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A study on Kalina solar system with an auxiliary superheater
Renewable Energy 41 (2012) 210e219
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A study on Kalina solar system with an auxiliary superheater Faming Sun*, Yasuyuki Ikegami, Baoju Jia Institute of Ocean Energy, Saga University, 840 8502, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 July 2011 Accepted 27 October 2011 Available online 16 November 2011
Based on the Kalina cycle, the solar-boosted system with an auxiliary superheater is investigated in the current paper. To predict the system performance, the corresponding calculation model is built. In accordance with engineering practice, the maximum pressure of the system is within 3 MW and the pinch point temperature difference of the regenerator is not less than 0.5 C in this paper. Then based on the characteristics of the Kalina solar system, the verification items are given to verify the correctness of the calculation model. Afterward the model is proven to be correct by sampling check a set of calculation data. Further, parameter performance analyses are carried out on the system. Results show that the system pressure difference is an important performance benchmark that can be used to evaluate the thermal efficiency of the power generation cycle. Furthermore, the relationship between the optimal mass flow rate and total heat transfer rate is noticeable in the solar system since solar radiation is changed with time. And the corresponding approximate expression is thus derived for optimal operation. Finally, an application case is designed by using direct normal solar radiation data in Tosashimizu city of Japan based on average hourly statistics. Ó 2011 Published by Elsevier Ltd.
Keywords: Kalina solar system System pressure difference System thermal efficiency Total heat transfer rate Superheater
1. Introduction Energy shortage and environmental pollution are two critical issues in this century that must be appropriately solved to save energy and reduce emission. Renewable energy is being considered as a more promising way to generate clean power, offering an excellent opportunity to supply electricity using non-CO2 emitting technology. Especially after the Fukushima nuclear accident in Japan, renewable energy has been gaining growing attention and respect throughout the world. Renewable energy is the energy which comes from natural resources such as sunlight, ocean thermal gradients, wind, rain, tides, and geothermal heat, etc. Recently, under the government policy guidance, solar energy, that is radiant energy produced by the sun, has attracted much attention. There are two main ways of converting solar radiation into energy: active and passive solar design [1]. Passive solar design is to design buildings for capturing the solar energy to save energy. The tenet for active solar design is collecting and converting solar radiation into heat or energy which can be stored. Many researchers devote themselves to active solar design and try to utilize solar clean renewable energy as heat source to generate inexhaustible power. Most of their studies utilize solar energy in
* Corresponding author. Tel.: þ81 955 202190; fax: þ81 955 202191. E-mail addresses: [email protected] (F.M. Sun), [email protected] (Y. Ikegami), [email protected] (B.J. Jia). 0960-1481/$ e see front matter Ó 2011 Published by Elsevier Ltd. doi:10.1016/j.renene.2011.10.026
Rankine cycle. Zhang et al. [2] first put forward the method using carbon dioxide for solar Rankine system in 2005. And the corresponding experimental model [3,4] and numerical model [5,6] were set up to test the characteristics and performance of the CO2-based thermodynamic cycle powered by solar energy. Later this method was developed by other researchers. Yamada [7] estimated the potential thermal efficiency and required effective area of a solar collector for a 100-kW SOTEC plant in 2009. Wang [8] proposed a low-temperature solar Rankine system utilizing R245fa as working fluid in 2010. In addition, the solar organic Rankine cycle (ORC) has also been developed by several researchers [9e13] in recent years. All their results show that utilization of solar energy provides an excellent way to supply clean power. However the thermal efficiency still needs to be improved. Therefore, some researchers attempt to utilize solar energy in Kalina cycle. It is well known that Kalina cycle has better performance than the traditional thermodynamic cycle (such as Rankine cycle) at the same temperature difference and shows a 10e20% improvement in thermal efficiency [14,15]. Later it is further confirmed that Kalina cycle can achieve a higher power output from a specified geothermal heat source when compared with organic Rankine cycle [16]. In the past few years, researchers have focused on ways to utilize the solar energy as the main heat source in Kalina cycle to improve the thermal efficiency. Lolos [17] investigated a Kalina cycle 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. Mittelman [18] proposed a combined
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
Nomenclature cp h _ m P Pmax Q_ s t Tt Dt U y W Ws;r
specific heat at constant pressure, 3.9 kJ/(kg K) specific enthalpy, kJ/kg mass flow rate, kg/s pressure, kPa maximum pressure of the system, kPa heat transfer rate, kW specific entropy, kJ/(kg K) temperature, C time, o’clock temperature difference, C overall heat transfer coefficient, kW/(m2 K) ammonia mass fraction, kg=kg power output, kW solar radiation, W=m2
Greek Letters D differential h thermal efficiency, % hs;co solar collector efficiency, [e] k heat transfer rate distribution ratio, [e] Subscripts abs absorber am ambient air c condenser
Rankine/Kalina cycle power block for concentrating solar thermal power (CSP). Arslan [19] used a new tool, the artificial neural network (ANN), to make a decision for the optimum working conditions of the processes in Kalina cycle system-34. All abovementioned results have suggested that the Kalina cycle provides an effective and efficient way to improve feasibility of the solar energy system. In summary, although many studies described that Kalina solar system could be a possible way to improve the practicability of the solar system and further to attain low cost, clean electricity. However, the real-time optimal control of the solar system for higher system thermal efficiency is scarcely considered even though it is significant for designing high performance solar system in engineering practice, since solar radiation varies with time during the day. It prompts us to carry out the present study. In this study, parameters influencing the Kalina solar system with an auxiliary superheater are initially discussed. Then the approximate expressions are derived by using fitting method. Finally an application case is designed for optimal operation with the aid of the direct normal solar radiation data in Tosashimizu city in Japan. Thus the way of high-efficiency utilization of solar energy in Kalina solar system is clarified.
2. Kalina solar system modeling 2.1. System description The proposed solar systems are mainly including a power generation cycle and a solar collector cycle. This study lays particular emphasis on qualitative analysis in power generation cycle with an auxiliary superheater that has a constant total heat transfer rate, and utilizes ammoniaewater mixture as the working fluid [20]. The main devices used in the system are listed below:
co cs csi cso cwf dif e el ewf E i net o opt pgc pp rg to tbn se sh sp kss scc wf wfp 0
➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢
211
collector cold seawater cold seawater at the inlet cold seawater at the outlet working fluid side in condenser diffuser evaporator exhaust loss working fluid side in evaporator exergy inlet net outlet optimal power generation cycle pinch point regenerator total turbine Solar-evaporator Superheater Separator Kalina solar system solar collector cycle working fluid working fluid pump environment state
A working fluid pump A regenerator A solar-evaporator A solar collector A separator A superheater A turbine A generator A diffuser An absorber A condenser
The Kalina solar system with an auxiliary superheater is proposed here based on the KCS-11 [21], which is commonly used in recovering energy from the low-temperature heat resources. The 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). The saturated vapor then becomes superheated vapor (11) in the superheater that is powered by an auxiliary heat source such as geothermal systems, solar concentrator modules or other similar sources. 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 boiled to become wet vapor using solar heat. Furthermore, the corresponding solar collector cycle can be designed by adjusting its solar collector area and mass flow rate.
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Fig. 1. Sketch of the Kalina solar system.
2.2. Basic parameters and general assumption
DTm ¼
In the solar collector cycle, heat rate absorbed from the solar collector is shown by
_ scc $cp $Dt Q_ ¼ m
(1)
_ scc is the mass flow rate of the solar collector cycle, cp in which, m represents the specific heat at constant pressure, and Dt means the temperature difference of the solar collector. Meanwhile, in the power generation cycle, heat rate supplied to the cycle (solarevaporator) is
_ wf $Dhkss;e Q_ ewf ¼ m
(2)
Heat rate rejected from the cycle (condenser) is given as
_ wf $Dhkss;c Q_ cwf ¼ m
(4)
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
(5)
Therefore, the heat transfer rate in the condenser is
Q_ c ¼ ðUAÞc ðDTm Þc
(6)
where
ðDTm Þc ¼
Dti Dto ðt tcso Þ ðt2 tcsi Þ ¼ 1 t tcso lnðDti =Dto Þ ln 1 t2 tcsi
(7)
In the same way, the LMTD of the evaporator and regenerator can also be given here. Meanwhile, in power generation cycle of the solar system, the thermal efficiency is shown as
W
(3)
_ wf is the mass flow rate of the working fluid. Dhkss;e and where, m Dhkss;c respectively represent the enthalpy difference of the evaporator and condenser in Kalina solar system. Also it is noticed that heat conduction of the heat exchanger is
Q_ ¼ UADTm
Dti Dto lnðDti =Dto Þ
hpgc ¼ _ net Q to
(8)
_ wf $ The corresponding net power output is Wnet ¼ m _ 6 =m _ 5. x1 ¼ m where Moreover, ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ, Q_ to ¼ Q_ se þ Q_ sh represents total heat transfer rate, which is regarded as a constant in this paper. Q_ se and Q_ sh represent the heat transfer rate in solar-evaporator and superheater, respectively. Further their relationship is introduced as k ¼ ðQ_ sh =Q_ to Þ 100%. Furthermore, the Kalina solar system thermal efficiency is
hkss ¼ hpgc $hs;co
(9)
where hs;co represents the solar collector efficiency. Fig. 2 gives its curve for the classical flat plate type collector from the Solar Rating
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
213
Fig. 2. Solar collector efficiency for flat plate type collector [22].
