Optimization of a modified double-turbine Kalina cycle by using Artificial Bee Colony algorithm

Applied Thermal Engineering 91 (2015) 19e32

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Optimization of a modified double-turbine Kalina cycle by using Artificial Bee Colony algorithm Sadegh Sadeghi*, Hamid Saffari, Nikrouz Bahadormanesh School of Mechanical Engineering, Iran University of Science and Technology (IUST), Tehran, Narmak, Iran

h i g h l i g h t s
A modified double-turbine Kalina cycle is modeled.
Adequate mass flow rate for the second turbine in appropriate pressure is supplied.
ABC algorithm is applied to calculate the optimum thermal efficiency more precisely.
Thermodynamic analysis and optimization are executed in Matlab software.
Effects of important parameters on the performance of the cycle are discussed.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 May 2015 Accepted 8 August 2015 Available online 15 August 2015

Owing to appropriate performance of ammonia-water as a working fluid over two-phase region when exploiting low-temperature heat sources, a modified low-temperature double-turbine Kalina cycle system is designed to boost thermal efficiency. Due to low pressure after the second turbine, it is not affordable to use more than two turbines. Input mass flow rate of the second turbine is supplied by adding heat to the output liquid ammonia-water mixture from the first separator, separating the vapor at the outlet of the first turbine before blending the two streams. In order to reach the optimum thermal efficiency of the cycle, ABC (Artificial Bee Colony) algorithm is implemented as a novel powerful multivariable optimization algorithm. Considering the structure of the algorithm, convergence speed and accuracy of solutions have been considerably enhanced when compared to those of GA, PSO and DE algorithms. Such a relative enhancement is indicated by limit parameter and reducing probability of occurrence of local optimum problem. In this paper, thermal efficiency is selected as the objective function of ABC algorithm where its optimum value for the suggested Kalina cycle is found to be 26.32%. Finally, effects of the first separator inlet pressure and temperature, basic ammonia mass fraction and mass flow rate of the ammonia-water working fluid on net power output, required heat energy for the cycle and thermal efficiency are investigated. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Kalina cycle Artificial Bee Colony algorithm Ammonia-water mixture Thermal efficiency

1. Introduction Today, due to continuous reduction in non-renewable resources' reserves such as fossil fuels and importance of decreasing environmental pollutions, researches are oriented toward using clean energies such as geothermal energy, solar energy and waste heat recovery as heat sources. Since renewable heat sources do not produce very high temperatures spontaneously, many low-grade temperature thermodynamic cycles have been designed to

* Corresponding author. E-mail address: [email protected] (S. Sadeghi). http://dx.doi.org/10.1016/j.applthermaleng.2015.08.014 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

improve thermal and energy efficiencies. Organic Rankine Cycle is one of those low-temperature cycles in which water is used as the working fluid [1e6]. Alexander Kalina conceived a new power generation cycle whose working fluid was a mixture of ammoniawater. Indeed, this cycle was an improved version of the Organic Rankine Cycle (ORC) [7e14]. Kalina cycle was first proposed as a bottoming cycle generating power from waste heat [2]. It was mainly applied as a combined cycle to mitigate heat losses [15]. Unlike pure water, saturation and temperature of ammonia-water mixture is not constant in two-phase region during heat absorption process at a constant pressure. This causes the working fluid temperature profile to approach heat source temperature profile more than pure water does as a working fluid, so as exergy losses

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Nomenclature h m P Q Qu S T u v W X

specific enthalpy, kJ/kg mass flow rate, kg/s pressure, bar heat transfer rate, kW quality, % entropy, kJ/kg-K temperature, K specific internal energy, kJ/kg specific volume, m3/kg power, kW ammonia mass fraction

