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Energy–exergy analysis and optimization of the solar-boosted Kalina cycle system 11 (KCS-11)
Renewable Energy 66 (2014) 268e279
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Energyeexergy analysis and optimization of the solar-boosted Kalina cycle system 11 (KCS-11) Faming Sun a, b, *, Weisheng Zhou c, Yasuyuki Ikegami d, Kenichi Nakagami c, Xuanming Su b a
Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan Ritsumeikan Global Innovation Research Organization, Ritsumeikan University, Kyoto 603-8577, Japan c College of Policy Science, Ritsumeikan University, Kyoto 603-8577, Japan d Institute of Ocean Energy, Saga University, 1-Honjo machi, Saga 840-8502, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2012 Accepted 11 December 2013 Available online 6 January 2014
Energyeexergy analysis and parameter design optimization of the KCS-11 solar system with an auxiliary superheater are studied in low-grade thermal energy conversion (LTEC). Firstly, from a thermodynamics point of view, the corresponding calculation model is built to solve the system state points as well as the exergy input/output/loss for each system component. And then, according to the characteristics of the KCS-11 solar system, the verification items are given to verify the correctness of the calculation model. Afterward the model is proved to be correct by sampling check a set of calculation data. On that basis, the corresponding parameter design optimization and system performance analysis are carried out from the viewpoint of the maximization of the exergy output in KCS-11 solar system at a certain scale. Results show that the mass flow rates of working fluid and solar collector subcycle and also ammonia mass fraction are important system operation parameters that should be optimized to deduce the irreversible behavior of the solar system for producing more useful energy. Meanwhile, the heat-transfer rate distribution ratio of the superheater should be large enough to ensure that the expanding vapor in the turbine is superheated. Finally, an optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. In this case, the maximum generated power is 491 kW showing 35.6% exergy efficiency and 6.48% energy efficiency of the system for the month of August. The size of the system in terms of power generated of each major equipment is listed as follows: solar evaporator (370 kW), superheater (106 kW), condenser (298 kW), turbine (491 kW), separator (43 kW), absorber (37 kW), pump (8 kW), regenerator (38 kW), and diffuser (17 kW). And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities. In this way, the maximum annual power generation of the KCS-11 solar system is about 553,520 kW h. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: KCS-11 solar system Energy analysis Exergy analysis Optimization design Power generation
1. Introduction In recent years, research on the conversion of low-grade heat from sources such as geothermal heat, waste heat, low-temperature solar thermal heat, etc. into electrical power or LTEC has received a lot of attention [1e4]. Ammoniaewater thermodynamic cycle is being considered as a more promising way for power generation in LTEC. Zamfirescu and Dincer [5] have undertaken a study to thermodynamically assess the performance of an ammoniaewater Rankine cycle that uses no boiler, but rather the saturated liquid is flashed by a positive displacement expander for
* Corresponding author. Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan. E-mail address: [email protected] (F. Sun). 0960-1481/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2013.12.015
power generation. Results showed that it has best performance when compared with the ones obtained for conventional organic Rankine cycle and a Kalina-kind cycle having a resorber instead of the usual distillation and condensation subsystem. It is known that the ammoniaewater Rankine cycle is in general known as Kalina cycle after the name of its inventor [6]. KCS-11 is a well-known Kalina cycle for low-temperature driven power generation and using ammoniaewater as its working fluid for this purpose. Many researchers tried their best to clear the characteristics of the KCS-11 for using various forms of low-temperature heat sources. Such as, Hettiarachchi and Worek et al. [7] examined the KCS-11 for lowtemperature geothermal heat sources and compared with an organic Rankine cycle (ORC). Results showed that the KCS-11 has better overall performance at moderate pressures than that of ORC. Lu et al. [8] also examined the KCS-11 for geothermal power
F. Sun et al. / Renewable Energy 66 (2014) 268e279
Nomenclature cp Ex h Io _ m P Q_ s t T
Dt DTm U y W Ws,r CPC ETC FPC LTEC OTEC KCS-11
specific heat at constant pressure, 3.9 kJ/kg K the exergy, kJ/s specific enthalpy, kJ/kg the exergy loss, kJ/s mass flow rate, kg/s pressure, kPa heat-transfer rate, kW specific entropy, kJ/kg K temperature, C absolute temperature, K temperature difference, C logarithmic mean temperature difference, C overall heat-transfer coefficient, kW/m2 K ammonia mass fraction, kg/kg power output, kW solar radiation intensity, W/m2 compound parabolic concentrating evacuated tube solar collector flat plate solar collector low-grade thermal energy conversion ocean thermal energy conversion Kalina cycle system 11
Greek letters a first order loss coefficient of the solar collector b second order loss coefficient of the solar collector D differential h thermal efficiency, % hsc solar collector efficiency [e] k heat-transfer rate distribution ratio of the superheater [e] _ 6 =m _ 5 [e] x1 ¼ m x1 Gt average monthly sunshine duration, h Subscripts a outlet of the solar collector abs absorber
generation and compared with the existing Kawerau ORMAT binary plant in New Zealand. And parametric sensitivity analysis of KCS-11 was carried out for the specific power output and net thermal efficiency by changing the temperatures of both heat source and heat sink for a given ammoniaewater composition. Meanwhile, Lolos [9] investigated the KCS-11 with a main heat source provided by flat plate solar collectors and an external heat source used for superheating the vapor to expand in the turbine. Later, Mittelman [10] proposed a combined Rankine/KCS-11 power block for concentrating solar thermal power (CSP). All their results show that the KCS-11 is a better choice for exploiting and utilizing the low-temperature thermal energy. However the heat source temperature of the KCS-11 is assumed constant in their research. So as for solar thermal power generation system, the optimal operation scheme of the KCS-11 should be paid much attention for designing high performance KCS-11 solar system in engineering practice, since the solar heat source varies with time as well as operation conditions. KCS-11 solar system is the hybrid of the power generation subcycle and solar collector subcycle. The power generation subcycle is constructed from Kalina cycle system 11. Sun et al. [11e13] have studied the performance of KCS-11 solar system from the viewpoint of energy analysis. Results show that the system pressure difference is an important performance benchmark in this system. Based on
c ca cs csc csi cso cwf dif exg f i ii in is k net o out opt pgc pp r rg s sc scc sds se sewf sh sl sp sv tbn to wf wfp 0
269
condenser no difference between the collector temperature and ambient temperature cold seawater cold seawater subcycle cold seawater at the inlet cold seawater at the outlet working fluid side in condenser diffuser exergy inlet of the solar collector heat exchanger end section (heat source inlet) number of the state point in KCS-11 solar system inlet isentropic process KCS-11 solar system net heat exchanger end section (heat source outlet) outlet optimal power generation subcycle pinch point solar radiation regenerator solar solar collector solar collector subcycle system dead state solar evaporator working fluid side in solar evaporator superheater saturated liquid separator saturated vapor turbine total working fluid working fluid pump environment state
this, a real-time optimal operation scheme is given for high system performance. However, the exergy analysis to deduce the irreversible behavior of the solar system for producing more useful energy is still not considered even though it is significant for designing high performance solar system in engineering practice. So, in this study, energyeexergy analysis of the KCS-11 solar system with an auxiliary superheater is studied in LTEC. The corresponding calculation model is built to solve the system state points as well as the exergy input/ output/loss for each system component. And then parameter design optimization is carried out in KCS-11 solar system for producing more useful energy. Finally, an optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. Thus the way of high-efficiency utilization of solar energy in KCS-11 solar system is clarified. 2. KCS-11 solar system modeling 2.1. System description The proposed solar systems are mainly including power generation subcycle with an auxiliary superheater, solar collector subcycle and cold seawater subcycle. And ammoniaewater mixture is the working fluid, whose thermodynamic properties are
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simulated by using Ibrahim’s data [14]. Therefrom, main devices of the system are listed and described as follows: ➢ A working fluid pump, a device used in this system to allow the flowing working fluid in liquid to overcome gravity and pressure loss. ➢ A regenerator, a device used in this system to preheat the compressed liquid before sending it to the solar evaporator by using exhaust waste heat of the system. ➢ A solar evaporator, a device used in this system for the evaporation of the compressed liquid to wet vapor by using solar heat. ➢ A solar collector, a device used in this system to collect heat by capturing solar radiation. ➢ A separator, a vaporeliquid device used in this system to separate the ammoniaewater mixture into saturated vapor and saturated liquid. ➢ A superheater, a device used in this system to heat up the saturated ammonia vapor to superheated ammonia vapor. ➢ A turbine, a device used in this system to extract thermal energy from pressurized ammonia vapor and use it to do mechanical work on a rotating output shaft. ➢ A generator, a device used in this system to convert mechanical energy to electrical energy. ➢ A diffuser, a device used in this system to releases pressure of the working fluid from compressed liquid state to saturated liquid state. ➢ An absorber, a device used in this system to mix the wet vapor with the saturated liquid. ➢ A condenser, a device used in this system for the condensation of the wet vapor into saturated liquid. Based on the KCS-11, which is commonly used in recovering energy from the low-temperature heat resources, the KCS-11 solar
system with an auxiliary superheater is proposed here, and its schematic diagram is shown in Fig. 1. The turbine exhaust wet vapor (10) is mixed with saturated liquid (9) in the absorber. And the wet vapor (1) leaving the absorber is cooled in the condenser to become the saturated liquid (2). Then it is compressed to the compressed liquid (3) by the working fluid pump. Meanwhile, the working fluid wet vapor (5) is separated into rich ammoniaewater mixture saturated vapor (6) and the poor ammoniaewater mixture saturated liquid (7), where the saturated vapor is superheated to the superheated vapor (11) in the superheater by auxiliary heat source, such as geothermal systems, solar concentrator module or other similar sources etc. And then the superheated vapor is expanded in the turbine to generate electricity by using a generator. Moreover, the compressed liquid (8) leaving the regenerator releases pressure in the diffuser to become saturated liquid. And the compressed liquid (4) reheated by the regenerator is sent to the solar evaporator, where it is heated to saturated liquid (40 ) and then boiled to wet vapor by the solar heat. Furthermore, the corresponding solar collector subcycle can be designed by adjusting its solar collector area and mass flow rate.
2.2. Basic parameters and general assumption In solar collector subcycle, the effective solar radiation energy gain at solar collector is given as
Q_ sc;r ¼ Ws;r $Asc $hsc
(1)
where Ws,r reflects solar radiation intensity, it comes from local weather conditions of the solar system. Asc represents the area of the solar collector and hsc means the efficiency of the solar collector, which can be expressed as follows.
