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Parametric analysis and optimization of a Kalina cycle driven by solar energy
Applied Thermal Engineering 50 (2013) 408e415
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Parametric analysis and optimization of a Kalina cycle driven by solar energy Jiangfeng Wang a, *, Zhequan Yan a, Enmin Zhou b, Yiping Dai a a b
Institute of Turbomachinery, School of Energy and Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, China China Aerodynamics Research and Development Center, Mianyang 621000, China
h i g h l i g h t s < A thermal storage system is introduced to provide stable power output. < A modified system efficiency is defined to evaluate the system performance. < The effects of thermodynamic parameters on the performance are examined. < Parametric optimization is conducted to find the optimum performance by GA.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 April 2012 Accepted 2 September 2012 Available online 10 September 2012
A solar-driven Kalina cycle is examined to utilize solar energy effectively due to using ammoniaewater’s varied temperature vaporizing characteristic. In order to ensure a continuous and stable operation for the system, a thermal storage system is introduced to store the collected solar energy and provide stable power when solar radiation is insufficient. A mathematical model is developed to simulate the solar-driven Kalina cycle under steady-state conditions, and a modified system efficiency is defined to evaluate the system performance over a period of time. A parametric analysis is conducted to examine the effects of some key thermodynamic parameters on the system performance. The solar-driven Kalina cycle is also optimized with the modified system efficiency as an objective function by means of genetic algorithm under the given conditions. Results indicate that there exists an optimal turbine inlet pressure under given conditions to maximize the net power output and the modified system efficiency. The net power output and the modified system efficiency are less sensitive to a change in the turbine inlet temperature. An optimal basic solution ammonia fraction can be identified that yields maximum net power output and modified system efficiency. The optimized modified system efficiency is 8.54% under the given conditions. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Kalina cycle Solar energy Sensitivity analysis Optimization
1. Introduction The Kalina cycle, which utilizes ammoniaewater as its working fluid, was originally conceived by Alexander Kalina [1]. The ammoniaewater has the advantage of variable-temperature evaporation and condensation at subcritical pressures in contrast to a pure fluid that evaporates and condenses at constant temperature, and could provide a better performance due to better thermal match achieved in the condenser and evaporator. Kalina cycle uses unique DCSS (Distiller Condenser Sub-System) to achieve ammoniaewater condensation process at low condensing pressure by changing the ammoniaewater mass fraction. Due to the superior to steam power cycle, many studies have been found to investigate Kalina cycle. El-Sayed and Tribus [2] * Corresponding author. Tel./fax: þ86 029 82668704. E-mail address: [email protected] (J. Wang). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.002
made a theoretical comparison between the Kalina cycle and Rankine cycle. The configurations developed by them were very much complicated because several heat exchangers had more than two steams. Marston [3] considered the parametric analysis of the Kalina cycle. He developed a method of balancing the Kalina cycle and identified the key parameters for optimizing the Kalina cycle. Rogdakis [4] developed correlations describing the optimum operation of the Kalina cycle. In addition, Nag and Gupta [5] studied exergy analysis of the Kalina cycle. Because of the advantage of recovering sensible heat source, Kalina cycle is generally used as a bottoming cycle to enhance energy conversion efficiency by recovering waste heat from gas turbine, diesel engine or industrial production such as cement line [6,7]. Marston [8] compared the performance of Kalina cycle with a triple-pressure steam cycle as the bottoming sections of a gas turbine combined cycle power plant. Jonsson et al. [9,10] examined the Kalina cycle as the bottoming cycle with gas engines and gas
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
Nomenclature A b C cp D F0 FR h
I k L _ m N p Q R s S T U V
area, m2 width of absorber, m concentration ratio of CPC specific heat, kJ kg1 K1 diameter, m collector efficiency factor heat removal factor enthalpy, kJ kg1 hourly radiation, W m2 heat transferring coefficient, W m2 K1 length, m mass flow rate, kg s1 number of tubes pressure, bar heat rate, kW tilt factor for radiation entropy, kJ kg1 K1 incident solar flux, W m2 temperature, C loss coefficient, W m2 k1; heat transfer coefficient, W m2 k1 volume, m3
diesel engines as prime movers to recover waste heat available from the exhaust gas. Bombarda et al. [11] conducted a thermodynamic comparison between Kalina cycle and ORC as the bottoming cycle to recover waste heat from diesel engines. Results showed the net electric power of Kalina cycle was a little larger than that of ORC under the reasonable design parameters and the same logarithmic mean temperature difference in the heat recovery exchanger. With the rapid industrialization and social growth, the demand for energy is growing faster. Conventional sources, such as coal, oil and natural gas, have limited reserves that are expected not to last for an extended period. Renewable energy resources are expected to play an increasing role in energy consumption due to these potentials in reducing fossil fuel consumption and alleviating environmental problems. So, Kalina cycle is also used to utilize renewable energy resources, such as geothermal heat sources. Madhawa Hettiarachchi et al. [12] evaluated the performance of the Kalina cycle system for low temperature geothermal heat sources, compared it with an organic Rankine cycle, and examined the effect of the ammonia fraction and turbine inlet pressure on the cycle performance in detail. Nasruddin et al. [13] conducted the energy and exergy analysis of kalina cycle utilizing lower temperature geothermal resources, and optimized the Kalina cycle on the mass fraction of working fluid and the turbine output pressure. Arslan [14] investigated Kalina cycle to generate electricity generation from Simav geothermal field. He determined the optimum operating conditions for the KCS-34 plant on the basis of the exergetic and life-cycle-cost concepts. Due to limitation of region for geothermal resources, some researchers paid attention to use solar energy, which is available everywhere, to drive Kalina cycle enabling the distributed power generation. Lolos [15] investigated a Kalina cycle using solar energy to produce power. He used flatplate solar collectors to heat the evaporator to make ammoniae water be partially vaporized and used an external heat source to superheat the ammoniaewater vapor before entering a turbine. In this study, a Kalina cycle driven by solar energy mainly as one heat source is investigated based on the thermodynamic analysis. A thermal storage system is added to store the collected solar energy
W x
409
power, kW; Width, m ammonia mass fraction
Greek letters a absorptivity of the absorber surface h efficiency r reflectivity of the concentrator surface; density, kg m3 s transmissivity of the cover Subscripts 0 environment b beam C condenser d diffuse fi inlet of solar collector fo outlet of solar collector i inlet l uniform; loss lo loss P pump s isentropic process sys system T turbine u useful
and to provide continuous power output when solar radiation is insufficient. A mathematical model is developed to simulate the solar-driven Kalina cycle under steady-state conditions, and a modified system efficiency is defined to evaluate the cycle performance over a period of time. A parametric analysis is conducted to examine the effects of some key thermodynamic parameters on the system performance. The solar-driven Kalina cycle is also optimized with the modified system efficiency as an objective function by means of genetic algorithm (GA) under the given conditions. 2. System description Fig. 1 illustrates a schematic diagram of the Kalina cycle driven by solar energy. The overall system is divided into two subsystems: the solar energy collecting and storing subsystem and the Kalina cycle. The solar energy collecting and storing subsystem consists of solar collectors, a thermal storage tank and an auxiliary heater. Compound parabolic collector (CPC) is used to collect the solar radiation to supply heat to the overall system because it can achieve higher concentration for large acceptance angle and requires only intermittent sun-tracking. In addition, the CPC can achieve a higher temperature than flat-plate solar collector. The thermal storage tank with thermal oil as working fluid is used as the heat source when solar radiation is not sufficient. The auxiliary heater is installed as the backup energy source to boost the temperature of thermal storage tank to the allowable temperature when the temperature of thermal storage tank drops below the allowable temperature. The Kalina cycle consists of two separators, a vapor evaporator, two recuperators, an air condenser, a feed pump, a turbine-generator and a throttle valve. The ammoniaewater mixture is heated in the vapor evaporator where it is partially vaporized by absorbing heat from thermal storage system. The twophase ammoniaewater mixture is sent to separator 1 where the ammoniaewater solution is separated into weak liquid solution and ammonia-rich vapor. The ammonia-rich vapor is expended to a low pressure through a turbine to drive a generator to generate
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3 Solar Radiation
c2
Auxiliary Heater
Turbine
Separator 1
2
s1
Generator
5 Recuperator 1
4
CPC
6
7 8
Valve Vapor Generator
c1
Thermal Storage Tank
s2
Recuperator 2
14
10
1 13
9 Separator 2
Pump
11 Condenser
12
Fig. 1. Schematic diagram of the Kalina cycle driven by solar energy.
electricity. The weak liquid solution, after recuperating some of the heat in recuperator 1, is throttled down to a low pressure and then mixed with the ammonia-rich solution coming from the turbine to form the ammoniaewater basic solution. After cooled down in recuperator 2, the ammoniaewater basic solution is sent to separator 2 separating the phases and condensed to ammoniaewater liquid in the condenser by cooling air. The ammoniaewater liquid is pumped to vapor evaporator again after preheated through the recuperators.
