1 xÞhlw þ hE slmix vlmix
¼ ¼
xsla þ ð1 xÞslw R½x ln x xvla þ ð1 xÞvlw þ vE
ð18Þ ð1 xÞ lnð1 xÞ þ s
E
ð19Þ ð20Þ
where hE, sE and vE are excess enthalpy, entropy and volume, respectively, of the liquid mixture, which are given as follows:
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
o ðGE =T Þ h ¼ T oT E oG s¼ oT p E oG v¼ op T
1077
ð21Þ ð22Þ ð23Þ
where GE is the Gibbs excess energy for liquid mixture. This convenient semi-empirical scheme, which combines the Gibbs free energy method for mixtures and bubble and dew point temperature correlations for phase equilibrium, has been adopted by Xu and Goswami [18]. And the calculated results have been compared to experimental mixture properties in the literature with good agreement. 5. Parametric analysis The combined power and refrigeration cycle can be heated by the exhaust flue gas from gas turbine, solar energy, geothermal heat or any other heat source. In this study, the waste heat, which is composed of 96.16% N2, 3.59% O2, 0.23% H2O, and 0.02% NO + NO2 by volume, is used as heat source for simulating the combined cycle. Tables 2 and 3 show the thermodynamic state of each point for the power and refrigeration cycle. Table 4 shows the results of thermodynamic simulation. The simulations were carried out using a simulation program written by authors. Iterative relative convergence error tolerance was 0.02%. Thermodynamic property of ammonia–water mixture were calculated by a convenient semi-empirical method, which combines the Gibbs free energy method for mixtures and bubble and dew point temperature correlations for phase equilibrium; the differences between calculated data and experimental data were less than 0.3% [18]. The parametric analysis is performed to evaluate the effects of each major parameter on the combined cycle performance, such as waste heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration. When one specific parameter is studied, other parameters are kept constant, as shown in Table 1. Fig. 2 shows the effect of heat source temperature on the net power output for different basic solution ammonia concentrations. It can be seen that the net power output increases with increasing heat source temperature. This is because a higher heat source temperature leads to a higher the turbine inlet temperature and a higher the vapor flow rate. In addition, it is found that the net power output increases with the decreasing basic solution ammonia concentration.
Table 2 Results of simulation for the combined power and refrigeration cycle State
t (°C)
p (MPa)
Dryness
h (kJ/kg)
s (kJ/kg K)
m (kg/s)
x
1 2 3 4 5 6 7 8 9 10 11 12 13
25 24.9922 5 25 25.7205 157.898 212.005 285 96.9438 61.5448 25 212.005 157.898
2.5 0.11941 0.11941 0.11941 2.5 2.5 2.5 2.5 0.11941 2.5 2.5 2.5 2.5
0 0.17169 1 0 0 0.175754 1 1 0.930298 1 0 1 0
118.177 118.177 1281.44 93.8817 88.7169 764.317 2540.24 2731.76 2245.41 1305.72 118.177 2540.24 543.591
0.414111 0.525818 5.27235 0.281065 0.290083 2.53483 6.20896 6.57701 6.80555 4.03228 0.414111 6.20896 1.96345
0.193084 0.193084 0.193084 1.46725 1.46725 1.46725 1.27416 1.27416 1.27416 0.386168 0.193084 0.026106 1.30027
0.9999 0.9999 0.9999 0.34 0.34 0.34 0.24 0.24 0.24 0.9999 0.9999 0.24 0.24
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Table 3 Results of simulation for the heat source fluid State
14 15 16 17
t (°C)
300 289.248 172.898 115.537
h (kJ/kg)
609.674 597.473 467.664 405.083
s (kJ/kg K)
m (kg/s)
7.41566 7.39417 7.13573 6.98558
20.0 20.0 20.0 20.0
Mole composition N2
O2
H2O
NO + NO2
0.9616 0.9616 0.9616 0.9616
0.00359 0.00359 0.00359 0.00359
0.0023 0.0023 0.0023 0.0023
0.0002 0.0002 0.0002 0.0002
Table 4 The performance of the combined power and refrigeration cycle Turbine work (kW) Pump work (kW) Absorber heat rejection (kW) Condenser heat rejection (kW) Refrigeration output (kW) Boiler heat input (kW) Superheat input (kW) Heat exchanger heat input (kW) Net power output (kW) Net power and refrigeration output (kW) Heat input (kW) Exergy input (kW) Thermal efficiency (%) Exergy efficiency (%)
619.699 7.57795 3246.18 458.59 224.608 2596.17 244.036 1251.61 612.121 836.728 4091.82 1846.34 20.45 35.54
1000
Net power output (kW)
Ammonia concentration x=0.30 x=0.34 x=0.38
900 800 700 600 500 400 520
540
560
580
600
620
Heat source temperature (K) Fig. 2. Effect of heat source temperature on net power output for different basic solution ammonia concentrations.
Fig. 3 shows the effect of heat source temperatures on the refrigeration output for different basic solution ammonia concentrations. It is evident that the refrigeration output increases as the heat source temperature increases. Although the inlet temperature of the evaporator does not vary with the heat source temperature, the increasing heat source temperature increases the mass flow rate through the evaporator. It is also found that higher basic solution ammonia concentration results in higher refrigeration output. Fig. 4 shows the effect of heat source temperature on the exergy efficiency for different basic solution ammonia concentrations. It is obvious that the exergy efficiency increases as the heat source temperature increases, as the high heat source temperature has high energy quality and increases turbine power output and refriger-
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
Refrigeration output (kW)
250
200
1079
Ammonia concentration x=0.30 x=0.34 x=0.38
150
100
50 520
540
560
580
600
620
Heat source temperature (K) Fig. 3. Effect of heat source temperature on refrigeration output for different basic solution ammonia concentrations.