Fig. 1. Schematic diagram of the KCS-11 solar system.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
hsc ¼ hsc;ca a
Dtsc Ws;r
Dtsc 2 b Ws;r
Dtsc ¼ tsc t0 tsc ¼
(2)
In addition, leave the influence of solar collector subcycle pump to the temperature out of consideration, which means ta ¼ tb ¼ tc ¼ td and tf ¼ te. And then the temperature tf is solved as following
(3)
. 2 ta þ tf
(4)
in which, ta and tf represent the outlet and inlet temperature of the solar collector, respectively. And t0 is the ambient air temperature; hsc,ca is the solar collector efficiency value when there is no difference between the collector temperature and ambient temperature; a and b are loss coefficients of the solar collector. In addition, the useful energy gain at solar collector is
_ scc $cp $Dt Q_ sc ¼ m
271
tf ¼
t5 t4 $e
UA Q_ se t5 þt4 $ _ scc $cp Q_ se m
1e
_
m_ Q se$c !scc p
UA Q_ se $ t5 þ t4 _ scc $cp Q_ se m
_ scc $cp þ tf and Q_ se is assumed to be same with Q_ sc thus, ta ¼ Q_ se =m here. And a calculation model is necessary for solving state points in KCS-11 solar system, the corresponding calculation flow chart is shown in Fig. 2. Then based on the given initial condition of Tables 1
(5)
_ scc is the mass flow rate of the solar collector subcycle, cp in which, m represents the specific heat at constant pressure, Dt ¼ ta tf means the temperature difference of the solar collector. According to heat _ scc can be expressed as balance in solar collector, the m
_ scc ¼ m
2 ! ðta þtf Þ=2t0 ðta þtf Þ=2t0 b$ Ws;r $Asc $ hsc;ca a$ Ws;r Ws;r cp $ ta tf (6)
Meanwhile, in power generation subcycle, heat rate supplied to the cycle (solar evaporator) is shown below
_ wf $Dhk;se Q_ sewf ¼ m
(7)
Heat rate rejected from the cycle (condenser) is given as
_ wf $Dhk;c Q_ cwf ¼ m
(8)
_ wf is the mass flow rate of the working fluid. Dhk,se and where, m Dhk,c respectively represent the enthalpy difference of the solar evaporator and condenser in KCS-11 solar system. Also it is noticed that heat conduction of the heat exchanger is
Q_ ¼ UADTm
(9)
where Q_ is the rate of heat transfer; U is the overall heat-transfer coefficient; A is the cross-section area normal to the direction of heat transfer; DTm is called the logarithmic mean temperature difference (LMTD) and gives
DTm ¼
Dti Dto lnðDti =Dto Þ
(10)
in which, Dti represents the temperature difference of heat exchanger end section (heat source inlet), Dto shows the temperature difference of heat exchanger end section (heat source outlet). Therefore, the heat-transfer rate in the condenser is
Q_ c ¼ ðUAÞc ðDTm Þc
(11)
where
ðDTm Þc ¼
Dti Dto ðt tcso Þ ðt2 tcsi Þ ¼ 1 lnðDti =Dto Þ ln t1 tcso
(12)
t2 tcsi
In the same way, the LMTD of the evaporator and regenerator can also be given here.
(13)
Fig. 2. Flow chart of the KCS-11 solar system.
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Thus based on aforementioned discussion, the KCS-11 solar system thermal efficiency is given as
Table 1 Weather data of the Kumejima Island [20,21]. Month
tcsi [ C]
t0 [ C]
Ws,r [W/m2]
Gt [h]
January February March April May June July August September October November December
4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5
16.4 16.7 18.0 21.7 23.6 27.3 29.1 28.4 27.3 25.0 20.8 18.0
334 336 408 412 422 473 612 651 573 516 388 365
77.92 88.68 115.41 116.58 138.47 144.67 253.02 235.62 197.85 160.56 105.42 98.760
Table 2 Initial condition for simulation. Environment pressure Performance of the solar evaporator and condenser Turbine isentropic efficiency Pump isentropic efficiency Solar collector area Mass flow rate of cold seawater Ammonia mass fraction Performance of the regenerator Heat-transfer rate proportion for superheater Mass flow rate of working fluid Efficiency of the CPC solar collector Sampling month
P0 ¼ 0.10135 [MPa] ðUA=Q_ Þ ¼ 0:2 ½1= C se;c
htbn ¼ 85 [%] hwfp ¼ 75 [%]
Asc ¼ 1.0 [ha] _ cs ¼ 150 ½kg=s m y5 ¼ 0.95 [kg/kg] ðUA=Q_ Þrg ¼ 0:2 ½1= C k ¼ 2% [e] _ wf ¼ 6:5 ½kg=s m hsc ¼ 60 [%] August
and 2, t4 and t5 can be solved here. Thus by combining with Eqs. (2) _ scc and (6), the value of mass flow rate of solar collect subcycle m could be found. Moreover, the basic equations obtained from the conservation law for energy in the components are given in Table 3. 2.3. System performance The overall KCS-11 solar system performance can be evaluated by its thermal efficiency, exergy efficiency and exergy output. In power generation subcycle of the solar system, the thermal efficiency is
W
hpgc ¼ _ net Q to
(14)
_ wf $ The corresponding net power output is Wnet ¼ m _ 6 =m _ 5 . Meanwhile, Q_ to ¼ ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ, where x1 ¼ m Q_ se þ Q_ sh represents total heat-transfer rate. And Q_ se with Q_ sh represent the heat-transfer rate in solar evaporator and superheater, respectively. And their relationship is introduced as k ¼ Q_ sh =Q_ to 100%.
hk ¼ hpgc $hsc
(15)
Furthermore, based on the researches [15e17], the exergy efficiency of the power generation subcycle in KCS-11 solar system is given as
hexg ¼
P Exin I o Exin
(16)
P where the item Exin I o represents the exergy output of the solar system, in which, Exin ¼ Exin,se þ Exin,sh þ Exin,c is the sum of the exergy input at solar evaporator (Exin,se), superheater (Exin,sh) and condenser (Exin,c). In which, the definition of exergy input at solar evaporator, superheater and condenser is given in Table 4, P o respectively. In addition, T0 ¼ tsds þ 273.15, I is the sum of the exergy losses in all the components, tsds is the temperature of the system when it is in the dead state, here it is assumed as ambient air temperature t0. And the exergy of each state point ii in KCS-11 solar system considers only the physical exergy and the chemical exergy of water and ammonia cancels out in the exergy balances as entering and leaving quantities are the same [18]. Thus it can be _ ii $½ðhii h0 Þ T0 ðsii s0 Þ. In this way, the expressed as Exii ¼ m exergy loss in each component of the power generation subcycle is given in Table 3. According to aforementioned discussion, the KCS-11 solar system exergy efficiency is given as
hk;exg ¼ hexg $hsc
(17)
Finally, it should be noted that the following assumptions should be applied to the system. ➢ Based on the research of Uehara [2,19], turbine and pump isentropic efficiencies are separately given in 85% and 75% as an example. ➢ The piping and other auxiliary are considered no heat losses in the system. Based on the above assumptions, initial condition of KCS-11 solar system is given in Tables 1 and 2. Meanwhile, the data of Table 1 comes from the weather conditions of Kumejima Island (Lat. 26-20N, Lng. 126-48E) in Japan since it is the planned construction site of the OTEC (ocean thermal energy conversion) plant and the deep-sea cold seawater can be supplied therefrom [20,21]. And in solar collector subcycle, the applicable solar collectors include, but not limited to, FPC (flat plate solar collector), ETC (evacuated tube solar collector), CPC (compound parabolic concentrating), etc. Here it takes CPC solar collector as an example since it can supply heat sources with good performance, all year round. Thus reference [22], the parameters of the solar collector are given as hsc,ca ¼ 0.7035, a ¼ 2.5896 and b ¼ 7.4878.
Table 3 Basic equations and exergy loss items in the components of the KCS-11. Components
Basic equations
Exergy loss items
Solar evaporator Separator Superheater Turbine Regenerator Diffuser Absorber Condenser Working fluid pump
_ se $ðh5 h4 Þ Q_ se ¼ Q_ sewf ¼ m _ 5 h5 ¼ m _ 6 h6 þ m _ 7 h7 , m _5 ¼ m _ 6 þm _7 m _ sh $ðh11 h6 Þ Q_ sh ¼ m _ tbn $ðh11 h10 Þ, htbn ¼ (h11 h10)/(h11 h10,is) Wtbn ¼ m _ 4 ðh4 h3 Þ ¼ m _ 7 ðh7 h8 Þ m h8 ¼ h9 _1 ¼ m _ 10 þ m _9 _ 1 ¼ h10 m _ 10 þ h9 m _ 9, m h1 m _ c $ðh1 h2 Þ Q_ c ¼ Q_ cwf ¼ m _ wfp $ðh3 h2 Þ, hwfp ¼ (h3,is h2)/(h3 h2) Wwfp ¼ m
Iose ¼ Exin,se,scc Exout,se,scc þ Exin,se,pgc Exout,se,pgc Iosp ¼ Exin,sp,pgc Exout1,sp,pgc Exout2,sp,pgc Iosh ¼ 0 Iotbn ¼ Exin,tbn,pgc Exout,tbn,pgc Wtbn Iorg ¼ Exin1,rg,pgc þ Exin2,rg,pgc Exout1,rg,pgc Exout2,rg,pgc Iodif ¼ Exin,dif,pgc Exout,dif,pgc Ioabs ¼ Exin1,abs,pgc þ Exin2,abs,pgc Exout,abs,pgc Ioc ¼ Exin,c,csc Exout,c,csc þ Exin,c,pgc Exout,c,pgc Iowfp ¼ Wwfp þ Exin,wfp,pgc Exout,wfp,pgc
F. Sun et al. / Renewable Energy 66 (2014) 268e279
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Table 4 Definition of exergy input at solar evaporator, superheater and condenser, respectively. Solar evaporator
Superheater
Condenser
Exin,se ¼ Exin,se,scc Exout,se,scc _ scc ððhd h0 Þ T0 ðsd s0 ÞÞ Exin;se;scc ¼ m _ scc ððhe h0 Þ T0 ðse s0 ÞÞ Exout;se;scc ¼ m
Exin,sh ¼ Exin,sh,pgc Exout,sh,pgc _ sh ððh11 h0 Þ T0 ðs11 s0 ÞÞ Exin;sh;pgc ¼ m _ sh ððh6 h0 Þ T0 ðs6 s0 ÞÞ Exout;sh;pgc ¼ m
Exin,c ¼ Exin,c,csc Exout,c,csc _ cs ððhcsi h0 Þ T0 ðscsi s0 ÞÞ Exin;c;csc ¼ m _ cs ððhcso h0 Þ T0 ðscso s0 ÞÞ Exout;c;csc ¼ m
3. Optimization design of the KCS-11 solar system 3.1. Result rationality analysis In order to verify correctness of the solar system simulation program, firstly we take out a set of sampling calculation data from KCS-11 solar system with the initial condition, which is given in Tables 1 and 2, as an example for checking. The corresponding results are shown in Table 5. In this case, the design requirements of the solar collector in solar collector subcycle are inlet temperature 28.149 [ C], outlet temperature 75.760 [ C], solar collector subcycle mass flow rate 21.0 [kg/s] and water as the heat-transfer medium of the subcycle. Based on the characteristics of the KCS-11 solar system, the verification items are listed as follows: 1. Check whether or not ðUA=Q_ Þc ¼ lnððt1 tcso Þ=ðt2 tcsi ÞÞ= ððt1 tcso Þ ðt2 tcsi ÞÞ matches the specified condition ððUA=Q_ Þc ¼ 0:2 ½1= CÞ as given in Table 2. 2. Check whether or not ðUA=Q_ Þse ¼ lnððtd t5 Þ=ðte t4 ÞÞ= ððtd t5 Þ ðte t4 ÞÞ matches the specified condition ððUA=Q_ Þse ¼ 0:2 ½1= CÞ as given in Table 2. 3. Check whether or not ðUA=Q_ Þrg ¼ lnððt7 t4 Þ=ðt8 t3 ÞÞ= ððt7 t4 Þ ðt8 t3 ÞÞ matches the specified condition ððUA=Q_ Þrg ¼ 0:2 ½1= CÞ as given in Table 2. 4. Check whether or not k ¼ Q_ sh =ðQ_ se þ Q_ sh Þ ¼ x1 $ðh11 h6 Þ= ððh5 h4 Þ þ x1 $ðh11 h6 ÞÞ 100% matches the specified condition (k ¼ 2%) as given in Table 2. 5. Check whether or not the following equation is true for the heat balance in the solar evaporator, which is _ wf ðh5 h4 Þ. Q_ sc ¼ Ws;r $Asc $hsc ¼ Q_ se ¼ m 6. Check whether or not the following equation is true, which is _ 6 =m _ 5 ¼ ðy5 y7 Þ=ðy6 y7 Þ. m 7. Check whether or not the following equation is true for the heat balance in the condenser, as shown by _ cs cp ðtcso tcsi Þ ¼ Q_ cwf ¼ m _ wf ðh1 h2 Þ. Q_ c ¼ m 8. Check whether or not the following equation is true for the _ 5 h5 ¼ m _ 6 h6 þ m _ 7 h7 . heat balance in the separator: m