Greek letters efficiency, %

h

Subscripts ABC artificial bee colony

caused by temperature difference of working fluid and heat source or heat sink are considerably lower in a Kalina cycle when compared to ORC [9,13,16,17]. After foundation of first Kalina cycle, researching on efficiency improvement of Kalina cycle gained more attention. Researchers have been investigating to calculate thermodynamic properties of ammonia-water mixture more accurately and to design different Kalina cycles to enhance thermal and exergy efficiencies. Ziegler and Trepp presented correlations to compute the mixture properties. El-Sayed and Tribus also provided correlations before comparing thermal efficiency of Kalina cycle with that of Rankine cycle by using similar heat sources showing 10e20% better thermal efficiency for Kalina cycle rather than Rankine cycle [12,13,18e21]. Important correlations for calculating ammoniawater mixture properties presented by Ibrahim and Klein were used in EES software [17,22]. Correlation of Reiner Thillner offered more accurate results and were implemented in NIST REFPROP software [16]. Ibrahim and Kovac compared another Kalina cycle with Rankine by considering hot exhaust gases of a gas turbine as a heat source [8]. Bombarda showed that bottoming Kalina cycle produces larger net power than ORC by recovering waste heat from exhaust gas of gas diesel engines [2]. Goswami proposed a new solar Kalina cycle. Then Xu and Goswami presented correlations of thermodynamic properties of ammonia-water mixture for power cycle applications [11,12,22e24]. Liu Y et al. proposed a Kalina cycle with seawater as its heat source while an LNG reservoir as its heat sink. Thermodynamic analysis and optimization of Liu Y proposed Kalina cycle was carried out by Wang J et al. via a genetic algorithm [8]. A combined Kalina cycle utilizing low-temperature waste heat and LNG cold energy was proposed and optimized via DE algorithm by Shi X. and Che D [9]. A Kalina power cycle driven by solar energy was offered by Lolos P. A. and Rogdakis E. D. for which operating pressures and optimum range of ammonia mass fraction in vapor phase were calculated [19]. The first plant using Kalina cycle was Canoga Park Demonstration Plant in California supplying 6 MW of electric power [7,17]. The first commercial plant was built by Sumitomo Metals Kashima Steelworks. It generated 3.1 MW of power by waste heat recovery. The first Kalina geothermal power plant was established in Husavic, Island. It produced 2 MW net electrical power [1]. In this paper, we have proposed a Kalina cycle heat source with a temperature range of 80  C to 200  C to drive two turbines. Mass flow rate of the second turbine is supplied by adding heat from the

Cond. D DE EES ES Evap. Exp. v. F Fit GA H.E. LNG NP ORC P PSO Sep. SN Tur.

condenser number of optimization parameters differential evolution engineering equation solver evolution strategy evaporator expansion valve cost function fitness genetic algorithm heat exchanger liquefied natural gas number of colony size organic rankine cycle probability partial swarm optimization separator food source number turbine

first separator and outlet vapor of the first turbine to liquid ammonia-water mixture. Due to pressure loss after the second turbine, using more than two turbines does not seem to be affordable. Thermodynamic analysis of the cycle has been implemented based on EES correlations for calculating ammonia-water mixture properties and by linking EES to Matlab. Optimum values of thermal efficiency in different conditions are obtained with a novel multi-objective optimization algorithm, ABC algorithm. Finally, effects of the first turbine inlet pressure, temperature, mass flow rate and basic ammonia mass fraction of the working fluid on the net power output, heat feed to the cycle, ratio of the highest to the lowest pressure of the cycle and thermal efficiency are presented. 2. System description and thermodynamic model Considering variable saturation temperature of ammonia-water mixture at a constant pressure over the saturation region shown in Fig. 1 and good performance of the mixture as a working fluid in low-grade temperature heat source cycles [15], we proposed a modified double-turbine Kalina cycle. Knowing the ammoniawater mixture characteristics on two-phase region, exergy losses related to the temperature difference between working fluid temperature profile and that of heat source or heat sink decrease remarkably. Schematic diagram of the suggested Kalina cycle is presented in Fig. 2a and b has shown T-S diagram of the cycle at optimum value of thermal efficiency. Heat is added to ammonia-water solution at the evaporator and two-phase working fluid (point 1) is sent to the first separator where the vapor component with a high fraction of ammonia (point 2) is separated from the liquid component having a low fraction of ammonia (point 5). The high-pressure saturated vapor with high fraction of ammonia becomes superheated by passing through the heat exchanger 1 (point 3) before it is driven to the first turbine where it is expanded to generate power (point 4). Saturated vapor of the expanded solution (point 8) is separated from the saturated liquid (point 7) at the second separator. High-pressure ammonia-water saturated liquid (point 5) passes through the first expansion valve (point 6) while its pressure approaches to that of the first turbine outlet and blends with the output liquid stream from the separator 2 at the first mixer (point 9). The stream absorbs heat and becomes saturated