The Kalina cycle driven by solar energy is modeled based on the mass, momentum and energy conservations. To simplify the theoretical model, some assumptions are made as follows: (1) The system reaches a steady state. (2) The pressure drops in compound parabolic collector, storage tank, auxiliary heater, vapor generator, separators, recuperators, condenser, and the connection tubes are neglected. (3) A well-mixed situation is assumed in the thermal storage tank where a uniform temperature varies only with time [16]. (4) There is no heat transfer with the environment for the Kalina cycle. (5) The vapor streams from the separators are saturated vapor and the liquid streams from the separators are saturated liquid. (6) The stream at the condenser outlet is saturated liquid, and the flows across the throttle valve are isenthalpic. (7) The pump and the turbine have a given isentropic efficiency, respectively. A CPC can accept both beam and diffuse radiation because of its large acceptance angle. The beam radiation flux falling on the aperture plane is IbRb, while the diffuse radiation flux within the acceptance angle is given by (Id/C). Thus, the total effective flux absorbed at the absorber surface is expressed as [16],
I Ib Rb þ d sre a C
The useful heat gain rate can be given by [16],
(1)
(2)
where
FR ¼
0 _ p mc F bUlo L 1 exp _ p bUlo L mc
(3)
and
1 1 b ¼ Ulo þ 0 F Ulo N pDi k
3. Mathematical model and performance criteria
S ¼
U Qu ¼ FR WL S lo Tfi T0 C
(4)
An insulated thermal oil storage tank is used to receive energy from an array of collectors and discharge energy to a load in the Kalina cycle. With a well-mixed model of the storage tank, the temperature of the thermal oil remains a uniform temperature Tl, which is defined as the thermal oil temperature in the tank after two streams from solar collector and vapor generator are wellmixed. An energy balance applied to thermal storage tank is expressed as
rVcp
dTl ¼ Qu Qload UAðTl T0 Þ dt
(5)
Furthermore, Qu and Qload, which represent the useful gain from the solar collectors and the energy discharged to the Kalina cycle, respectively, can be calculated as
_ oil;1 cp Tfo Tl Qu ¼ m
(6)
_ oil;2 cp ðTl Ti Þ Qload ¼ m
(7)
The detailed descriptions about the mathematical model of the compound parabolic collector and the thermal storage tank are given in Ref. [17]. In the vapor generator, due to using an ammoniaewater mixture, the more volatile ammonia tends to vaporize first at a lower temperature than a pure water. The temperature of the remaining two-phase liquid rises as the ammonia concentration decreases. Thus, a better match between heat ejection of hot oil
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
from thermal storage tank and heat absorption of ammoniaewater is performed using ammoniaewater’s characteristic of varied vaporizing temperature during the vaporizing process, as shown in Fig. 2 with two heat exchanging sections, namely, an economizer and an evaporator. Energy balance for the evaporator is
_ oil;2 hs1 hga ¼ m _ 1 ðh2 haw Þ m
(8)
_ oil;2 hga hs2 ¼ m _ 1 ðhaw h1 Þ m
_ 10 þ m _ 11 ¼ m _9 m
(10)
_ 11 x11 þ m _ 10 x10 ¼ m _ 9 x9 m
x9 x11 _ $m x10 x11 9
(20)
_ 3 x3 þ m _ 4 x4 ¼ m _ 2 x2 m
(11)
The mass flow rate of saturated vapor separated by the separator 1 is
x2 x4 _ $m x3 x4 2
(12)
_ 4 ðh4 h6 Þ ¼ m _ 1 ðh1 h14 Þ m
(13)
For the turbine, the isentropic efficiency of the turbine can be expressed as
h3 h5 h3 h5s
(22)
In the pump, the isentropic efficiencies is
hP ¼
h13s h12 h13 h12
(23)
The works input by the pump is
_ 12 ðh13 h12 Þ WP ¼ m
In the recuperator 1, the energy balance equation is
(21)
In the condenser, the energy balance equation is
_ 10 h10 þ m _ 11 h11 m _ 12 h12 QC ¼ m
The ammonia mass balance equation is
(24)
Previous researchers in this field have defined the system efficiency as the ratio of the power output to the total solar energy input [18] to evaluate the overall system performance. This is fairly advisable to evaluate the instantaneous performance of the solardriven power cycle at a given time of the day. The instantaneous efficiency is defined as:
(14)
hinstant ¼
The power output of ammoniaewater turbine is given by:
_ 3 ðh3 h5 Þ WT ¼ m
(15)
In the mixed point, the mass and energy balance equation are
_ 5 x5 þ m _ 7 x7 ¼ m _ 8 x8 m
(16)
_ 7 h7 ¼ m _ 8 h8 _ 5 h5 þ m m
(17)
In the recuperator 2, the energy balance equation is
Economizer
Evaporator
Thermal oil Tga
T2
Taw
Ammonia-water ΔT
Pinch point
T1
Q Fig. 2. Thermal oil/ammoniaewater temperature profile.
Wnet Qu
(25)
However, when determining the system performance over a period of time or a whole day, such assessment index suffers from intrinsic limitations. On one hand, the useful heat gain Qu varies greatly with the radiation intensity, reaching its peak in midday and dropping sharply toward zero when the sun sets at around 18:00. Thus the WneteQu ratio seems less demonstrative in the late afternoon as it is in the morning. On the other hand, for the system equipped with a thermal storage tank, the power generation could be sustained long after sunset. Then the instantaneous efficiency would be unable to evaluate the system performance in the evening or at night. Therefore, we introduce an alternative to demonstrate the whole-day performance of the system. A modified system efficiency based on WneteQu ratio is defined to replace instantaneous efficiency by integrating the net power output and Qu over a period of time, which is expressed as follows:
Zt2
Ts1
Ts2
(19)
The ammonia mass balance equation is
_ 10 ¼ m
_ 3þm _4 ¼ m _2 m
T
In the separator 2, the mass balance equation is
(9)
In the separator 1, the mass balance equation is
hT ¼
(18)
The mass flow rate of saturated vapor separated by the separator 2 is
Energy balance for the economizer is
_3 ¼ m
_ 14 ðh14 h13 Þ ¼ m _ 8 ðh8 h9 Þ m
411
Wnet ðtÞdt
hsys ¼
t1
(26)
Zt2 Qu ðtÞdt t1
4. Methodology for parametric optimization In order to improve the utilization efficiency of solar energy, it is necessary to optimize the performance of the solar-driven Kalina cycle. The genetic algorithm is used to achieve the parameter optimization with the modified system efficiency as objective function in the present study.
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Firstly introduced by John Holland [19], the genetic algorithm is based on the theory of the natural selection in the biological genetic progress which was developed by Charles Darwin. The GA (Genetic Algorithm) considers every parameter as a gene as well as a solution as a chromosome by encoding them as binary numbers. Different combinations of genes make up a population of variable chromosome-like structure. Before the GA, a group of chromosomes are given, called the original population. The better approximations in the original population generates a new generation and the better approximations to potential results are selected as the new population. Then the new population continues to generate next generation and stops when the population converges to the optimal result. In the GA, the fitness value is assessed by the fitness function. Bigger fitness value corresponds to better adaptability of the chromosome-like structure. Fig. 3 shows a basic flow chart of genetic algorithm. In this optimization, the modified system efficiency is selected as the fitness function. The GA encodes a potential solution to a specific domain problem on a simple chromosome-like data structure, where genes are parameters of the problem to be solved. In the present study, the float-point coding is used to perform parameter optimization for the Kalina cycle.