Exergy efficiency (%)
40
38
Ammonia concentration x=0.30 x=0.34 x=0.38
36
34
32
30 520
540
560
580
600
620
Heat source temperature (K) Fig. 4. Effect of heat source temperature on exergy efficiency for different basic solution ammonia concentrations.
ation output, thus the exergy efficiency increases. In addition, higher ammonia concentration of the basic solution accords with higher exergy efficiency. Fig. 5 shows the effect of turbine inlet pressure on net power output at different environment temperatures. It can be seen that the exergy efficiency increases first to maximum and then decreases as the turbine inlet pressure increases. It is known that the enthalpy drop across the turbine increases as the pressure ratio increases. This is why the net power output increases at first. But the enthalpy gains from an increased pressure ratio do not make up for the decrease in vapor flow rate, thus the net power output decreases afterwards. In addition, the net power output decreases as the environment temperature increases. It is obvious that the condensing temperature in the absorber increases with the increasing environment temperature, and this leads to the increasing turbine back pressure. Thus the increasing turbine back pressure makes the turbine power output decreases. Fig. 6 shows the effect of the turbine inlet pressure on the refrigeration output at different environment temperatures. It can be seen that the refrigeration output drops as the turbine inlet pressure increases, as the increasing turbine inlet pressure reduces the mass flow rate through the evaporator. As shown in Fig. 6, the refrigeration output drops with the increasing environment temperature. Because the evaporator inlet temperature increases with the increasing environment temperature, the refrigeration output decreases. Due to the
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Net power output (kW)
700
Environment temperature 288.15K 293.15K 298.15K
680 660 640 620 600 580 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 5. Effect of turbine inlet pressure on net power output for different environment temperatures.
Refrigeration output (kW)
155
Environment temperature
150
288.15K 293.15K 298.15K
145 140 135 130 125 120 115 110 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 6. Effect of turbine inlet pressure on cooling capacity for different environment temperatures.
combined effects of net power output and refrigeration output on the performance of the combined cycle, the exergy efficiency increases first to a maximum and then decreases, as shown in Fig. 7. Fig. 8 shows the effect of refrigeration temperature on the net power output at different turbine inlet temperatures. It can be seen that the net power output keeps constant as the refrigeration temperature increases. And the higher turbine inlet temperature, the larger is the net power output. Because the variation of refrigeration temperature can not change the turbine inlet and outlet conditions and the pump inlet and outlet conditions, the net power output can not change as the refrigeration temperature increases. In addition, higher turbine inlet temperature increases the turbine power output which lead to higher net power output of the system. Fig. 9 shows the effect of refrigeration temperature on the refrigeration output at different turbine inlet temperatures. As the refrigeration temperature increases, the refrigeration output increases correspondingly, and higher turbine inlet temperature leads to lower refrigeration output. It is observed that it is difficult to obtain the refrigeration output when the refrigeration temperature is very low. Fig. 10 shows the effect of refrigeration temperature on exergy efficiency at different turbine inlet temperatures. It is found that the exergy efficiency increases as the refrigeration increases, and a higher turbine inlet temperature conforms to a higher exergy efficiency.
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
1081
38.0
Environment temperature
Exergy efficiency (%)
37.5
288.15K 293.15K 298.15K
37.0 36.5 36.0 35.5 35.0 34.5 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 7. Effect of turbine inlet pressure on exergy efficiency for different environment temperatures.
690
Net power output (kW)
Turbine inlet temperature 558.15K 548.15K 538.15K
685
680
675
670 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 8. Effect of refrigeration temperature on net power output for different turbine inlet temperatures.
Refrigeration output (kW)
150 149 148
Turbine inlet temperature 558.15K 548.15K 538.15K
147 146 145 144 143 142 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 9. Effect of refrigeration temperature on cooling capacity for different turbine inlet temperatures.
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Exergy efficiency (%)
37.30
37.25
Turbine inlet temperature 558.15K 548.15K 538.15K
37.20
37.15
37.10
37.05 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 10. Effect of refrigeration temperature on exergy efficiency for different turbine inlet temperatures.
From the discussions presented above, the effects of a given parameter on the net power output, Refrigeration output and exergy efficiency are different. In order to evaluate the performance of the combined power and refrigeration cycle, it is necessary to optimize the exergy efficiency for the combined cycle. 6. Optimization Parametric analysis of the combined power and refrigeration cycle shows the potential for the cycle to be optimized. For practical operation, the combined cycle has many parameters that are varied together, presenting a multi-dimensional surface on which an optimum can be found. Optimization of the operating parameters in the cycle is possible for each heat source and heat sink temperature. The cycle may be optimized based on the first low efficiency, second law efficiency, power output or refrigeration output, depending on the intended application and heat source. For the waste heat recovery, optimization of the combined cycle for maximum second law efficiency is most appropriate, because the second law efficiency can reflect the performance for cogeneration from the viewpoint of thermodynamics. In this study, parameter optimization is achieved by means of genetic algorithm to reach the maximum exergy efficiency. 6.1. Optimization method The genetic algorithm, which is presented firstly by professor Hooland in America [19], is a stochastic global search method that simulates natural biological evolution. Based on the Darwinian survival-of-fittest principle, the genetic algorithm operates on a population of potential solutions to produce better and better approximations to the optimal solution. The genetic algorithm differs from more traditional optimization techniques because it involves a search from a population of solutions and not from a single point. The genetic algorithm encodes a potential solution to a specific domain problem on a simple chromosomelike data structure (which constitutes an individual), where genes are parameters of the problem to be solved. In this study, the float-point coding is used in the genetic algorithm to solve the problem of parameter optimization in the combined power and refrigeration system. Each chromosome vector is coded as a vector of floating point numbers of the same length as the dimension of the search space. Chromosome is defined as a real number vector, X = (x1, x2, . . . , xn), xi eR, i = 1, 2,. . ., n, where n = 3, x1 is the turbine inlet pressure, x2 is the turbine inlet temperature, x3 is the basic solution ammonia concentration. The genetic algorithm only used fitness function to evaluate adaptability of individual without external information in the evolution search. The adaptability is expressed by the fitness value. A bigger fitness value means a better adaptability to constraints and a better viability of the individual. Fitness function which is not constrained by definition domain, continuity and differentiability, requires that the objective function is
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
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defined as the form of non-negative maximum. In this optimization, the exergy efficiency is selected as the fitness function. The basic genetic algorithm operators include selection operator, crossover operator and mutation operator. Selection operator is responsible for selecting the parents to create the next generation of solutions. The parent is chosen with a probability based on its fitness. The higher the fitness, the higher is the probability of selection. The rank-based model is selected for this optimization of the combined cycle. Crossover operator is the basic operator for producing new chromosomes. It produces new individuals that have some parts of both parent’s genetic material. The simple arithmetic crossover is applied to this optimization problem due to very simple operation, which is presented as follows: cc1 ¼ af1 þ ð1 aÞf2 ð15Þ c2 ¼ af2 þ ð1 aÞf1 where a is a random number between 0 and 1, f1 and f2 are parents individuals which are selected to crossover each other, c1 and c2 are children individuals which are produced by crossover. To avoid the local solution, the mutation operator is randomly applied with low probability to modify values in the chromosomes. Random mutation was adopted to optimize the parameters for the combined cycle. It is performed by selecting individuals from the range of the parameter according to mutation probability. The steps of genetic algorithm are made as follows: (1) Initialize the population size, crossover probability, mutation probability, stop generation, and generate the initial population randomly. (2) Calculate the fitness of each individual for parent generation, and order the fitness. (3) Select the individuals from parent generation, and create the children generation using crossover and mutation operators. (4) Calculate the fitness of each individual for children generation. If the maximum fitness of children generation is less than that of parent generation, substitute the maximum fitness of parent generation for that of children generation. (5) If generation reaches the stop generation, stop the optimization. Otherwise go back to step 3.