and Certification Corporation (SRCC) site [22]. The vertical axis shows efficiency ðhs;co Þ. And the horizontal axis shows the difference between the average collector temperature ðtco Þ and the ambient air temperature ðtam Þ. It is clear that the solar collector efficiency is not a constant. It depends strongly on the temperature difference ðDts;co ¼ tco tam Þ between the solar collector and the outside air. Thus, according to Fig. 2, the approximate expression of the classical flat plate type collector efficiency is given as
hs;co ¼ 0:0032Dts;co þ 0:74
(10)
where, Dts;co ¼ tco tam , and tco ¼ ðta þ tf Þ=2. ta and tf represent the outlet and inlet temperature of the solar collector respectively. Moreover, it should be noticed that the following assumptions should be applied to the system. ➢ The constant total heat transfer rate is assumed in the system. ➢ The power generation cycle is regarded as an ideal cycle. Turbine efficiency and pump efficiency are given ideally. ➢ It is assumed that there are no heat losses in the system from piping and other auxiliary items. Based on these assumptions, the initial condition of the Kalina solar system is given in Table 1. In accordance with engineering practice, the maximum pressure of the system is maintained within 3 MPa and the pinch point temperature difference of the regenerator is never less than 0.5 C (Dtrg;pp 0:5 C) in this paper. 2.3. Calculation model
Q_ to $ð1 kÞ _ wf m
_ cs ½kg=s m k½
y5 ½kg=kg _ wf ½kg=s m
(11)
Meanwhile, with knowing y5 and P5 , state of point 5 can be obtained. Thus the separator exit points (Point 6 and 7: saturated vapor and liquid) are calculated with the aid of P6 ¼ P5 and t6 ¼ t5 . Herefrom, with the heat balance in superheater, enthalpy of point 11 (superheated vapor) can be given as
h11 ¼ h6 þ
Table 1 Initial condition for simulation. ðUA=Q_ Þse;c ¼ 0:4½1= C Q_ to ½kW
conditions P2 and y2 ¼ y5 . After that, state of point 3 (compressed liquid) can be solved with P3 ¼ P5 , y3 ¼ y5 and s3 ¼ s2 . And then h4 is assumed for the simulation of point 4 (compressed liquid) with the aid of P4 ¼ P5 and y4 ¼ y5 . Afterward by using the heat balance in solar-evaporator, enthalpy of point 5 (wet vapor) is known as
h5 ¼ h4 þ
As mentioned above, a calculation model is necessary for solving state points in Kalina solar system to predict its performance. And then the thermodynamic quantitative analysis of the system can be discussed. Fig. 3 shows the calculation flow chart. Firstly, P2 and P5 are assumed as shown in Fig. 3. Then based on the given initial condition from Table 1, the state of the condenser exit point (Point 2: saturated liquid) can be calculated by using the
tcsi ¼ 4:0½ C ðUA=Q_ Þrg ½1= C
Fig. 3. Flow chart of the Kalina solar system.
Q_ to $k _ wf $x1 m
(12)
Knowing y11 ¼ y6 and P11 ¼ P6 , state of point 11 can be found. Moreover, as the Kalina solar system shown that P9 ¼ P2 and
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y9 ¼ y7 , the state of the outlet of the diffuser (Point 9: saturated liquid) can be given. Then the state of the point 8 (compressed liquid) can be obtained by using P8 ¼ P5 , y8 ¼ y7 and h8 ¼ h9 . Thus by checking whether or not the heat balance of regenerator is matched, it is possible to decide whether h4 is suitable or not. As the system shows that s10 ¼ s6 , y10 ¼ y6 and P10 ¼ P2 , the state of point 10 (wet vapor) can be calculated. Further according to _ 1 ¼ h10 m _ 10 þ h9 m _ 9 or the heat balance at absorber h1 m _5 ¼ m _ 6þm _ 7 , then _ 5 ¼ h10 m _ 6 þ h9 m _ 7 and mass balance m h1 m
h1 ¼ h9 ð1 x1 Þ þ h10 x1
(13)
_ 6 =m _ 5 , and the solar system is in the condition where where x1 ¼ m y1 ¼ y2 and P1 ¼ P2 . So the state of point 1 can be given. Afterward, by checking whether or not ðUA=Q_ Þrg match the specified conditions, it is also possible to deduce whether the P5 is suitable or not. Thus by solving the following equation,
t tcso ln 1 UA t2 tcsi ¼ ðt1 tcso Þ ðt2 tcsi Þ Q_ c
(14)
the cold source temperature outlet tcso can clearly be deduced. Finally, by checking whether or not Q_ c ¼ Q_ cwf , that is the heat _ cs cP ðtcso tcsi ÞÞ is transfer rate released from the system ðQ_ c ¼ m _ wf ðh1 h2 ÞÞ, it equal to that absorbed by the cold source ðQ_ cwf ¼ m is possible to decide whether P2 is suitable or not. Moreover, by disregarding any influence of the solar collector cycle pump on the temperature, we can assume that ta ¼ tb ¼ tc ¼ td and te ¼ tf . And using Equations (1) and (4) from the solar-evaporator, the temperature te can be solved as follows
UA Q_
te ¼
t5 t4 $e
Q_ to $ð1kÞ
_ scc $cp Q_ to $ð1 kÞ m se _ scc $cp m Q_ to $ð1kÞ UA $
$
1e
se
_ scc $cp m
Point
(15)
t5 þt4
1 9.562 2 5.117 3 5.403 4 15.379 5 60.169 6 60.169 7 60.169 8 11.902 9 12.157 10 4.378 11 68.714 te ¼ 22:917½ C, td ¼
3. Result and discussion
y½kg=kg
h [kJ/kg]
0.494 0.950000 1120.478 0.494 0.950000 187.313 1.944 0.950000 189.524 1.944 0.950000 235.993 1.944 0.950000 1285.993 1.944 0.998575 1533.178 1.944 0.760292 320.623 1.944 0.760292 92.674 0.494 0.760292 92.674 0.494 0.998575 1383.650 1.944 0.998575 1560.094 60:610½ C, tcso ¼ 4:837½ C, hpgc
s [kJ/(kg*K)]
_ 5 ½ _ n =m m
4.428 1.088 1.088 1.252 4.509 5.198 1.814 1.076 1.083 5.278 5.278 ¼ 12:90½%
1.0000 1.0000 1.0000 1.0000 1.0000 0.7961 0.2039 0.2039 0.2039 0.7961 0.7961
2. We check whether or not ðUA=Q_ Þse matches the specified conditions as given in Table 1.
t t5 ln d te t4 UA=Q_ se ¼ ðtd t5 Þ ðte t4 Þ 60:610 60:169 ln 22:917 15:379 ¼ ð60:610 60:169Þ ð22:917 15:379Þ ¼ 0:4½1= C
(17)
3. We check whether or not ðUA=Q_ Þrg matches the specified conditions as given for Table 2.
t7 t4 t8 t3 UA=Q_ rg ¼ ðt7 t4 Þ ðt8 t3 Þ 60:169 15:379 ln 11:902 5:403 ¼ ð60:169 15:379Þ ð11:902 5:403Þ ¼ 0:05½1= C
3.1. Result rationality validation In order to verify the correctness of the solar system calculation model, firstly we take out a set of calculation data as an example for checking, see Table 2, from the Kalina solar system with the initial conditions shown in Table 1. The design requirements of the solar collector are inlet temperature 22.917 C, outlet temperature 60.610 C, mass flow rate 1.0 kg/s, and water as the working fluid. Based on the characteristics of the Kalina solar system, the verification items are listed below: 1. We check whether or not ðUA=Q_ Þc matches the specified conditions as given in Table 1.
Check is successful.
Pressure [MPa]
ln
_ scc $cp Þ þ te : and td ¼ Q_ to $ð1 kÞ=ðm
t tcso ln 1 t2 tcsi UA=Q_ c ¼ ðt1 tcso Þ ðt2 tcsi Þ 9:562 4:837 ln 5:117 4 ¼ 0:4½1= C ¼ ð9:562 4:837Þ ð5:117 4Þ
Temperature ½ C
Check is successful.
t5 þt4
Q_
Table 2 _ cs ¼ 40½kg=s, _ wf ¼ 0:140½kg=s, m Kalina solar system on the condition of m Q_ to ¼ 150½kW, y5 ¼ 0:95½kg=kg, ðUA=Q_ Þrg ¼ 0:05½1= C, k ¼ 2%½ and _ scc ¼ 1:0½kg=s. m
Check is successful. 4. We check whether or not Q_ to matches the specified conditions as given for Table 2.
_ wf ððh5 h4 Þ þ x1 ðh11 h6 ÞÞ Q_ to ¼ Q_ se þ Q_ sh ¼ m ¼ 0:140 ðð1285:993 235:993Þ þ 0:7961 ð1560:094 1533:178ÞÞ ¼ 150½kW
(19)
Check is successful. 5. We check whether or not k matches the specified conditions as given for Table 2.
Q_
k ¼ _ sh 100% ¼ Q to ¼ (16)
(18)
_ wf ,x1 ,ðh11 h6 Þ m 100% 150
0:140 0:7961 ð1560:094 1533:178Þ 100% ¼ 2% 150 (20)
Check is successful.