9. Check whether or not the following equation is true for the _ 1 h1 ¼ m _ 9 h9 þ m _ 10 h10 . heat balance in the absorber: m 10. Check whether or not the following equation is true for the _ 4 ðh4 h3 Þ ¼ m _ 7 ðh7 h8 Þ. heat balance in the regenerator: m 11. Check whether or not hpgc ¼ Wnet =Q_ to ¼ ðx1 $ðh11 h10 Þ ðh3 h2 ÞÞ=ððh5 h4 Þ þ x1 $ðh11 h6 ÞÞ matches the calculation result (hpgc ¼ 7.17 [%]) as shown in Table 5. 12. Check whether or not hsc ¼ 0.7035 2.5896(Dtsc) 7.4878(Dtsc)2 matches the specified condition (hsc ¼ 60 [%]) as given in Table 2, in which, Dtsc ¼ ((ta þ tf)/2 t0)/Ws,r. _ scc ¼ ðWs;r $Asc $hsc Þ=ðcp $ðta tf ÞÞ 13. Check whether or not m _ scc ¼ 21:0 ½kg=s) as shown matches the calculation result (m in Table 5. _ _ 14. Check whether or not tf ¼ ðt5 t4 eðUA=Q Þse $ðQ se =ðm_ scc cp Þt5 þt4 Þ _ scc cp ÞÞ=ð1 eðUA=Q_ Þse $ðQ_ se =ðm_ scc cp Þt5 þt4 Þ Þ and ta ¼ Q_ se = Q_ se =ðm _ scc $cp Þ þ tf match the calculation results (tf ¼ 28.149 [ C], ðm ta ¼ 75.760 [ C]) as shown in Table 5. 15. Check whether or not htbn ¼ (h11 h10)/(h11 h10,is) and hwfp ¼ (h3,is h2)/(h3 h2) match the specified conditions (htbn ¼ 85 [%] and hwfp ¼ 75 [%]) as given in Table 2. From these results, it is proven that the simulation programs designed for KCS-11 solar system is rational. And then based on aforementioned assumptions (see Tables 1 and 2) and calculations (see Tables 3 and 5), the corresponding system exergy analysis results are calculated and listed in Table 6. It should be clarified that percentage of the component exergy loss, as shown in the table, is defined as the ratio of exergy loss of the corresponding component and total exergy input of the cycle. Based on this, each of the components (i.e. solar evaporator, separator, superheater, turbine, absorber, condenser, pump, regenerator and diffuser) is estimated. As a result, the exergy loss is mainly in components of solar evaporator, condenser and turbine. And solar evaporator exergy loss takes up the largest proportion that is 23.1 [%]. That means that system parametric optimization analysis should be expected to decrease the system thermodynamic irreversibility in the following part. In addition, it is also found that the system exergy output (Table 6) calculated by using second law of thermodynamics is the
Table 5 Sampling results for KCS-11 solar system under condition of Tables 1 and 2. Point
t [ C]
P [MPa]
y [kg/kg]
h [kJ/kg]
s [kJ/(kg K)]
1 13.691 0.638 0.950000 791.028 3.199 2 12.493 0.638 0.950000 221.781 1.209 3 12.784 1.528 0.950000 223.620 1.211 3is 12.686 1.528 0.950000 223.161 1.209 4 28.102 1.528 0.950000 296.121 1.458 40 41.272 1.528 0.950000 360.130 1.666 5 42.978 1.528 0.950000 897.044 3.370 6 42.978 1.528 0.999738 1502.724 5.203 7 42.978 1.528 0.903777 334.156 1.665 8 13.667 1.528 0.903777 194.279 1.201 9 13.783 0.638 0.903777 194.279 1.206 10 11.305 0.638 0.999738 1433.149 5.342 10is 11.241 0.638 0.999738 1416.379 5.283 11 51.201 1.528 0.999738 1528.184 5.283 _ scc ¼ 21:0 ½kg=s, hpgc ¼ 7.17 [%], hk ¼ 4.30 [%], Wnet ¼ 285.606 [kW] ta ¼ 75.760 [ C], tf ¼ 28.149 [ C], tcso ¼ 10.828 [ C], m
v [m3/kg]
_ n =m _ 5 ½ m
0.0939 0.0016 0.0016 0.0015 0.0016 0.0016 0.0016 0.0865 0.0016 0.0015 0.0015 0.1920 0.1893 0.0903
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4817 0.5183 0.5183 0.5183 0.4817 0.4817 0.4817
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Table 6 Exergy input/output/loss for the KCS-11 solar system. Design parameters
Exergy input
k ¼ 2% [e], hsc ¼ 60% [e], y5,opt ¼ 0.94 [kg/kg] Amount (kW)
Percentage (%)
Percentage (%)
Exergy efficiency Operation conditions
295.819 49.8 4.183 0.7 294.328 49.5 285.606 48.1 137.482 23.1 24.926 4.2 0 0 55.706 9.4 25.015 4.2 93.884 15.8 3.920 0.7 12.740 2.1 5.080 0.8 hexg ¼ 48.1 [%], hk,exg ¼ 28.9 [%] _ wf ¼ 6:5 ½kg=s, m _ scc ¼ 21:0 ½kg=s m
301.612 50.5 7.226 1.2 288.793 48.3 374.811 62.7 12.906 2.2 29.012 4.9 0 0 74.374 12.4 28.922 4.8 93.456 15.6 6.749 1.1 26.090 4.4 9.157 1.5 hexg ¼ 62.7 [%], hk,exg ¼ 37.6 [%] _ wf;opt ¼ 7:46 ½kg=s, m _ scc ¼ 40:03 ½kg=s m
Design parameters
k ¼ 2% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/
k ¼ 14% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/ kg]
Exergy output Exergy loss
Solar evaporator Superheater Condenser
k ¼ 2% [e], hsc ¼ 60% [e], y5 ¼ 0.95 [kg/kg] Amount (kW)
Solar evaporator Separator Superheater Turbine Absorber Condenser Pump Regenerator Diffuser
kg] Amount (kW) Exergy input
Exergy output Exergy loss
Exergy efficiency Operation conditions
Solar evaporator Superheater Condenser Solar evaporator Separator Superheater Turbine Absorber Condenser Pump Regenerator Diffuser
Percentage (%)
370.174 57.1 8.494 1.3 269.266 41.6 391.389 60.4 23.975 3.7 42.362 6.5 0 0 79.790 12.3 39.622 6.1 82.932 12.8 8.187 1.3 42.166 6.5 16.756 2.6 hexg ¼ 60.4 [%], hk,exg ¼ 33.8 [%] _ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:59 ½kg=s m
Amount (kW)
Percentage (%)
370.165 47.9 105.661 13.6 297.555 38.5 490.999 63.5 23.957 3.1 43.142 5.6 0 0 92.019 11.9 36.908 4.8 96.764 12.5 8.187 1.0 38.472 5.0 16.748 2.2 hexg ¼ 63.5 [%], hk,exg ¼ 35.6 [%] _ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:40 ½kg=s m
Fig. 3. Relationship between ammonia mass fraction y5 and exergy input/output/loss.
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Fig. 4. Relationship between solar collector efficiency hsc and exergy input/output/loss.
same as the system net power (Table 5) calculated by using first law of thermodynamics. This thermodynamic property is known as an inherent characteristic of the proposed KCS-11 solar system in this paper and it is proved that the designed calculation model for system exergy analysis is also rational.
3.2. System parametric optimization analysis From the point of view of the maximization of the exergy output in KCS-11 solar system at a certain scale or size, it is observed that the significant system operation parameters are the mass flow rates of the working fluid in power generation subcycle, cold seawater _ wf , m _ cs and m _ scc ), heatsubcycle and solar collector subcycle (m transfer rate distribution ratio of the superheater k, efficiency of the solar collector hsc, ammonia mass fraction y5 and weather data etc. And then the main objective of the parametric analysis is focused on optimization of these system operation parameters to find the maximum value of the exergy output, and its initial conditions are shown in Tables 1 and 2. Meanwhile, the corresponding system constraint conditions are assumed as 0.80 [kg/kg] y5 0.98 [kg/ kg], 0.05 [e] hsc 0.70 [e] and 0 [%] k 18 [%]. Furthermore, it _ wf under is worth noting that there is a convergence range for the m the abovementioned initial and constraint conditions in KCS-11 _ wf should be located in a solar system, which means that the m limited range to satisfy that all the increased ammoniaewater mixture working fluid can be converted from compressed liquid state to wet vapor state in the solar evaporator. In addition, according to the real productivity scale of the deep-sea cold seawater in Kumejima Island, the mass flow rate of cold seawater subcycle is _ cs ¼ 150 ½kg=s in this case as shown in Table 2. And it given as m should be noted that the constraint condition 0.05 [e] hsc 0.70 [e] can be obtained by adjusting the mass flow rate of the solar _ scc , appropriately. collector subcycle m
Based on aforementioned discussion, Fig. 3(a) shows the relationship between y5 and total exergy input of the solar system with the initial conditions (Table 2) by way of solar evaporator, superheater and condenser, respectively. Meanwhile, Fig. 3(b) gives exergy inputs of the solar system in terms of a percentage. From these figures it is known that the y5 has little effect on the exergy inputs of condenser, superheater and solar evaporator. Fig. 3(c) illustrates the exergy output and exergy loss of each component in the solar system. And Fig. 3(d) displays the exergy output and exergy losses of the solar system in percentage terms. As shown in the two figures, it is true that the sum of the exergy output and the
Fig. 5. Relationship between y5 and exergy output with hsc,opt.
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Fig. 6. Relationship between ammonia mass fraction y5 and exergy input/output/loss with hsc,opt.
total exergy loss is equal to the total exergy input. And it is also noticed that the exergy loss of the absorber is minus. The reason is that heat is released when ammonia gas dissolves in water in the absorber. In addition, it is found that when y5 is equal to 0.94 [kg/
kg], the exergy output of the power generation subcycle in KCS-11 solar system are maximum, which is 374.811 [kW] (Table 6). So the following parametric optimization analysis takes y5 ¼ 0.94 [kg/kg] as an example.
Fig. 7. Relationship between heat-transfer rate distribution ratio k and exergy input/output/loss.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
Fig. 8. Relationship between temperature and enthalpy in KCS-11 solar system.