6.2. Optimization results For this optimization, the waste heat mentioned above is considered as the heat source, and the environment temperature and the refrigeration temperature are assumed constant. Thus, the parameters chosen for optimizing this combined power and refrigeration cycle are turbine inlet pressure, turbine inlet temperature, Table 5 Condition of the parameter optimization Environment temperature (°C) Environment pressure (MPa) Heat source temperature (°C) Heat source mass rate (kg/s) Refrigeration temperature (°C) Turbine isentropic efficiency (%) Turbine minimum exhaust degree of dryness Pump isentropic efficiency (%) Pinch point temperature difference (°C) Population size Crossover probability Mutation probability Stop generation The range of turbine inlet pressure (MPa) The range of turbine inlet temperature (°C) The range of basic solution ammonia–water concentration
20 0.10135 300 20 5 85 0.88 70 15 50 0.95 0.05 200 1.64.0 265285 0.280.38
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Table 6 The optimization results of the parameters for the combined cycle Turbine inlet pressure (MPa) Turbine inlet temperature (°C) Basic solution ammonia–water concentration Turbine work (kW) Pump work (kW) Refrigeration output (kW) Net power output (kW) Net power and refrigeration output (kW) Exergy input (kW) Exergy efficiency (%)
1.706 280.4 0.305 722.764 8.30644 168.647 714.457 883.104 1846.34 43.06
the basic solution ammonia–water concentration. Table 5 shows the condition of the parameter optimization. Table 6 lists the optimization results for the combined power and refrigeration cycle. 7. Discussion The aim of this research is to conduct a parametric analysis and optimization of a combined power and refrigeration cycle. The proposed combined cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or an independent cycle using low temperature sources such as geothermal and solar energy or waste heat. The combined cycle presented in this paper can provide more refrigeration output using a relatively simpler system configuration. In addition, genetic algorithm is used to optimize multi-parameter system. The combined cycle can be optimized for the first low efficiency, second law efficiency, power output or refrigeration output, depending on the intended application and heat source. However, owing to lack experimental data for this combined cycle, the experimental study will be carried out to validate the feasibility of the combined power and refrigeration cycle in the future. In addition, thermoeconomic optimization for this combined cycle will be carried out in the coming research, because the optimization based on the second law efficiency as the objective function can only evaluate the system performance from the viewpoint of thermodynamics, not reflect the cost of performance improvement financially. 8. Conclusions A combined power and refrigeration cycle using ammonia–water mixtures as the working fluid is proposed, which combines the Rankine cycle and absorption refrigeration cycle. Parametric analysis is conducted to investigate the effects of several thermodynamic parameters on the cycle performances. It is shown that heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration have significant effects on the net power output, refrigeration output and exergy efficiency. This parametric analysis of the cycle showed the potential for the cycle to be optimized. Optimization of the thermal parameters in the cycle is achieved using exergy efficiency as the objective function by means of genetic algorithm. It is found that the combined cycle has a maximum exergy efficiency of 43.06% when turbine inlet pressure, turbine inlet temperature and basic solution ammonia concentration are 1.706 MPa, 280.4 °C and 0.305, respectively. References [1] Maloney JD, Robertson RC. Thermodynamic study of ammonia–water heat power cycles. Oak Ridge National Laboratory Report 1953; CF-53-8-43. [2] Kalina AI. Combined cycle system with novel bottoming cycle. ASME J Eng Gas Turb Power 1984;106:737–42. [3] Xu F, Goswami DY, Bhagwat SS. A combined power/cooling cycle. Energy 2000;25:233–46. [4] Sadrameli SM, Goswami DY. Optimum operating conditions for a combined power and cooling thermodynamic cycle. Appl Energ 2007;84:254–65.
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[5] Yidal A, Best R, Rivero R, Cervantes J. Analysis of a combined power and refrigeration cycle by the exergy method. Energy 2006;31:3401–14. [6] Tamm G, Goswami DY, Lu S, Hasan AA. Theoretical and experimental investigation of an ammonia–water power and refrigeration thermodynamic cycle. Sol Energy 2004;76:217–28. [7] Vijayaraghavan S, Goswami DY. A combined power and cooling cycle modified to improve resource utilization efficiency using a distillation stage. Energy 2006;31:1177–96. [8] Martin C, Goswami DY. Effectiveness of cooling production with a combined power and cooling thermodynamic cycle. Appl Therm Eng 2006;26:576–82. [9] Hasan AA, Goswami GY, Vijayaraghavan S. First and second law analysis of a new power and refrigeration thermodynamic cycle using a solar heat source. Sol Energy 2002;73:385–93. [10] Zheng D, Chen B, Qi Y, Jin H. Thermodynamic analysis of a novel absorption power/cooling combined-cycle. Appl Energ 2006;83:311–23. [11] Liu M, Zhang N. Proposal and analysis of a novel ammonia–water cycle for power and refrigeration cogeneration. Energy 2007;32:961–70. [12] Zhang N, Cai R, Lior N. A novel ammonia–water cycle for power and refrigeration cogeneration. Proceedings of the ASME Advanced Energy Systems Division, 2004; 183–96. [13] Zhang N, Lior N. Development of a novel combined absorption cycle for power generation and refrigeration. ASME J Energ Res 2007;129:254–65. [14] Zhang N, Lior N. Methodology for thermal design of novel combined refrigeration/power binary fluid systems. Int J Refrig 2007;30:1072–85. [15] Cengel YA, Boles MA. Thermodynamics: an engineering approach. 3rd ed. New York: McGraw-Hill Inc.; 1984. [16] El-Sayed YM, Tribus M. Thermodynamic properties of water–ammonia mixtures theoretical implementation for use in power cycles analysis. American Society of Mechanical Engineers, Advanced Energy Systems Division (Publication) AES 1985;1:89–95. [17] Ziegler B, Trepp C. Equation of state for ammonia–water mixtures. Int J Refrig 1984;7:101–6. [18] Xu F, Goswami DY. Thermodynamic properties of ammonia–water mixtures for use in power cycles. Energy 1999;24:525–36. [19] Holland JH. Adaptation in nature and artificial systems: an introductory analysis with applications to biology, control and artificial intelligence. Massachusetts: MIT Press; 1992.