S. Sadeghi et al. / Applied Thermal Engineering 91 (2015) 19e32

21

950

P=40 bar, X=1

P=40 bar, X=0.8

850

P=40 bar, X=0.6

T (K)

750

P=40 bar, X=0.4 P=40 bar, X=0.2

650

P=40 bar, X=0

550 450 350 250 0

2

4

6

Entropy (kJ/kg-K) Fig. 1. TemperatureeEntropy diagram of ammonia-water mixture for different ammonia mass fraction at pressure 40 bar.

ammonia-water solution (point 10) before being introduced into the third separator where ammonia-water saturated vapor (point 11) is separated from the ammonia-water liquid (point 12). The vapor solution is mixed with the second separator output vapor at the second mixer (point 13) and then fed to the second turbine where the working fluid pressure is approached to the environment pressure (point 14). Since output pressure of the second turbine is close to that of environment and there is probable leakage problem, utilizing more turbines does not seem to be affordable. Pressure of the saturated liquid coming out of the separator 3 declines to output pressure of the turbine 2 at the second expansion valve (point 15) before the stream is mixed with the second turbine output stream at the third mixer (point 16) and enters the condenser after passing through the heat exchanger 3 (point 17). Mixer 3 exhaust is condensed to ammonia-water saturated liquid (quality is zero) e by rejecting heat (point 18) e which is subsequently sent to the feed pump. Feed pump increases the pressure of the working fluid to the required pressure (point 19). The pressurized working fluid reaches the evaporator (point 21) after absorbing heat at the heat exchanger 3 (point 20). 2.1. Mass and energy analysis Assumptions taken to simulate the Kalina cycle are as follows:
All processes reach a steady state.
Pressure losses in pipes are negligible.
Cycle components are isolated and heat losses are inconsiderable.
Quality of working fluid after the turbines is higher than 98%.
Expansion process in expansion valves are isenthalpic.
Effectiveness of heat exchangers is 40%.
Minimum temperature difference in heat exchangers is 5 K while that in evaporator and condenser is 6 K.
Pressure reductions in evaporator, condenser and heat exchangers are equal to 2% of the stream inlet pressure, respectively.
Mixture is at saturation region at the outlet of evaporator. If not, the condition is considered to be out of working.
Efficiencies of turbine and pump are hT and hP, respectively. Mass and energy conservation equations are generally written as follows:

X

min ¼

Q W ¼

X X

mout mout hout 

(1) X

min hin

(2)

And the balance equations for every component of the proposed cycle are defined as 1st turbine:

m3 ¼ m4

(3)

x3 ¼ x4

(4)

WTur: 1 ¼ m3 ðh3  h4 Þ

(5)

hT ¼

h3  h4 h3  h4s

(6)

2nd turbine:

m13 ¼ m14

(7)

x13 ¼ x14

(8)

WTur: 2 ¼ m13 ðh13  h14 Þ

(9)

hT ¼

h13  h14 h13  h14s

(10)

Evaporator:

m21 ¼ m1

(11)

x21 ¼ x1

(12)

QEvap: ¼ m1 ðh1  h21 Þ

(13)

1st separator:

m1 ¼ m2 þ m5

(14)

m1 x1 ¼ m2 x2 þ m5 x5

(15)

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a

b

3

440 1 5

2

Temperature [K]

390

11

12 10

340

9

6

7 21

4

15

8

20 16

290

14

17

19 18

240 0

1

2

3

4

5

6

Entropy [Kj/Kg-K] Fig. 2. a Schematic diagram of proposed Kalina cycle. b T-S diagram of proposed Kalina cycle.