Fig. 4 shows the relationship between hsc and exergy input/ output/loss of the solar system by using the initial conditions of Fig. 3 with y5 ¼ 0.94 [kg/kg]. It is known that the larger hsc within its effective range, the larger quantity energy obtained in solar evaporator. However, from Fig. 4(a) and (b) it can be seen that the exergy input of the solar system decreases with increasing hsc. The reason is that the larger hsc, the lower temperature of the solar evaporator, and then the smaller exergy input by way of solar evaporator. As shown in Fig. 4(c) and (d), there is an optimal hsc (hsc,opt ¼ 60% [e]) that maximizes the exergy output (374.811 [kW]) of the solar
277
system. Reason resulting in such phenomena is that the larger hsc within its effective range, the smaller exergy input of the solar system. Meanwhile, when the hsc gets smaller within its effective range, the exergy loss of the solar system gets larger as shown in the figure. In addition, from Figs. 3 and 4 it is known that the (hsc ¼ 60% [e], y5,opt ¼ 0.94 [kg/kg]) or (y5 ¼ 0.94 [kg/kg], hsc,opt ¼ 60% [e]) is a locally optimal solution for maximizing the exergy output of the solar system. To get the global optimal solution of the system, Fig. 5 shows the locally maximum exergy output of the solar system and the locally hsc,opt for each y5. And the corresponding exergy input/ output/loss is shown in Fig. 6. Thus it can be seen from these figures that the global optimal solution of the solar system is hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/kg]. And the global maximum exergy output is known as 391.389 [kW]. Meanwhile, the detail data of the exergy input/output/loss and the corresponding optimal operation pa_ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:59 ½kg=s) in this rameters (m case are listed in Table 6. In sum, the hsc,opt and y5,opt are chosen as an example for further discussion. Fig. 7 shows the influence of the superheater on exergy input/ output/loss of the KCS-11 solar system in terms of heat-transfer rate distribution ratio k. It’s worth mentioning here that the case (k ¼ 0% [e]) means the KCS-11 solar system without a superheater. Thus, from Fig. 7(a) and (b) it can be seen that the total exergy input of the solar system is increasing with increasing k since the exergy input of the superheater is increased markedly in this process. And it is shown from Fig. 7(c) and (d) that the larger k, the larger exergy output. Meanwhile, the exergy loss of each system component is nearly a constant and the system exergy efficiency is increasing slightly. Thus based on abovementioned simulation results and analysis, it is known that the superheater (k) has little influence on
Table 7 Optimal results for KCS-11 solar system under condition of Tables 1 and 2 with k ¼ 14% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/kg]. Point
t [ C]
P [MPa]
y [kg/kg]
h [kJ/kg]
1 13.893 0.604 0.900000 598.598 2 12.264 0.604 0.900000 184.442 3 12.777 2.354 0.900000 187.932 3is 12.590 2.354 0.900000 187.059 4 46.424 2.354 0.900000 348.531 40 60.230 2.354 0.900000 417.505 5 62.462 2.354 0.900000 751.360 6 62.462 2.354 0.999103 1516.378 7 62.462 2.354 0.853776 394.541 8 13.505 2.354 0.853776 159.034 9 13.762 0.604 0.853776 159.034 10 35.828 0.604 0.999103 1541.024 10is 23.919 0.604 0.999103 1508.989 11 130.512 2.354 0.999103 1722.552 ta ¼ 71.054 [ C], tf ¼ 49.008 [ C], tcso ¼ 10.905 [ C], hpgc ¼ 11.58 [%], hk ¼ 6.48 [%], Wnet ¼ 490.884 [kW]
s [kJ/(kg K)]
v [m3/kg]
_ n =m _ 5 ½ m
2.626 1.179 1.182 1.179 1.713 1.924 2.922 5.069 1.921 1.163 1.172 5.737 5.631 5.631
0.0720 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016 0.0569 0.0016 0.0015 0.0015 0.2351 0.2233 0.0768
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3181 0.6819 0.6819 0.6819 0.3181 0.3181 0.3181
Table 8 _ ½kg=s. Optimum KCS-11 solar system operating conditions in Kumejima Island m Month
_ wf;opt ½kg=s m
_ scc;opt ½kg=s m
hsc,opt [e]
Exergy output [kW]
Other conditions
January February March April May June July August September October November December
1.98 2.08 3.64 4.08 4.39 5.75 8.35 9.05 7.53 6.26 3.56 2.81
6.99 8.44 15.49 16.03 16.30 26.82 33.32 42.40 31.24 23.07 16.70 10.84
0.24 0.25 0.36 0.40 0.42 0.49 0.55 0.56 0.53 0.49 0.37 0.31
110.736 117.981 205.145 227.458 244.828 320.816 454.144 490.999 411.909 342.916 201.559 157.188
P0 ¼ 0.10135 [MPa] ðUA=Q_ Þse;c ¼ 0:2 ½1= C htbn ¼ 85 [%] hwfp ¼ 75 [%] Asc ¼ 104 [m2] _ cs ¼ 150 ½kg=s m y5 ¼ 0.90 [kg/kg] ðUA=Q_ Þrg ¼ 0:2 ½1= C k ¼ 14% [e]
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Fig. 9. Exergy input/output/loss of the KCS-11 solar system in Kumejima Island for a year.
the system optimal solution (hsc,opt, y5,opt) from a thermodynamics point of view. Therefore from the point of view of system economy and device safety, the further discussion still takes the hsc,opt and y5,opt as an example to find the appropriate scale of the superheater (k) to satisfy the superheated vapor expansions in the turbine. It can be seen from the temperatureeentropy diagram (Fig. 8) of the KCS11 solar system that k ¼ 14% [e] (the real line with star mark) is the appropriate value to avoid damage to turbine since the superheated vapor expansion process does not contain the liquid particles. Meanwhile, the real line with cycle mark represents entropy flows of the initial conditions (Table 2) for comparison. Obviously, in this expansion process, the superheated vapor will condense out to liquid particles. As a result from the parametric optimization analysis, the following system case design in Kumejima Island for power generation will take k ¼ 14% [e] for an example. In addition, the corresponding detail data of the exergy input/output/loss of the optimal KCS-11 solar system and its state points in this case are listed in Tables 6 and 7.
optimization analysis results for sampling month (August) in Kumejima Island. And from the viewpoint of economics, the system y5 is set to a fixed value as 0.90 [kg/kg], which is the optimal value _ wf and hsc) need to be optifor August. As a result, parameters (m mized for the maximum annual power generation in the Kumejima Island. In which, the different hsc can be gotten by adjusting the _ scc . Finally, the mass flow rate of the solar collector subcycle m corresponding optimum solar system operating conditions can be calculated with aforementioned method and listed in Table 8. Fig. 9 shows exergy input/output/loss of the KCS-11 solar system in Kumejima Island for a year with its corresponding optimum operation conditions (Table 8). Concurring with expectations, the
4. An application case designed in Kumejima Island Based on the above discussion, suggestions could be given on selection of the system parameters for the maximum annual power generation with the help of the Kumejima Island weather data (Table 1) as follows. It is known that the larger the solar system scale, the larger the power generation. However, from an economic point of view and because of the limited conditions of the local area, the solar system should be in a certain scale. Therefore, as mentioned above, most system parameters are designed as shown in Table 2 as an example except some operating parameters, such as ammonia mass fraction y5, heat-transfer rate proportion for su_ wf , efficiency of the perheater k, mass flow rate of working fluid m solar collector hsc, etc. In which, the k for the annual power generation is given as 14 [%], which is based on the abovementioned
Fig. 10. Power generation of the KCS-11 solar system in Kumejima Island for a year.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
total exergy input of the solar system is largest in summer as shown in Fig. 9(a). It is also noted from Fig. 9(b) that percentage of exergy input in the solar system by way of condenser is largest in the summer months. Reason resulting in such phenomena is the temperature difference of the ambient air and cold seawater, which varies with seasons. Meanwhile, it can be seen from Fig. 9(c) that the exergy output of the solar system in August is the largest, which is about 491 kW. And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities. Further, from Fig. 9(d), we know that the exergy efficiency and percentage of the exergy loss in each component are almost constant under their respective _ wf;opt , m _ scc;opt ). Meanwhile, it also optimum operation conditions (m shows a basis for the performance estimation of the optimum solar system. Based on this, the generated electrical energy for each month using the KCS-11 solar system under the optimum operation conditions of each month (Table 8) and weather data of Kumejima Island (Table 1) is shown in Fig. 10. In which, the dot line with ‘cycle’ mark and dash dot line with ‘square’ mark show the relationship _ wf;opt , m _ scc;opt and months, respectively. And then, the between m corresponding annual power generation of the KCS-11 solar system can be calculated therefrom, which is about 553520 kW h.
5. Conclusions The KCS-11 solar system with an auxiliary superheater is analyzed in the present study from both the first and the second law point of view providing a rational procedure for producing more useful energy in LTEC. Here, some concluding remarks have been summarized as follows: The system state points as well as the exergy input/output/loss for each system component are solved and proved to be correct with the help of the verification items in KCS-11 solar system. The parameter design optimization and system performance analysis are carried out and shown that the key operating parameters, which affect the system as a whole, have been iden_ wf ) and solar tified as the mass flow rates of working fluid (m _ scc ) and also ammonia mass fraction (y5). collector subcycle (m And, they all have an optimum value for a set of other operating parameters to realize the maximum exergy output of the system. The heat-transfer rate distribution ratio of the superheater (k) should be large enough to ensure that the expanding vapor in the turbine is superheated from the viewpoint of the device safety. An optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. In this case, the maximum generated power is 491 kW showing 35.6% exergy efficiency and 6.48% energy efficiency of the system for the month of August. The size of the system in terms of power generated of each major equipment is listed as follows: solar evaporator (370 kW), superheater (106 kW), condenser (298 kW), turbine (491 kW), separator (43 kW), absorber (37 kW), pump (8 kW), regenerator (38 kW), diffuser (17 kW). And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities.
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The exergy efficiency and percentage of the exergy loss in each component for each month are almost constant under their respective optimum operation conditions. Meanwhile, it also shows a basis for the performance estimation of the optimum solar system. The maximum annual power generation of the KCS-11 solar system is about 553,520 kW h in Kumejima Island of Japan. Acknowledgment The authors gratefully acknowledge the financial support of this work by the AY2012 Research Promotion Program (Young Scientist) (Ritsumeikan University). References [1] Kalina AI, Leibowitz HM. Application of the Kalina cycle technology to geothermal power generation. Geotherm Res Council Trans 1989;13:605e11. [2] Uehara H, Ikegami Y. Optimization of a closed-cycle OTEC system. J Sol Energy Eng 1990;112:247e56. [3] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. A feasibility study of CO2-based Rankine cycle powered by solar energy. JSME Int J Ser B (Fluids Therm Eng) 2005;48:540e7. [4] Sun FM, Ikegami Y. Direct method to maximize net power output of Rankine cycle in low-grade thermal energy conversion. J Therm Sci Eng Appl 2010;2: 0210031e7. [5] Zamfirescu C, Dincer I. Thermodynamic analysis of a novel ammoniaewater trilateral Rankine cycle. Thermochim Acta 2008;477(1-2):7e15. [6] Kalina A. Combined-cycle system with novel bottoming cycle. J Eng Gas Turbines Power 1984;106(4):737e42. [7] Madhawa Hettiarachchi HD, Golubovic M, Worek WM, Ikegami Y. The performance of the Kalina cycle system 11 (KCS-11) with low-temperature heat sources. J Energy Res Technol 2007;129:243e7. [8] Lu XL, Watson A, Deans J. Analysis of the thermodynamic performance of Kalina cycle system 11 (KCS11) for geothermal power plant: comparison with Kawerau ORMAT binary plant. In: ASME 2009 3rd international conference on energy sustainability collocated with the heat transfer and InterPACK09 conferences (ES2009) July 19e23, 2009. pp. 357e8. San Francisco, California, USA. [9] Lolos PA, Rogdakis ED. A Kalina power cycle driven by renewable energy sources. Energy 2009;34(4):457e64. [10] Mittelman G, Epstein M. A novel power block for CSP systems. Sol Energy 2010;84:1761e71. [11] Sun FM, Ikegami Y, Jia BJ. A study on Kalina solar system with an auxiliary superheater. Renew Energy 2012;41:210e9. [12] Sun FM, Ikegami Y, Arima H, Zhou WS. Performance analysis of the low temperature solar-boosted power generation system e part I: comparison between Kalina solar system and Rankine solar system. J Sol Energy Eng 2013;135:011006.1e.11. [13] Sun FM, Ikegami Y, Arima H, Zhou WS. Performance analysis of the low temperature solar-boosted power generation system e part II: thermodynamic characteristics of the Kalina solar system. J Sol Energy Eng 2013;135: 011007.1e.8. [14] Ibrahim OM, Klein SA. Thermodynamic properties of ammoniaewater mixtures. In: ASHRAE transactions: symposia, CH-93-21-2 1993. [15] Nag PK, Gupta AVSSKS. Exergy analysis of the Kalina cycle. Appl Therm Eng 1998;18(6):427e39. [16] Wang JF, Dai YP, Gao L. Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry. Appl Energy 2009;86(6):941e8. [17] Sun FM, Ikegami Y, Jia BJ, Arima H. Optimization design and exergy analysis of organic Rankine cycle in ocean thermal energy conversion. Appl Ocean Res 2012;35:38e46. [18] Kotas T. The exergy method of thermal plant analysis. Melbourne, Florida, USA: Krieger Publishing Company; 1995. [19] Uehara H, Miyara A, Ikegami Y, Nakaoka T. Performance analysis of an OTEC plant and a desalination plant using an integrated hybrid cycle. J Sol Energy Eng 1996;118:115e22. [20] Weather data:. [21] World ocean data: . [22] Tripanagnostopoulos Y, Yianoulis P, Papaefthimiou S, Zafeiratos S. CPC solar collectors with flat bifacial absorbers. Sol Energy 2000;69(3):191e203.