The operators of the GA consist of selection, crossover and mutation. First, the selection operator selects parents to generate the children of solutions. When chosen to generate the next generation, the parents are conducted by crossover operator under a probability. In the process of the optimization, mutation is a nonignorable operator because only selection and crossover operators producing new solutions can tend to converge rapidly and lose some potential solutions. In the solar-driven Kalina cycle, the rankbased model is used as the selection operator, and the simple arithmetic crossover is applied to this optimization problem due to very simple operation. In addition, random mutation is adopted, which is achieved by selecting individuals from the range of the parameter according to mutation probability. 5. Results and discussion In the present study, the compound parabolic collector is assumed to be located in Xi’an (34.27N, 108.95E) and mounted on a horizontal eastewest axis and oriented with its aperture plane sloping at an angle of 10 . The heat collected at the absorber surface is transferred to thermal oil through two tubes with an outer diameter of 0.018 m and an inner diameter of 0.014 m attached to the bottom side. June 21st is chosen as a typical day to simulate the whole system. Thermodynamic properties of the ammoniaewater mixture were calculated by a convenient semi-empirical method, which combined the Gibbs free energy method for single phase [20] and empirical correlations for phase equilibrium [21]; the differences between calculated data and experimental data of the bubble and dew point temperatures were less than 0.3% with good agreement [22]. The conditions of simulation for the solar-driven Kalina cycle are summarized in Table 1. Table 2 lists the thermodynamic parameters of each node in the system, and Table 3 shows the results of thermodynamic simulation for the solar-driven Kalina cycle at 14:00 pm. Fig. 4 shows the variation of the thermal oil temperature in the thermal storage tank and net power output of the system, along with the useful heat gain and collector outlet temperature in 24 h on a daily basis. It can be seen that from 6:00 to 18:00, due to the useful heat gain from solar radiation, the collector outlet temperature is higher than the tank thermal oil temperature. The useful heat gain increases from 6:00 to reach the maximum at 12:00 then begins to decrease until 18:00. With the radiation of the useful heat
Table 1 Conditions of simulation for the solar-driven Kalina cycle. Environment temperature Environment pressure CPC concentration ratio Width of CPC absorber plane Length of CPC absorber plane Transmissivity of the cover Reflectivity of concentrator Absorptivity of absorber surface Number of CPC arrays Specific heat capacity of thermal oil Diameter of cylindrical thermal oil storage tank Height of cylindrical thermal oil storage tank Number of thermal oil storage tank Turbine inlet pressure Turbine inlet temperature Turbine isentropic efficiency Minimum quality of turbine exhaust Ammonia mass fraction of basic solution Pump isentropic efficiency Pinch point temperature difference Fig. 3. Flow chart of genetic algorithm.
20.00 C 0.10135 Mpa 10 0.06 m 2.00 m 0.89 0.87 0.94 600 2.8 kJ kg1 K1 1.5 m 1.8 m 4 18 bar 106 C 80.00% 0.88 0.68 70.00% 6.0 C
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
600 500
State T/ C
p/bar
Quality h/kJ kg1
_ s/kJ kg1 K1 m/kg s1 x
400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 s1 s2 c1 c2
18.000 18.000 18.000 18.000 6.167 18.000 6.167 6.167 6.167 6.167 6.167 6.167 18.000 18.000 e e e e
0.000 0.507 1.000 0.000 0.962 0.000 0.035 0.504 0.484 1.000 0.000 0.000 0.000 0.000 e e e e
0.586 3.060 4.744 1.326 4.843 0.995 1.000 2.952 2.821 4.991 0.788 0.246 0.248 0.396 e e e e
300
13.7965 895.403 1520.2 252.056 1384.69 131.092 131.092 767.06 722.091 1432.18 57.659 92.9248 90.7702 45.8012 e e e e
0.1643 0.1643 0.0834 0.0809 0.0834 0.0809 0.0809 0.1643 0.1643 0.0795 0.0848 0.1643 0.1643 0.1643 0.9000 0.9000 15.000 15.000
0.6800 0.6800 0.9568 0.3949 0.9568 0.3949 0.3949 0.6800 0.6800 0.9808 0.3982 0.6800 0.6800 0.6800 e e e e
gain, the collector outlet temperature also increases to its peak after 12:00. The sufficient solar energy is stored by the thermal oil tank, so the thermal oil temperature lags behind the collector outlet temperature to reach its maximum value at about 15:00. Then the tank thermal oil temperature decreases as the useful heat gain decreases sharply. As the thermal oil is used to heat the ammoniae water mixture in the vapor generator for the Kalina cycle, the net power output undergoes almost the same variation with the thermal oil tank temperature. Thus, the purpose of the storage tank is fulfilled by taking care of the short term mismatch between supply and demand of energy over a day. Noted that the tank temperature fluctuates by about 15 C. The magnitude of this fluctuation primarily depends on the volume of thermal oil in the tank. If the volume of the thermal oil was increased, the fluctuation of the tank temperature would be weakened. On a given time of the day, the parametric analysis is achieved to evaluate the effects of some key parameters, namely, turbine inlet temperature, turbine inlet pressure and the basic solution ammonia fraction, on the system performance, respectively. In the parametric analysis, when one parameter varies, the other parameters are kept constant as those in Table 1. Fig. 5 shows the effect of turbine inlet pressure on the net power output in 24 h on a given day. Due to the thermal heat storage tank, the solar-powered Kalina cycle can operate over a whole day (day and night). It can been seen that the net power output decreases to its minimum at around 6:00 due to no useful heat gain at night, then it increases with the increasing useful heat gain and reaches to its maximum at about 15:00. As the turbine inlet pressure increases, the net power output increases firstly, reaches to its peak and then declines. It is known that the enthalpy drop across the turbine increases with the increasing turbine inlet pressure, thus the turbine power output increases. By subtracting pump input from the turbine power output, the net power output increases.
Qu
TT = 106
160
xbasic= 0.68
Tfo Qu, Wnet /kW
47.81 106.00 106.00 106.00 64.95 79.67 68.20 67.28 63.67 63.67 63.67 25.00 25.30 35.00 122.48 65.00 122.48 131.91
200
PT = 18bar
200
120
Tl 80
100
40
Wnet 0
0 0
2
4
6
8
10
12
14
16
18
20
22
Time /h Fig. 4. The variation of key parameters for the solar-powered Kalina cycle in 24 h over a whole day.
This is why the net power output increases at first. But the enthalpy gains from an increasing turbine inlet pressure do not make up for a decrease in mass flow rate of ammoniaewater mixture across the turbine, since the vapor flow rate of ammoniaewater mixture generated in vapor generator decreases with the increasing turbine inlet pressure, thus the net power output decreases afterward. Fig. 6 shows the variation of the modified system efficiency based on WneteQu ratio with the increasing turbine inlet pressure. It indicates that there is an optimal value of turbine inlet pressure to maximize the modified system efficiency based on WneteQu ratio under the given conditions. It can be observed from Fig. 7 that as turbine inlet temperature increases, the net power output remains nearly unchanged. It is because that the increasing turbine inlet temperature results in a decrease in mass flow rate of ammoniaewater mixture generated in vapor generator, but the enthalpy difference across ammoniae water turbine increases due to the increasing turbine inlet temperature. The two factors have combined to counterbalance the influence of one another, resulting in an unchanged net power output. It can also be seen from Fig. 8 that as turbine inlet temperature increases, the modified system efficiency increases
Table 3 Performance of the solar-driven Kalina cycle at 14:00 pm. Useful heat gain from solar collector Heat input in vapor generator Turbine power Pump power Condenser heat rejection Net power output Thermal efficiency of the power cycle System instantaneous efficiency
Tl, Tfo /
Table 2 Results of simulation for the solar-driven Kalina cycle.
413
396.21 kW 144.85 kW 11.30 kW 0.35 kW 133.97 kW 10.94 kW 7.55% 2.76% Fig. 5. Effect of turbine inlet pressure on the net power output.
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J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415 7 .5
7.20
TT = 106 xbasic = 0.68
7.15
ηsys /%
ηsys /%
7 .0
PT = 18bar
7.10
xbasic = 0.68
6 .5
7.05
6 .0
7.00
14
16
18
20
22
24
26
PT /bar
98
100
102
104
106
108
TT /
Fig. 6. Effect of turbine inlet pressure on the modified system efficiency based on WneteQu ratio.