APPLIED ENERGY Applied Energy 85 (2008) 1071–1085 www.elsevier.com/locate/apenergy
Parametric analysis and optimization for a combined power and refrigeration cycle Jiangfeng Wang *, Yiping Dai, Lin Gao Institute of Turbomachinery, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, PR China Received 25 December 2007; received in revised form 19 February 2008; accepted 21 February 2008 Available online 18 April 2008
Abstract A combined power and refrigeration cycle is proposed, which combines the Rankine cycle and the absorption refrigeration cycle. This combined cycle uses a binary ammonia–water mixture as the working fluid and produces both power output and refrigeration output simultaneously with only one heat source. A parametric analysis is conducted to evaluate the effects of thermodynamic parameters on the performance of the combined cycle. It is shown that heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration have significant effects on the net power output, refrigeration output and exergy efficiency of the combined cycle. A parameter optimization is achieved by means of genetic algorithm to reach the maximum exergy efficiency. The optimized exergy efficiency is 43.06% under the given condition. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Ammonia–water; Exergy efficiency; Combined cycle; Optimization
1. Introduction In recent years, there are a great deal of waste heats being released into environment, such as exhaust gas from turbines and engines, and waste heat from industrial plant, which lead to serious environmental pollution. In addition, there are also abundant geothermal resources and solar energy available in the world. Therefore, it is very important to focus on utilizing these waste heats and renewable energy for their potential in reducing fossil fuel consumption and alleviating environmental problems. Binary component mixtures exhibit variable boiling temperatures during the boiling process. This allows a small temperature difference for a good thermal match between the variable temperature heat sources and the working fluid, and consequently reduces irreversibility loss in the heat addition process. The ammonia–water mixture is a typical binary mixture, which not only has excellent thermo-physical properties, but also is an environmentally-friendly material. It is also the best substitute for the CFCs for solving global-warming prob-
*
Corresponding author. Tel./fax: +86 029 82668704. E-mail addresses: [email protected], [email protected] (J. Wang).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.02.014
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Nomenclature E G h m p Q s t T v W x
exergy (kJ/s) Gibbs free energy (kJ/kg) enthalpy (kJ/kg) mass flow rate (kg/s) pressure (MPa) heat addition (kJ/s) entropy (kJ/(kg K)) temperature (°C) temperature (K) specific volume (m3/kg) power (kW) mass fraction
Greek symbol g efficiency Subscripts a ammonia b bubble point d dew point eva refrigeration output eva,i evaporator inlet eva,o evaporator outlet g heat source i,j,k,l state points in inlet mix mixture net net w water 0 environment state 1 first law of thermodynamics 2 second law of thermodynamics Superscripts g vapor l liquid E excess
lem. Maloney and Robertson [1] first used an ammonia–water mixture as the working fluid in an absorption power cycle in the early 1950s. However, the condensation process took place at a variable temperature resulting in a higher turbine back pressure than that of the conventional steam Rankin cycle. Higher turbine back pressure was good to prevent air leakage into the system, but unfavorable to the power generation and cycle efficiency. Kalina [2] proposed a power cycle which employed an ammonia–water mixture as the bottoming cycle working fluid, and solved the problem of higher turbine back pressure by replacing the condensation process with an absorption process. A combined thermal power and refrigeration cycle was proposed by Goswami [3], and some further researches on the cycle performance were carried out [4–9]. It could provide power output as well as refrigeration and used an absorption condensation instead of the conventional condensation process. One of the char-
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acteristics of this cycle is that it can use low heat source temperatures bellow 200 °C in comparison with other dual-output concepts. Since this cycle employs the ammonia-rich vapor in the turbine to generate power, and then the turbine exhaust passes through a heat exchanger (cooler) transferring sensible heat to the chilled water, the refrigeration output is relatively small. In order to produce a larger refrigeration output, the fluid should go through a phase change in the cooler. Zheng et al. [10] proposed an absorption combined power/ cooling cycle based on the Kalina cycle. The flash tank in Kalina cycle was replaced by a rectifier which could obtain a higher concentration ammonia–water vapor for refrigeration. A condenser and an evaporator were introduced between the rectifier and the second absorber. The cycle was able to provide power and refrigeration with these modifications. Liu and Zhang [11] proposed a novel ammonia–water cycle for the cogeneration of power and refrigeration. They introduced a splitting/absorption unit into the combined power and refrigeration system. Zhang et al. [12,13] proposed a new ammonia–water system for the cogeneration of refrigeration and power. The plant operated in a parallel combined cycle mode with an ammonia–water Rankine cycle and an ammonia refrigeration cycle, interconnected by absorption, separation and heat transfer processes. They investigated the influences of the key thermodynamic parameters on both energy and exergy efficiencies. Zhang et al. [14] proposed several novel combined refrigeration and power systems using ammonia–water as working fluid, and summarized some guidelines for integration of refrigeration and power systems to produce higher energy and exergy efficiencies. Although these cycles showed higher energy and exergy efficiency, the systems were relatively complicated, resulting in higher capital investment. In this study, a combined power and refrigeration cycle is proposed, which is a marginal variation of the cycle in Ref. [12]. The most significant difference between this proposed cycle and the one in Ref. [12] is that the pump and the condenser before and after the turbine are eliminated. It is enough to increase the turbine inlet pressure by the pump which is used to send basic fluid to rectifier, because the turbine inlet pressure which is too high can result in reduction of the degree of dryness in the last stage of the turbine, that would influence turbine’s safe operation. In addition, the turbine exhaust with pressure which is higher than environment pressure can be condensed in the absorber. Thus, it is not necessary to add a feed pump to increase the turbine inlet pressure and add a condenser to condense the turbine exhaust. The advantage of the proposed cycle compared to the cycle in Ref. [12] is that the system is relatively simple, resulting in reduction of cost for investment. This cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or an independent cycle using low temperature sources such as geothermal and solar energy or waste heat. In this study, the parametric analysis for this cycle is performed, and the effects of thermodynamic parameters on the cycle performance are examined. In addition, parameter optimization is conducted with exergy efficiency as the objective function by means of genetic algorithm under the given condition. 2. Cycle description and assumptions 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 ammonia–water mixtures as a working fluid, which reduces the heat transfer irreversibility, especially for low temperature heat sources such as solar energy and geothermal heat. As shown in Fig. 1, the basic concentration saturated solution which leaves the absorber is pumped to a high pressure. After being heated in a heat exchanger, it is sent to the rectifier, where the basic solution is separated into ammonia-rich vapor and a weak solution. The bottom of the rectifier is boiler, where weak solution absorbs heat and becomes saturated vapor. The weak saturated solution is superheated through the superheater and then expanded through the turbine to produce power. The ammonia-rich vapor is condensed to liquid in the condenser. The liquid ammonia passes through a valve, and is throttled to a low pressure. This stream which is almost pure ammonia, evaporates completely to vapor in the evaporator for refrigeration. It is then absorbed by the weak solution which is brought to absorber after expansion through the turbine, to form the basic ammonia–water saturated liquid solution to complete the cycle. The heat source passes through superheater firstly, and then flows into boiler, and finally exhausts into environment through heat exchanger. It was assumed that the system reached a steady state, and the pressure drops and heat losses in pipe lines were neglected. Assuming the ammonia-rich solution at the evaporator outlet was saturated vapor. The low pressure was determined by absorber outlet temperature. The basic solution concentration was determined by