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Energyeexergy analysis and optimization of the solar-boosted Kalina cycle system 11 (KCS-11) Faming Sun a, b, *, Weisheng Zhou c, Yasuyuki Ikegami d, Kenichi Nakagami c, Xuanming Su b a
Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan Ritsumeikan Global Innovation Research Organization, Ritsumeikan University, Kyoto 603-8577, Japan c College of Policy Science, Ritsumeikan University, Kyoto 603-8577, Japan d Institute of Ocean Energy, Saga University, 1-Honjo machi, Saga 840-8502, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2012 Accepted 11 December 2013 Available online 6 January 2014
Energyeexergy analysis and parameter design optimization of the KCS-11 solar system with an auxiliary superheater are studied in low-grade thermal energy conversion (LTEC). Firstly, from a thermodynamics point of view, the corresponding calculation model is built to solve the system state points as well as the exergy input/output/loss for each system component. And then, according to the characteristics of the KCS-11 solar system, the verification items are given to verify the correctness of the calculation model. Afterward the model is proved to be correct by sampling check a set of calculation data. On that basis, the corresponding parameter design optimization and system performance analysis are carried out from the viewpoint of the maximization of the exergy output in KCS-11 solar system at a certain scale. Results show that the mass flow rates of working fluid and solar collector subcycle and also ammonia mass fraction are important system operation parameters that should be optimized to deduce the irreversible behavior of the solar system for producing more useful energy. Meanwhile, the heat-transfer rate distribution ratio of the superheater should be large enough to ensure that the expanding vapor in the turbine is superheated. Finally, an optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. In this case, the maximum generated power is 491 kW showing 35.6% exergy efficiency and 6.48% energy efficiency of the system for the month of August. The size of the system in terms of power generated of each major equipment is listed as follows: solar evaporator (370 kW), superheater (106 kW), condenser (298 kW), turbine (491 kW), separator (43 kW), absorber (37 kW), pump (8 kW), regenerator (38 kW), and diffuser (17 kW). And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities. In this way, the maximum annual power generation of the KCS-11 solar system is about 553,520 kW h. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: KCS-11 solar system Energy analysis Exergy analysis Optimization design Power generation
1. Introduction In recent years, research on the conversion of low-grade heat from sources such as geothermal heat, waste heat, low-temperature solar thermal heat, etc. into electrical power or LTEC has received a lot of attention [1e4]. Ammoniaewater thermodynamic cycle is being considered as a more promising way for power generation in LTEC. Zamfirescu and Dincer [5] have undertaken a study to thermodynamically assess the performance of an ammoniaewater Rankine cycle that uses no boiler, but rather the saturated liquid is flashed by a positive displacement expander for
* Corresponding author. Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan. E-mail address: [email protected] (F. Sun). 0960-1481/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2013.12.015
power generation. Results showed that it has best performance when compared with the ones obtained for conventional organic Rankine cycle and a Kalina-kind cycle having a resorber instead of the usual distillation and condensation subsystem. It is known that the ammoniaewater Rankine cycle is in general known as Kalina cycle after the name of its inventor [6]. KCS-11 is a well-known Kalina cycle for low-temperature driven power generation and using ammoniaewater as its working fluid for this purpose. Many researchers tried their best to clear the characteristics of the KCS-11 for using various forms of low-temperature heat sources. Such as, Hettiarachchi and Worek et al. [7] examined the KCS-11 for lowtemperature geothermal heat sources and compared with an organic Rankine cycle (ORC). Results showed that the KCS-11 has better overall performance at moderate pressures than that of ORC. Lu et al. [8] also examined the KCS-11 for geothermal power
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Nomenclature cp Ex h Io _ m P Q_ s t T
Dt DTm U y W Ws,r CPC ETC FPC LTEC OTEC KCS-11
specific heat at constant pressure, 3.9 kJ/kg K the exergy, kJ/s specific enthalpy, kJ/kg the exergy loss, kJ/s mass flow rate, kg/s pressure, kPa heat-transfer rate, kW specific entropy, kJ/kg K temperature, C absolute temperature, K temperature difference, C logarithmic mean temperature difference, C overall heat-transfer coefficient, kW/m2 K ammonia mass fraction, kg/kg power output, kW solar radiation intensity, W/m2 compound parabolic concentrating evacuated tube solar collector flat plate solar collector low-grade thermal energy conversion ocean thermal energy conversion Kalina cycle system 11
Greek letters a first order loss coefficient of the solar collector b second order loss coefficient of the solar collector D differential h thermal efficiency, % hsc solar collector efficiency [e] k heat-transfer rate distribution ratio of the superheater [e] _ 6 =m _ 5 [e] x1 ¼ m x1 Gt average monthly sunshine duration, h Subscripts a outlet of the solar collector abs absorber
generation and compared with the existing Kawerau ORMAT binary plant in New Zealand. And parametric sensitivity analysis of KCS-11 was carried out for the specific power output and net thermal efficiency by changing the temperatures of both heat source and heat sink for a given ammoniaewater composition. Meanwhile, Lolos [9] investigated the KCS-11 with a main heat source provided by flat plate solar collectors and an external heat source used for superheating the vapor to expand in the turbine. Later, Mittelman [10] proposed a combined Rankine/KCS-11 power block for concentrating solar thermal power (CSP). All their results show that the KCS-11 is a better choice for exploiting and utilizing the low-temperature thermal energy. However the heat source temperature of the KCS-11 is assumed constant in their research. So as for solar thermal power generation system, the optimal operation scheme of the KCS-11 should be paid much attention for designing high performance KCS-11 solar system in engineering practice, since the solar heat source varies with time as well as operation conditions. KCS-11 solar system is the hybrid of the power generation subcycle and solar collector subcycle. The power generation subcycle is constructed from Kalina cycle system 11. Sun et al. [11e13] have studied the performance of KCS-11 solar system from the viewpoint of energy analysis. Results show that the system pressure difference is an important performance benchmark in this system. Based on
c ca cs csc csi cso cwf dif exg f i ii in is k net o out opt pgc pp r rg s sc scc sds se sewf sh sl sp sv tbn to wf wfp 0
269
condenser no difference between the collector temperature and ambient temperature cold seawater cold seawater subcycle cold seawater at the inlet cold seawater at the outlet working fluid side in condenser diffuser exergy inlet of the solar collector heat exchanger end section (heat source inlet) number of the state point in KCS-11 solar system inlet isentropic process KCS-11 solar system net heat exchanger end section (heat source outlet) outlet optimal power generation subcycle pinch point solar radiation regenerator solar solar collector solar collector subcycle system dead state solar evaporator working fluid side in solar evaporator superheater saturated liquid separator saturated vapor turbine total working fluid working fluid pump environment state
this, a real-time optimal operation scheme is given for high system performance. However, the exergy analysis to deduce the irreversible behavior of the solar system for producing more useful energy is still not considered even though it is significant for designing high performance solar system in engineering practice. So, in this study, energyeexergy analysis of the KCS-11 solar system with an auxiliary superheater is studied in LTEC. The corresponding calculation model is built to solve the system state points as well as the exergy input/ output/loss for each system component. And then parameter design optimization is carried out in KCS-11 solar system for producing more useful energy. Finally, an optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. Thus the way of high-efficiency utilization of solar energy in KCS-11 solar system is clarified. 2. KCS-11 solar system modeling 2.1. System description The proposed solar systems are mainly including power generation subcycle with an auxiliary superheater, solar collector subcycle and cold seawater subcycle. And ammoniaewater mixture is the working fluid, whose thermodynamic properties are
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simulated by using Ibrahim’s data [14]. Therefrom, main devices of the system are listed and described as follows: ➢ A working fluid pump, a device used in this system to allow the flowing working fluid in liquid to overcome gravity and pressure loss. ➢ A regenerator, a device used in this system to preheat the compressed liquid before sending it to the solar evaporator by using exhaust waste heat of the system. ➢ A solar evaporator, a device used in this system for the evaporation of the compressed liquid to wet vapor by using solar heat. ➢ A solar collector, a device used in this system to collect heat by capturing solar radiation. ➢ A separator, a vaporeliquid device used in this system to separate the ammoniaewater mixture into saturated vapor and saturated liquid. ➢ A superheater, a device used in this system to heat up the saturated ammonia vapor to superheated ammonia vapor. ➢ A turbine, a device used in this system to extract thermal energy from pressurized ammonia vapor and use it to do mechanical work on a rotating output shaft. ➢ A generator, a device used in this system to convert mechanical energy to electrical energy. ➢ A diffuser, a device used in this system to releases pressure of the working fluid from compressed liquid state to saturated liquid state. ➢ An absorber, a device used in this system to mix the wet vapor with the saturated liquid. ➢ A condenser, a device used in this system for the condensation of the wet vapor into saturated liquid. Based on the KCS-11, which is commonly used in recovering energy from the low-temperature heat resources, the KCS-11 solar
system with an auxiliary superheater is proposed here, and its schematic diagram is shown in Fig. 1. The turbine exhaust wet vapor (10) is mixed with saturated liquid (9) in the absorber. And the wet vapor (1) leaving the absorber is cooled in the condenser to become the saturated liquid (2). Then it is compressed to the compressed liquid (3) by the working fluid pump. Meanwhile, the working fluid wet vapor (5) is separated into rich ammoniaewater mixture saturated vapor (6) and the poor ammoniaewater mixture saturated liquid (7), where the saturated vapor is superheated to the superheated vapor (11) in the superheater by auxiliary heat source, such as geothermal systems, solar concentrator module or other similar sources etc. And then the superheated vapor is expanded in the turbine to generate electricity by using a generator. Moreover, the compressed liquid (8) leaving the regenerator releases pressure in the diffuser to become saturated liquid. And the compressed liquid (4) reheated by the regenerator is sent to the solar evaporator, where it is heated to saturated liquid (40 ) and then boiled to wet vapor by the solar heat. Furthermore, the corresponding solar collector subcycle can be designed by adjusting its solar collector area and mass flow rate.
2.2. Basic parameters and general assumption In solar collector subcycle, the effective solar radiation energy gain at solar collector is given as
Q_ sc;r ¼ Ws;r $Asc $hsc
(1)
where Ws,r reflects solar radiation intensity, it comes from local weather conditions of the solar system. Asc represents the area of the solar collector and hsc means the efficiency of the solar collector, which can be expressed as follows.
Fig. 1. Schematic diagram of the KCS-11 solar system.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
hsc ¼ hsc;ca a
Dtsc Ws;r
Dtsc 2 b Ws;r
Dtsc ¼ tsc t0 tsc ¼
(2)
In addition, leave the influence of solar collector subcycle pump to the temperature out of consideration, which means ta ¼ tb ¼ tc ¼ td and tf ¼ te. And then the temperature tf is solved as following
(3)
. 2 ta þ tf
(4)
in which, ta and tf represent the outlet and inlet temperature of the solar collector, respectively. And t0 is the ambient air temperature; hsc,ca is the solar collector efficiency value when there is no difference between the collector temperature and ambient temperature; a and b are loss coefficients of the solar collector. In addition, the useful energy gain at solar collector is
_ scc $cp $Dt Q_ sc ¼ m
271
tf ¼
t5 t4 $e
UA Q_ se t5 þt4 $ _ scc $cp Q_ se m
1e
_
m_ Q se$c !scc p
UA Q_ se $ t5 þ t4 _ scc $cp Q_ se m
_ scc $cp þ tf and Q_ se is assumed to be same with Q_ sc thus, ta ¼ Q_ se =m here. And a calculation model is necessary for solving state points in KCS-11 solar system, the corresponding calculation flow chart is shown in Fig. 2. Then based on the given initial condition of Tables 1
(5)
_ scc is the mass flow rate of the solar collector subcycle, cp in which, m represents the specific heat at constant pressure, Dt ¼ ta tf means the temperature difference of the solar collector. According to heat _ scc can be expressed as balance in solar collector, the m
_ scc ¼ m
2 ! ðta þtf Þ=2t0 ðta þtf Þ=2t0 b$ Ws;r $Asc $ hsc;ca a$ Ws;r Ws;r cp $ ta tf (6)
Meanwhile, in power generation subcycle, heat rate supplied to the cycle (solar evaporator) is shown below
_ wf $Dhk;se Q_ sewf ¼ m
(7)
Heat rate rejected from the cycle (condenser) is given as
_ wf $Dhk;c Q_ cwf ¼ m
(8)
_ wf is the mass flow rate of the working fluid. Dhk,se and where, m Dhk,c respectively represent the enthalpy difference of the solar evaporator and condenser in KCS-11 solar system. Also it is noticed that heat conduction of the heat exchanger is
Q_ ¼ UADTm
(9)
where Q_ is the rate of heat transfer; U is the overall heat-transfer coefficient; A is the cross-section area normal to the direction of heat transfer; DTm is called the logarithmic mean temperature difference (LMTD) and gives
DTm ¼
Dti Dto lnðDti =Dto Þ
(10)
in which, Dti represents the temperature difference of heat exchanger end section (heat source inlet), Dto shows the temperature difference of heat exchanger end section (heat source outlet). Therefore, the heat-transfer rate in the condenser is
Q_ c ¼ ðUAÞc ðDTm Þc
(11)
where
ðDTm Þc ¼
Dti Dto ðt tcso Þ ðt2 tcsi Þ ¼ 1 lnðDti =Dto Þ ln t1 tcso
(12)
t2 tcsi
In the same way, the LMTD of the evaporator and regenerator can also be given here.