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m1 h1 ¼ m2 h2 þ m5 h5

(16)

Qin 1 ¼ m2 ðh3  h2 Þ

23

(40)

2nd heat exchanger:

2nd separator:

m4 ¼ m7 þ m8

(17)

m9 ¼ m10

(41)

m4 x4 ¼ m7 x7 þ m8 x8

(18)

x9 ¼ x10

(42)

m4 h4 ¼ m7 h7 þ m8 h8

(19)

Qin 2 ¼ m9 ðh10  h9 Þ

(43)

3rd heat exchanger:

3rd separator:

m10 ¼ m11 þ m12

(20)

m16 ¼ m17 ;

m10 x10 ¼ m11 x11 þ m12 x12

(21)

x16 ¼ x17 ;

x19 ¼ x20

(45)

m10 h10 ¼ m11 h11 þ m12 h12

(22)

m16 ðh16  h17 Þ ¼ m19 ðh19  h20 Þ

(46)

1st mixer:

ε¼

m19 ¼ m20

h16  h17 h16  h20

(44)

(47)

m6 þ m7 ¼ m9

(23)

m6 x6 þ m7 x7 ¼ m9 x9

(24)

m20 ¼ m21

(48)

m6 h6 þ m7 h7 ¼ m9 h9

(25)

x20 ¼ x21

(49)

Qin 3 ¼ m20 ðh21  h20 Þ

(50)

4th heat exchanger:

2nd mixer:

m8 þ m11 ¼ m13

(26)

m8 x8 þ m11 x11 ¼ m13 x13

(27)

m17 ¼ m18

(51)

m8 h8 þ m11 h11 ¼ m13 h13

(28)

x17 ¼ x18

(52)

QCond: ¼ m17 ðh17  h18 Þ

(53)

3rd mixer:

Condenser:

m14 þ m15 ¼ m16

(29)

m14 x14 þ m15 x15 ¼ m16 x16

(30)

m18 ¼ m19

(54)

m14 h14 þ m15 h15 ¼ m16 h16

(31)

x18 ¼ x19

(55)

WPump ¼ m18 ðh19  h18 Þ

(56)

1st expansion valve:

m5 ¼ m6

(32)

x5 ¼ x6

(33)

h5 ¼ h6

(34)

Pump:

hP ¼

h19s  h18 h19  h18

(57)

And thermal efficiency is

hThermal ¼

2nd expansion valve:

WTur: 1 þ WTur: 2  WPump QEvap: þ Qin 1 þ Qin 2 þ Qin 3

(58)

m12 ¼ m15

(35)

x12 ¼ x15

(36)

2.2. Optimization algorithm

h12 ¼ h15

(37)

Optimization algorithms have been widely used during the last decade specifically for energy system applications ranging from a simple power generation system to more sophisticated multigeneration systems [25,26]. Thermal efficiency, exergy efficiency and cost assessment of cycle components in different lowtemperature combined cycles such as Kalina cycle and organic Rankine cycle which, respectively, apply exhausted heat from a

1st heat exchanger:

m2 ¼ m3

(38)

x2 ¼ x3

(39)

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micro turbine or gas turbine and heat generated from a bio mass combustor as their heat sources, have been optimized by using evolutionary algorithms such as genetic algorithm to determine the best design for the proposed cycles [9,11,25,26]. In this paper, we employed a novel optimization algorithm, ABC algorithm, proposed by Dervis Karaboga [27e29] to achieve optimum thermal efficiency of the Kalina cycle. Based on analysis and optimizations carried out by Karaboga and Akay, artificial bee colony algorithm has important advantages in multi-variable problems in comparison with other well-known optimization algorithms such as GA, PSO, DE and ES [30,31]. ABC algorithm has fewer constraints while it considers a limiting parameter to increase the convergence speed of optimization. Local optimum or premature convergence problem is less seen in ABC than in GA and PSO algorithms [30e32]. It does not employ crossover operators like GA and DE algorithms. ABC algorithm generates new solutions by a simple operation based on considering the difference of randomly determined child components of the parent and a randomly selected solution from the population. This accelerates searching cycle and converging into an optimum value. Unlike DE, ABC choses solutions depending on their qualities. Indeed, solutions with higher fitness values are selected which leads to a quick and detailed search over search space on each cycle of optimization. One other important advantages of ABC algorithm is its better or at least similar function to that of optimization algorithms, although it has less control parameters making ABC algorithm more efficient in optimizing multimodal and multi-dimensional problems [30]. ABC consists of three significant components [25e27,30,31]:
Food source: food sources are points chosen on the function among which we are to find the optimum one.
Employed bees: the bees which are particularly sent to the food sources to calculate fitness value and probability of each food source.
Unemployed bees: unemployed bees are of two types: I. Scouts: the bees sent randomly to food sources at initial stage II. Onlookers: the bees randomly allocated to generate new solutions, calculate the fitness of each food source, compare the fitness and save information to share them with other bees. Important parameters calculated in ABC are expressed as follows [27,28,30,31]: i. Fitness value:

Fiti ¼

1 1 þ Fi

i ¼ 1; 2; …; D

(59)

ii. Probability value:

Fit Pi ¼ PSN i n¼1 Fitn

(60)

iii. New food source position from that of the old food source is calculated by:

  nij ¼ xij þ ∅ij xij  xik

(61)

k є {1,2, …,SN}, j є {1,2, …,SN}, ∅ ¼ random number є [1,1], K s j iv. Limit: limit is applied in order to abandon solutions which are not improved during optimization process to increase optimization process speed.

Generally, optimizing procedure of ABC algorithm can be mentioned as follows [28e33]: ➢ Generating initial solutions by scouts. ➢ Sending specifically the employed bees to the food sources in order to compute the fitness value and probability. ➢ Sending randomly the onlooker bees to the food sources to calculate the fitness and to share information with the employed bees. ➢ Selecting food sources with the preferred fitness value. ➢ Sending scouts who have abandoned the low-fitness food sources to find new food sources. ➢ Memorizing the best fitness value food source. Flowchart of ABC algorithm used for optimization of the suggested Kalina cycle is shown in Fig. 3a. 3. Results and discussion In this study, an ABC algorithm is employed in order to optimize the proposed Kalina cycle. Initial conditions and variable ranges considered in the algorithm for converging thermal efficiency to the optimum value are presented in Table 1. Thermodynamic analysis of the Kalina cycle is carried out by using Matlab software and thermodynamic properties of ammoniawater mixture are calculated by EES academic professional v. 8.4. Linking EES to Matlab in order to increase the accuracy of calculation of thermodynamic properties of the mixture is executed by creating EES macro file. Assumptions taken in thermodynamic analysis of the cycle are presented in Table 2. Parameters such as pressure, temperature, ammonia mass fraction and mass flow rate of working fluid have higher impacts on thermal efficiency. Effects of these parameters on net output power, heat addition to the cycle and thermal efficiency are shown subsequently. Fig. 3b illustrates the convergence behavior of ABC algorithm for optimizing thermal efficiency according to the stages mentioned in Fig. 3a. Objective function, 100  hth., has been minimized. It can be observed from Fig. 3b that although a set of randomly selected food sources is not accurate in ABC algorithm but it is quickly converged to the optimum thermal efficiency at almost 60 cycles of foraging. Optimum values are presented in Table 3 considering constraints and conditions taken for optimization mentioned in Table 1. Thermodynamic properties of each point of the proposed Kalina cycle are presented in Table 4. 3.1. Net power output Inlet pressure and temperature of the first separator, basic ammonia mass fraction and basic mass flow rate have important influences on the net power output. Fig. 4 illustrates the effect of the first separator pressure on net power with respect to the conditions presented in Table 1 and results are shown for ammonia mass fractions of 0.85, 0.9, and 0.95, and temperatures of 130 and 140  C, respectively. It is evident that the net power output of the proposed Kalina cycle varies between 320 and 430 kW. In the considered range of pressure, maximum net power output occurs at the temperature of 140  C, pressure of 20 bar and ammonia mass fraction of 0.85. Owing to Fig. 4, the net output power initially drops and then rises with an increase in pressure at the temperature of 130  C. The net power output declines with an increase in pressure at the temperature of 140  C for the considered pressure range. It can be observed that at 140  C, changes of net power output with the pressure are investigated in shorter range of pressure. That is because the system state enters the superheat region outside the

S. Sadeghi et al. / Applied Thermal Engineering 91 (2015) 19e32

Fig. 3. a Flowchart of ABC algorithm. b Convergence behavior of ABC algorithm optimizing hth.