Fig. 8. Effect of turbine inlet temperature on the modified system efficiency based on WneteQu ratio.
slightly. It has little contribution to an increase of the modified system efficiency. Fig. 9 shows the effect of basic solution ammonia fraction on the net power output over a whole day. It also reveals that the net power output lies in minimum at around 6:00 and reaches to maximum at about 15:00 over a whole day. As basic solution ammonia fraction increases, the net power output increases firstly, reaches its peak at about 80% and then decreases. Since the specific heat capacity of ammonia is smaller than that of water, the vapor flow rate of ammoniaewater mixture generated in vapor generator increases with the increasing ammonia fraction of ammoniaewater mixture. This also leads to an increase in mass flow rate across the ammoniaewater turbine, resulting in an increase in turbine power output. This is why the net power output increases at first. In addition, the increasing basic solution ammonia fraction makes turbine inlet ammonia fraction increase, resulting in a decrease in enthalpy difference across ammoniaewater turbine. The increasing mass flow rate does not make up for a decrease in enthalpy
difference across ammoniaewater turbine, thus the net power output decreases afterward. As shown in Fig. 10, it is also seen that as the basic solution ammonia fraction increases, the modified system efficiency increases firstly, reaches to its peak and then declines. There is an optimal value of basic solution ammonia fraction to maximize the modified system efficiency based on WneteQu ratio under the given conditions. Through parameter analysis above, turbine inlet pressure, turbine inlet temperature and basic solution ammonia fraction can influence the system performance, so we use GA to achieve the parametric optimization. The selected thermodynamic parameters, the ranges of the parameters, operation parameters of GA and optimization results are listed in Table 4. The optimal modified system efficiency could reach 8.54% under the given conditions. Thermo-economic analysis and optimization will be carried out in the coming research, because thermodynamic analysis and optimization can only evaluate the system performance from the
Fig. 7. Effect of turbine inlet temperature on the net power output.
Fig. 9. Effect of basic solution ammonia fraction on the net power output.
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
(3) An optimal turbine inlet pressure can be achieved in a given condition, which could lead to the maximum net power output and maximum system efficiency. (4) The net power output and the system efficiency are less sensitive to a change in the turbine inlet temperature. (5) There is an optimal value of basic solution ammonia fraction to maximize the modified system efficiency based on WneteQu ratio under the given conditions. (6) Through parametric optimization, the optimized modified system efficiency is 8.54% under the given conditions.
8
7
6
ηsys /%
415
TT = 106 PT = 18bar 5
Acknowledgements 4
3 0.4
0.5
0.6
0.7
0.8
0.9
1.0
xbasic Fig. 10. Effect of basic solution ammonia fraction on the modified system efficiency based on WneteQu ratio.
Table 4 Data of the parameter optimization. Population size Crossover probability Mutation probability Stop generation The range of turbine inlet pressure The range of turbine inlet temperature The range of basic solution ammoniaewater concentration The optimal turbine inlet pressure The optimal turbine inlet temperature The optimal basic solution ammoniaewater concentration The optimal modified system efficiency
20 0.95 0.02 100 14e30 bar 271.15e281.15 K 0.5e0.9 25.73 bar 380.96 K 0.898 8.54%
viewpoint of thermodynamics, not reflect the cost of performance improvement financially. In addition, experimental study is required to validate the feasibility of system.
6. Conclusions In the present study, a solar-driven Kalina cycle is investigated based on the thermodynamic analysis. A thermal storage tank is added to this system to store the collected solar energy, and a modified system efficiency is defined to assess the cycle performance over a long period. By establishing the mathematical model, we have obtained a better understanding of the system performance by examining the effects of some key thermodynamic parameters. In addition, the system is optimized with the modified system efficiency as the objective function by means of GA. The main conclusions drawn from the study are summarized as follows: (1) By introducing a thermal storage tank into the system, the solar-driven Kalina cycle can achieve a continuous and stable operation over a long time. (2) The modified system efficiency based on WneteQu ratio by integrating both power and useful heat gain over a period of time is able to provide a more accurate evaluation for the system performance.
The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant No. 51106117), the Natural Science Foundation of Shaanxi Province (Grant No. 2011JQ7002) and the Fundamental Research Funds for the Central Universities. References [1] A.I. Kalina, Combined cycle system with novel bottoming cycle, ASME J. Eng. Gas Turb. Power 106 (1984) 737e742. [2] Y.M. El-Sayed, M. Tribus, Theoretical comparison of Rankine and Kalina cycles, ASME Adv. Energy Syst. Div. (1985) 97e102. [3] C.H. Marston, Parametric analysis of the Kalina cycle, ASME J. Eng. Gas Turb. Power 112 (1990) 107e116. [4] E.D. Rogdakis, Thermodynamic analysis, parametric study and optimum operation of the Kalina cycle, Int. J. Energy Res. 20 (1994) 359e370. [5] P.K. Nag, A. Gupta, Exergy analysis of the Kalina cycle, Appl. Therm. Eng. 18 (1998) 427e439. [6] M. D. Mirolli. The Kalina cycle for cement kiln waste heat recovery power plants, IEEE cement industry technical conference record (2005) 330e336. [7] M. D. Mirolli, Ammonia-water based thermal conversion technology: applications in waste heat recovery for the cement industry, IEEE cement industry technical conference record (2007) 234e241. [8] C.H. Marston, Gas turbine bottoming cycles: triple-pressure steam versus Kalina, ASME J. Eng. Gas Turb. Power 117 (1995) 10e15. [9] M. Jonsson, J. Yan, Exergy and pinch analysis of diesel engine bottoming cycles with ammonia-water mixtures as working Fluid, J. Appl. Thermodyn. 3 (2000) 57e71. [10] M. Jonsson, J. Yan, Ammonia-water bottoming cycles: a comparison between gas engines and gas diesel engines as prime movers, Energy 26 (2001) 31e44. [11] P. Bombarda, C.M. Invernizzi, C. Pietra, Heat recovery from Diesel engines: a thermodynamic comparison between Kalina and ORC cycles, Appl. Therm. Eng. 30 (2010) 212e219. [12] H.D. Madhawa Hettiarachchi, M. Golubovic, W.M. Worek, Y. Lkegami, The performance of the kalina cycle system 11 (KCS-11) with low-temperature heat sources, ASME J. Energy Resour. 129 (2007) 243e247. [13] Nasruddin, R. Usvika, M. Rifaldi, A. Noor, Energy and exergy analysis of kalina cycle system (KCS) 34 with mass fraction ammonia-water mixture variation, J. Mech. Sci. Technol. 23 (2009) 1871e1876. [14] O. Arslan, Exergoeconomic evaluation of electricity generation by the medium temperature geothermal resources, using a Kalina cycle: simav case study, Int. J. Therm. Sci. 49 (2010) 1866e1873. [15] P.A. Lolos, E.D. Rogdakisa, A Kalina power cycle driven by renewable energy sources, Energy 34 (2009) 457e464. [16] S.P. Sukhatme, Solar Energy-principles of Thermal Collection and Storage, Tata McGraw-Hill Publishing Company Limited, India, 1984. [17] J.F. Wang, Y.P. Dai, L. Gao, S.L. Ma, A new combined cooling, heating and power system driven by solar energy, Renew Energy 34 (2009) 2780e2788. [18] Y. Chen, Dynamic simulation of a solar-driven carbon dioxide transcritical power system for small scale combined heat and power production, Sol. Energy 84 (2010) 1103e1110. [19] J. Holland, Adaptation in Nature and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, MIT Press, Massachusetts, 1992. [20] B. Ziegler, C. Trepp, Equation of state for ammonia-water mixtures, Int. J. Refrig. 7 (1984) 101e116. [21] Y.M. El-Sayed, M. Tribus, Thermodynamic properties of water-ammonia mixtures theoretical implementation for use in power cycles analysis, ASME Adv. Energy Syst. Div. 1 (1985) 89e95. [22] F. Xu, D.Y. Goswami, Thermodynamic properties of ammonia water mixtures for use in power-cycle applications, Energy 24 (1999) 525e536.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Parametric analysis and optimization of a Kalina cycle driven by solar energy Jiangfeng Wang a, *, Zhequan Yan a, Enmin Zhou b, Yiping Dai a a b
Institute of Turbomachinery, School of Energy and Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, China China Aerodynamics Research and Development Center, Mianyang 621000, China
h i g h l i g h t s < A thermal storage system is introduced to provide stable power output. < A modified system efficiency is defined to evaluate the system performance. < The effects of thermodynamic parameters on the performance are examined. < Parametric optimization is conducted to find the optimum performance by GA.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 April 2012 Accepted 2 September 2012 Available online 10 September 2012