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10 condenser
11
rectifier
1
6 12 13
7
16
boiler 15
Throttle valve
turbine
8 14 superheater
heatex changer
5
Generator
2
9
17
evaporator
pump
3 absorber
4 Fig. 1. Schematic diagram of the combined power and refrigeration cycle.
the absorber outlet temperature and pressure. The absorber outlet temperature (pump inlet) was assumed to be approximately 5 °C higher than the assumed environment temperature. The ammonia-rich vapor separated from rectifier was saturated vapor, and the weak solution separated from rectifier was saturated liquid. The condenser outlet state was saturated liquid, and its temperature was assumed to be approximately 5 °C higher than the environment temperature. The main assumptions were shown in Table 1. 3. Mathematical model and performance criteria The cycle consists of some relatively simple units, such as the turbine, pump, heat exchanger, valve, combined with other relatively complex components, such as the absorber and rectifier. Each component can be treated as a control volume with inlet and outlet streams, heat transfer and work interactions. The basic models for all of the components involve mass and energy balance equations Table 1 Main assumptions for the combined power and refrigeration cycle Environment temperature (°C) Environment pressure (MPa) Turbine inlet pressure (MPa) Turbine inlet temperature (°C) Turbine isentropic efficiency (%) Minimum degree of dryness of turbine exhaust Refrigeration temperature (°C) Heat source temperature (°C) Heat source mass rate (kg/s) Ammonia mass fraction of basic solution Pump isentropic efficiency (%) Pinch point temperature difference (°C)
20 0.10135 2.5 285.0 85 0.88 5.0 300 20.0 0.34 70 15.0
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
Din out
X
! mi
¼0
i
Din out
X
1075
! mi hi
i
þ Din out
ð1Þ X
! Qj
j
þ Din out
X
! Wk
¼0
ð2Þ
k
In addition, the rectifier and absorber involve ammonia mass balance equation ! X in xl m l ¼ 0 Dout
ð3Þ
l
In this study, the thermal efficiency and exergy efficiency are adopted for the cycle performance evaluation. The first law or thermal efficiency is defined as the useful energy output divided by the total energy input, given by g1 ¼
W net þ Qeva Qin
ð4Þ
where W net is the power output from the turbine, reduced by the power input to the pump, Qeva is the refrigeration output and Qin is the total heat added to the cycle from the heat source in both the boiler and superheater. From the viewpoint of the first law of thermodynamics and energy conservation used to determine the overall thermal efficiency, work and heat are equivalent. On the other hand, exergy, based on the second law of thermodynamics, quantifies the difference between work and heat in terms of irreversibility, or change in energy quality. Therefore, the exergy efficiency is chosen to be the criterion for the cycle performance evaluation. Exergy is defined as the maximum reversible work a substance can do during the process of reaching equilibrium with its environment. Exergy efficiency is defined as the exergy output divided by the exergy input to the cycle [15]. The exergy input is taken as the available energy change of the heat source. The exergy output is the exergy of the net work and the exergy of the refrigeration. g2 ¼
W net þ Eeva Ein
ð5Þ
where Ein is the exergy of the heat source fluid, which is given as Ein ¼ mg ½ðhg h0 Þ T 0 ðsg s0 Þ
ð6Þ
Since the heat source fluid is finally exhausted into the environment, the calculation of the exergy input is based on the difference between its initial state and the environment state. Eeva is the exergy associated with the refrigeration output, which is calculated as the working fluid exergy difference across the evaporator. Eeva ¼ meva ½ðheva;i heva;o Þ T 0 ðseva;i seva;o Þ
ð7Þ
4. Thermodynamic property data of ammonia–water mixture The study of the combined power and refrigeration cycle requires the thermodynamic properties of an ammonia–water mixture. El-sayed and Tribus [16] developed correlations to represent the phase behavior of ammonia–water mixture system. Ziegler and Trepp [17] developed equations of state for ammonia–water mixture, which represented the Gibbs free energy of the mixture as a function of pressure, temperature and mixture composition. In the two phase region, the vapor–liquid fractions are always different and their fractions change continuously at constant pressure between the bubble point and dew point with the variation of mixture composition. To specify a pure substance, two degrees of freedom (i.e. pressure and temperature) are sufficient. But for a binary mixture, a third degree of freedom (i.e. concentration) is needed to specify the equilibrium state. In the equilibrium state, Eqs. (8) and (9), developed in [16], can be used to calculate the bubble and dew point
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temperatures, respectively. This avoids the complicated method of calculating the fugacity coefficient of a component in a mixture to determine the bubble and dew point temperatures. ! 7 10 X X i j Tb ¼ Tc ci þ cij x ½lnðpc =pÞ ð8Þ ij
i¼1
and Td ¼ Tc
6 X
( ai þ
i¼1
4 X
) Aij ½lnð1:0001 xÞ
j
i
½lnðpc =pÞ
ð9Þ
j¼1
where T c ¼ T cw
4 X
ai xi
ð10Þ
i¼1
pc ¼ pcw exp
8 X
! bi x
i
ð11Þ
i¼1