25

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Table 1 Converging conditions and constraints used in optimization. Parameters

Symbol

Unit

Value

Number of colony size (employed bees þ onlooker bees) Number of food sources Food source which could not be improved though trials Number of cycles for foraging {stopping criteria} Number of parameters of the problem to be optimized Iterative relative convergence error tolerance The range of point1 pressure of the cycle The range of point 1 temperature of the cycle The range of point 1 temperature of the cycle The range of basic ammonia mass fraction of working fluid The range of basic mass flow rate The range of point 18 pressure of the cycle The range of outlet quality of the turbines Condition of point 1 of the cycle

NP Food Number Limit Max Cycle D e P1 T1 T3 X m P18 Qu e

e e e e e % bar  C  C % kg/s bar % e

20 10 100 100 1 0.05 20e50 105e165 150e200 55e95 10e30 >1.1 >98 saturated

Table 2 Parameters applied in thermodynamic analysis. Parameter

Unit

Value

Turbine isentropic efficiency Pump isentropic efficiency Pressure loss in evaporator and condenser Pressure loss in heat exchangers Pinch temperature difference Approach temperature difference in heat exchanges Minimum quality of turbine exhaust Environment pressure

% % % %  C  C % bar

90 85 2 2 6 5 98 1.1

Table 3 Optimum values of ABC optimizing of the Kalina cycle. Parameter

Symbol

Unit

Optimum value

1st separator inlet temperature 1st separator inlet pressure Basic ammonia mass fraction Ammonia-water mass flow rate Net power output Inlet heat addition Thermal efficiency

T1 P1 x1 m1 W Qin



135.85 39.35 94.08 12 5203 19,770 26.32

hThermal

C bar % kg/s kW kW %

range at point 1, which contradicts the considered optimization constraints. Thermodynamic properties of working fluid predominantly at high ammonia mass fractions, approach ammonia thermodynamic properties. Whereas, the enthalpy difference of pure ammonia is more than the enthalpy difference of pure water between two certain pressures, so the net power output at high ammonia mass fraction is more than the net power at low ammonia mass fraction, which can be implied from Fig. 4. The effect of the first separator inlet temperature on net power output is shown in Fig. 5. It is observed that the net power output increases once, then decreases with further increase in the first separator inlet temperature, although it increases again with less slope. The net output power of the cycle varies between 340 and 478 kW. Since Kalina cycle systems use low-grade temperature heat sources, optimum values of the net power output of the proposed Kalina cycle occur in temperatures between 110 and 120  C. Regarding Fig. 5, the net power output curves increase again after an approximate temperature of 120  C, but they do not reach the maximum net power generated before 120  C in the considered range of temperature. The effect of basic ammonia mass fraction on net power output is illustrated in Fig. 6. Net output power varies between 220 and 400 kW. Regarding Fig. 6, net power output increases with an increase in ammonia mass fraction, and variation of net power output

Table 4 Thermodynamic properties of each point of the cycle at optimum thermal efficiency. Point

T (K)

P (bar)

h (kJ/kg)

s (kJ/kg-K)

u (kJ/kg)

v (m3/kg)

x (%)

Qu (%)

m (kg/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

409 409 467.6 327.8 409 335.1 327.8 327.8 329.7 353.8 353.8 353.8 328.5 297 326.8 300 266.5 248.1 252.7 294 328.1

39.35 39.35 38.56 3.62 39.35 3.62 3.62 3.62 3.62 3.55 3.55 3.55 3.62 1.116 1.116 1.116 1.111 1.106 41.81 40.97 40.15

1520.50 1541.20 1722.4 1364.3 396.05 396.05 25.364 1430.0 131.80 529.25 1585.0 192.64 1432.5 1339.0 192.64 1284.4 1044.6 191.60 184.61 55.147 221.82

4.43 4.48 4.9 5.02 1.7 1.86 0.68 5.24 1.02 2.18 5.64 1.07 5.25 5.52 1.09 5.32 4.48 0.56 0.53 0.34 0.87

1354.2 1372.0 1514.1 1216.3 390.4 358.5 25.0 1275.0 120.8 488.4 1417.5 192.2 1277.0 1230.5 182.7 1149.0 938.0 191.7 190.5 48.7 215.0

0.0423 0.0430 0.0540 0.3973 0.0014 0.1036 0.0012 0.4286 0.0303 0.1148 0.4712 0.0011 0.4290 1.1958 0.0927 1.2685 1.0199 0.0014 0.0014 0.0016 0.0017