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
W
hpgc ¼ _ net ¼ Q to
215
_ wf $ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ m Q_ to
0:140 ð0:7961 ð1560:094 1383:650Þ ð189:524 187:313ÞÞ ¼ 100% ¼ 12:90½% 150
6. We check whether or not the following equation is true, that is _ 5 ¼ ðy5 y7 Þ=ðy6 y7 Þ. _ 6 =m m
_6 m ¼ 0:7961 _5 m
(21)
y5 y7 0:95 0:760292 ¼ ¼ 0:7961 y6 y7 0:998575 0:760292
(22)
The error is 0.00 [%]. Therefore the check is successful. 7. We check whether or not the following equation is true for the _ cs cP heat balance in the condenser, as shown by Q_ c ¼ m _ wf ðh1 h2 Þ. ðtcso tcsi Þ ¼ Q_ cwf ¼ m
_ cs cP ðtcso tcsi Þ ¼ 40 3:9 ð4:837 4Þ Q_ c ¼ m ¼ 130:572½kJ=s
(23)
_ wf ðh1 h2 Þ ¼ 0:140 ð1120:478 187:313Þ Q_ cwf ¼ m ¼ 130:643½kJ=s
(24)
The error is 0.05 [%]. Therefore the check is successful. 8. We check whether or not the following equation is true for the _ 6 h6 þ m _ 7 h7 . _ 5 h5 ¼ m heat balance in the separator: m
_ 5 h5 ¼ 0:140 1285:993 ¼ 180:039½kJ=s m
(25)
_ 7 h7 ¼ 0:140 0:7961 1533:178 þ 0:140 0:2039 _ 6 h6 þ m m 320:623 ¼ 180:031½kJ=s
(26)
The error is 0.00 [%]. So the check is successful. 9. We check whether or not the following equation is true for the _ 9 h9 þ m _ 10 h10 . _ 1 h1 ¼ m heat balance in the absorber: m
_ 1 h1 ¼ 0:140 1120:478 ¼ 156:867½kJ=s m
(27)
_ 10 h10 ¼ 0:140 0:2039 92:674 þ 0:140 0:7961 _ 9 h9 þ m m 1383:650 ¼ 156:859½kJ=s
(31)
Check is successful. From these results, it is proven that the simulation programs designed for Kalina solar system is rational. As a result, the corresponding parameter performance analyses of the solar system are carried out. 3.2. Performance and parameter analysis It is known that increasing the pressure difference in the turbine appropriately will make the turbine more productive. To further know its effectiveness to power generation thermal efficiency of the proposed solar system, Fig. 4 shows system pressure difference DP ¼ P5 P2 versus power generation efficiency hpgc for significant cases ð1 i 22Þ listed in Table 3 where Pmax 3½MPa and Dtrg;pp 0:5½ C in accordance with engineering practice. In which, the cases from <1> to <5> represent the effectiveness of the heat transfer rate distribution ratio k to the relationship. Meanwhile, the cases from <6 > to <9 > reflect the influence of the regenerator performance ðUA=Q_ Þrg to the relationship. And the cases from <10> to <12> stand for the effect of the ammonia mass fraction of point 5 y5 to the relationship. Moreover, the cases from <13> to <17> represent the action of the total heat transfer rate Q_ to to the relationship. Finally, the cases from <18> to <22> show _ cs to the the effectiveness of the cold sources mass flow rate m relationship. Furthermore, the different DP can be gotten by _ wf . From this it adjusting the mass flow rate of the working fluid m can be seen from Fig. 4 that the DP can be considered as a key factor in performance evaluation of the solar energy system. Although _ cs and many operating parameters, such as k, ðUA=Q_ Þrg , y5 , Q_ to , m _ wf , have a significant influence on the Kalina solar system presm sure difference, the relationship between DP and hpgc remains relatively constancy as shown in this figure. This result leads up to the performance criterion of the power generation cycle in Kalina solar system by using fitting method, which is given below.
hpgc ¼ 0:64DP 3 4:90DP 2 þ 14:67DP þ 0:22
(32)
In which, DP has an effective range of 2.5 MPa. And Fig. 4 shows the fitting effect of the relationship. All the mark points represent
(28)
The error is 0.01 [%]. So the check is successful. 10. We check whether or not the following equation is true for the _ 7 ðh7 h8 Þ. _ 4 ðh4 h3 Þ ¼ m heat balance in the regenerator: m
_ 4 ðh4 h3 Þ ¼ 0:140 ð235:993 189:524Þ ¼ 6:506½kJ=s m
(29)
_ 7 ðh7 h8 Þ ¼ 0:140 0:2039 ð320:623 92:674Þ m ¼ 6:507½kJ=s
(30)
The error is 0.02 [%]. So the check is successful. 11. We check whether or not hpgc matches the results as shown in Table 2.
Fig. 4. Relationship between DP½MPa and hpgc ½% in case of ð1 i 22Þ
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the simulation cases shown in Table 3. The real line shows the relationship from Eq. (32). It can be seen from this figure that the equation mirrors the relationship between DP and hpgc quit strongly. And thence this equation can supply a performance benchmark DP for designing a new Kalina solar system. Because in practice, the maximum pressure of the solar system is limited, so the DP is also limited. For this reason, if we take DP as a standard, many thermodynamic parameters are investigated as follows to try to find an optimal way to design the Kalina solar system. _ wf and DP with different Fig. 5 shows the relationship between m k, which is listed in Table 3. The line with ‘o’ mark for case 1 represents k ¼ 0%, which means that the superheater does not play
a role in the Kalina solar system. Meanwhile, the other cases from 2 to 5 reflect the effectiveness of the superheater as shown in the figure. As can be seen in this figure, the maximum value of DP in each case with condition Pmax 3½MPa is almost the same by _ wf;opt . _ wf to m adjusting the corresponding operating parameter m _ wf is an important parameter in the Kalina This implies that the m solar system, showing that the superheater has little influence on _ wf;opt . On the power generation efficiency under the condition of m _ wf;opt of the Kalina solar the other hand, the corresponding m system with the superheater is smaller than that without superheater, which means that the superheater can reduce the system scale for same power generation and generating efficiency. In addition, the superheated vapor isentropic expansions in the turbine in practice can avoid damage to equipment since the vapor does not contain fluid particles and it decreases in temperature within limits that will not condense out to liquid particles. Thus the turbine efficiency is increased. Therefrom, the following discussion takes k ¼ 4% as an example. _ wf and DP with different Fig. 6 shows the relationship between m ðUA=Q_ Þrg . Here it should be noticed that there is a convergence _ wf in each case under the initial condition of Table 1 and range for m Table 3. In which the convergence range of case ð7 i 9Þ is determined by the limiting condition of the pinch point temperature difference in regenerator Dtrg;pp 0:5½ C. Meanwhile, the other case is determined by the side condition of maximum system pressure Pmax 3½MPa. As can be seen in this figure, the effective _ wf becomes wider as the value of ðUA=Q_ Þrg increases. range of m _ wf in Kalina solar This means that in practice the operability of m system becomes easier with better regenerator performance. Moreover, the maximum of DPðDPmax Þ in case <3> and <6> is nearly the same. And DPmax in case ð7 i 9Þ is decreased with increasing ðUA=Q_ Þrg . On this basis, the performance design of the regenerator in Kalina solar system will be decided by its Pmax . For example, Pmax ¼ 3½MPa is used in the design for a Kalina solar system. The best performance for the regenerator design shows that less than ðUA=Q_ Þrg ¼ 0:10½1= C is enough since the larger ðUA=Q_ Þrg needs a smaller pinch point temperature difference in the regenerator to satisfy its design condition Pmax ¼ 3½MPa as shown in Fig. 6. Furthermore, it is known that the smaller pinch point temperature difference in regenerator is difficult to realize in practice, so the following discussion takes ðUA=Q_ Þrg ¼ 0:05½1= C as an example.
_ wf ½kg=s and DP½MPa in case of ð1 i 5Þ Fig. 5. Relationship between m
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 6 i 9Þ Fig. 6. Relationship between m
Table 3 Significant cases ð1 i 22Þ in Kalina solar system. Case <1> <2> <3> <4> <5> Case <3> <6> <7> <8> <9> Case <10> <11> <12> <3> Case <13> <14> <3> <15> <16> <17> Case <18> <19> <20> <21> <3> <22>
k½ 0% 2% 4% 6% 8% ðUA=Q_ Þrg ½1= C 0.05 0.10 0.15 0.20 0.25 y5 ½kg=kg 0.80 0.85 0.90 0.95 Q_ to ½kW 50 100 150 200 250 300 _ cs ½kg=s m 5 10 20 30 40 50
Constant: ðUA=Q_ Þrg ¼ 0:05½1= C, y5 ¼ 0:95½kg=kg, _ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m Constant:
k ¼ 4%½, y5 ¼ 0:95½kg=kg,
_ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m
Constant: k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, _ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m Constant: k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, _ cs ¼ 40½kg=s y5 ¼ 0:95½kg=kg, m Variables: _ wf ½kg=s m
Constant:
k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, y5 ¼ 0:95½kg=kg, Q_ to ¼ 150½kW Variables: _ wf ½kg=s m
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 10 i 12Þ Fig. 7. Relationship between m
_ wf and DP with different Fig. 7 shows the relationship between m y5 . As can be seen in this figure, the range of convergence is wider _ wf for Kalina with decreasing y5 . This means that the operability of m solar system in practice becomes easier with the smaller ammonia mass fraction of point 5. Meanwhile, the maximum of DP in each case with condition Pmax 3½MPa is almost the same. However the _ wf;opt is significantly corresponding operating parameter m _ wf;opt is needed under the different. The larger y5 the smaller m condition of DPmax . This implies that the larger ammonia mass fraction of point 5 in Kalina solar system will reduce the system scale for same power generation and generating efficiency. In sum, the y5 ¼ 0:95½kg=kg is chosen as an example for further discussion. _ wf and DP with different Fig. 8 shows the relationship between m _ wf;opt is Q_ to . As can be seen in this figure, although the larger m needed under the condition of DPmax for the larger Q_ to, the DPmax in each case with condition Pmax 3½MPa is almost the same. This implies that the energy consumption of working fluid pump is increased with increasing the total heat transfer rate in a Kalina solar system. The corresponding net power output is increased since its power generation efficiency remains almost unchanged under the condition of DPmax . In brief, the large-scale solar system is cost-effective for the development and utilization of solar energy. _ wf and DP with different Fig. 9 shows the relationship between m _ cs . As can be seen in this figure, the DPmax for each case where m _ cs in a certain Pmax 3½MPa decreases slightly with decreasing m _ cs with limits has no effect on the extent. This implies that the m power generation thermal efficiency in Kalina solar system. _ cs will limit the scale of the solar system. For However the smaller m _ cs to a certain degree is preferred to the reason that the smaller m design the solar system since it can ease the burden of the cold source pump for the same power generation efficiency. _ wf;opt and Q_ to for DPmax with In brief, the relationship between m condition Pmax 3½MPa is noticeable in Kalina solar system since solar radiation changes with time. And according to the corresponding case ði ¼ 3; 13 i 17Þ, approximate expression of _ wf ;opt is given as the optimal operating parameter m
_ wf ;opt ¼ 0:9579 103 Q_ to þ 0:1786 103 m
(33)
217
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 13 i 17Þ Fig. 8. Relationship between m
statistics for example as shown in Fig. 10, the approximate expression of the solar radiation Ws;r is assumed as
Ws;r ¼ 0:0162Tt5 þ 0:9220Tt4 20:4622Tt3 þ 208:3654Tt2 849:4552Tt þ 919:1667
ð34Þ
This is represented by a dash line and Tt represents the daylight hours from 6:30 to 17:30. Thus the total heat transfer rate Q_ to can be expressed by
Ws;r $As;co $hs;co;opt Q_ to ¼ 1k
(35)
Where As;co reflects the area of the solar collector. Combine with Eq. (10) and case ði ¼ 3; 13 i 17Þ, the design case of the Kalina solar system is shown as follows. The temperature of ambient air is assumed as tam ¼ 25:0½ C. The optimal temperature of point 4 and 5 respectively is ðt4 Þopt ¼ 22:4½ C; ðt5 Þopt ¼ 77:2½ C with the help of case ði ¼ 3; 13 i 17Þ. Meanwhile, based on these cases, approximate _ scc;opt is given as expression of the optimal operating parameter m
_ scc;opt ¼ m
Q_ to
(36)
l
Here l is a constant. Thus we have the following equations
UA tf ;opt ¼
ðt5 Þopt ðt4 Þopt $e
Q_
se
UA 1e
Q_
se
$
$
l$ð1kÞ cp
l$ð1kÞ cp
ðt5 Þ
opt
þ ðt Þ 4
opt
ðt5 Þ
opt
þ ðt Þ 4
l$ð1 kÞ cp
opt
(37) ta;opt ¼ tco;opt ¼
l$ð1 kÞ cp
þ tf ;opt
ta;opt þ tf ;opt
. 2
(38) (39)
4. An application design case for Kalina solar system
Dts;co;opt ¼ tco;opt tam
(40)
As mentioned above, take the direct normal solar radiation data in Tosashimizu city of Japan [23] in the form of average hourly
hs;co;opt ¼ 0:0032Dts;co;opt þ 0:74
(41)
218
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 18 i 22Þ Fig. 9. Relationship between m
From these equations, we know that hs;co;opt is a constant in this case. Therefore the optimal Kalina solar system thermal efficiency is decided by the following equation
hkss;opt ¼ hpgc;opt $hs;co;opt
(42)
_ wf;opt and To summarize, by operating the parameters m _ scc;opt during daylight hours in this case, the Kalina solar m system optimal thermal efficiency hkss;opt remains steady at 10.61%. In which, l ¼ 200½kJ=kg, tf ;opt ¼ 28:6½ C, ta;opt ¼ 77:9½ C, Dts;co;opt ¼ 28:3½ C, x1;opt ¼ 0:765, tco;opt ¼ 53:3½ C, hs;co;opt ¼ 0:65, hpgc;opt ¼ 16:27%, As;co ¼ 1000½m2 . Based on _ wf;opt aforementioned discussion, the control scheme of the m _ scc;opt in Tosashimizu city of Japan from 6:30 to 17:30 for and m Kalina solar system is shown in Fig. 11, which is represented by the dash-dot line and dash line, respectively. In addition, the relationship between Q_ to and Tt is shown in this figure in terms
Fig. 10. Average hourly statistics for direct normal solar radiation in Tosashimizu city of Japan.
_ scc;opt , m _ wf ;opt , Q_ to ½kW and Tt ½o’clock for the design Fig. 11. Relationship between m case in Tosashimizu city of Japan.
_ scc;opt;case for case of a real line, while the ‘o’ mark shows m ði ¼ 3; 13 i 17Þ. It can be seen from this figure that _ scc;opt under the condition of case _ scc;opt;case agrees well with m m ði ¼ 3; 13 i 17Þ. To sum up, the application design case is found to be rational. 5. Conclusions The Kalina solar system, which utilizes an auxiliary superheater, is studied in the paper. Based on the characteristics of the Kalina solar system, the verification items are given to verify the correctness of the calculation model, and the rationality is confirmed by checking its random sampling result. Subsequently, most system _ cs , m _ wf and DP, are disparameters, such as k, ðUA=Q_ Þrg , y5 , Q_ to , m cussed for high performance power generation. Results show that the superheater in the Kalina solar system makes a little influence _ wf properly. to the power generation efficiency by adjusting the m However from the point of view of system scale, economy and device safety, the superheater is important. Meanwhile it is found that the system pressure difference is an important performance benchmark which can be used to evaluate the power generation cycle thermal efficiency. Normally, the larger system pressure difference, the better power generation thermal efficiency obtained. And by using fitting method, its approximate expression is derived. Furthermore in practice, the maximum pressure Pmax of the solar system is limited. The corresponding DPmax is restrained. Results show that the DPmax for each case in this paper with condition of constant Pmax is almost the same, here it is about 2.5 MPa. Therefore, the mass flow rate corresponding to the DPmax is optimal in the Kalina solar system. And then the approximate expression of the optimal mass flow rate with total heat transfer rate is given since the solar radiation is changed with time. Finally, by using the direct normal solar radiation data in Tosashimizu city of Japan in the form of average hourly statistics, an application case is designed. The general relational expression of Kalina solar system thermal efficiency is derived by using flat plate solar collector. The _ scc;opt to ensure that _ scc is for optimal m control scheme of the m hs;co;opt is a constant, at about 0.65 in this case. As a result, its system thermal efficiency remains almost constant at 10.58%. Moreover, by comparing with the cases results, the optimal mass flow rate expression is proven to be rational.
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
Acknowledgment This study was performed under the Research Program of IOES. References [1] Banos R, Manzano-Agugliaro F, Montoya FG, Gil C, Alcayde A, Gomez J. Optimization methods applied to renewable and sustainable energy: a review. Renewable and Sustainable Energy Reviews 2011;15:1753e66. [2] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. A feasibility study of CO2-based Rankine cycle powered by solar energy. JSME International Journal, Series. B (Fluids and Thermal Engineering) 2005;48:540e7. [3] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. Study of solar energy powered transcritical cycle using supercritical carbon dioxide. International Journal of Energy Research 2006;30:1117e29. [4] Zhang XR, Yamaguchi H, Uneno D. Experimental study on the performance of solar Rankine system using supercritical CO2. Renewable Energy 2007;32: 2617e28. [5] Zhang XR, Yamaguchi H, Uneno D, Fujima K, Enomoto M, Sawada N. Analysis of a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide. Renewable Energy 2006; 31(12):1839e54. [6] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. Theoretical analysis of a thermodynamic cycle for power and heat generation using supercritical carbon dioxide. Energy 2007;32:591e9. [7] Yamada N, Hoshi A, Ikegami Y. Performance simulation of solar-boosted ocean thermal energy conversion plant. Renewable Energy 2009;34:1752e8. [8] Wang XD, Zhao L, Wang JL, Zhang WZ, Zhao XZ, Wu W. Performance evaluation of a low-temperature solar Rankine cycle system utilizing R245fa. Solar Energy 2010;84(3):353e64. [9] Delgado-Torres AM, Garcia-Rodriguez L. Comparison of solar technologies for driving a desalination system by means of an organic Rankine cycle. Desalination 2007;216(1e3):276e91.
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[10] Manolakos D, Papadakis G, Kyritsis S. Experimental evaluation of an autonomous low-temperature solar Rankine cycle system for reverse osmosis desalination. Desalination 2007;203(1e3):366e74. [11] Bruno JC, Lopez-Villada J, Letelier E, Romera S, Coronas A. Modelling and optimisation of solar organic rankine cycle engines for reverse osmosis desalination. Applied Thermal Engineering 2008;28(17e18):2212e26. [12] Delgado-Torres AM, Garcia-Rodriguez L. Analysis and optimization of the lowtemperature solar organic Rankine cycle (ORC). Energy Conversion and Management 2010;51(12):2846e56. [13] Wang JL, Zhao L, Wang XD. A comparative study of pure and zeotropic mixtures in low-temperature solar Rankine cycle. Applied Energy 2010; 87(11):3366e73. [14] El-Sayed YM, Tribus M. A theoretical comparison of the Rankine and Kalina cycles. ASME Special Publications. AES-1; 1985. 97e102. [15] Ibrahim MB, Kovach RM. A Kalina cycle application for power generation. Energy 1993;18(9):961e9. [16] Kalina AI, Leibowitz HM. Application of the Kalina cycle technology to geothermal power generation. Geothermal Resources Council Transactions 1989;13:605e11. [17] Lolos PA, Rogdakis ED. A Kalina power cycle driven by renewable energy sources. Energy 2009;34(4):457e64. [18] Mittelman G, Epstein M. A novel power block for CSP systems. Solar Energy 2010;84:1761e71. [19] Arslan O. Power generation from medium temperature geothermal resources: ANN-based optimization of Kalina cycle system-34. Energy 2011;36(5): 2528e34. [20] Ibrahim OM, Klein SA. Thermodynamic properties of ammonia-water mixtures. ASHRAE Transactions: Symposia; 1993. CH-93-21-2. [21] Madhawa Hettiarachchi HD, Golubovic M, Worek WM, Ikegami Y. The performance of the Kalina cycle system 11(KCS-11) with low-temperature heat sources. Journal of Energy Resources Technology 2007;129:243e7. [22] Solar Rating and Certification Corporation (SRCC) site:. [23] Solar radiation data: .
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A study on Kalina solar system with an auxiliary superheater Faming Sun*, Yasuyuki Ikegami, Baoju Jia Institute of Ocean Energy, Saga University, 840 8502, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 July 2011 Accepted 27 October 2011 Available online 16 November 2011
Based on the Kalina cycle, the solar-boosted system with an auxiliary superheater is investigated in the current paper. To predict the system performance, the corresponding calculation model is built. In accordance with engineering practice, the maximum pressure of the system is within 3 MW and the pinch point temperature difference of the regenerator is not less than 0.5 C in this paper. Then based on the characteristics of the Kalina solar system, the verification items are given to verify the correctness of the calculation model. Afterward the model is proven to be correct by sampling check a set of calculation data. Further, parameter performance analyses are carried out on the system. Results show that the system pressure difference is an important performance benchmark that can be used to evaluate the thermal efficiency of the power generation cycle. Furthermore, the relationship between the optimal mass flow rate and total heat transfer rate is noticeable in the solar system since solar radiation is changed with time. And the corresponding approximate expression is thus derived for optimal operation. Finally, an application case is designed by using direct normal solar radiation data in Tosashimizu city of Japan based on average hourly statistics. Ó 2011 Published by Elsevier Ltd.
Keywords: Kalina solar system System pressure difference System thermal efficiency Total heat transfer rate Superheater
1. Introduction Energy shortage and environmental pollution are two critical issues in this century that must be appropriately solved to save energy and reduce emission. Renewable energy is being considered as a more promising way to generate clean power, offering an excellent opportunity to supply electricity using non-CO2 emitting technology. Especially after the Fukushima nuclear accident in Japan, renewable energy has been gaining growing attention and respect throughout the world. Renewable energy is the energy which comes from natural resources such as sunlight, ocean thermal gradients, wind, rain, tides, and geothermal heat, etc. Recently, under the government policy guidance, solar energy, that is radiant energy produced by the sun, has attracted much attention. There are two main ways of converting solar radiation into energy: active and passive solar design [1]. Passive solar design is to design buildings for capturing the solar energy to save energy. The tenet for active solar design is collecting and converting solar radiation into heat or energy which can be stored. Many researchers devote themselves to active solar design and try to utilize solar clean renewable energy as heat source to generate inexhaustible power. Most of their studies utilize solar energy in
* Corresponding author. Tel.: þ81 955 202190; fax: þ81 955 202191. E-mail addresses: [email protected] (F.M. Sun), [email protected] (Y. Ikegami), [email protected] (B.J. Jia). 0960-1481/$ e see front matter Ó 2011 Published by Elsevier Ltd. doi:10.1016/j.renene.2011.10.026
Rankine cycle. Zhang et al. [2] first put forward the method using carbon dioxide for solar Rankine system in 2005. And the corresponding experimental model [3,4] and numerical model [5,6] were set up to test the characteristics and performance of the CO2-based thermodynamic cycle powered by solar energy. Later this method was developed by other researchers. Yamada [7] estimated the potential thermal efficiency and required effective area of a solar collector for a 100-kW SOTEC plant in 2009. Wang [8] proposed a low-temperature solar Rankine system utilizing R245fa as working fluid in 2010. In addition, the solar organic Rankine cycle (ORC) has also been developed by several researchers [9e13] in recent years. All their results show that utilization of solar energy provides an excellent way to supply clean power. However the thermal efficiency still needs to be improved. Therefore, some researchers attempt to utilize solar energy in Kalina cycle. It is well known that Kalina cycle has better performance than the traditional thermodynamic cycle (such as Rankine cycle) at the same temperature difference and shows a 10e20% improvement in thermal efficiency [14,15]. Later it is further confirmed that Kalina cycle can achieve a higher power output from a specified geothermal heat source when compared with organic Rankine cycle [16]. In the past few years, researchers have focused on ways to utilize the solar energy as the main heat source in Kalina cycle to improve the thermal efficiency. Lolos [17] investigated a Kalina cycle 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. Mittelman [18] proposed a combined
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
Nomenclature cp h _ m P Pmax Q_ s t Tt Dt U y W Ws;r
specific heat at constant pressure, 3.9 kJ/(kg K) specific enthalpy, kJ/kg mass flow rate, kg/s pressure, kPa maximum pressure of the system, kPa heat transfer rate, kW specific entropy, kJ/(kg K) temperature, C time, o’clock temperature difference, C overall heat transfer coefficient, kW/(m2 K) ammonia mass fraction, kg=kg power output, kW solar radiation, W=m2
Greek Letters D differential h thermal efficiency, % hs;co solar collector efficiency, [e] k heat transfer rate distribution ratio, [e] Subscripts abs absorber am ambient air c condenser
Rankine/Kalina cycle power block for concentrating solar thermal power (CSP). Arslan [19] used a new tool, the artificial neural network (ANN), to make a decision for the optimum working conditions of the processes in Kalina cycle system-34. All abovementioned results have suggested that the Kalina cycle provides an effective and efficient way to improve feasibility of the solar energy system. In summary, although many studies described that Kalina solar system could be a possible way to improve the practicability of the solar system and further to attain low cost, clean electricity. However, the real-time optimal control of the solar system for higher system thermal efficiency is scarcely considered even though it is significant for designing high performance solar system in engineering practice, since solar radiation varies with time during the day. It prompts us to carry out the present study. In this study, parameters influencing the Kalina solar system with an auxiliary superheater are initially discussed. Then the approximate expressions are derived by using fitting method. Finally an application case is designed for optimal operation with the aid of the direct normal solar radiation data in Tosashimizu city in Japan. Thus the way of high-efficiency utilization of solar energy in Kalina solar system is clarified.
2. Kalina solar system modeling 2.1. System description The proposed solar systems are mainly including a power generation cycle and a solar collector cycle. This study lays particular emphasis on qualitative analysis in power generation cycle with an auxiliary superheater that has a constant total heat transfer rate, and utilizes ammoniaewater mixture as the working fluid [20]. The main devices used in the system are listed below:
co cs csi cso cwf dif e el ewf E i net o opt pgc pp rg to tbn se sh sp kss scc wf wfp 0
➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢
211
collector cold seawater cold seawater at the inlet cold seawater at the outlet working fluid side in condenser diffuser evaporator exhaust loss working fluid side in evaporator exergy inlet net outlet optimal power generation cycle pinch point regenerator total turbine Solar-evaporator Superheater Separator Kalina solar system solar collector cycle working fluid working fluid pump environment state
A working fluid pump A regenerator A solar-evaporator A solar collector A separator A superheater A turbine A generator A diffuser An absorber A condenser
The Kalina solar system with an auxiliary superheater is proposed here based on the KCS-11 [21], which is commonly used in recovering energy from the low-temperature heat resources. The 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). The saturated vapor then becomes superheated vapor (11) in the superheater that is powered by an auxiliary heat source such as geothermal systems, solar concentrator modules or other similar sources. 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 boiled to become wet vapor using solar heat. Furthermore, the corresponding solar collector cycle can be designed by adjusting its solar collector area and mass flow rate.
212
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
Fig. 1. Sketch of the Kalina solar system.
2.2. Basic parameters and general assumption
DTm ¼
In the solar collector cycle, heat rate absorbed from the solar collector is shown by
_ scc $cp $Dt Q_ ¼ m
(1)
_ scc is the mass flow rate of the solar collector cycle, cp in which, m represents the specific heat at constant pressure, and Dt means the temperature difference of the solar collector. Meanwhile, in the power generation cycle, heat rate supplied to the cycle (solarevaporator) is
_ wf $Dhkss;e Q_ ewf ¼ m
(2)
Heat rate rejected from the cycle (condenser) is given as
_ wf $Dhkss;c Q_ cwf ¼ m
(4)
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
(5)
Therefore, the heat transfer rate in the condenser is
Q_ c ¼ ðUAÞc ðDTm Þc
(6)
where
ðDTm Þc ¼
Dti Dto ðt tcso Þ ðt2 tcsi Þ ¼ 1 t tcso lnðDti =Dto Þ ln 1 t2 tcsi
(7)
In the same way, the LMTD of the evaporator and regenerator can also be given here. Meanwhile, in power generation cycle of the solar system, the thermal efficiency is shown as
W
(3)
_ wf is the mass flow rate of the working fluid. Dhkss;e and where, m Dhkss;c respectively represent the enthalpy difference of the evaporator and condenser in Kalina solar system. Also it is noticed that heat conduction of the heat exchanger is
Q_ ¼ UADTm
Dti Dto lnðDti =Dto Þ
hpgc ¼ _ net Q to
(8)
_ wf $ The corresponding net power output is Wnet ¼ m _ 6 =m _ 5. x1 ¼ m where Moreover, ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ, Q_ to ¼ Q_ se þ Q_ sh represents total heat transfer rate, which is regarded as a constant in this paper. Q_ se and Q_ sh represent the heat transfer rate in solar-evaporator and superheater, respectively. Further their relationship is introduced as k ¼ ðQ_ sh =Q_ to Þ 100%. Furthermore, the Kalina solar system thermal efficiency is
hkss ¼ hpgc $hs;co
(9)
where hs;co represents the solar collector efficiency. Fig. 2 gives its curve for the classical flat plate type collector from the Solar Rating
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
213
Fig. 2. Solar collector efficiency for flat plate type collector [22].
and Certification Corporation (SRCC) site [22]. The vertical axis shows efficiency ðhs;co Þ. And the horizontal axis shows the difference between the average collector temperature ðtco Þ and the ambient air temperature ðtam Þ. It is clear that the solar collector efficiency is not a constant. It depends strongly on the temperature difference ðDts;co ¼ tco tam Þ between the solar collector and the outside air. Thus, according to Fig. 2, the approximate expression of the classical flat plate type collector efficiency is given as
hs;co ¼ 0:0032Dts;co þ 0:74
(10)
where, Dts;co ¼ tco tam , and tco ¼ ðta þ tf Þ=2. ta and tf represent the outlet and inlet temperature of the solar collector respectively. Moreover, it should be noticed that the following assumptions should be applied to the system. ➢ The constant total heat transfer rate is assumed in the system. ➢ The power generation cycle is regarded as an ideal cycle. Turbine efficiency and pump efficiency are given ideally. ➢ It is assumed that there are no heat losses in the system from piping and other auxiliary items. Based on these assumptions, the initial condition of the Kalina solar system is given in Table 1. In accordance with engineering practice, the maximum pressure of the system is maintained within 3 MPa and the pinch point temperature difference of the regenerator is never less than 0.5 C (Dtrg;pp 0:5 C) in this paper. 2.3. Calculation model
Q_ to $ð1 kÞ _ wf m
_ cs ½kg=s m k½
y5 ½kg=kg _ wf ½kg=s m
(11)
Meanwhile, with knowing y5 and P5 , state of point 5 can be obtained. Thus the separator exit points (Point 6 and 7: saturated vapor and liquid) are calculated with the aid of P6 ¼ P5 and t6 ¼ t5 . Herefrom, with the heat balance in superheater, enthalpy of point 11 (superheated vapor) can be given as
h11 ¼ h6 þ
Table 1 Initial condition for simulation. ðUA=Q_ Þse;c ¼ 0:4½1= C Q_ to ½kW
conditions P2 and y2 ¼ y5 . After that, state of point 3 (compressed liquid) can be solved with P3 ¼ P5 , y3 ¼ y5 and s3 ¼ s2 . And then h4 is assumed for the simulation of point 4 (compressed liquid) with the aid of P4 ¼ P5 and y4 ¼ y5 . Afterward by using the heat balance in solar-evaporator, enthalpy of point 5 (wet vapor) is known as
h5 ¼ h4 þ
As mentioned above, a calculation model is necessary for solving state points in Kalina solar system to predict its performance. And then the thermodynamic quantitative analysis of the system can be discussed. Fig. 3 shows the calculation flow chart. Firstly, P2 and P5 are assumed as shown in Fig. 3. Then based on the given initial condition from Table 1, the state of the condenser exit point (Point 2: saturated liquid) can be calculated by using the
tcsi ¼ 4:0½ C ðUA=Q_ Þrg ½1= C
Fig. 3. Flow chart of the Kalina solar system.
Q_ to $k _ wf $x1 m
(12)
Knowing y11 ¼ y6 and P11 ¼ P6 , state of point 11 can be found. Moreover, as the Kalina solar system shown that P9 ¼ P2 and
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F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
y9 ¼ y7 , the state of the outlet of the diffuser (Point 9: saturated liquid) can be given. Then the state of the point 8 (compressed liquid) can be obtained by using P8 ¼ P5 , y8 ¼ y7 and h8 ¼ h9 . Thus by checking whether or not the heat balance of regenerator is matched, it is possible to decide whether h4 is suitable or not. As the system shows that s10 ¼ s6 , y10 ¼ y6 and P10 ¼ P2 , the state of point 10 (wet vapor) can be calculated. Further according to _ 1 ¼ h10 m _ 10 þ h9 m _ 9 or the heat balance at absorber h1 m _5 ¼ m _ 6þm _ 7 , then _ 5 ¼ h10 m _ 6 þ h9 m _ 7 and mass balance m h1 m
h1 ¼ h9 ð1 x1 Þ þ h10 x1
(13)
_ 6 =m _ 5 , and the solar system is in the condition where where x1 ¼ m y1 ¼ y2 and P1 ¼ P2 . So the state of point 1 can be given. Afterward, by checking whether or not ðUA=Q_ Þrg match the specified conditions, it is also possible to deduce whether the P5 is suitable or not. Thus by solving the following equation,
t tcso ln 1 UA t2 tcsi ¼ ðt1 tcso Þ ðt2 tcsi Þ Q_ c
(14)
the cold source temperature outlet tcso can clearly be deduced. Finally, by checking whether or not Q_ c ¼ Q_ cwf , that is the heat _ cs cP ðtcso tcsi ÞÞ is transfer rate released from the system ðQ_ c ¼ m _ wf ðh1 h2 ÞÞ, it equal to that absorbed by the cold source ðQ_ cwf ¼ m is possible to decide whether P2 is suitable or not. Moreover, by disregarding any influence of the solar collector cycle pump on the temperature, we can assume that ta ¼ tb ¼ tc ¼ td and te ¼ tf . And using Equations (1) and (4) from the solar-evaporator, the temperature te can be solved as follows
UA Q_
te ¼
t5 t4 $e
Q_ to $ð1kÞ
_ scc $cp Q_ to $ð1 kÞ m se _ scc $cp m Q_ to $ð1kÞ UA $
$
1e
se
_ scc $cp m
Point
(15)
t5 þt4
1 9.562 2 5.117 3 5.403 4 15.379 5 60.169 6 60.169 7 60.169 8 11.902 9 12.157 10 4.378 11 68.714 te ¼ 22:917½ C, td ¼
3. Result and discussion
y½kg=kg
h [kJ/kg]
0.494 0.950000 1120.478 0.494 0.950000 187.313 1.944 0.950000 189.524 1.944 0.950000 235.993 1.944 0.950000 1285.993 1.944 0.998575 1533.178 1.944 0.760292 320.623 1.944 0.760292 92.674 0.494 0.760292 92.674 0.494 0.998575 1383.650 1.944 0.998575 1560.094 60:610½ C, tcso ¼ 4:837½ C, hpgc
s [kJ/(kg*K)]
_ 5 ½ _ n =m m
4.428 1.088 1.088 1.252 4.509 5.198 1.814 1.076 1.083 5.278 5.278 ¼ 12:90½%
1.0000 1.0000 1.0000 1.0000 1.0000 0.7961 0.2039 0.2039 0.2039 0.7961 0.7961
2. We check whether or not ðUA=Q_ Þse matches the specified conditions as given in Table 1.
t t5 ln d te t4 UA=Q_ se ¼ ðtd t5 Þ ðte t4 Þ 60:610 60:169 ln 22:917 15:379 ¼ ð60:610 60:169Þ ð22:917 15:379Þ ¼ 0:4½1= C
(17)
3. We check whether or not ðUA=Q_ Þrg matches the specified conditions as given for Table 2.
t7 t4 t8 t3 UA=Q_ rg ¼ ðt7 t4 Þ ðt8 t3 Þ 60:169 15:379 ln 11:902 5:403 ¼ ð60:169 15:379Þ ð11:902 5:403Þ ¼ 0:05½1= C
3.1. Result rationality validation In order to verify the correctness of the solar system calculation model, firstly we take out a set of calculation data as an example for checking, see Table 2, from the Kalina solar system with the initial conditions shown in Table 1. The design requirements of the solar collector are inlet temperature 22.917 C, outlet temperature 60.610 C, mass flow rate 1.0 kg/s, and water as the working fluid. Based on the characteristics of the Kalina solar system, the verification items are listed below: 1. We check whether or not ðUA=Q_ Þc matches the specified conditions as given in Table 1.
Check is successful.
Pressure [MPa]
ln
_ scc $cp Þ þ te : and td ¼ Q_ to $ð1 kÞ=ðm
t tcso ln 1 t2 tcsi UA=Q_ c ¼ ðt1 tcso Þ ðt2 tcsi Þ 9:562 4:837 ln 5:117 4 ¼ 0:4½1= C ¼ ð9:562 4:837Þ ð5:117 4Þ
Temperature ½ C
Check is successful.
t5 þt4
Q_
Table 2 _ cs ¼ 40½kg=s, _ wf ¼ 0:140½kg=s, m Kalina solar system on the condition of m Q_ to ¼ 150½kW, y5 ¼ 0:95½kg=kg, ðUA=Q_ Þrg ¼ 0:05½1= C, k ¼ 2%½ and _ scc ¼ 1:0½kg=s. m
Check is successful. 4. We check whether or not Q_ to matches the specified conditions as given for Table 2.
_ wf ððh5 h4 Þ þ x1 ðh11 h6 ÞÞ Q_ to ¼ Q_ se þ Q_ sh ¼ m ¼ 0:140 ðð1285:993 235:993Þ þ 0:7961 ð1560:094 1533:178ÞÞ ¼ 150½kW
(19)
Check is successful. 5. We check whether or not k matches the specified conditions as given for Table 2.
Q_
k ¼ _ sh 100% ¼ Q to ¼ (16)
(18)
_ wf ,x1 ,ðh11 h6 Þ m 100% 150
0:140 0:7961 ð1560:094 1533:178Þ 100% ¼ 2% 150 (20)
Check is successful.
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
W
hpgc ¼ _ net ¼ Q to
215
_ wf $ðx1 ðh11 h10 Þ ðh3 h2 ÞÞ m Q_ to
0:140 ð0:7961 ð1560:094 1383:650Þ ð189:524 187:313ÞÞ ¼ 100% ¼ 12:90½% 150
6. We check whether or not the following equation is true, that is _ 5 ¼ ðy5 y7 Þ=ðy6 y7 Þ. _ 6 =m m
_6 m ¼ 0:7961 _5 m
(21)
y5 y7 0:95 0:760292 ¼ ¼ 0:7961 y6 y7 0:998575 0:760292
(22)
The error is 0.00 [%]. Therefore the check is successful. 7. We check whether or not the following equation is true for the _ cs cP heat balance in the condenser, as shown by Q_ c ¼ m _ wf ðh1 h2 Þ. ðtcso tcsi Þ ¼ Q_ cwf ¼ m
_ cs cP ðtcso tcsi Þ ¼ 40 3:9 ð4:837 4Þ Q_ c ¼ m ¼ 130:572½kJ=s
(23)
_ wf ðh1 h2 Þ ¼ 0:140 ð1120:478 187:313Þ Q_ cwf ¼ m ¼ 130:643½kJ=s
(24)
The error is 0.05 [%]. Therefore the check is successful. 8. We check whether or not the following equation is true for the _ 6 h6 þ m _ 7 h7 . _ 5 h5 ¼ m heat balance in the separator: m
_ 5 h5 ¼ 0:140 1285:993 ¼ 180:039½kJ=s m
(25)
_ 7 h7 ¼ 0:140 0:7961 1533:178 þ 0:140 0:2039 _ 6 h6 þ m m 320:623 ¼ 180:031½kJ=s
(26)
The error is 0.00 [%]. So the check is successful. 9. We check whether or not the following equation is true for the _ 9 h9 þ m _ 10 h10 . _ 1 h1 ¼ m heat balance in the absorber: m
_ 1 h1 ¼ 0:140 1120:478 ¼ 156:867½kJ=s m
(27)
_ 10 h10 ¼ 0:140 0:2039 92:674 þ 0:140 0:7961 _ 9 h9 þ m m 1383:650 ¼ 156:859½kJ=s
(31)
Check is successful. From these results, it is proven that the simulation programs designed for Kalina solar system is rational. As a result, the corresponding parameter performance analyses of the solar system are carried out. 3.2. Performance and parameter analysis It is known that increasing the pressure difference in the turbine appropriately will make the turbine more productive. To further know its effectiveness to power generation thermal efficiency of the proposed solar system, Fig. 4 shows system pressure difference DP ¼ P5 P2 versus power generation efficiency hpgc for significant cases ð1 i 22Þ listed in Table 3 where Pmax 3½MPa and Dtrg;pp 0:5½ C in accordance with engineering practice. In which, the cases from <1> to <5> represent the effectiveness of the heat transfer rate distribution ratio k to the relationship. Meanwhile, the cases from <6 > to <9 > reflect the influence of the regenerator performance ðUA=Q_ Þrg to the relationship. And the cases from <10> to <12> stand for the effect of the ammonia mass fraction of point 5 y5 to the relationship. Moreover, the cases from <13> to <17> represent the action of the total heat transfer rate Q_ to to the relationship. Finally, the cases from <18> to <22> show _ cs to the the effectiveness of the cold sources mass flow rate m relationship. Furthermore, the different DP can be gotten by _ wf . From this it adjusting the mass flow rate of the working fluid m can be seen from Fig. 4 that the DP can be considered as a key factor in performance evaluation of the solar energy system. Although _ cs and many operating parameters, such as k, ðUA=Q_ Þrg , y5 , Q_ to , m _ wf , have a significant influence on the Kalina solar system presm sure difference, the relationship between DP and hpgc remains relatively constancy as shown in this figure. This result leads up to the performance criterion of the power generation cycle in Kalina solar system by using fitting method, which is given below.
hpgc ¼ 0:64DP 3 4:90DP 2 þ 14:67DP þ 0:22
(32)
In which, DP has an effective range of 2.5 MPa. And Fig. 4 shows the fitting effect of the relationship. All the mark points represent
(28)
The error is 0.01 [%]. So the check is successful. 10. We check whether or not the following equation is true for the _ 7 ðh7 h8 Þ. _ 4 ðh4 h3 Þ ¼ m heat balance in the regenerator: m
_ 4 ðh4 h3 Þ ¼ 0:140 ð235:993 189:524Þ ¼ 6:506½kJ=s m
(29)
_ 7 ðh7 h8 Þ ¼ 0:140 0:2039 ð320:623 92:674Þ m ¼ 6:507½kJ=s
(30)
The error is 0.02 [%]. So the check is successful. 11. We check whether or not hpgc matches the results as shown in Table 2.
Fig. 4. Relationship between DP½MPa and hpgc ½% in case of ð1 i 22Þ
216
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
the simulation cases shown in Table 3. The real line shows the relationship from Eq. (32). It can be seen from this figure that the equation mirrors the relationship between DP and hpgc quit strongly. And thence this equation can supply a performance benchmark DP for designing a new Kalina solar system. Because in practice, the maximum pressure of the solar system is limited, so the DP is also limited. For this reason, if we take DP as a standard, many thermodynamic parameters are investigated as follows to try to find an optimal way to design the Kalina solar system. _ wf and DP with different Fig. 5 shows the relationship between m k, which is listed in Table 3. The line with ‘o’ mark for case 1 represents k ¼ 0%, which means that the superheater does not play
a role in the Kalina solar system. Meanwhile, the other cases from 2 to 5 reflect the effectiveness of the superheater as shown in the figure. As can be seen in this figure, the maximum value of DP in each case with condition Pmax 3½MPa is almost the same by _ wf;opt . _ wf to m adjusting the corresponding operating parameter m _ wf is an important parameter in the Kalina This implies that the m solar system, showing that the superheater has little influence on _ wf;opt . On the power generation efficiency under the condition of m _ wf;opt of the Kalina solar the other hand, the corresponding m system with the superheater is smaller than that without superheater, which means that the superheater can reduce the system scale for same power generation and generating efficiency. In addition, the superheated vapor isentropic expansions in the turbine in practice can avoid damage to equipment since the vapor does not contain fluid particles and it decreases in temperature within limits that will not condense out to liquid particles. Thus the turbine efficiency is increased. Therefrom, the following discussion takes k ¼ 4% as an example. _ wf and DP with different Fig. 6 shows the relationship between m ðUA=Q_ Þrg . Here it should be noticed that there is a convergence _ wf in each case under the initial condition of Table 1 and range for m Table 3. In which the convergence range of case ð7 i 9Þ is determined by the limiting condition of the pinch point temperature difference in regenerator Dtrg;pp 0:5½ C. Meanwhile, the other case is determined by the side condition of maximum system pressure Pmax 3½MPa. As can be seen in this figure, the effective _ wf becomes wider as the value of ðUA=Q_ Þrg increases. range of m _ wf in Kalina solar This means that in practice the operability of m system becomes easier with better regenerator performance. Moreover, the maximum of DPðDPmax Þ in case <3> and <6> is nearly the same. And DPmax in case ð7 i 9Þ is decreased with increasing ðUA=Q_ Þrg . On this basis, the performance design of the regenerator in Kalina solar system will be decided by its Pmax . For example, Pmax ¼ 3½MPa is used in the design for a Kalina solar system. The best performance for the regenerator design shows that less than ðUA=Q_ Þrg ¼ 0:10½1= C is enough since the larger ðUA=Q_ Þrg needs a smaller pinch point temperature difference in the regenerator to satisfy its design condition Pmax ¼ 3½MPa as shown in Fig. 6. Furthermore, it is known that the smaller pinch point temperature difference in regenerator is difficult to realize in practice, so the following discussion takes ðUA=Q_ Þrg ¼ 0:05½1= C as an example.
_ wf ½kg=s and DP½MPa in case of ð1 i 5Þ Fig. 5. Relationship between m
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 6 i 9Þ Fig. 6. Relationship between m
Table 3 Significant cases ð1 i 22Þ in Kalina solar system. Case <1> <2> <3> <4> <5> Case <3> <6> <7> <8> <9> Case <10> <11> <12> <3> Case <13> <14> <3> <15> <16> <17> Case <18> <19> <20> <21> <3> <22>
k½ 0% 2% 4% 6% 8% ðUA=Q_ Þrg ½1= C 0.05 0.10 0.15 0.20 0.25 y5 ½kg=kg 0.80 0.85 0.90 0.95 Q_ to ½kW 50 100 150 200 250 300 _ cs ½kg=s m 5 10 20 30 40 50
Constant: ðUA=Q_ Þrg ¼ 0:05½1= C, y5 ¼ 0:95½kg=kg, _ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m Constant:
k ¼ 4%½, y5 ¼ 0:95½kg=kg,
_ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m
Constant: k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, _ cs ¼ 40½kg=s Q_ to ¼ 150½kW, m Variables: _ wf ½kg=s m Constant: k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, _ cs ¼ 40½kg=s y5 ¼ 0:95½kg=kg, m Variables: _ wf ½kg=s m
Constant:
k ¼ 4%½, ðUA=Q_ Þrg ¼ 0:05½1= C, y5 ¼ 0:95½kg=kg, Q_ to ¼ 150½kW Variables: _ wf ½kg=s m
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 10 i 12Þ Fig. 7. Relationship between m
_ wf and DP with different Fig. 7 shows the relationship between m y5 . As can be seen in this figure, the range of convergence is wider _ wf for Kalina with decreasing y5 . This means that the operability of m solar system in practice becomes easier with the smaller ammonia mass fraction of point 5. Meanwhile, the maximum of DP in each case with condition Pmax 3½MPa is almost the same. However the _ wf;opt is significantly corresponding operating parameter m _ wf;opt is needed under the different. The larger y5 the smaller m condition of DPmax . This implies that the larger ammonia mass fraction of point 5 in Kalina solar system will reduce the system scale for same power generation and generating efficiency. In sum, the y5 ¼ 0:95½kg=kg is chosen as an example for further discussion. _ wf and DP with different Fig. 8 shows the relationship between m _ wf;opt is Q_ to . As can be seen in this figure, although the larger m needed under the condition of DPmax for the larger Q_ to, the DPmax in each case with condition Pmax 3½MPa is almost the same. This implies that the energy consumption of working fluid pump is increased with increasing the total heat transfer rate in a Kalina solar system. The corresponding net power output is increased since its power generation efficiency remains almost unchanged under the condition of DPmax . In brief, the large-scale solar system is cost-effective for the development and utilization of solar energy. _ wf and DP with different Fig. 9 shows the relationship between m _ cs . As can be seen in this figure, the DPmax for each case where m _ cs in a certain Pmax 3½MPa decreases slightly with decreasing m _ cs with limits has no effect on the extent. This implies that the m power generation thermal efficiency in Kalina solar system. _ cs will limit the scale of the solar system. For However the smaller m _ cs to a certain degree is preferred to the reason that the smaller m design the solar system since it can ease the burden of the cold source pump for the same power generation efficiency. _ wf;opt and Q_ to for DPmax with In brief, the relationship between m condition Pmax 3½MPa is noticeable in Kalina solar system since solar radiation changes with time. And according to the corresponding case ði ¼ 3; 13 i 17Þ, approximate expression of _ wf ;opt is given as the optimal operating parameter m
_ wf ;opt ¼ 0:9579 103 Q_ to þ 0:1786 103 m
(33)
217
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 13 i 17Þ Fig. 8. Relationship between m
statistics for example as shown in Fig. 10, the approximate expression of the solar radiation Ws;r is assumed as
Ws;r ¼ 0:0162Tt5 þ 0:9220Tt4 20:4622Tt3 þ 208:3654Tt2 849:4552Tt þ 919:1667
ð34Þ
This is represented by a dash line and Tt represents the daylight hours from 6:30 to 17:30. Thus the total heat transfer rate Q_ to can be expressed by
Ws;r $As;co $hs;co;opt Q_ to ¼ 1k
(35)
Where As;co reflects the area of the solar collector. Combine with Eq. (10) and case ði ¼ 3; 13 i 17Þ, the design case of the Kalina solar system is shown as follows. The temperature of ambient air is assumed as tam ¼ 25:0½ C. The optimal temperature of point 4 and 5 respectively is ðt4 Þopt ¼ 22:4½ C; ðt5 Þopt ¼ 77:2½ C with the help of case ði ¼ 3; 13 i 17Þ. Meanwhile, based on these cases, approximate _ scc;opt is given as expression of the optimal operating parameter m
_ scc;opt ¼ m
Q_ to
(36)
l
Here l is a constant. Thus we have the following equations
UA tf ;opt ¼
ðt5 Þopt ðt4 Þopt $e
Q_
se
UA 1e
Q_
se
$
$
l$ð1kÞ cp
l$ð1kÞ cp
ðt5 Þ
opt
þ ðt Þ 4
opt
ðt5 Þ
opt
þ ðt Þ 4
l$ð1 kÞ cp
opt
(37) ta;opt ¼ tco;opt ¼
l$ð1 kÞ cp
þ tf ;opt
ta;opt þ tf ;opt
. 2
(38) (39)
4. An application design case for Kalina solar system
Dts;co;opt ¼ tco;opt tam
(40)
As mentioned above, take the direct normal solar radiation data in Tosashimizu city of Japan [23] in the form of average hourly
hs;co;opt ¼ 0:0032Dts;co;opt þ 0:74
(41)
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F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
_ wf ½kg=s and DP½MPa in case of ði ¼ 3; 18 i 22Þ Fig. 9. Relationship between m
From these equations, we know that hs;co;opt is a constant in this case. Therefore the optimal Kalina solar system thermal efficiency is decided by the following equation
hkss;opt ¼ hpgc;opt $hs;co;opt
(42)
_ wf;opt and To summarize, by operating the parameters m _ scc;opt during daylight hours in this case, the Kalina solar m system optimal thermal efficiency hkss;opt remains steady at 10.61%. In which, l ¼ 200½kJ=kg, tf ;opt ¼ 28:6½ C, ta;opt ¼ 77:9½ C, Dts;co;opt ¼ 28:3½ C, x1;opt ¼ 0:765, tco;opt ¼ 53:3½ C, hs;co;opt ¼ 0:65, hpgc;opt ¼ 16:27%, As;co ¼ 1000½m2 . Based on _ wf;opt aforementioned discussion, the control scheme of the m _ scc;opt in Tosashimizu city of Japan from 6:30 to 17:30 for and m Kalina solar system is shown in Fig. 11, which is represented by the dash-dot line and dash line, respectively. In addition, the relationship between Q_ to and Tt is shown in this figure in terms
Fig. 10. Average hourly statistics for direct normal solar radiation in Tosashimizu city of Japan.
_ scc;opt , m _ wf ;opt , Q_ to ½kW and Tt ½o’clock for the design Fig. 11. Relationship between m case in Tosashimizu city of Japan.
_ scc;opt;case for case of a real line, while the ‘o’ mark shows m ði ¼ 3; 13 i 17Þ. It can be seen from this figure that _ scc;opt under the condition of case _ scc;opt;case agrees well with m m ði ¼ 3; 13 i 17Þ. To sum up, the application design case is found to be rational. 5. Conclusions The Kalina solar system, which utilizes an auxiliary superheater, is studied in the paper. Based on the characteristics of the Kalina solar system, the verification items are given to verify the correctness of the calculation model, and the rationality is confirmed by checking its random sampling result. Subsequently, most system _ cs , m _ wf and DP, are disparameters, such as k, ðUA=Q_ Þrg , y5 , Q_ to , m cussed for high performance power generation. Results show that the superheater in the Kalina solar system makes a little influence _ wf properly. to the power generation efficiency by adjusting the m However from the point of view of system scale, economy and device safety, the superheater is important. Meanwhile it is found that the system pressure difference is an important performance benchmark which can be used to evaluate the power generation cycle thermal efficiency. Normally, the larger system pressure difference, the better power generation thermal efficiency obtained. And by using fitting method, its approximate expression is derived. Furthermore in practice, the maximum pressure Pmax of the solar system is limited. The corresponding DPmax is restrained. Results show that the DPmax for each case in this paper with condition of constant Pmax is almost the same, here it is about 2.5 MPa. Therefore, the mass flow rate corresponding to the DPmax is optimal in the Kalina solar system. And then the approximate expression of the optimal mass flow rate with total heat transfer rate is given since the solar radiation is changed with time. Finally, by using the direct normal solar radiation data in Tosashimizu city of Japan in the form of average hourly statistics, an application case is designed. The general relational expression of Kalina solar system thermal efficiency is derived by using flat plate solar collector. The _ scc;opt to ensure that _ scc is for optimal m control scheme of the m hs;co;opt is a constant, at about 0.65 in this case. As a result, its system thermal efficiency remains almost constant at 10.58%. Moreover, by comparing with the cases results, the optimal mass flow rate expression is proven to be rational.
F.M. Sun et al. / Renewable Energy 41 (2012) 210e219
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