The thermodynamic property of mixture is the sum of analogous properties of pure components weighted with their fractional composition and the property change during mixing process. In the vapor phase, assuming that it is as an ideal solution, the property change during mixing process is neglected. The enthalpy, entropy, and volume of the vapor mixture are given as follows [17]: hgmix ¼ xhga þ ð1 xÞhgw sgmix vgmix
¼ ¼
xsga þ ð1 xÞsgw xvga þ ð1 xÞvgw
ð12Þ R½x ln x ð1 xÞ lnð1 xÞ
ð13Þ ð14Þ
where hga , sga and vga are the enthalpy, entropy and volume of pure ammonia vapor, and hgw , sgw and vgw are the enthalpy, entropy and volume of pure water vapor. The molar specific enthalpy, entropy, and volume of pure ammonia or water are related to Gibbs free energy by o ðG=T Þ h ¼ T ð15Þ oT p oG s¼ ð16Þ oT p oG v¼ ð17Þ op T where G is the Gibbs free energy and their values of the pure component in both vapor and liquid phases are taken from Ziegler and Trepp [17]. In the liquid phase, ammonia–water mixture deviates from ideal solution behavior, thus we must consider the Gibbs excess energy which influences liquid mixture. The enthalpy, entropy, and volume of the liquid mixture are given as: hlmix ¼ xhla þ ð1 xÞhlw þ hE slmix vlmix
¼ ¼
xsla þ ð1 xÞslw R½x ln x xvla þ ð1 xÞvlw þ vE
ð18Þ ð1 xÞ lnð1 xÞ þ s
E
ð19Þ ð20Þ
where hE, sE and vE are excess enthalpy, entropy and volume, respectively, of the liquid mixture, which are given as follows:
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
o ðGE =T Þ h ¼ T oT E oG s¼ oT p E oG v¼ op T
1077
ð21Þ ð22Þ ð23Þ
where GE is the Gibbs excess energy for liquid mixture. This convenient semi-empirical scheme, which combines the Gibbs free energy method for mixtures and bubble and dew point temperature correlations for phase equilibrium, has been adopted by Xu and Goswami [18]. And the calculated results have been compared to experimental mixture properties in the literature with good agreement. 5. Parametric analysis The combined power and refrigeration cycle can be heated by the exhaust flue gas from gas turbine, solar energy, geothermal heat or any other heat source. In this study, the waste heat, which is composed of 96.16% N2, 3.59% O2, 0.23% H2O, and 0.02% NO + NO2 by volume, is used as heat source for simulating the combined cycle. Tables 2 and 3 show the thermodynamic state of each point for the power and refrigeration cycle. Table 4 shows the results of thermodynamic simulation. The simulations were carried out using a simulation program written by authors. Iterative relative convergence error tolerance was 0.02%. Thermodynamic property of ammonia–water mixture were calculated by a convenient semi-empirical method, which combines the Gibbs free energy method for mixtures and bubble and dew point temperature correlations for phase equilibrium; the differences between calculated data and experimental data were less than 0.3% [18]. The parametric analysis is performed to evaluate the effects of each major parameter on the combined cycle performance, such as waste heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration. When one specific parameter is studied, other parameters are kept constant, as shown in Table 1. Fig. 2 shows the effect of heat source temperature on the net power output for different basic solution ammonia concentrations. It can be seen that the net power output increases with increasing heat source temperature. This is because a higher heat source temperature leads to a higher the turbine inlet temperature and a higher the vapor flow rate. In addition, it is found that the net power output increases with the decreasing basic solution ammonia concentration.
Table 2 Results of simulation for the combined power and refrigeration cycle State
t (°C)
p (MPa)
Dryness
h (kJ/kg)
s (kJ/kg K)
m (kg/s)
x
1 2 3 4 5 6 7 8 9 10 11 12 13
25 24.9922 5 25 25.7205 157.898 212.005 285 96.9438 61.5448 25 212.005 157.898
2.5 0.11941 0.11941 0.11941 2.5 2.5 2.5 2.5 0.11941 2.5 2.5 2.5 2.5
0 0.17169 1 0 0 0.175754 1 1 0.930298 1 0 1 0
118.177 118.177 1281.44 93.8817 88.7169 764.317 2540.24 2731.76 2245.41 1305.72 118.177 2540.24 543.591
0.414111 0.525818 5.27235 0.281065 0.290083 2.53483 6.20896 6.57701 6.80555 4.03228 0.414111 6.20896 1.96345
0.193084 0.193084 0.193084 1.46725 1.46725 1.46725 1.27416 1.27416 1.27416 0.386168 0.193084 0.026106 1.30027
0.9999 0.9999 0.9999 0.34 0.34 0.34 0.24 0.24 0.24 0.9999 0.9999 0.24 0.24
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Table 3 Results of simulation for the heat source fluid State
14 15 16 17
t (°C)
300 289.248 172.898 115.537
h (kJ/kg)
609.674 597.473 467.664 405.083
s (kJ/kg K)
m (kg/s)
7.41566 7.39417 7.13573 6.98558
20.0 20.0 20.0 20.0
Mole composition N2
O2
H2O
NO + NO2
0.9616 0.9616 0.9616 0.9616
0.00359 0.00359 0.00359 0.00359
0.0023 0.0023 0.0023 0.0023
0.0002 0.0002 0.0002 0.0002
Table 4 The performance of the combined power and refrigeration cycle Turbine work (kW) Pump work (kW) Absorber heat rejection (kW) Condenser heat rejection (kW) Refrigeration output (kW) Boiler heat input (kW) Superheat input (kW) Heat exchanger heat input (kW) Net power output (kW) Net power and refrigeration output (kW) Heat input (kW) Exergy input (kW) Thermal efficiency (%) Exergy efficiency (%)
619.699 7.57795 3246.18 458.59 224.608 2596.17 244.036 1251.61 612.121 836.728 4091.82 1846.34 20.45 35.54
1000
Net power output (kW)
Ammonia concentration x=0.30 x=0.34 x=0.38
900 800 700 600 500 400 520
540
560
580
600
620
Heat source temperature (K) Fig. 2. Effect of heat source temperature on net power output for different basic solution ammonia concentrations.