A solar-driven Kalina cycle is examined to utilize solar energy effectively due to using ammoniaewater’s varied temperature vaporizing characteristic. In order to ensure a continuous and stable operation for the system, a thermal storage system is introduced to store the collected solar energy and provide stable power when solar radiation is insufficient. A mathematical model is developed to simulate the solar-driven Kalina cycle under steady-state conditions, and a modified system efficiency is defined to evaluate the system performance over a period of time. A parametric analysis is conducted to examine the effects of some key thermodynamic parameters on the system performance. The solar-driven Kalina cycle is also optimized with the modified system efficiency as an objective function by means of genetic algorithm under the given conditions. Results indicate that there exists an optimal turbine inlet pressure under given conditions to maximize the net power output and the modified system efficiency. The net power output and the modified system efficiency are less sensitive to a change in the turbine inlet temperature. An optimal basic solution ammonia fraction can be identified that yields maximum net power output and modified system efficiency. The optimized modified system efficiency is 8.54% under the given conditions. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Kalina cycle Solar energy Sensitivity analysis Optimization
1. Introduction The Kalina cycle, which utilizes ammoniaewater as its working fluid, was originally conceived by Alexander Kalina [1]. The ammoniaewater has the advantage of variable-temperature evaporation and condensation at subcritical pressures in contrast to a pure fluid that evaporates and condenses at constant temperature, and could provide a better performance due to better thermal match achieved in the condenser and evaporator. Kalina cycle uses unique DCSS (Distiller Condenser Sub-System) to achieve ammoniaewater condensation process at low condensing pressure by changing the ammoniaewater mass fraction. Due to the superior to steam power cycle, many studies have been found to investigate Kalina cycle. El-Sayed and Tribus [2] * Corresponding author. Tel./fax: þ86 029 82668704. E-mail address: [email protected] (J. Wang). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.002
made a theoretical comparison between the Kalina cycle and Rankine cycle. The configurations developed by them were very much complicated because several heat exchangers had more than two steams. Marston [3] considered the parametric analysis of the Kalina cycle. He developed a method of balancing the Kalina cycle and identified the key parameters for optimizing the Kalina cycle. Rogdakis [4] developed correlations describing the optimum operation of the Kalina cycle. In addition, Nag and Gupta [5] studied exergy analysis of the Kalina cycle. Because of the advantage of recovering sensible heat source, Kalina cycle is generally used as a bottoming cycle to enhance energy conversion efficiency by recovering waste heat from gas turbine, diesel engine or industrial production such as cement line [6,7]. Marston [8] compared the performance of Kalina cycle with a triple-pressure steam cycle as the bottoming sections of a gas turbine combined cycle power plant. Jonsson et al. [9,10] examined the Kalina cycle as the bottoming cycle with gas engines and gas
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
Nomenclature A b C cp D F0 FR h
I k L _ m N p Q R s S T U V
area, m2 width of absorber, m concentration ratio of CPC specific heat, kJ kg1 K1 diameter, m collector efficiency factor heat removal factor enthalpy, kJ kg1 hourly radiation, W m2 heat transferring coefficient, W m2 K1 length, m mass flow rate, kg s1 number of tubes pressure, bar heat rate, kW tilt factor for radiation entropy, kJ kg1 K1 incident solar flux, W m2 temperature, C loss coefficient, W m2 k1; heat transfer coefficient, W m2 k1 volume, m3
diesel engines as prime movers to recover waste heat available from the exhaust gas. Bombarda et al. [11] conducted a thermodynamic comparison between Kalina cycle and ORC as the bottoming cycle to recover waste heat from diesel engines. Results showed the net electric power of Kalina cycle was a little larger than that of ORC under the reasonable design parameters and the same logarithmic mean temperature difference in the heat recovery exchanger. With the rapid industrialization and social growth, the demand for energy is growing faster. Conventional sources, such as coal, oil and natural gas, have limited reserves that are expected not to last for an extended period. Renewable energy resources are expected to play an increasing role in energy consumption due to these potentials in reducing fossil fuel consumption and alleviating environmental problems. So, Kalina cycle is also used to utilize renewable energy resources, such as geothermal heat sources. Madhawa Hettiarachchi et al. [12] evaluated the performance of the Kalina cycle system for low temperature geothermal heat sources, compared it with an organic Rankine cycle, and examined the effect of the ammonia fraction and turbine inlet pressure on the cycle performance in detail. Nasruddin et al. [13] conducted the energy and exergy analysis of kalina cycle utilizing lower temperature geothermal resources, and optimized the Kalina cycle on the mass fraction of working fluid and the turbine output pressure. Arslan [14] investigated Kalina cycle to generate electricity generation from Simav geothermal field. He determined the optimum operating conditions for the KCS-34 plant on the basis of the exergetic and life-cycle-cost concepts. Due to limitation of region for geothermal resources, some researchers paid attention to use solar energy, which is available everywhere, to drive Kalina cycle enabling the distributed power generation. Lolos [15] investigated a Kalina cycle using solar energy to produce power. He used flatplate solar collectors to heat the evaporator to make ammoniae water be partially vaporized and used an external heat source to superheat the ammoniaewater vapor before entering a turbine. In this study, a Kalina cycle driven by solar energy mainly as one heat source is investigated based on the thermodynamic analysis. A thermal storage system is added to store the collected solar energy
W x
409
power, kW; Width, m ammonia mass fraction
Greek letters a absorptivity of the absorber surface h efficiency r reflectivity of the concentrator surface; density, kg m3 s transmissivity of the cover Subscripts 0 environment b beam C condenser d diffuse fi inlet of solar collector fo outlet of solar collector i inlet l uniform; loss lo loss P pump s isentropic process sys system T turbine u useful
and to provide continuous power output when solar radiation is insufficient. A mathematical model is developed to simulate the solar-driven Kalina cycle under steady-state conditions, and a modified system efficiency is defined to evaluate the cycle performance over a period of time. A parametric analysis is conducted to examine the effects of some key thermodynamic parameters on the system performance. The solar-driven Kalina cycle is also optimized with the modified system efficiency as an objective function by means of genetic algorithm (GA) under the given conditions. 2. System description Fig. 1 illustrates a schematic diagram of the Kalina cycle driven by solar energy. The overall system is divided into two subsystems: the solar energy collecting and storing subsystem and the Kalina cycle. The solar energy collecting and storing subsystem consists of solar collectors, a thermal storage tank and an auxiliary heater. Compound parabolic collector (CPC) is used to collect the solar radiation to supply heat to the overall system because it can achieve higher concentration for large acceptance angle and requires only intermittent sun-tracking. In addition, the CPC can achieve a higher temperature than flat-plate solar collector. The thermal storage tank with thermal oil as working fluid is used as the heat source when solar radiation is not sufficient. The auxiliary heater is installed as the backup energy source to boost the temperature of thermal storage tank to the allowable temperature when the temperature of thermal storage tank drops below the allowable temperature. The Kalina cycle consists of two separators, a vapor evaporator, two recuperators, an air condenser, a feed pump, a turbine-generator and a throttle valve. The ammoniaewater mixture is heated in the vapor evaporator where it is partially vaporized by absorbing heat from thermal storage system. The twophase ammoniaewater mixture is sent to separator 1 where the ammoniaewater solution is separated into weak liquid solution and ammonia-rich vapor. The ammonia-rich vapor is expended to a low pressure through a turbine to drive a generator to generate
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3 Solar Radiation
c2
Auxiliary Heater
Turbine
Separator 1
2
s1
Generator
5 Recuperator 1
4
CPC
6
7 8
Valve Vapor Generator
c1
Thermal Storage Tank
s2
Recuperator 2
14
10
1 13
9 Separator 2
Pump
11 Condenser
12
Fig. 1. Schematic diagram of the Kalina cycle driven by solar energy.
electricity. The weak liquid solution, after recuperating some of the heat in recuperator 1, is throttled down to a low pressure and then mixed with the ammonia-rich solution coming from the turbine to form the ammoniaewater basic solution. After cooled down in recuperator 2, the ammoniaewater basic solution is sent to separator 2 separating the phases and condensed to ammoniaewater liquid in the condenser by cooling air. The ammoniaewater liquid is pumped to vapor evaporator again after preheated through the recuperators.
The Kalina cycle driven by solar energy is modeled based on the mass, momentum and energy conservations. To simplify the theoretical model, some assumptions are made as follows: (1) The system reaches a steady state. (2) The pressure drops in compound parabolic collector, storage tank, auxiliary heater, vapor generator, separators, recuperators, condenser, and the connection tubes are neglected. (3) A well-mixed situation is assumed in the thermal storage tank where a uniform temperature varies only with time [16]. (4) There is no heat transfer with the environment for the Kalina cycle. (5) The vapor streams from the separators are saturated vapor and the liquid streams from the separators are saturated liquid. (6) The stream at the condenser outlet is saturated liquid, and the flows across the throttle valve are isenthalpic. (7) The pump and the turbine have a given isentropic efficiency, respectively. A CPC can accept both beam and diffuse radiation because of its large acceptance angle. The beam radiation flux falling on the aperture plane is IbRb, while the diffuse radiation flux within the acceptance angle is given by (Id/C). Thus, the total effective flux absorbed at the absorber surface is expressed as [16],
I Ib Rb þ d sre a C
The useful heat gain rate can be given by [16],
(1)
(2)
where
FR ¼
0 _ p mc F bUlo L 1 exp _ p bUlo L mc
(3)
and
1 1 b ¼ Ulo þ 0 F Ulo N pDi k
3. Mathematical model and performance criteria
S ¼
U Qu ¼ FR WL S lo Tfi T0 C
(4)
An insulated thermal oil storage tank is used to receive energy from an array of collectors and discharge energy to a load in the Kalina cycle. With a well-mixed model of the storage tank, the temperature of the thermal oil remains a uniform temperature Tl, which is defined as the thermal oil temperature in the tank after two streams from solar collector and vapor generator are wellmixed. An energy balance applied to thermal storage tank is expressed as
rVcp
dTl ¼ Qu Qload UAðTl T0 Þ dt
(5)
Furthermore, Qu and Qload, which represent the useful gain from the solar collectors and the energy discharged to the Kalina cycle, respectively, can be calculated as
_ oil;1 cp Tfo Tl Qu ¼ m
(6)
_ oil;2 cp ðTl Ti Þ Qload ¼ m
(7)
The detailed descriptions about the mathematical model of the compound parabolic collector and the thermal storage tank are given in Ref. [17]. In the vapor generator, due to using an ammoniaewater mixture, the more volatile ammonia tends to vaporize first at a lower temperature than a pure water. The temperature of the remaining two-phase liquid rises as the ammonia concentration decreases. Thus, a better match between heat ejection of hot oil
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
from thermal storage tank and heat absorption of ammoniaewater is performed using ammoniaewater’s characteristic of varied vaporizing temperature during the vaporizing process, as shown in Fig. 2 with two heat exchanging sections, namely, an economizer and an evaporator. Energy balance for the evaporator is
_ oil;2 hs1 hga ¼ m _ 1 ðh2 haw Þ m
(8)
_ oil;2 hga hs2 ¼ m _ 1 ðhaw h1 Þ m
_ 10 þ m _ 11 ¼ m _9 m
(10)
_ 11 x11 þ m _ 10 x10 ¼ m _ 9 x9 m
x9 x11 _ $m x10 x11 9
(20)
_ 3 x3 þ m _ 4 x4 ¼ m _ 2 x2 m
(11)
The mass flow rate of saturated vapor separated by the separator 1 is
x2 x4 _ $m x3 x4 2
(12)
_ 4 ðh4 h6 Þ ¼ m _ 1 ðh1 h14 Þ m
(13)
For the turbine, the isentropic efficiency of the turbine can be expressed as
h3 h5 h3 h5s
(22)
In the pump, the isentropic efficiencies is
hP ¼
h13s h12 h13 h12
(23)
The works input by the pump is
_ 12 ðh13 h12 Þ WP ¼ m
In the recuperator 1, the energy balance equation is
(21)
In the condenser, the energy balance equation is
_ 10 h10 þ m _ 11 h11 m _ 12 h12 QC ¼ m
The ammonia mass balance equation is
(24)
Previous researchers in this field have defined the system efficiency as the ratio of the power output to the total solar energy input [18] to evaluate the overall system performance. This is fairly advisable to evaluate the instantaneous performance of the solardriven power cycle at a given time of the day. The instantaneous efficiency is defined as:
(14)
hinstant ¼
The power output of ammoniaewater turbine is given by:
_ 3 ðh3 h5 Þ WT ¼ m
(15)
In the mixed point, the mass and energy balance equation are
_ 5 x5 þ m _ 7 x7 ¼ m _ 8 x8 m
(16)
_ 7 h7 ¼ m _ 8 h8 _ 5 h5 þ m m
(17)
In the recuperator 2, the energy balance equation is
Economizer
Evaporator
Thermal oil Tga
T2
Taw
Ammonia-water ΔT
Pinch point
T1
Q Fig. 2. Thermal oil/ammoniaewater temperature profile.
Wnet Qu
(25)
However, when determining the system performance over a period of time or a whole day, such assessment index suffers from intrinsic limitations. On one hand, the useful heat gain Qu varies greatly with the radiation intensity, reaching its peak in midday and dropping sharply toward zero when the sun sets at around 18:00. Thus the WneteQu ratio seems less demonstrative in the late afternoon as it is in the morning. On the other hand, for the system equipped with a thermal storage tank, the power generation could be sustained long after sunset. Then the instantaneous efficiency would be unable to evaluate the system performance in the evening or at night. Therefore, we introduce an alternative to demonstrate the whole-day performance of the system. A modified system efficiency based on WneteQu ratio is defined to replace instantaneous efficiency by integrating the net power output and Qu over a period of time, which is expressed as follows:
Zt2
Ts1
Ts2
(19)
The ammonia mass balance equation is
_ 10 ¼ m
_ 3þm _4 ¼ m _2 m
T
In the separator 2, the mass balance equation is
(9)
In the separator 1, the mass balance equation is
hT ¼
(18)
The mass flow rate of saturated vapor separated by the separator 2 is
Energy balance for the economizer is
_3 ¼ m
_ 14 ðh14 h13 Þ ¼ m _ 8 ðh8 h9 Þ m
411
Wnet ðtÞdt
hsys ¼
t1
(26)
Zt2 Qu ðtÞdt t1
4. Methodology for parametric optimization In order to improve the utilization efficiency of solar energy, it is necessary to optimize the performance of the solar-driven Kalina cycle. The genetic algorithm is used to achieve the parameter optimization with the modified system efficiency as objective function in the present study.
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J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
Firstly introduced by John Holland [19], the genetic algorithm is based on the theory of the natural selection in the biological genetic progress which was developed by Charles Darwin. The GA (Genetic Algorithm) considers every parameter as a gene as well as a solution as a chromosome by encoding them as binary numbers. Different combinations of genes make up a population of variable chromosome-like structure. Before the GA, a group of chromosomes are given, called the original population. The better approximations in the original population generates a new generation and the better approximations to potential results are selected as the new population. Then the new population continues to generate next generation and stops when the population converges to the optimal result. In the GA, the fitness value is assessed by the fitness function. Bigger fitness value corresponds to better adaptability of the chromosome-like structure. Fig. 3 shows a basic flow chart of genetic algorithm. In this optimization, the modified system efficiency is selected as the fitness function. The GA encodes a potential solution to a specific domain problem on a simple chromosome-like data structure, where genes are parameters of the problem to be solved. In the present study, the float-point coding is used to perform parameter optimization for the Kalina cycle.
The operators of the GA consist of selection, crossover and mutation. First, the selection operator selects parents to generate the children of solutions. When chosen to generate the next generation, the parents are conducted by crossover operator under a probability. In the process of the optimization, mutation is a nonignorable operator because only selection and crossover operators producing new solutions can tend to converge rapidly and lose some potential solutions. In the solar-driven Kalina cycle, the rankbased model is used as the selection operator, and the simple arithmetic crossover is applied to this optimization problem due to very simple operation. In addition, random mutation is adopted, which is achieved by selecting individuals from the range of the parameter according to mutation probability. 5. Results and discussion In the present study, the compound parabolic collector is assumed to be located in Xi’an (34.27N, 108.95E) and mounted on a horizontal eastewest axis and oriented with its aperture plane sloping at an angle of 10 . The heat collected at the absorber surface is transferred to thermal oil through two tubes with an outer diameter of 0.018 m and an inner diameter of 0.014 m attached to the bottom side. June 21st is chosen as a typical day to simulate the whole system. Thermodynamic properties of the ammoniaewater mixture were calculated by a convenient semi-empirical method, which combined the Gibbs free energy method for single phase [20] and empirical correlations for phase equilibrium [21]; the differences between calculated data and experimental data of the bubble and dew point temperatures were less than 0.3% with good agreement [22]. The conditions of simulation for the solar-driven Kalina cycle are summarized in Table 1. Table 2 lists the thermodynamic parameters of each node in the system, and Table 3 shows the results of thermodynamic simulation for the solar-driven Kalina cycle at 14:00 pm. Fig. 4 shows the variation of the thermal oil temperature in the thermal storage tank and net power output of the system, along with the useful heat gain and collector outlet temperature in 24 h on a daily basis. It can be seen that from 6:00 to 18:00, due to the useful heat gain from solar radiation, the collector outlet temperature is higher than the tank thermal oil temperature. The useful heat gain increases from 6:00 to reach the maximum at 12:00 then begins to decrease until 18:00. With the radiation of the useful heat
Table 1 Conditions of simulation for the solar-driven Kalina cycle. Environment temperature Environment pressure CPC concentration ratio Width of CPC absorber plane Length of CPC absorber plane Transmissivity of the cover Reflectivity of concentrator Absorptivity of absorber surface Number of CPC arrays Specific heat capacity of thermal oil Diameter of cylindrical thermal oil storage tank Height of cylindrical thermal oil storage tank Number of thermal oil storage tank Turbine inlet pressure Turbine inlet temperature Turbine isentropic efficiency Minimum quality of turbine exhaust Ammonia mass fraction of basic solution Pump isentropic efficiency Pinch point temperature difference Fig. 3. Flow chart of genetic algorithm.
20.00 C 0.10135 Mpa 10 0.06 m 2.00 m 0.89 0.87 0.94 600 2.8 kJ kg1 K1 1.5 m 1.8 m 4 18 bar 106 C 80.00% 0.88 0.68 70.00% 6.0 C
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
600 500
State T/ C
p/bar
Quality h/kJ kg1
_ s/kJ kg1 K1 m/kg s1 x
400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 s1 s2 c1 c2
18.000 18.000 18.000 18.000 6.167 18.000 6.167 6.167 6.167 6.167 6.167 6.167 18.000 18.000 e e e e
0.000 0.507 1.000 0.000 0.962 0.000 0.035 0.504 0.484 1.000 0.000 0.000 0.000 0.000 e e e e
0.586 3.060 4.744 1.326 4.843 0.995 1.000 2.952 2.821 4.991 0.788 0.246 0.248 0.396 e e e e
300
13.7965 895.403 1520.2 252.056 1384.69 131.092 131.092 767.06 722.091 1432.18 57.659 92.9248 90.7702 45.8012 e e e e
0.1643 0.1643 0.0834 0.0809 0.0834 0.0809 0.0809 0.1643 0.1643 0.0795 0.0848 0.1643 0.1643 0.1643 0.9000 0.9000 15.000 15.000
0.6800 0.6800 0.9568 0.3949 0.9568 0.3949 0.3949 0.6800 0.6800 0.9808 0.3982 0.6800 0.6800 0.6800 e e e e
gain, the collector outlet temperature also increases to its peak after 12:00. The sufficient solar energy is stored by the thermal oil tank, so the thermal oil temperature lags behind the collector outlet temperature to reach its maximum value at about 15:00. Then the tank thermal oil temperature decreases as the useful heat gain decreases sharply. As the thermal oil is used to heat the ammoniae water mixture in the vapor generator for the Kalina cycle, the net power output undergoes almost the same variation with the thermal oil tank temperature. Thus, the purpose of the storage tank is fulfilled by taking care of the short term mismatch between supply and demand of energy over a day. Noted that the tank temperature fluctuates by about 15 C. The magnitude of this fluctuation primarily depends on the volume of thermal oil in the tank. If the volume of the thermal oil was increased, the fluctuation of the tank temperature would be weakened. On a given time of the day, the parametric analysis is achieved to evaluate the effects of some key parameters, namely, turbine inlet temperature, turbine inlet pressure and the basic solution ammonia fraction, on the system performance, respectively. In the parametric analysis, when one parameter varies, the other parameters are kept constant as those in Table 1. Fig. 5 shows the effect of turbine inlet pressure on the net power output in 24 h on a given day. Due to the thermal heat storage tank, the solar-powered Kalina cycle can operate over a whole day (day and night). It can been seen that the net power output decreases to its minimum at around 6:00 due to no useful heat gain at night, then it increases with the increasing useful heat gain and reaches to its maximum at about 15:00. As the turbine inlet pressure increases, the net power output increases firstly, reaches to its peak and then declines. It is known that the enthalpy drop across the turbine increases with the increasing turbine inlet pressure, thus the turbine power output increases. By subtracting pump input from the turbine power output, the net power output increases.
Qu
TT = 106
160
xbasic= 0.68
Tfo Qu, Wnet /kW
47.81 106.00 106.00 106.00 64.95 79.67 68.20 67.28 63.67 63.67 63.67 25.00 25.30 35.00 122.48 65.00 122.48 131.91
200
PT = 18bar
200
120
Tl 80
100
40
Wnet 0
0 0
2
4
6
8
10
12
14
16
18
20
22
Time /h Fig. 4. The variation of key parameters for the solar-powered Kalina cycle in 24 h over a whole day.
This is why the net power output increases at first. But the enthalpy gains from an increasing turbine inlet pressure do not make up for a decrease in mass flow rate of ammoniaewater mixture across the turbine, since the vapor flow rate of ammoniaewater mixture generated in vapor generator decreases with the increasing turbine inlet pressure, thus the net power output decreases afterward. Fig. 6 shows the variation of the modified system efficiency based on WneteQu ratio with the increasing turbine inlet pressure. It indicates that there is an optimal value of turbine inlet pressure to maximize the modified system efficiency based on WneteQu ratio under the given conditions. It can be observed from Fig. 7 that as turbine inlet temperature increases, the net power output remains nearly unchanged. It is because that the increasing turbine inlet temperature results in a decrease in mass flow rate of ammoniaewater mixture generated in vapor generator, but the enthalpy difference across ammoniae water turbine increases due to the increasing turbine inlet temperature. The two factors have combined to counterbalance the influence of one another, resulting in an unchanged net power output. It can also be seen from Fig. 8 that as turbine inlet temperature increases, the modified system efficiency increases
Table 3 Performance of the solar-driven Kalina cycle at 14:00 pm. Useful heat gain from solar collector Heat input in vapor generator Turbine power Pump power Condenser heat rejection Net power output Thermal efficiency of the power cycle System instantaneous efficiency
Tl, Tfo /
Table 2 Results of simulation for the solar-driven Kalina cycle.
413
396.21 kW 144.85 kW 11.30 kW 0.35 kW 133.97 kW 10.94 kW 7.55% 2.76% Fig. 5. Effect of turbine inlet pressure on the net power output.
414
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415 7 .5
7.20
TT = 106 xbasic = 0.68
7.15
ηsys /%
ηsys /%
7 .0
PT = 18bar
7.10
xbasic = 0.68
6 .5
7.05
6 .0
7.00
14
16
18
20
22
24
26
PT /bar
98
100
102
104
106
108
TT /
Fig. 6. Effect of turbine inlet pressure on the modified system efficiency based on WneteQu ratio.
Fig. 8. Effect of turbine inlet temperature on the modified system efficiency based on WneteQu ratio.
slightly. It has little contribution to an increase of the modified system efficiency. Fig. 9 shows the effect of basic solution ammonia fraction on the net power output over a whole day. It also reveals that the net power output lies in minimum at around 6:00 and reaches to maximum at about 15:00 over a whole day. As basic solution ammonia fraction increases, the net power output increases firstly, reaches its peak at about 80% and then decreases. Since the specific heat capacity of ammonia is smaller than that of water, the vapor flow rate of ammoniaewater mixture generated in vapor generator increases with the increasing ammonia fraction of ammoniaewater mixture. This also leads to an increase in mass flow rate across the ammoniaewater turbine, resulting in an increase in turbine power output. This is why the net power output increases at first. In addition, the increasing basic solution ammonia fraction makes turbine inlet ammonia fraction increase, resulting in a decrease in enthalpy difference across ammoniaewater turbine. The increasing mass flow rate does not make up for a decrease in enthalpy
difference across ammoniaewater turbine, thus the net power output decreases afterward. As shown in Fig. 10, it is also seen that as the basic solution ammonia fraction increases, the modified system efficiency increases firstly, reaches to its peak and then declines. There is an optimal value of basic solution ammonia fraction to maximize the modified system efficiency based on WneteQu ratio under the given conditions. Through parameter analysis above, turbine inlet pressure, turbine inlet temperature and basic solution ammonia fraction can influence the system performance, so we use GA to achieve the parametric optimization. The selected thermodynamic parameters, the ranges of the parameters, operation parameters of GA and optimization results are listed in Table 4. The optimal modified system efficiency could reach 8.54% under the given conditions. Thermo-economic analysis and optimization will be carried out in the coming research, because thermodynamic analysis and optimization can only evaluate the system performance from the
Fig. 7. Effect of turbine inlet temperature on the net power output.
Fig. 9. Effect of basic solution ammonia fraction on the net power output.
J. Wang et al. / Applied Thermal Engineering 50 (2013) 408e415
(3) An optimal turbine inlet pressure can be achieved in a given condition, which could lead to the maximum net power output and maximum system efficiency. (4) The net power output and the system efficiency are less sensitive to a change in the turbine inlet temperature. (5) There is an optimal value of basic solution ammonia fraction to maximize the modified system efficiency based on WneteQu ratio under the given conditions. (6) Through parametric optimization, the optimized modified system efficiency is 8.54% under the given conditions.
8
7
6
ηsys /%
415
TT = 106 PT = 18bar 5
Acknowledgements 4
3 0.4
0.5
0.6
0.7
0.8
0.9
1.0
xbasic Fig. 10. Effect of basic solution ammonia fraction on the modified system efficiency based on WneteQu ratio.
Table 4 Data of the parameter optimization. Population size Crossover probability Mutation probability Stop generation The range of turbine inlet pressure The range of turbine inlet temperature The range of basic solution ammoniaewater concentration The optimal turbine inlet pressure The optimal turbine inlet temperature The optimal basic solution ammoniaewater concentration The optimal modified system efficiency
20 0.95 0.02 100 14e30 bar 271.15e281.15 K 0.5e0.9 25.73 bar 380.96 K 0.898 8.54%
viewpoint of thermodynamics, not reflect the cost of performance improvement financially. In addition, experimental study is required to validate the feasibility of system.
6. Conclusions In the present study, a solar-driven Kalina cycle is investigated based on the thermodynamic analysis. A thermal storage tank is added to this system to store the collected solar energy, and a modified system efficiency is defined to assess the cycle performance over a long period. By establishing the mathematical model, we have obtained a better understanding of the system performance by examining the effects of some key thermodynamic parameters. In addition, the system is optimized with the modified system efficiency as the objective function by means of GA. The main conclusions drawn from the study are summarized as follows: (1) By introducing a thermal storage tank into the system, the solar-driven Kalina cycle can achieve a continuous and stable operation over a long time. (2) The modified system efficiency based on WneteQu ratio by integrating both power and useful heat gain over a period of time is able to provide a more accurate evaluation for the system performance.
The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant No. 51106117), the Natural Science Foundation of Shaanxi Province (Grant No. 2011JQ7002) and the Fundamental Research Funds for the Central Universities. References [1] A.I. Kalina, Combined cycle system with novel bottoming cycle, ASME J. Eng. Gas Turb. Power 106 (1984) 737e742. [2] Y.M. El-Sayed, M. Tribus, Theoretical comparison of Rankine and Kalina cycles, ASME Adv. Energy Syst. Div. (1985) 97e102. [3] C.H. Marston, Parametric analysis of the Kalina cycle, ASME J. Eng. Gas Turb. Power 112 (1990) 107e116. [4] E.D. Rogdakis, Thermodynamic analysis, parametric study and optimum operation of the Kalina cycle, Int. J. Energy Res. 20 (1994) 359e370. [5] P.K. Nag, A. Gupta, Exergy analysis of the Kalina cycle, Appl. Therm. Eng. 18 (1998) 427e439. [6] M. D. Mirolli. The Kalina cycle for cement kiln waste heat recovery power plants, IEEE cement industry technical conference record (2005) 330e336. [7] M. D. Mirolli, Ammonia-water based thermal conversion technology: applications in waste heat recovery for the cement industry, IEEE cement industry technical conference record (2007) 234e241. [8] C.H. Marston, Gas turbine bottoming cycles: triple-pressure steam versus Kalina, ASME J. Eng. Gas Turb. Power 117 (1995) 10e15. [9] M. Jonsson, J. Yan, Exergy and pinch analysis of diesel engine bottoming cycles with ammonia-water mixtures as working Fluid, J. Appl. Thermodyn. 3 (2000) 57e71. [10] M. Jonsson, J. Yan, Ammonia-water bottoming cycles: a comparison between gas engines and gas diesel engines as prime movers, Energy 26 (2001) 31e44. [11] P. Bombarda, C.M. Invernizzi, C. Pietra, Heat recovery from Diesel engines: a thermodynamic comparison between Kalina and ORC cycles, Appl. Therm. Eng. 30 (2010) 212e219. [12] H.D. Madhawa Hettiarachchi, M. Golubovic, W.M. Worek, Y. Lkegami, The performance of the kalina cycle system 11 (KCS-11) with low-temperature heat sources, ASME J. Energy Resour. 129 (2007) 243e247. [13] Nasruddin, R. Usvika, M. Rifaldi, A. Noor, Energy and exergy analysis of kalina cycle system (KCS) 34 with mass fraction ammonia-water mixture variation, J. Mech. Sci. Technol. 23 (2009) 1871e1876. [14] O. Arslan, Exergoeconomic evaluation of electricity generation by the medium temperature geothermal resources, using a Kalina cycle: simav case study, Int. J. Therm. Sci. 49 (2010) 1866e1873. [15] P.A. Lolos, E.D. Rogdakisa, A Kalina power cycle driven by renewable energy sources, Energy 34 (2009) 457e464. [16] S.P. Sukhatme, Solar Energy-principles of Thermal Collection and Storage, Tata McGraw-Hill Publishing Company Limited, India, 1984. [17] J.F. Wang, Y.P. Dai, L. Gao, S.L. Ma, A new combined cooling, heating and power system driven by solar energy, Renew Energy 34 (2009) 2780e2788. [18] Y. Chen, Dynamic simulation of a solar-driven carbon dioxide transcritical power system for small scale combined heat and power production, Sol. Energy 84 (2010) 1103e1110. [19] J. Holland, Adaptation in Nature and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, MIT Press, Massachusetts, 1992. [20] B. Ziegler, C. Trepp, Equation of state for ammonia-water mixtures, Int. J. Refrig. 7 (1984) 101e116. [21] Y.M. El-Sayed, M. Tribus, Thermodynamic properties of water-ammonia mixtures theoretical implementation for use in power cycles analysis, ASME Adv. Energy Syst. Div. 1 (1985) 89e95. [22] F. Xu, D.Y. Goswami, Thermodynamic properties of ammonia water mixtures for use in power-cycle applications, Energy 24 (1999) 525e536.