(13)
Fig. 2. Flow chart of the KCS-11 solar system.
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Thus based on aforementioned discussion, the KCS-11 solar system thermal efficiency is given as
Table 1 Weather data of the Kumejima Island [20,21]. Month
tcsi [ C]
t0 [ C]
Ws,r [W/m2]
Gt [h]
January February March April May June July August September October November December
4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5
16.4 16.7 18.0 21.7 23.6 27.3 29.1 28.4 27.3 25.0 20.8 18.0
334 336 408 412 422 473 612 651 573 516 388 365
77.92 88.68 115.41 116.58 138.47 144.67 253.02 235.62 197.85 160.56 105.42 98.760
Table 2 Initial condition for simulation. Environment pressure Performance of the solar evaporator and condenser Turbine isentropic efficiency Pump isentropic efficiency Solar collector area Mass flow rate of cold seawater Ammonia mass fraction Performance of the regenerator Heat-transfer rate proportion for superheater Mass flow rate of working fluid Efficiency of the CPC solar collector Sampling month
P0 ¼ 0.10135 [MPa] ðUA=Q_ Þ ¼ 0:2 ½1= C se;c
htbn ¼ 85 [%] hwfp ¼ 75 [%]
Asc ¼ 1.0 [ha] _ cs ¼ 150 ½kg=s m y5 ¼ 0.95 [kg/kg] ðUA=Q_ Þrg ¼ 0:2 ½1= C k ¼ 2% [e] _ wf ¼ 6:5 ½kg=s m hsc ¼ 60 [%] August
and 2, t4 and t5 can be solved here. Thus by combining with Eqs. (2) _ scc and (6), the value of mass flow rate of solar collect subcycle m could be found. Moreover, the basic equations obtained from the conservation law for energy in the components are given in Table 3. 2.3. System performance The overall KCS-11 solar system performance can be evaluated by its thermal efficiency, exergy efficiency and exergy output. In power generation subcycle of the solar system, the thermal efficiency is
W
hpgc ¼ _ net Q to
(14)
_ wf $ The corresponding net power output is Wnet ¼ m _ 6 =m _ 5 . Meanwhile, Q_ to ¼ ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ, where x1 ¼ m Q_ se þ Q_ sh represents total heat-transfer rate. And Q_ se with Q_ sh represent the heat-transfer rate in solar evaporator and superheater, respectively. And their relationship is introduced as k ¼ Q_ sh =Q_ to 100%.
hk ¼ hpgc $hsc
(15)
Furthermore, based on the researches [15e17], the exergy efficiency of the power generation subcycle in KCS-11 solar system is given as
hexg ¼
P Exin I o Exin
(16)
P where the item Exin I o represents the exergy output of the solar system, in which, Exin ¼ Exin,se þ Exin,sh þ Exin,c is the sum of the exergy input at solar evaporator (Exin,se), superheater (Exin,sh) and condenser (Exin,c). In which, the definition of exergy input at solar evaporator, superheater and condenser is given in Table 4, P o respectively. In addition, T0 ¼ tsds þ 273.15, I is the sum of the exergy losses in all the components, tsds is the temperature of the system when it is in the dead state, here it is assumed as ambient air temperature t0. And the exergy of each state point ii in KCS-11 solar system considers only the physical exergy and the chemical exergy of water and ammonia cancels out in the exergy balances as entering and leaving quantities are the same [18]. Thus it can be _ ii $½ðhii h0 Þ T0 ðsii s0 Þ. In this way, the expressed as Exii ¼ m exergy loss in each component of the power generation subcycle is given in Table 3. According to aforementioned discussion, the KCS-11 solar system exergy efficiency is given as
hk;exg ¼ hexg $hsc
(17)
Finally, it should be noted that the following assumptions should be applied to the system. ➢ Based on the research of Uehara [2,19], turbine and pump isentropic efficiencies are separately given in 85% and 75% as an example. ➢ The piping and other auxiliary are considered no heat losses in the system. Based on the above assumptions, initial condition of KCS-11 solar system is given in Tables 1 and 2. Meanwhile, the data of Table 1 comes from the weather conditions of Kumejima Island (Lat. 26-20N, Lng. 126-48E) in Japan since it is the planned construction site of the OTEC (ocean thermal energy conversion) plant and the deep-sea cold seawater can be supplied therefrom [20,21]. And in solar collector subcycle, the applicable solar collectors include, but not limited to, FPC (flat plate solar collector), ETC (evacuated tube solar collector), CPC (compound parabolic concentrating), etc. Here it takes CPC solar collector as an example since it can supply heat sources with good performance, all year round. Thus reference [22], the parameters of the solar collector are given as hsc,ca ¼ 0.7035, a ¼ 2.5896 and b ¼ 7.4878.
Table 3 Basic equations and exergy loss items in the components of the KCS-11. Components
Basic equations
Exergy loss items
Solar evaporator Separator Superheater Turbine Regenerator Diffuser Absorber Condenser Working fluid pump
_ se $ðh5 h4 Þ Q_ se ¼ Q_ sewf ¼ m _ 5 h5 ¼ m _ 6 h6 þ m _ 7 h7 , m _5 ¼ m _ 6 þm _7 m _ sh $ðh11 h6 Þ Q_ sh ¼ m _ tbn $ðh11 h10 Þ, htbn ¼ (h11 h10)/(h11 h10,is) Wtbn ¼ m _ 4 ðh4 h3 Þ ¼ m _ 7 ðh7 h8 Þ m h8 ¼ h9 _1 ¼ m _ 10 þ m _9 _ 1 ¼ h10 m _ 10 þ h9 m _ 9, m h1 m _ c $ðh1 h2 Þ Q_ c ¼ Q_ cwf ¼ m _ wfp $ðh3 h2 Þ, hwfp ¼ (h3,is h2)/(h3 h2) Wwfp ¼ m
Iose ¼ Exin,se,scc Exout,se,scc þ Exin,se,pgc Exout,se,pgc Iosp ¼ Exin,sp,pgc Exout1,sp,pgc Exout2,sp,pgc Iosh ¼ 0 Iotbn ¼ Exin,tbn,pgc Exout,tbn,pgc Wtbn Iorg ¼ Exin1,rg,pgc þ Exin2,rg,pgc Exout1,rg,pgc Exout2,rg,pgc Iodif ¼ Exin,dif,pgc Exout,dif,pgc Ioabs ¼ Exin1,abs,pgc þ Exin2,abs,pgc Exout,abs,pgc Ioc ¼ Exin,c,csc Exout,c,csc þ Exin,c,pgc Exout,c,pgc Iowfp ¼ Wwfp þ Exin,wfp,pgc Exout,wfp,pgc
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Table 4 Definition of exergy input at solar evaporator, superheater and condenser, respectively. Solar evaporator
Superheater
Condenser
Exin,se ¼ Exin,se,scc Exout,se,scc _ scc ððhd h0 Þ T0 ðsd s0 ÞÞ Exin;se;scc ¼ m _ scc ððhe h0 Þ T0 ðse s0 ÞÞ Exout;se;scc ¼ m
Exin,sh ¼ Exin,sh,pgc Exout,sh,pgc _ sh ððh11 h0 Þ T0 ðs11 s0 ÞÞ Exin;sh;pgc ¼ m _ sh ððh6 h0 Þ T0 ðs6 s0 ÞÞ Exout;sh;pgc ¼ m
Exin,c ¼ Exin,c,csc Exout,c,csc _ cs ððhcsi h0 Þ T0 ðscsi s0 ÞÞ Exin;c;csc ¼ m _ cs ððhcso h0 Þ T0 ðscso s0 ÞÞ Exout;c;csc ¼ m
3. Optimization design of the KCS-11 solar system 3.1. Result rationality analysis In order to verify correctness of the solar system simulation program, firstly we take out a set of sampling calculation data from KCS-11 solar system with the initial condition, which is given in Tables 1 and 2, as an example for checking. The corresponding results are shown in Table 5. In this case, the design requirements of the solar collector in solar collector subcycle are inlet temperature 28.149 [ C], outlet temperature 75.760 [ C], solar collector subcycle mass flow rate 21.0 [kg/s] and water as the heat-transfer medium of the subcycle. Based on the characteristics of the KCS-11 solar system, the verification items are listed as follows: 1. Check whether or not ðUA=Q_ Þc ¼ lnððt1 tcso Þ=ðt2 tcsi ÞÞ= ððt1 tcso Þ ðt2 tcsi ÞÞ matches the specified condition ððUA=Q_ Þc ¼ 0:2 ½1= CÞ as given in Table 2. 2. Check whether or not ðUA=Q_ Þse ¼ lnððtd t5 Þ=ðte t4 ÞÞ= ððtd t5 Þ ðte t4 ÞÞ matches the specified condition ððUA=Q_ Þse ¼ 0:2 ½1= CÞ as given in Table 2. 3. Check whether or not ðUA=Q_ Þrg ¼ lnððt7 t4 Þ=ðt8 t3 ÞÞ= ððt7 t4 Þ ðt8 t3 ÞÞ matches the specified condition ððUA=Q_ Þrg ¼ 0:2 ½1= CÞ as given in Table 2. 4. Check whether or not k ¼ Q_ sh =ðQ_ se þ Q_ sh Þ ¼ x1 $ðh11 h6 Þ= ððh5 h4 Þ þ x1 $ðh11 h6 ÞÞ 100% matches the specified condition (k ¼ 2%) as given in Table 2. 5. Check whether or not the following equation is true for the heat balance in the solar evaporator, which is _ wf ðh5 h4 Þ. Q_ sc ¼ Ws;r $Asc $hsc ¼ Q_ se ¼ m 6. Check whether or not the following equation is true, which is _ 6 =m _ 5 ¼ ðy5 y7 Þ=ðy6 y7 Þ. m 7. Check whether or not the following equation is true for the heat balance in the condenser, as shown by _ cs cp ðtcso tcsi Þ ¼ Q_ cwf ¼ m _ wf ðh1 h2 Þ. Q_ c ¼ m 8. Check whether or not the following equation is true for the _ 5 h5 ¼ m _ 6 h6 þ m _ 7 h7 . heat balance in the separator: m