Fig. 3 shows the effect of heat source temperatures on the refrigeration output for different basic solution ammonia concentrations. It is evident that the refrigeration output increases as the heat source temperature increases. Although the inlet temperature of the evaporator does not vary with the heat source temperature, the increasing heat source temperature increases the mass flow rate through the evaporator. It is also found that higher basic solution ammonia concentration results in higher refrigeration output. Fig. 4 shows the effect of heat source temperature on the exergy efficiency for different basic solution ammonia concentrations. It is obvious that the exergy efficiency increases as the heat source temperature increases, as the high heat source temperature has high energy quality and increases turbine power output and refriger-
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
Refrigeration output (kW)
250
200
1079
Ammonia concentration x=0.30 x=0.34 x=0.38
150
100
50 520
540
560
580
600
620
Heat source temperature (K) Fig. 3. Effect of heat source temperature on refrigeration output for different basic solution ammonia concentrations.
Exergy efficiency (%)
40
38
Ammonia concentration x=0.30 x=0.34 x=0.38
36
34
32
30 520
540
560
580
600
620
Heat source temperature (K) Fig. 4. Effect of heat source temperature on exergy efficiency for different basic solution ammonia concentrations.
ation output, thus the exergy efficiency increases. In addition, higher ammonia concentration of the basic solution accords with higher exergy efficiency. Fig. 5 shows the effect of turbine inlet pressure on net power output at different environment temperatures. It can be seen that the exergy efficiency increases first to maximum and then decreases as the turbine inlet pressure increases. It is known that the enthalpy drop across the turbine increases as the pressure ratio increases. This is why the net power output increases at first. But the enthalpy gains from an increased pressure ratio do not make up for the decrease in vapor flow rate, thus the net power output decreases afterwards. In addition, the net power output decreases as the environment temperature increases. It is obvious that the condensing temperature in the absorber increases with the increasing environment temperature, and this leads to the increasing turbine back pressure. Thus the increasing turbine back pressure makes the turbine power output decreases. Fig. 6 shows the effect of the turbine inlet pressure on the refrigeration output at different environment temperatures. It can be seen that the refrigeration output drops as the turbine inlet pressure increases, as the increasing turbine inlet pressure reduces the mass flow rate through the evaporator. As shown in Fig. 6, the refrigeration output drops with the increasing environment temperature. Because the evaporator inlet temperature increases with the increasing environment temperature, the refrigeration output decreases. Due to the
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Net power output (kW)
700
Environment temperature 288.15K 293.15K 298.15K
680 660 640 620 600 580 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 5. Effect of turbine inlet pressure on net power output for different environment temperatures.
Refrigeration output (kW)
155
Environment temperature
150
288.15K 293.15K 298.15K
145 140 135 130 125 120 115 110 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 6. Effect of turbine inlet pressure on cooling capacity for different environment temperatures.
combined effects of net power output and refrigeration output on the performance of the combined cycle, the exergy efficiency increases first to a maximum and then decreases, as shown in Fig. 7. Fig. 8 shows the effect of refrigeration temperature on the net power output at different turbine inlet temperatures. It can be seen that the net power output keeps constant as the refrigeration temperature increases. And the higher turbine inlet temperature, the larger is the net power output. Because the variation of refrigeration temperature can not change the turbine inlet and outlet conditions and the pump inlet and outlet conditions, the net power output can not change as the refrigeration temperature increases. In addition, higher turbine inlet temperature increases the turbine power output which lead to higher net power output of the system. Fig. 9 shows the effect of refrigeration temperature on the refrigeration output at different turbine inlet temperatures. As the refrigeration temperature increases, the refrigeration output increases correspondingly, and higher turbine inlet temperature leads to lower refrigeration output. It is observed that it is difficult to obtain the refrigeration output when the refrigeration temperature is very low. Fig. 10 shows the effect of refrigeration temperature on exergy efficiency at different turbine inlet temperatures. It is found that the exergy efficiency increases as the refrigeration increases, and a higher turbine inlet temperature conforms to a higher exergy efficiency.
J. Wang et al. / Applied Energy 85 (2008) 1071–1085
1081
38.0
Environment temperature
Exergy efficiency (%)
37.5
288.15K 293.15K 298.15K
37.0 36.5 36.0 35.5 35.0 34.5 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Turbine inlet pressure (MPa) Fig. 7. Effect of turbine inlet pressure on exergy efficiency for different environment temperatures.
690
Net power output (kW)
Turbine inlet temperature 558.15K 548.15K 538.15K
685
680
675
670 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 8. Effect of refrigeration temperature on net power output for different turbine inlet temperatures.
Refrigeration output (kW)
150 149 148
Turbine inlet temperature 558.15K 548.15K 538.15K
147 146 145 144 143 142 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 9. Effect of refrigeration temperature on cooling capacity for different turbine inlet temperatures.
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Exergy efficiency (%)
37.30
37.25
Turbine inlet temperature 558.15K 548.15K 538.15K
37.20
37.15
37.10
37.05 258
260
262
264
266
268
Refrigeration temperature (K) Fig. 10. Effect of refrigeration temperature on exergy efficiency for different turbine inlet temperatures.
From the discussions presented above, the effects of a given parameter on the net power output, Refrigeration output and exergy efficiency are different. In order to evaluate the performance of the combined power and refrigeration cycle, it is necessary to optimize the exergy efficiency for the combined cycle. 6. Optimization Parametric analysis of the combined power and refrigeration cycle shows the potential for the cycle to be optimized. For practical operation, the combined cycle has many parameters that are varied together, presenting a multi-dimensional surface on which an optimum can be found. Optimization of the operating parameters in the cycle is possible for each heat source and heat sink temperature. The cycle may be optimized based on the first low efficiency, second law efficiency, power output or refrigeration output, depending on the intended application and heat source. For the waste heat recovery, optimization of the combined cycle for maximum second law efficiency is most appropriate, because the second law efficiency can reflect the performance for cogeneration from the viewpoint of thermodynamics. In this study, parameter optimization is achieved by means of genetic algorithm to reach the maximum exergy efficiency. 6.1. Optimization method The genetic algorithm, which is presented firstly by professor Hooland in America [19], is a stochastic global search method that simulates natural biological evolution. Based on the Darwinian survival-of-fittest principle, the genetic algorithm operates on a population of potential solutions to produce better and better approximations to the optimal solution. The genetic algorithm differs from more traditional optimization techniques because it involves a search from a population of solutions and not from a single point. The genetic algorithm encodes a potential solution to a specific domain problem on a simple chromosomelike data structure (which constitutes an individual), where genes are parameters of the problem to be solved. In this study, the float-point coding is used in the genetic algorithm to solve the problem of parameter optimization in the combined power and refrigeration system. Each chromosome vector is coded as a vector of floating point numbers of the same length as the dimension of the search space. Chromosome is defined as a real number vector, X = (x1, x2, . . . , xn), xi eR, i = 1, 2,. . ., n, where n = 3, x1 is the turbine inlet pressure, x2 is the turbine inlet temperature, x3 is the basic solution ammonia concentration. The genetic algorithm only used fitness function to evaluate adaptability of individual without external information in the evolution search. The adaptability is expressed by the fitness value. A bigger fitness value means a better adaptability to constraints and a better viability of the individual. Fitness function which is not constrained by definition domain, continuity and differentiability, requires that the objective function is
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defined as the form of non-negative maximum. In this optimization, the exergy efficiency is selected as the fitness function. The basic genetic algorithm operators include selection operator, crossover operator and mutation operator. Selection operator is responsible for selecting the parents to create the next generation of solutions. The parent is chosen with a probability based on its fitness. The higher the fitness, the higher is the probability of selection. The rank-based model is selected for this optimization of the combined cycle. Crossover operator is the basic operator for producing new chromosomes. It produces new individuals that have some parts of both parent’s genetic material. The simple arithmetic crossover is applied to this optimization problem due to very simple operation, which is presented as follows: cc1 ¼ af1 þ ð1 aÞf2 ð15Þ c2 ¼ af2 þ ð1 aÞf1 where a is a random number between 0 and 1, f1 and f2 are parents individuals which are selected to crossover each other, c1 and c2 are children individuals which are produced by crossover. To avoid the local solution, the mutation operator is randomly applied with low probability to modify values in the chromosomes. Random mutation was adopted to optimize the parameters for the combined cycle. It is performed by selecting individuals from the range of the parameter according to mutation probability. The steps of genetic algorithm are made as follows: (1) Initialize the population size, crossover probability, mutation probability, stop generation, and generate the initial population randomly. (2) Calculate the fitness of each individual for parent generation, and order the fitness. (3) Select the individuals from parent generation, and create the children generation using crossover and mutation operators. (4) Calculate the fitness of each individual for children generation. If the maximum fitness of children generation is less than that of parent generation, substitute the maximum fitness of parent generation for that of children generation. (5) If generation reaches the stop generation, stop the optimization. Otherwise go back to step 3.
6.2. Optimization results For this optimization, the waste heat mentioned above is considered as the heat source, and the environment temperature and the refrigeration temperature are assumed constant. Thus, the parameters chosen for optimizing this combined power and refrigeration cycle are turbine inlet pressure, turbine inlet temperature, Table 5 Condition of the parameter optimization Environment temperature (°C) Environment pressure (MPa) Heat source temperature (°C) Heat source mass rate (kg/s) Refrigeration temperature (°C) Turbine isentropic efficiency (%) Turbine minimum exhaust degree of dryness Pump isentropic efficiency (%) Pinch point temperature difference (°C) Population size Crossover probability Mutation probability Stop generation The range of turbine inlet pressure (MPa) The range of turbine inlet temperature (°C) The range of basic solution ammonia–water concentration
20 0.10135 300 20 5 85 0.88 70 15 50 0.95 0.05 200 1.64.0 265285 0.280.38
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Table 6 The optimization results of the parameters for the combined cycle Turbine inlet pressure (MPa) Turbine inlet temperature (°C) Basic solution ammonia–water concentration Turbine work (kW) Pump work (kW) Refrigeration output (kW) Net power output (kW) Net power and refrigeration output (kW) Exergy input (kW) Exergy efficiency (%)
1.706 280.4 0.305 722.764 8.30644 168.647 714.457 883.104 1846.34 43.06
the basic solution ammonia–water concentration. Table 5 shows the condition of the parameter optimization. Table 6 lists the optimization results for the combined power and refrigeration cycle. 7. Discussion The aim of this research is to conduct a parametric analysis and optimization of a combined power and refrigeration cycle. The proposed combined cycle can be used as a bottoming cycle using waste heat from a conventional power cycle or an independent cycle using low temperature sources such as geothermal and solar energy or waste heat. The combined cycle presented in this paper can provide more refrigeration output using a relatively simpler system configuration. In addition, genetic algorithm is used to optimize multi-parameter system. The combined cycle can be optimized for the first low efficiency, second law efficiency, power output or refrigeration output, depending on the intended application and heat source. However, owing to lack experimental data for this combined cycle, the experimental study will be carried out to validate the feasibility of the combined power and refrigeration cycle in the future. In addition, thermoeconomic optimization for this combined cycle will be carried out in the coming research, because the optimization based on the second law efficiency as the objective function can only evaluate the system performance from the viewpoint of thermodynamics, not reflect the cost of performance improvement financially. 8. Conclusions A combined power and refrigeration cycle using ammonia–water mixtures as the working fluid is proposed, which combines the Rankine cycle and absorption refrigeration cycle. Parametric analysis is conducted to investigate the effects of several thermodynamic parameters on the cycle performances. It is shown that heat source temperature, environment temperature, refrigeration temperature, turbine inlet pressure, turbine inlet temperature, and basic solution ammonia concentration have significant effects on the net power output, refrigeration output and exergy efficiency. This parametric analysis of the cycle showed the potential for the cycle to be optimized. Optimization of the thermal parameters in the cycle is achieved using exergy efficiency as the objective function by means of genetic algorithm. It is found that the combined cycle has a maximum exergy efficiency of 43.06% when turbine inlet pressure, turbine inlet temperature and basic solution ammonia concentration are 1.706 MPa, 280.4 °C and 0.305, respectively. References [1] Maloney JD, Robertson RC. Thermodynamic study of ammonia–water heat power cycles. Oak Ridge National Laboratory Report 1953; CF-53-8-43. [2] Kalina AI. Combined cycle system with novel bottoming cycle. ASME J Eng Gas Turb Power 1984;106:737–42. [3] Xu F, Goswami DY, Bhagwat SS. A combined power/cooling cycle. Energy 2000;25:233–46. [4] Sadrameli SM, Goswami DY. Optimum operating conditions for a combined power and cooling thermodynamic cycle. Appl Energ 2007;84:254–65.
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