94.08 94.95 94.95 94.95 47.05 47.05 35.61 97.67 38.9 38.9 89.34 22.81 97.54 97.54 22.81 94.08 94.08 94.08 94.08 94.08 94.08

98.2 1 1.001 95.44 0 23.45 0 1 6.78 24.18 1 0 1 98.3 6.24 93.67 85.57 0 0.001 8.09 16.68

12.00 11.78 11.78 11.78 0.217 0.217 0.538 11.25 0.754 0.754 0.182 0.572 11.42 11.42 0.572 12.00 12.00 12.00 12.00 12.00 12.00

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27

T=130 C, X=0.85

Net power output (KW)

4.40E+02

T=130 C, X=0.9 T=130 C, X=0.95

4.20E+02

T=140 C, X=0.85 T=140 C, X=0.9

4.00E+02

T=140 C, X=0.95

3.80E+02 3.60E+02 3.40E+02 3.20E+02 3.00E+02 18

23

28

33

38

43

48

53

1st separator pressure (bar) Fig. 4. Effects of 1st separator inlet pressure on the net power output.

Fig. 5. Effect of 1st separator temperature on net power output.

is scarce with an increase in the first turbine inlet pressure and temperature. Enthalpy drop occurring in turbines increases with an increase in basic ammonia mass fraction of working fluid, leading to a net output power boost.

Fig. 7 shows the effect of basic mass flow rate of working fluid on net power output. It can be seen that net power output increases with an increase in basic mass flow rate and varies between 4.5 and 9.5 MW. It can be understood from Fig. 7 the generated net power

Fig. 6. Effect of ammonia mass fraction on net power output.

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S. Sadeghi et al. / Applied Thermal Engineering 91 (2015) 19e32

Fig. 7. Effect of basic mass flow rate on the net power output.

increases remarkably with an increase in basic mass flow rate, and the order of generated power is about 10 times larger than the order of power generated in the ranges of the first separator inlet pressure, temperature, and basic ammonia mass fraction ranges discussed in previous paragraphs. 3.2. Heat addition Fig. 8 illustrates the effect of the first separator inlet pressure on required heat for the cycle. It can be observed that the required heat at 130  C initially decreases and then increases with an increase in pressure. The required heat for the cycle decreases with an increase in pressure at 140  C. Regarding Fig. 8, the maximum required heat for the cycle equals 1.79 MW occurring at pressure of 20 bar, temperature of 140  C, and ammonia mass fraction of 0.85; and the minimum value of required heat for the cycle equals 1.4 MW occurring at pressure of 50 bar, temperature of 140  C, and ammonia mass fraction of 0.85. The required heat increases in a range of temperature, then decreases and eventually increases again as illustrated in Fig. 9. The state of Point 1 in the cycle enters the superheat region over the investigated range of temperatures, so that variation of required heat with the temperature has been plotted in the range of saturation state. As can be seen, the procedure of variations is analogous

with those of the net power output, but at pressure of 35 and 40 bar, with same ammonia mass fraction of 0.85, the maximum required heat values occur after 120  C at about 160 and 168  C, respectively. The maximum value of required heat for the cycle equals 1.75 MW and occurs at pressure of 35 bar, temperature of 116  C, and ammonia mass fraction of 0.95, and the minimum value of required heat for the cycle equals 1.4 MW and occurs at pressure of 40 bar, temperature of 105  C, and ammonia mass fraction of 0.85. The effect of ammonia mass fraction on heat addition is investigated in Fig. 10. It is observed that, the required heat increases with an increase in basic ammonia mass fraction. The values of required heat of the Kalina cycle vary between 1.16 and 1.62 MW depending on ammonia fraction, first separator inlet pressure, and temperature. The effect of basic mass flow rate of the working fluid on heat addition is shown in Fig. 11. Looking at Fig. 11, one may see that heat addition increases linearly with an increasing basic mass flow rate of the cycle. As it can be observed, the maximum value of heat required for the cycle equals 46 MW and occurs at pressure of 35 bar, temperature of 130  C, and ammonia mass fraction of 0.95, and the minimum value of heat required for the cycle equals 16 MW and occurs at pressure of 40 bar, temperature of 130  C, and ammonia mass fraction of 0.85.

Fig. 8. Effect of 1st separator inlet pressure on the heat addition to the cycle.

S. Sadeghi et al. / Applied Thermal Engineering 91 (2015) 19e32

29

Fig. 9. Effect of 1st separator inlet temperature on the heat addition.

Fig. 10. Effect of basic ammonia mass fraction on the heat addition.

3.3. Thermal efficiency Effects of the first separator inlet pressure, temperature, basic ammonia mass fraction, and basic mass flow rate on thermal efficiency were investigated. According to the assumptions and

conditions presented in Tables 1 and 2, the thermal efficiency of the proposed Kalina cycle varies between 21.8% and 26.32%. Fig. 12 shows the effect of the first separator pressure on thermal efficiency in an optimum value of basic ammonia mass fraction and mass flow rate presented in Table 3. As can be seen at 140  C and

Fig. 11. Effect of basic mass flow rate on the heat addition.

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Fig. 12. Effect of 1st separator inlet pressure on the thermal efficiency in x ¼ 94.08%.

Fig. 13. Effect of 1st separator inlet temperature on the thermal efficiency in x ¼ 94.08%.

Fig. 14. Effect of basic ammonia mass fraction on the thermal efficiency.

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Fig. 15. Effect of basic mass flow rate on the thermal efficiency.

150  C, variations of thermal efficiency with pressure are investigated in shorter range of pressure. That is because the working fluid state enters the superheat region outside the range at Point 1. Regarding Fig. 12, at 140  C and 150  C, thermal efficiency increases continuously with increasing the first separator inlet pressure, but at 130  C, thermal efficiency initially increases and then decreases with an increase in pressure. The effect of the first separator inlet temperature on thermal efficiency in optimum values of basic ammonia mass fraction and mass flow rate is shown in Fig. 13. It can be seen that at pressures of 40 and 45 bar, thermal efficiency increases with an increase in the first separator inlet temperature and the optimum values of thermal efficiency occur in about 120  C, but at pressures of 30 and 35 bar, optimum values of thermal efficiency occur in temperatures 162 and 165  C, respectively. The effect of pressure on thermal efficiency is less intense in lower temperatures rather than that at higher temperatures. Fig. 14 illustrates the effect of basic ammonia mass fraction on thermal efficiency in basic mass flow rate of 15 kg/s. It is observed that thermal efficiency increases with an increase in basic ammonia mass fraction. In this case, thermal efficiency of the proposed cycle varies between 17.9% and 24.6%. Fig. 14 portrays that thermal efficiency is affected scarcely with basic ammonia mass fraction and the curves are approaching to each other. The effect of basic mass flow rate on thermal efficiency is shown in Fig. 15. In order to examine the effect better, we allow point 1 to enter the superheat region. In this case, thermal efficiency varies between 19.5% and 28.3%. As it can be observed, thermal efficiency decreases with an increase in basic mass flow rate of the working fluid, and the curves are closely affected by different inlet pressures and temperatures of the first turbine as well as basic ammonia mass fraction.

4. Conclusions In this paper, we proposed a modified low-temperature doubleturbine Kalina cycle to improve thermal efficiency of the Kalina cycle. The Kalina cycle was optimized by using a novel multivariable optimization algorithm, namely Artificial Bee Colony algorithm (ABC). The effects of the first separator inlet pressure, the first separator inlet temperature, basic ammonia mass fraction, and basic mass flow rate of working fluid on the net power output required heat for the cycle and thermal efficiency were investigated based on calculated ammonia-water mixture properties with EES Academic Professional v.8.4 Software as well as thermodynamic

analysis of the cycle using Matlab software. The main conclusions drawn from the present work are listed as follows:
Although ABC algorithm may not select an appropriate random food source at the initializing stage of finding the optimum thermal efficiency, but it can rapidly converge to the optimum value.
Mainly, the net power output and the required heat for the cycle decrease with an increase in the first separator inlet pressure.
Mainly, the net power output and the required heat for the cycle increase with an increase in basic ammonia mass fraction.
Mainly, the net power output and the required heat for the cycle increase with an increase in basic mass flow rate of the working fluid.
There is an optimum value of the first separator inlet pressure, the first separator inlet pressure temperature and basic ammonia mass fraction of the working fluid at which the maximum thermal efficiency is attained.
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