9. Check whether or not the following equation is true for the _ 1 h1 ¼ m _ 9 h9 þ m _ 10 h10 . heat balance in the absorber: m 10. Check whether or not the following equation is true for the _ 4 ðh4 h3 Þ ¼ m _ 7 ðh7 h8 Þ. heat balance in the regenerator: m 11. Check whether or not hpgc ¼ Wnet =Q_ to ¼ ðx1 $ðh11 h10 Þ ðh3 h2 ÞÞ=ððh5 h4 Þ þ x1 $ðh11 h6 ÞÞ matches the calculation result (hpgc ¼ 7.17 [%]) as shown in Table 5. 12. Check whether or not hsc ¼ 0.7035 2.5896(Dtsc) 7.4878(Dtsc)2 matches the specified condition (hsc ¼ 60 [%]) as given in Table 2, in which, Dtsc ¼ ((ta þ tf)/2 t0)/Ws,r. _ scc ¼ ðWs;r $Asc $hsc Þ=ðcp $ðta tf ÞÞ 13. Check whether or not m _ scc ¼ 21:0 ½kg=s) as shown matches the calculation result (m in Table 5. _ _ 14. Check whether or not tf ¼ ðt5 t4 eðUA=Q Þse $ðQ se =ðm_ scc cp Þt5 þt4 Þ _ scc cp ÞÞ=ð1 eðUA=Q_ Þse $ðQ_ se =ðm_ scc cp Þt5 þt4 Þ Þ and ta ¼ Q_ se = Q_ se =ðm _ scc $cp Þ þ tf match the calculation results (tf ¼ 28.149 [ C], ðm ta ¼ 75.760 [ C]) as shown in Table 5. 15. Check whether or not htbn ¼ (h11 h10)/(h11 h10,is) and hwfp ¼ (h3,is h2)/(h3 h2) match the specified conditions (htbn ¼ 85 [%] and hwfp ¼ 75 [%]) as given in Table 2. From these results, it is proven that the simulation programs designed for KCS-11 solar system is rational. And then based on aforementioned assumptions (see Tables 1 and 2) and calculations (see Tables 3 and 5), the corresponding system exergy analysis results are calculated and listed in Table 6. It should be clarified that percentage of the component exergy loss, as shown in the table, is defined as the ratio of exergy loss of the corresponding component and total exergy input of the cycle. Based on this, each of the components (i.e. solar evaporator, separator, superheater, turbine, absorber, condenser, pump, regenerator and diffuser) is estimated. As a result, the exergy loss is mainly in components of solar evaporator, condenser and turbine. And solar evaporator exergy loss takes up the largest proportion that is 23.1 [%]. That means that system parametric optimization analysis should be expected to decrease the system thermodynamic irreversibility in the following part. In addition, it is also found that the system exergy output (Table 6) calculated by using second law of thermodynamics is the
Table 5 Sampling results for KCS-11 solar system under condition of Tables 1 and 2. Point
t [ C]
P [MPa]
y [kg/kg]
h [kJ/kg]
s [kJ/(kg K)]
1 13.691 0.638 0.950000 791.028 3.199 2 12.493 0.638 0.950000 221.781 1.209 3 12.784 1.528 0.950000 223.620 1.211 3is 12.686 1.528 0.950000 223.161 1.209 4 28.102 1.528 0.950000 296.121 1.458 40 41.272 1.528 0.950000 360.130 1.666 5 42.978 1.528 0.950000 897.044 3.370 6 42.978 1.528 0.999738 1502.724 5.203 7 42.978 1.528 0.903777 334.156 1.665 8 13.667 1.528 0.903777 194.279 1.201 9 13.783 0.638 0.903777 194.279 1.206 10 11.305 0.638 0.999738 1433.149 5.342 10is 11.241 0.638 0.999738 1416.379 5.283 11 51.201 1.528 0.999738 1528.184 5.283 _ scc ¼ 21:0 ½kg=s, hpgc ¼ 7.17 [%], hk ¼ 4.30 [%], Wnet ¼ 285.606 [kW] ta ¼ 75.760 [ C], tf ¼ 28.149 [ C], tcso ¼ 10.828 [ C], m
v [m3/kg]
_ n =m _ 5 ½ m
0.0939 0.0016 0.0016 0.0015 0.0016 0.0016 0.0016 0.0865 0.0016 0.0015 0.0015 0.1920 0.1893 0.0903
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.4817 0.5183 0.5183 0.5183 0.4817 0.4817 0.4817
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Table 6 Exergy input/output/loss for the KCS-11 solar system. Design parameters
Exergy input
k ¼ 2% [e], hsc ¼ 60% [e], y5,opt ¼ 0.94 [kg/kg] Amount (kW)
Percentage (%)
Percentage (%)
Exergy efficiency Operation conditions
295.819 49.8 4.183 0.7 294.328 49.5 285.606 48.1 137.482 23.1 24.926 4.2 0 0 55.706 9.4 25.015 4.2 93.884 15.8 3.920 0.7 12.740 2.1 5.080 0.8 hexg ¼ 48.1 [%], hk,exg ¼ 28.9 [%] _ wf ¼ 6:5 ½kg=s, m _ scc ¼ 21:0 ½kg=s m
301.612 50.5 7.226 1.2 288.793 48.3 374.811 62.7 12.906 2.2 29.012 4.9 0 0 74.374 12.4 28.922 4.8 93.456 15.6 6.749 1.1 26.090 4.4 9.157 1.5 hexg ¼ 62.7 [%], hk,exg ¼ 37.6 [%] _ wf;opt ¼ 7:46 ½kg=s, m _ scc ¼ 40:03 ½kg=s m
Design parameters
k ¼ 2% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/
k ¼ 14% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/ kg]
Exergy output Exergy loss
Solar evaporator Superheater Condenser
k ¼ 2% [e], hsc ¼ 60% [e], y5 ¼ 0.95 [kg/kg] Amount (kW)
Solar evaporator Separator Superheater Turbine Absorber Condenser Pump Regenerator Diffuser
kg] Amount (kW) Exergy input
Exergy output Exergy loss
Exergy efficiency Operation conditions
Solar evaporator Superheater Condenser Solar evaporator Separator Superheater Turbine Absorber Condenser Pump Regenerator Diffuser
Percentage (%)
370.174 57.1 8.494 1.3 269.266 41.6 391.389 60.4 23.975 3.7 42.362 6.5 0 0 79.790 12.3 39.622 6.1 82.932 12.8 8.187 1.3 42.166 6.5 16.756 2.6 hexg ¼ 60.4 [%], hk,exg ¼ 33.8 [%] _ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:59 ½kg=s m
Amount (kW)
Percentage (%)
370.165 47.9 105.661 13.6 297.555 38.5 490.999 63.5 23.957 3.1 43.142 5.6 0 0 92.019 11.9 36.908 4.8 96.764 12.5 8.187 1.0 38.472 5.0 16.748 2.2 hexg ¼ 63.5 [%], hk,exg ¼ 35.6 [%] _ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:40 ½kg=s m
Fig. 3. Relationship between ammonia mass fraction y5 and exergy input/output/loss.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
275
Fig. 4. Relationship between solar collector efficiency hsc and exergy input/output/loss.
same as the system net power (Table 5) calculated by using first law of thermodynamics. This thermodynamic property is known as an inherent characteristic of the proposed KCS-11 solar system in this paper and it is proved that the designed calculation model for system exergy analysis is also rational.
3.2. System parametric optimization analysis From the point of view of the maximization of the exergy output in KCS-11 solar system at a certain scale or size, it is observed that the significant system operation parameters are the mass flow rates of the working fluid in power generation subcycle, cold seawater _ wf , m _ cs and m _ scc ), heatsubcycle and solar collector subcycle (m transfer rate distribution ratio of the superheater k, efficiency of the solar collector hsc, ammonia mass fraction y5 and weather data etc. And then the main objective of the parametric analysis is focused on optimization of these system operation parameters to find the maximum value of the exergy output, and its initial conditions are shown in Tables 1 and 2. Meanwhile, the corresponding system constraint conditions are assumed as 0.80 [kg/kg] y5 0.98 [kg/ kg], 0.05 [e] hsc 0.70 [e] and 0 [%] k 18 [%]. Furthermore, it _ wf under is worth noting that there is a convergence range for the m the abovementioned initial and constraint conditions in KCS-11 _ wf should be located in a solar system, which means that the m limited range to satisfy that all the increased ammoniaewater mixture working fluid can be converted from compressed liquid state to wet vapor state in the solar evaporator. In addition, according to the real productivity scale of the deep-sea cold seawater in Kumejima Island, the mass flow rate of cold seawater subcycle is _ cs ¼ 150 ½kg=s in this case as shown in Table 2. And it given as m should be noted that the constraint condition 0.05 [e] hsc 0.70 [e] can be obtained by adjusting the mass flow rate of the solar _ scc , appropriately. collector subcycle m
Based on aforementioned discussion, Fig. 3(a) shows the relationship between y5 and total exergy input of the solar system with the initial conditions (Table 2) by way of solar evaporator, superheater and condenser, respectively. Meanwhile, Fig. 3(b) gives exergy inputs of the solar system in terms of a percentage. From these figures it is known that the y5 has little effect on the exergy inputs of condenser, superheater and solar evaporator. Fig. 3(c) illustrates the exergy output and exergy loss of each component in the solar system. And Fig. 3(d) displays the exergy output and exergy losses of the solar system in percentage terms. As shown in the two figures, it is true that the sum of the exergy output and the
Fig. 5. Relationship between y5 and exergy output with hsc,opt.
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Fig. 6. Relationship between ammonia mass fraction y5 and exergy input/output/loss with hsc,opt.
total exergy loss is equal to the total exergy input. And it is also noticed that the exergy loss of the absorber is minus. The reason is that heat is released when ammonia gas dissolves in water in the absorber. In addition, it is found that when y5 is equal to 0.94 [kg/
kg], the exergy output of the power generation subcycle in KCS-11 solar system are maximum, which is 374.811 [kW] (Table 6). So the following parametric optimization analysis takes y5 ¼ 0.94 [kg/kg] as an example.
Fig. 7. Relationship between heat-transfer rate distribution ratio k and exergy input/output/loss.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
Fig. 8. Relationship between temperature and enthalpy in KCS-11 solar system.
Fig. 4 shows the relationship between hsc and exergy input/ output/loss of the solar system by using the initial conditions of Fig. 3 with y5 ¼ 0.94 [kg/kg]. It is known that the larger hsc within its effective range, the larger quantity energy obtained in solar evaporator. However, from Fig. 4(a) and (b) it can be seen that the exergy input of the solar system decreases with increasing hsc. The reason is that the larger hsc, the lower temperature of the solar evaporator, and then the smaller exergy input by way of solar evaporator. As shown in Fig. 4(c) and (d), there is an optimal hsc (hsc,opt ¼ 60% [e]) that maximizes the exergy output (374.811 [kW]) of the solar
277
system. Reason resulting in such phenomena is that the larger hsc within its effective range, the smaller exergy input of the solar system. Meanwhile, when the hsc gets smaller within its effective range, the exergy loss of the solar system gets larger as shown in the figure. In addition, from Figs. 3 and 4 it is known that the (hsc ¼ 60% [e], y5,opt ¼ 0.94 [kg/kg]) or (y5 ¼ 0.94 [kg/kg], hsc,opt ¼ 60% [e]) is a locally optimal solution for maximizing the exergy output of the solar system. To get the global optimal solution of the system, Fig. 5 shows the locally maximum exergy output of the solar system and the locally hsc,opt for each y5. And the corresponding exergy input/ output/loss is shown in Fig. 6. Thus it can be seen from these figures that the global optimal solution of the solar system is hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/kg]. And the global maximum exergy output is known as 391.389 [kW]. Meanwhile, the detail data of the exergy input/output/loss and the corresponding optimal operation pa_ wf;opt ¼ 9:05 ½kg=s, m _ scc;opt ¼ 42:59 ½kg=s) in this rameters (m case are listed in Table 6. In sum, the hsc,opt and y5,opt are chosen as an example for further discussion. Fig. 7 shows the influence of the superheater on exergy input/ output/loss of the KCS-11 solar system in terms of heat-transfer rate distribution ratio k. It’s worth mentioning here that the case (k ¼ 0% [e]) means the KCS-11 solar system without a superheater. Thus, from Fig. 7(a) and (b) it can be seen that the total exergy input of the solar system is increasing with increasing k since the exergy input of the superheater is increased markedly in this process. And it is shown from Fig. 7(c) and (d) that the larger k, the larger exergy output. Meanwhile, the exergy loss of each system component is nearly a constant and the system exergy efficiency is increasing slightly. Thus based on abovementioned simulation results and analysis, it is known that the superheater (k) has little influence on
Table 7 Optimal results for KCS-11 solar system under condition of Tables 1 and 2 with k ¼ 14% [e], hsc,opt ¼ 56% [e], y5,opt ¼ 0.90 [kg/kg]. Point
t [ C]
P [MPa]
y [kg/kg]
h [kJ/kg]
1 13.893 0.604 0.900000 598.598 2 12.264 0.604 0.900000 184.442 3 12.777 2.354 0.900000 187.932 3is 12.590 2.354 0.900000 187.059 4 46.424 2.354 0.900000 348.531 40 60.230 2.354 0.900000 417.505 5 62.462 2.354 0.900000 751.360 6 62.462 2.354 0.999103 1516.378 7 62.462 2.354 0.853776 394.541 8 13.505 2.354 0.853776 159.034 9 13.762 0.604 0.853776 159.034 10 35.828 0.604 0.999103 1541.024 10is 23.919 0.604 0.999103 1508.989 11 130.512 2.354 0.999103 1722.552 ta ¼ 71.054 [ C], tf ¼ 49.008 [ C], tcso ¼ 10.905 [ C], hpgc ¼ 11.58 [%], hk ¼ 6.48 [%], Wnet ¼ 490.884 [kW]
s [kJ/(kg K)]
v [m3/kg]
_ n =m _ 5 ½ m
2.626 1.179 1.182 1.179 1.713 1.924 2.922 5.069 1.921 1.163 1.172 5.737 5.631 5.631
0.0720 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016 0.0569 0.0016 0.0015 0.0015 0.2351 0.2233 0.0768
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3181 0.6819 0.6819 0.6819 0.3181 0.3181 0.3181
Table 8 _ ½kg=s. Optimum KCS-11 solar system operating conditions in Kumejima Island m Month
_ wf;opt ½kg=s m
_ scc;opt ½kg=s m
hsc,opt [e]
Exergy output [kW]
Other conditions
January February March April May June July August September October November December
1.98 2.08 3.64 4.08 4.39 5.75 8.35 9.05 7.53 6.26 3.56 2.81
6.99 8.44 15.49 16.03 16.30 26.82 33.32 42.40 31.24 23.07 16.70 10.84
0.24 0.25 0.36 0.40 0.42 0.49 0.55 0.56 0.53 0.49 0.37 0.31
110.736 117.981 205.145 227.458 244.828 320.816 454.144 490.999 411.909 342.916 201.559 157.188
P0 ¼ 0.10135 [MPa] ðUA=Q_ Þse;c ¼ 0:2 ½1= C htbn ¼ 85 [%] hwfp ¼ 75 [%] Asc ¼ 104 [m2] _ cs ¼ 150 ½kg=s m y5 ¼ 0.90 [kg/kg] ðUA=Q_ Þrg ¼ 0:2 ½1= C k ¼ 14% [e]
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Fig. 9. Exergy input/output/loss of the KCS-11 solar system in Kumejima Island for a year.
the system optimal solution (hsc,opt, y5,opt) from a thermodynamics point of view. Therefore from the point of view of system economy and device safety, the further discussion still takes the hsc,opt and y5,opt as an example to find the appropriate scale of the superheater (k) to satisfy the superheated vapor expansions in the turbine. It can be seen from the temperatureeentropy diagram (Fig. 8) of the KCS11 solar system that k ¼ 14% [e] (the real line with star mark) is the appropriate value to avoid damage to turbine since the superheated vapor expansion process does not contain the liquid particles. Meanwhile, the real line with cycle mark represents entropy flows of the initial conditions (Table 2) for comparison. Obviously, in this expansion process, the superheated vapor will condense out to liquid particles. As a result from the parametric optimization analysis, the following system case design in Kumejima Island for power generation will take k ¼ 14% [e] for an example. In addition, the corresponding detail data of the exergy input/output/loss of the optimal KCS-11 solar system and its state points in this case are listed in Tables 6 and 7.
optimization analysis results for sampling month (August) in Kumejima Island. And from the viewpoint of economics, the system y5 is set to a fixed value as 0.90 [kg/kg], which is the optimal value _ wf and hsc) need to be optifor August. As a result, parameters (m mized for the maximum annual power generation in the Kumejima Island. In which, the different hsc can be gotten by adjusting the _ scc . Finally, the mass flow rate of the solar collector subcycle m corresponding optimum solar system operating conditions can be calculated with aforementioned method and listed in Table 8. Fig. 9 shows exergy input/output/loss of the KCS-11 solar system in Kumejima Island for a year with its corresponding optimum operation conditions (Table 8). Concurring with expectations, the
4. An application case designed in Kumejima Island Based on the above discussion, suggestions could be given on selection of the system parameters for the maximum annual power generation with the help of the Kumejima Island weather data (Table 1) as follows. It is known that the larger the solar system scale, the larger the power generation. However, from an economic point of view and because of the limited conditions of the local area, the solar system should be in a certain scale. Therefore, as mentioned above, most system parameters are designed as shown in Table 2 as an example except some operating parameters, such as ammonia mass fraction y5, heat-transfer rate proportion for su_ wf , efficiency of the perheater k, mass flow rate of working fluid m solar collector hsc, etc. In which, the k for the annual power generation is given as 14 [%], which is based on the abovementioned
Fig. 10. Power generation of the KCS-11 solar system in Kumejima Island for a year.
F. Sun et al. / Renewable Energy 66 (2014) 268e279
total exergy input of the solar system is largest in summer as shown in Fig. 9(a). It is also noted from Fig. 9(b) that percentage of exergy input in the solar system by way of condenser is largest in the summer months. Reason resulting in such phenomena is the temperature difference of the ambient air and cold seawater, which varies with seasons. Meanwhile, it can be seen from Fig. 9(c) that the exergy output of the solar system in August is the largest, which is about 491 kW. And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities. Further, from Fig. 9(d), we know that the exergy efficiency and percentage of the exergy loss in each component are almost constant under their respective _ wf;opt , m _ scc;opt ). Meanwhile, it also optimum operation conditions (m shows a basis for the performance estimation of the optimum solar system. Based on this, the generated electrical energy for each month using the KCS-11 solar system under the optimum operation conditions of each month (Table 8) and weather data of Kumejima Island (Table 1) is shown in Fig. 10. In which, the dot line with ‘cycle’ mark and dash dot line with ‘square’ mark show the relationship _ wf;opt , m _ scc;opt and months, respectively. And then, the between m corresponding annual power generation of the KCS-11 solar system can be calculated therefrom, which is about 553520 kW h.
5. Conclusions The KCS-11 solar system with an auxiliary superheater is analyzed in the present study from both the first and the second law point of view providing a rational procedure for producing more useful energy in LTEC. Here, some concluding remarks have been summarized as follows: The system state points as well as the exergy input/output/loss for each system component are solved and proved to be correct with the help of the verification items in KCS-11 solar system. The parameter design optimization and system performance analysis are carried out and shown that the key operating parameters, which affect the system as a whole, have been iden_ wf ) and solar tified as the mass flow rates of working fluid (m _ scc ) and also ammonia mass fraction (y5). collector subcycle (m And, they all have an optimum value for a set of other operating parameters to realize the maximum exergy output of the system. The heat-transfer rate distribution ratio of the superheater (k) should be large enough to ensure that the expanding vapor in the turbine is superheated from the viewpoint of the device safety. An optimization calculation case is designed for illustration by using the monthly mean solar radiation statistics in Kumejima Island of Japan. In this case, the maximum generated power is 491 kW showing 35.6% exergy efficiency and 6.48% energy efficiency of the system for the month of August. The size of the system in terms of power generated of each major equipment is listed as follows: solar evaporator (370 kW), superheater (106 kW), condenser (298 kW), turbine (491 kW), separator (43 kW), absorber (37 kW), pump (8 kW), regenerator (38 kW), diffuser (17 kW). And the main system exergy losses are associated with internal consumptions of exergy in turbine (92 kW) and condenser (97 kW) due to irreversibilities.
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The exergy efficiency and percentage of the exergy loss in each component for each month are almost constant under their respective optimum operation conditions. Meanwhile, it also shows a basis for the performance estimation of the optimum solar system. The maximum annual power generation of the KCS-11 solar system is about 553,520 kW h in Kumejima Island of Japan. Acknowledgment The authors gratefully acknowledge the financial support of this work by the AY2012 Research Promotion Program (Young Scientist) (Ritsumeikan University). References [1] Kalina AI, Leibowitz HM. Application of the Kalina cycle technology to geothermal power generation. Geotherm Res Council Trans 1989;13:605e11. [2] Uehara H, Ikegami Y. Optimization of a closed-cycle OTEC system. J Sol Energy Eng 1990;112:247e56. [3] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. A feasibility study of CO2-based Rankine cycle powered by solar energy. JSME Int J Ser B (Fluids Therm Eng) 2005;48:540e7. [4] Sun FM, Ikegami Y. Direct method to maximize net power output of Rankine cycle in low-grade thermal energy conversion. J Therm Sci Eng Appl 2010;2: 0210031e7. [5] Zamfirescu C, Dincer I. Thermodynamic analysis of a novel ammoniaewater trilateral Rankine cycle. Thermochim Acta 2008;477(1-2):7e15. [6] Kalina A. Combined-cycle system with novel bottoming cycle. J Eng Gas Turbines Power 1984;106(4):737e42. [7] Madhawa Hettiarachchi HD, Golubovic M, Worek WM, Ikegami Y. The performance of the Kalina cycle system 11 (KCS-11) with low-temperature heat sources. J Energy Res Technol 2007;129:243e7. [8] Lu XL, Watson A, Deans J. Analysis of the thermodynamic performance of Kalina cycle system 11 (KCS11) for geothermal power plant: comparison with Kawerau ORMAT binary plant. In: ASME 2009 3rd international conference on energy sustainability collocated with the heat transfer and InterPACK09 conferences (ES2009) July 19e23, 2009. pp. 357e8. San Francisco, California, USA. [9] Lolos PA, Rogdakis ED. A Kalina power cycle driven by renewable energy sources. Energy 2009;34(4):457e64. [10] Mittelman G, Epstein M. A novel power block for CSP systems. Sol Energy 2010;84:1761e71. [11] Sun FM, Ikegami Y, Jia BJ. A study on Kalina solar system with an auxiliary superheater. Renew Energy 2012;41:210e9. [12] Sun FM, Ikegami Y, Arima H, Zhou WS. Performance analysis of the low temperature solar-boosted power generation system e part I: comparison between Kalina solar system and Rankine solar system. J Sol Energy Eng 2013;135:011006.1e.11. [13] Sun FM, Ikegami Y, Arima H, Zhou WS. Performance analysis of the low temperature solar-boosted power generation system e part II: thermodynamic characteristics of the Kalina solar system. J Sol Energy Eng 2013;135: 011007.1e.8. [14] Ibrahim OM, Klein SA. Thermodynamic properties of ammoniaewater mixtures. In: ASHRAE transactions: symposia, CH-93-21-2 1993. [15] Nag PK, Gupta AVSSKS. Exergy analysis of the Kalina cycle. Appl Therm Eng 1998;18(6):427e39. [16] Wang JF, Dai YP, Gao L. Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry. Appl Energy 2009;86(6):941e8. [17] Sun FM, Ikegami Y, Jia BJ, Arima H. Optimization design and exergy analysis of organic Rankine cycle in ocean thermal energy conversion. Appl Ocean Res 2012;35:38e46. [18] Kotas T. The exergy method of thermal plant analysis. Melbourne, Florida, USA: Krieger Publishing Company; 1995. [19] Uehara H, Miyara A, Ikegami Y, Nakaoka T. Performance analysis of an OTEC plant and a desalination plant using an integrated hybrid cycle. J Sol Energy Eng 1996;118:115e22. [20] Weather data: