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Energy and exergy analyses of a modified combined cooling, heating, and power system using supercritical CO2
Energy xxx (2015) 1e9
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Energy and exergy analyses of a modified combined cooling, heating, and power system using supercritical CO2 Xiao Xiao Xu*, Chao Liu, Xiang Fu, Hong Gao, Yourong Li Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 May 2014 Received in revised form 10 April 2015 Accepted 11 April 2015 Available online xxx
In aim to reduce the greenhouse-gas emissions and improve the low-grade heat efficiency, a modified CCHP (combined cooling, heating, and power) system is proposed using supercritical CO2. This cycle combines a Brayton cycle and a transcritical ejector refrigeration cycle by adding an extraction turbine. A mathematical model is developed to simulate the modified CCHP system. Parametric analysis and exergy analysis are conducted to investigate the effects of key thermodynamic parameters on the performance and exergy destruction. Due to the difficulties in the thermal efficiency evaluation for CCHP system, a more practical performance metric is introduced in order to quantify system performance. The results indicate that both higher extraction rate and extraction pressure are helpful to gain more refrigeration. For the conditions considered, the exergy efficiency of the modified CCHP with the extraction turbine is higher than that of the CCHP with the no-extraction turbine from 10.4% to 22.5%. Furthermore, there is a large increase in the turbine power output and the exergy efficiency with increased turbine inlet temperature. It reveals that a rise of heat source quality benefits the system performance. © 2015 Elsevier Ltd. All rights reserved.
Keywords: CCHP CO2 Transcritical cycle Ejector Exergy Simulation
1. Introduction The advantages of the CCHP (combined cooling, heating, and power) are higher primary energy efficiency, more environmental benefits, and better economic feasibility [1]. CCHP is a suitable solution in the case of a medium- and small-scale basis (below 1 or 2 MWe) [2]. In particular, the application of CCHP in municipal energy systems and food industry demanding cold and heat simultaneously can be significant [3]. Recent studies revealed that the novel CCHP cycle combined a Rankine cycle or a Kalina cycle with an absorption refrigeration cycle or an ejector refrigeration cycle. Wang et al. [4] proposed a novel solar energy-driven CCHP system, which integrated an organic Rankine cycle and an ejector refrigeration cycle, and conducted a parameter optimization to obtain the best performance. Zhai et al. [5] proposed a hybrid solar heating, cooling, and power generation system based on helical screw expander and silica gel-water adsorption chiller. Al-Sulaiman et al. [6] presented performance assessment of a novel CCHP system combined an organic Rankine cycle and a single-effect absorption chiller. Li and Wu [7] constructed a novel micro CCHP
* Corresponding author. Tel./fax: þ86 023 65112469. E-mail address: [email protected] (X.X. Xu).
system based on two bed silica gel-water adsorption chillers. The working fluids of the novel CCHP cycles are concentrated on some organic working fluids and binary working pairs, such as ammonia/ water and water/lithium bromide. Few studies can be found in the open literatures using CO2 as the working fluid in the CCHP system. However, CO2 is a non-flammable natural refrigerant with zero ODP (Ozone Depression Potential) and a negligible GWP (Global Warming Potential). The lower critical temperature (31.1 C) of CO2 results in the transcritical cycle. It can take advantage of thermophysical properties of CO2 near the critical region, and allow better matching of the refrigerant temperature with the secondary fluid during the heat rejection process with a relatively small compressor pressure ratio. Therefore, studies on transcritical carbon dioxide refrigeration systems have been dramatically promoted in recent years. For the transcritical CO2 ejector system (shown in Fig. 1), a two-phase ejector is used as a substitute for an expansion valve to recover the expansion process losses and reduce the compression work. More attention has been paid to reduce the throttle losses by introducing CO2 ejector [8,9], but the fact may be ignored that the compressor outlet temperature could reach 80 Ce150 C in the transcritical CO2 ejector system. In general, the heat from the compressor outlet is cooled and discharged into the environment by the gas cooler, which leads to the waste of low-
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Nomenclature E gc I m h pf s sf Q mf m n p n1 T n2 u s x i
exergy (kW) gas cooler exergy destruction (kW) mixing section of ejector specific enthalpy (kJ kg1) primary flow specific entropy (kJ kg1 K1) secondary flow heat load (kW) mixed fluid mass flow rate (kg s1) nozzle pressure (MPa) inlet of nozzle temperature ( C) outlet of nozzle velocity (m s1) isentropic process vapor quality () component
grade heat as well being unfriendly to environment. An attractive alternative solution is to use low-grade heat sources (such as solar energy, geothermal energy and industrial waste heats, etc.) to further raise the temperature of the heat generated from the compressor outlet, thus the grade of heat is enhanced to produce cooling output, heating output, and power output simultaneously. For the innovation, Wang et al. [10] firstly propose a novel CCHP system using natural substance CO2 as the working fluid. The novel CCHP combines a Brayton cycle and a transcritical CO2 ejector refrigeration cycle. It not only takes advantage of the low-grade heat sources and the waste heat from the compressor outlet in trancritical CO2 compression system, but also produces high-grade energy for cooling, heating, and power. However, the turbine expands to a lower supercritical pressure as the primary pressure of the ejector, which leads to a relatively small amount of refrigeration output. So, the novel CCHP is not adaptable to the large refrigeration application. On basis of the above-mentioned review, a modified CCHP system using supercritical CO2 is proposed. This system combines the Brayton cycle and the transcritical ejector system cycle by
COP a,b
coefficient of performance () inlet/outlet state of point
Subscripts 0 environment state c compressor Q heating source g gas heater EJE ejector cycle e evaporator EUE energy utilization v valve Greek h x t m ej h d
heater ratio turbine entrainment ratio ejector efficiency diffuser section of ejector
adding an extraction turbine. The extraction turbine not only extracts a relatively high-pressure fluid as a primary stream of ejector for large refrigeration output, but the remaining fluid in the extraction turbine also continues to expander a lower pressure for more power output. The modified CCHP cycle presented in this paper has some parts in common with Wang et al. [10]. There are some differences are summarized as follows: (1) the present cycle adds an extraction turbine. One stream extracted from the extraction turbine expands to a low supercritical pressure as the ejector primary stream, and the remaining stream continues to expand until left the extraction turbine, then is drawn into the compressor directly. (2) The extraction turbine extracted a relatively high-pressure fluid as a primary stream of ejector is helpful to gain more refrigeration. This view has been confirmed by Elbel et al. [11]. Considering the present cycle combined the power cycle and vapor compression cycle, a more practical performance metric is introduced in order to quantify system performance. The thermal efficiency is defined separately by energy utilization efficiency (hEUE ) and refrigeration coefficient (COP). In addition, in order to prove the superiority of the modified CCHP system, the exergy efficiency between the modified CCHP cycle with the extraction turbine and the CCHP with the no-extraction turbine (the same as Wang et al. [10]’s cycle) is compared. Meanwhile, the COPs between the modified CCHP system and the transcritical CO2 ejector system is also compared. 2. System description
Fig. 1. Schematic diagram of transcritical CO2 ejector system.
Fig. 2 shows the schematic diagram of the modified CCHP system (Fig. 2a) and the processes of the corresponding cycle in a temperature-specific entropy diagram (Fig. 2b). As can be seen in Fig. 2, the system includes a compressor, a gas heater, an extraction turbine, a heater, a gas cooler, an ejector, a separator, an evaporator, and throttle valves. CO2 is used as the working refrigerant for the system. The compressor compresses the CO2 stream to its supercritical state. The temperature of the supercritical CO2 continues to increase at the gas heater by absorbing the heat from heat sources, and then enters the extraction turbine. The stream extracted from
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3
Fig. 2. A modified combined cooling, heating and power system (a) Schematic diagram, (b) Temperature-entropy chart.
the extraction turbine expands to a low supercritical pressure, and the remaining stream continues to expand until leaving the extraction turbine. Both types of streams flow into the heater to supply the heat for the user, and then reject heat in the gas cooler. The primary stream is utilized to entrain refrigerant exiting from the evaporator, and then both streams come into contact in the mixing chamber. The two-phase CO2 stream pressure continues to increase at the diffuser, then leaves the ejector and flows into the separator, where it is divided into saturated liquid and saturated vapor. The saturated liquid enters the evaporator through a throttle valve by absorbing heat to produce the cooling effect, and a part of the saturated vapor is fed back to the evaporator through a throttle valve. The other part of the saturated vapor stream is drawn into the compressor with the remaining stream from the extraction turbine. Compared with the transcritical CO2 ejector refrigeration system, the modified CCHP system has the following advantages: (1) The supercritical CO2 stream can be expanded through the extraction turbine to generate power. (2) The supercritical CO2 stream, exiting from the compressor, can be further heated by gas heater. It cannot only increase the turbine power output but also upgrade the heat quality. (3) Part of supercritical CO2 stream is extracted from the extraction turbine as the ejector primary flow, which is utilized to entrain refrigerant exiting from the evaporator. The ejector pre-compresses the mass flow rate of the evaporator, and the compressor work decreases.
3.1. Ejector model Following assumptions are made for the ejector model: (1) The primary stream and the entrained stream are not mixed until they reach the mixing chamber; (2) The working fluid flow is one-dimensional and uniform; (3) The kinetic energy at the inlets of the primary nozzle and the suction chamber and at the diffuser exit is negligible. Based on the above assumptions, the mass, momentum, and energy equations are applied to each section of the ejector. Three independent efficiencies of the motive nozzle, mixing section, and diffuser are defined by Eqs. (1)e(3). The efficiencies are assumed as 0.9 [14], 0.85 [15], and 0.85 [16]. The ratio of the mass flow of the entrained stream to the primary stream is defined as the entrainment ratio, which is characterized as the important parameters of the ejector performance, as demonstrated by Eq. (4)
hn ¼
hm ¼
hd ¼
hpf;n1 hpf;n2 hpf ;n1 hpf;n2;s u2mf;m u2mf;m;s hmf;d;s hmf;m hmf;d hmf;m
msf mpf
(1)
(2)
(3)
3. Mathematical model
m¼
The ejector is the key component in the combined cycle. The ejector mathematical model is calculated based on a onedimensional constant pressure flow model. The basic principle of the model is introduced by Keenan et al. [12]. Based on reference [13], the detailed descriptions of the ejector mathematical model are presented.
Fig. 3 illustrates the iterative structure of the ejector calculation routine and presents the governing equations involved. The iteration completes when the value of the entrainment ratio (m) could be obtained. The convergence condition is that the absolute errors of the actual outlet enthalpy of the mixed fluid (hmf;d ) in both equations are less than 104. One equation neglects the outlet velocity of
(4)
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(6) The compressor and the turbine have a given isentropic efficiency. The basic equations obtained from the conservation law for energy in the components are given as follows: For evaporator
Qe ¼ me ðh8b h8a Þ
(5)
For gas heater
Qg ¼ mg ðh2 h1 Þ
(6)
For heater user
Qh ¼ m3 ðh3a h3b Þ þ m4 ðh4a h4b Þ
(7)
For turbine
Wt ¼ m3 ðh2 h3a Þ þ m4 ðh2 h4a Þ
(8)
For compressor
Wc ¼ mc ðh1 h12 Þ
(9)
3.3. System performance
Fig. 3. Flowchart of iterative calculation routine for ejector.
the mixed fluid (umf;m;d ), and the other equation is based on the isentropic efficiency of the diffuser in the ejector (hd ).
It is difficult to evaluating the efficiency of the CCHP cycle. The reason is that there are different quality outputs, such as cooling, heating, and power outputs. Khaliq [17] defined as the ratio of all the useful energy extracted from the system (electricity, process heat, and cold) to the energy of fuel input for the first law efficiency of gas turbine trigeneration system. Ghaeb et al. [18] also defined as the ratio of useful energies produced by the system (cold, heat and power) to the input energy of fuel for evaluating the thermal efficiency of a CCHP system with gas turbine prime mover. The first law efficiency counted different kinds of outputs together is not a satisfactory criterion. Vijayaraghavan et al. [19] pointed that the thermal efficiency of the combined cycle approaches that of Carnot cycle or even exceeds them using this definition in some cases. In contrast with the other CCHP, the energy input of the modified CCHP system includes not only the heat from heat source, but also the work from the compressor. The thermal efficiency of the overall system cannot be defined exactly by the first thermodynamic law or the energy conservation law. Considering the modified cycle combined with the power cycle and vapor compression cycle, the thermal efficiency is defined separately by energy utilization efficiency (hEUE ) and refrigeration coefficient COP. Meanwhile, the ratio of COP (x) between the modified combined cycle and the ejector cycle is developed to describe the improvement of the system refrigeration performance.
hEUE ¼
Qh þ Wt Wc Qg
(10)
COP ¼
Qe Wc Wt
(11)
Qe; EJE Wc; EJE
(12)
3.2. System model Based on the mass, momentum, and energy conservations, the modified CCHP system is presented. To simplify the theoretical model, the following assumptions are made: (1) The system runs in a steady state; (2) The pressure drops in the gas heater, the heater, the gas cooler, the separator, the evaporator, and the connection tubes are neglected; (3) The vapor stream from the separator is saturated vapor, and the liquid stream from the separator is saturated liquid; (4) The stream at the evaporator outlet is saturated vapor; (5) The flows across the throttle valves are isenthalpic;
COPEJE ¼
x¼
COP COPEJE
(13)
where,
Qe;EJE ¼ me;EJE ðh4 h11 Þ
(14)
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Wc;EJE ¼ mc;EJE ðh2 h1 Þ
(15)
Qe,EJE is the refrigeration output and Wc,EJE is the compressor work of the transcritical CO2 ejector refrigeration cycle. Refer to Fig. 1 for the subscripts of Eqs (14) and (15). Exergy efficiency, based on the second law of thermodynamics, is used to calculate the efficiency of CCHP system, taking into account the different thermodynamic values of different energy forms and quantities. Therefore, the exergy efficiency (hEXG ) is chosen to be the criterion for the cycle performance evaluation.
hEXG ¼
EQ ;e þ EQ ;h þ Wt Wc EQ ;g
(16)
The exergy inputs to the gas heater and the evaporator from low-grade heat source and refrigeration room, correspondingly. The exergy outputs to the heater and the gas cooler from heater user and cooling water, correspondingly. The equation can be expressed as follows:
EQ ;i ¼ Qi
T 1 0 TQ ;i
! (17)
Exergy analysis of a complex system can be performed by analyzing each component of the system, which will have a potential suggestion to improve the system efficiency from main exergy destruction. The definitions of the exergy destructions are referred to the literatures [20,21]. The exergy of each state point can be considered as
Ei ¼ mi ½ðhi h0 Þ T0 ðsi s0 Þ
(18)
For the combined cycle, the exergy destruction of each component can be expressed as follows:
Ii ¼
X i
" Qi 1
# X X T0 Ein;i Eout;i Wi þ TQ ;i i
(19)
i
The exergy destruction in the gas heater can be estimated by
Ig ¼ Ein;g Eout;g þ EQ ;g
(20)
The exergy destruction in the turbine can be given as
It ¼ Ein;t Eout1;t Eout2;t Wt
(21)
5
Igc ¼ Ein1;gc Eout1;gc EQ ;gc1 þ Ein2;gc Eout2;gc EQ ;gc2
(27)
3.4. Simulation conditions Table 1 lists the detailed conditions for the simulations of the modified CCHP cycle. The proposed system with a level of 200 kW low-grade heats is simulated to validate the system feasibility and performance improvement. Parts of parameter selections are based on the reference [10]. The thermodynamic properties of CO2 were calculated by REFPROP [22]. Li [13] pointed out that it is difficult to control a real transcritical CO2 ejector refrigeration system working in its steady-state, which satisfied the mass conservation constraint x ¼ 1=ð1 þ mÞ. He modifies the cycle by feeding back part of the vapor in the separator to the evaporator inlet through a throttle valve, which relaxes the constraints between the entrainment ratio of the ejector and the quality of the ejector outlet stream. In this work, the extraction turbine and the gas heater are introduced into the Li's modified cycle. Therefore, it should be noted that the entrainment ratio of the ejector and the ejector outlet quality must satisfy x > 1=ð1 þ mÞ in order to realize the cycle. 4. Results and discussion Based on the above model and conditions, a simulation program is developed. Table 2 and Table 3 show the thermodynamic state of each point and system performance for the modified CCHP system. Exergy analysis is performed to evaluate the exergy destruction for each component in the system as shown in Table 4. According to the percentage of the exergy destruction, most exergy destruction occurs in the heater, gas heater, and gas cooler. It means that the exergy destruction could be decreased by reducing the heat transfer temperature difference in those heat exchangers. It is found that the exergy destruction of compressor is up to 17.19%. It is partly due to the remaining stream (4c, Fig 2a) with relatively high temperature. The remaining stream is drawn into the compressor that leads to an increase of the compressor inlet temperature, thus causing the compressor efficiency to decrease and the exergy destruction to increase. In addition, using high-efficiency turbine and compressor could reduce the exergy destruction in the turbine and compressor. Fig. 4 shows the effect of extraction rate on the system performance. As the extraction rate increases, more supercritical fluid CO2 is extracted from turbine to ejector as the driving force, which
The exergy destruction in the evaporator can be given as
Ie ¼ Ein;e Eout;e þ EQ ;e
(22)
The exergy destruction in the compressor can be given as
Ic ¼ Ein;c Eout;c þ Wc
(23)
The exergy destruction in the ejector can be given as
Ic ¼ Ein1;EJE þ Ein2;EJE Eout;EJE
(24)
The exergy destruction in throttle valve is given as
Iv ¼ Ein;v1 Eout;v1 þ Ein;v2 Eout;v2
(25)
The exergy destruction in heater is given as
Ih ¼ Ein1;h Eout1;h EQ ;h1 þ Ein2;h Eout2;h EQ ;h2 The exergy destruction in gas cooler is given as
(26)
Table 1 The simulation conditions of the modified CCHP cycle. Parameters
Amount
Mass flow rate of working fluid Environment temperature Environment pressure Turbine inlet temperature Turbine inlet pressure Turbine extraction pressure Turbine extraction rate Ejector inlet temperature Ejector back pressure Heater outlet temperature Gas cooler outlet temperature Evaporation temperature Cooling room temperature Turbine isentropic efficiency Compressor isentropic efficiency Mass flow rate of flue Approach temperature difference of heat exchanger
1.4 kg/s 15 C 0.1013 MPa 220 C 12 MPa 8.4 MPa 0.55 36 C 4.6 MPa 70 C 36 C 5 C 10 C 0.85 0.8 5 kg/s 10 C
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Table 2 Results of simulation for the modified CCHP cycle. State
t( C)
p(MPa)
x
h(kJ kg1)
s(kJ kg1 K1)
m(kg s1)
1 2 3a 3b 3c 4a 4b 4c 5a 6 7 8a 8b 9 10 11 12 13
103.5 220 188 70 36 138.7 70 36 10.87 10.87 5 5 5 5 5 10.87 20.35 10.87
12 12 8.4 8.4 8.4 4.6 4.6 4.6 4.6 4.6 3.969 3.969 3.969 3.969 3.969 4.6 4.6 4.6
1 1 1 1 1 1 1 1 0.6769 0 0.07266 0.1011 1 1 0.9742 1 1 1
13.28 142.6 117.6 35.55 181.6 79.64 3.399 39.82 147.5 278.6 278.6 272.5 79.29 79.29 84.84 84.84 64.58 84.84
0.8625 0.4993 0.4897 0.8769 1.335 0.472 0.6748 0.8076 1.181 1.643 1.639 1.617 0.9227 0.9227 0.9426 0.9602 0.8899 0.9602
1.4 1.4 0.77 0.77 0.77 0.63 0.63 0.63 1.156 0.3734 0.3734 0.3855 0.3855 0.3855 0.01215 0.7821 1.4 0.01215
Table 3 The performance of the modified CCHP cycle. Parameters
Amount
Turbine power Refrigeration output Heating output Heat absorption from heat source Compressor power COP Energy utilization efficiency Exergy efficiency
58.88 kW 74.51 kW 166 kW 218.2 kW 71.82 kW 5.755 0.7013 0.2567
Table 4 The exergy destructions of the modified CCHP cycle. Component
Amount (kW)
Percentage (%)
Compressor Ejector Evaporator Gas cooler Gas heater Heater Turbine Throttle
11.08 5.58 1.36 13.94 15.93 9.12 7.09 0.40
17.19 8.65 2.11 21.61 24.70 14.14 11.00 0.62
drives the entrained flow into the suction chamber, thus the flow rate of entrained flow and refrigeration output increase. At the same time, the increase of the supercritical fluid CO2 extracted leads to the decrease of the turbine power output. Comparatively, the decrease of the turbine power output far outpaces the increase of the refrigeration output. Therefore, the COP decreases. It can be seen that the heat output increases with increasing extraction rate, mainly because of the high temperature of the working fluid extracted, resulting in an increase in energy utilization efficiency. It is found that the system exergy efficiency decreases with increasing extraction rate. Table 5 shows the trends of the exergy destructions of components with variable extraction rate. It can be observed that the high heat transfer temperature difference in the gas heater and the gas cooler contribute to the decrease of the exergy efficiency. In addition, more working fluid CO2 extracted from the turbine further reduces the power output, which also causes the decrease of the exergy efficiency. Fig. 5 shows the effect of turbine inlet temperature on the system performance. There is a large increase in the turbine power output and the exergy efficiency with the increase of turbine inlet temperature. It reveals that a rise of heat source quality benefits the system performance. Increasing in turbine power output leads to decreasing in the net power input of the system, when the compressor power input keeps almost unchanged, thus the COP increase. It is also found that the energy utilization efficiency keeps rising. This could be explained by the higher turbine exhausting temperature, which could generate more heat output from the heater as the turbine inlet temperature increases. Fig. 6 shows the effect of the compressor outlet pressure on the system performance. It can be clearly seen that, as the compressor outlet pressure increases, both turbine power output and compressor power input increase correspondingly owing to the increasing pressure ratio across the turbine and the compressor. The exergy destructions of the turbine and the compressor, however, increase along with the compressor outlet pressure increases, and the proportion of the exergy destruction in the turbine and the compressor is relatively large. Therefore, the exergy efficiency decreases. It is found that the heat output decreases as the compressor outlet pressure increases. The reason mainly is that the turbine exhausting temperature can be reduced with the increase of the compressor outlet pressure. On the other hand, the compressor outlet temperature increases with the increase of the compressor outlet pressure increases. With constant turbine inlet temperature, the heat absorption from heat source decreases. From the reasons presented above, the energy utilization efficiency decreases. It is also found that the COP increases first and then decreases, which indicates that the system exists an optimum highside pressure to get high system performance. Fig. 7 shows the effect of extraction pressure on the system performance. It is obvious that the power output of the expander decreases as the extraction pressure increases. As the extraction
Table 5 Trend of exergy destructions with variable extraction rate.
Fig. 4. Effect of extraction ratio on the system performance.
e
Ic(kW)
Ie(kW)
Iej(kW)
Ig(kW)
Igc(kW)
Ih(kW)
It(kW)
Iv(kW)
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
11.4 11.29 11.19 11.08 10.97 10.85 10.74 10.62 10.5 10.39
0.991 1.115 1.239 1.363 1.487 1.611 1.735 1.859 1.982 2.106
4.06 4.567 5.075 5.582 6.09 6.597 7.105 7.612 8.12 8.627
15.49 16.07 16.67 17.28 17.9 18.52 19.16 19.81 20.47 21.13
12.02 12.66 13.30 13.94 14.57 15.21 15.85 16.49 17.13 17.77
8.465 8.683 8.901 9.12 9.338 9.556 9.774 9.992 10.21 10.43
8.159 7.801 7.444 7.087 6.729 6.372 6.014 5.657 5.3 4.942
0.2915 0.328 0.3644 0.4009 0.4373 0.4737 0.5102 0.5466 0.5831 0.6195
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Fig. 5. Effect of turbine inlet temperature on the system performance.
Fig. 6. Effect of compressor outlet pressure on the system performance.
pressure increases, the refrigeration output increases more quickly. It is because the higher the extraction pressure, the lower the quality of the ejector outlet at a given entrainment ratio. The decrease of the quality of the ejector outlet leads to an increase of the liquid stream from the separator to evaporator and a decrease of the gas stream from the separator fed back to evaporator, then it
Fig. 7. Effect of extraction pressure on the system performance.
7
results in the refrigeration output increasing. It can be observed that the increase in the energy utilization efficiency, exergy efficiency, and the COP of the system follows the increasing extraction pressure. In general, the vapor extracted from the expander reduces the net power output of the expander, which decreases the system performance. However, the modified system of this work not only takes advantage of the remaining heat output, but also produces more refrigeration output, when it works in the higher extraction pressure. Therefore, the gain from refrigeration and heat output is the main factor, making the improvement in both the thermal efficiency and the exergy efficiency of the system. Compared to the no-extraction turbine, the extraction turbine extracted a relatively high-pressure fluid as a primary stream of ejector is helpful to gain more refrigeration. Fig. 8 shows the effect of compressor outlet pressure on the COPs of the modified CCHP system and the transcritical CO2 ejector system. The result is based on the same conditions, including the evaporation temperature, the ejector isentropic efficiency, the compressor isentropic efficiency, and the turbine isentropic efficiency. It can be seen that in the modified CCHP system there exists an optimal high-side pressure that gives a maximum COP. For a conventional transcritical CO2 system with expansion valve, Elbel [23] explained that the increasing of the high-side pressure increases the cooling capacity at the expense of the incremental increase in compressor power. A COP maximum exists when the incremental capacity increase equals the incremental increase in compressor power. This method of finding the COP maximizing high-side pressure can also apply to the transcritical CO2 ejector system and the modified CCHP cycle. The COP maximizing highside pressure of the modified CCHP system of approximately 12 MPa is higher than that of the transcritical CO2 ejector system. The difference of the COP maximizing high-side pressure in the modified CCHP cycle and the transcritical CO2 ejector system is that the net work equals compressor work subtract turbine power output, not equals compressor work. It can be also seen that the ratio of COPs between the modified CCHP cycle and the transcritical CO2 ejector cycle increases from 1.29 to 2.43 with the increasing of the compressor outlet pressure. Fig. 9 shows the exergy efficiency of the modified CCHP system and Wang et al. [10]’s CCHP system as a function of the compressor outlet pressure, one is the modified CCHP system with extraction turbine, the other is Wang et al. [10]’s CCHP system with noextraction turbine. For the case of the extraction turbine, it has higher exergy efficiency in comparison to the no-extraction
Fig. 8. Performance comparison of the modified CCHP system and the transcritical CO2 ejector system.
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X.X. Xu et al. / Energy xxx (2015) 1e9 Table 7 Trend of exergy destructions with variable turbine inlet pressure (Wang et al. [10]’s CCHP cycle with no-extraction turbine).
Fig. 9. Exergy efficiency comparison of the modified CCHP system and Wang et al. [10]’s CCHP system.
turbine. The range of an increase in the exergy efficiency values of the two cases is about 10.4%e22.5%. A higher ejector primary inlet pressure in the case of the no-extraction turbine results in a lower turbine power output, which is accounted as low exergy efficiency of this cycle. In order to clearly understand how the exergy efficiency is sensitive to the specific component for the two cases, the exergy destructions of all components are listed in Table 6 and Table 7. Both the exergy destructions of the compressor and turbine in the case of the extraction turbine are higher than that of the noextraction turbine, but all heat exchangers in the case of the extraction turbine have lower exergy destructions in comparison to the no-extraction turbine. It is also observed that the exergy destructions of the ejector in the case of the extraction turbine are lower than that of the no-extraction turbine. The increased flow rate to the ejector results in the higher exergy destructions of the ejector in the case of the no-extraction turbine.
5. Conclusion A modified combined cooling, heating, and power system using supercritical CO2 is proposed. From thermodynamic points of view, it is provable that the combination of the Brayton cycle and the transcritical ejector refrigeration cycle by adding an extraction turbine is highly efficient. Using low-grade heat source to further increase the temperature of the heat generated from the compressor outlet enhances the heat source quality, which benefits the system performance. The following conclusions can be drawn from this work:
Table 6 Trend of exergy destructions with variable turbine inlet pressure (The modified CCHP cycle with extraction turbine). P2(MPa) Ic(kW)
Ie(kW) Iej(kW) Ig(kW) Igc(kW) Ih(kW) It(kW) Iv(kW)
9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363
8.594 9.147 9.669 10.16 10.63 11.08 11.5 11.91 12.3 12.68
5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582
22.34 20.84 19.47 18.2 17.02 15.93 14.92 13.97 13.1 12.28
13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94
10.37 10.11 9.85 9.601 9.357 9.12 8.887 8.658 8.434 8.213
4.455 5.031 5.58 6.104 6.606 7.087 7.548 7.991 8.417 8.827
0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009
P2(MPa) Ic(kW)
Ie(kW) Iej(kW) Ig(kW) Igc(kW) Ih(kW) It(kW) Iv(kW)
9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478
7.746 8.25 8.726 9.178 9.608 10.02 10.41 10.79 11.15 11.5
10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15
28.99 27.28 25.69 24.22 22.85 21.58 20.39 19.28 18.24 17.27
19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68
12.11 11.9 11.69 11.48 11.28 11.08 10.89 10.7 10.51 10.32
1.329 1.885 2.415 2.921 3.406 3.87 4.316 4.744 5.157 5.554
0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288
(1) The modified CCHP system exists an optimal high-side pressure that gives a maximum COP, and the COP maximizing high-side pressure of the modified CCHP system is higher than that of the transcritical CO2 ejector system. (2) The ratio of COPs between the modified CCHP cycle and the transcritical CO2 ejector cycle increases from 1.29 to 2.43. (3) The range of an increase in the exergy efficiency of the modified CCHP system with extraction turbine is about 10.4%e22.5% compared to Wang et al. [10]’s CCHP system with no-extraction turbine. (4) Although the extraction turbine extracted relatively highpressure fluid results in a decrease in the exergy destruction of the turbine, the gains from refrigeration and heat output are the main factors making the improvement of the thermal efficiency and the exergy efficiency of the system.
Acknowledgment This work is supported by National Natural Science Foundation of China (Project No. 51206197), National Basic Research Program of China (973 Program, Project No. 2011CB710701), Fundamental Research Funds for the Central Universities (Project No. cdjzr12140032) and Chongqing Natural Science Foundation (Project No. CSTC2011BB6094).
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X.X. Xu et al. / Energy xxx (2015) 1e9 [11] Elbel SW, Hrnjak PS. Experimental validation of a prototype ejector designed to reduce throttling losses encountered in transcritical R744 system operation. Int J Refrig 2008;31(3):411e22. [12] Keenan J, Neumann E, Lustwerk F. An investigation of ejector design by analysis and experiment. J Appl Mech Trans ASME 1950;17(3):299e309. [13] Dai YP, Wang JF, Gao L. Exergy analysis, parametric analysis and optimization for a novel combined power and ejector refrigeration cycle. Appl Therm Eng 2009;29:1983e90. [14] Li DQ, Groll EA. Transcritical CO2 refrigeration cycle with ejector-expansion device. Int J Refrig 2005;28(5):766e73. [15] Huang BJ, Chang JM, Wang CP, Petrenko VA. A 1-D analysis of ejector performance. Int J Refrig 1999;22:354e64. [16] Cizungu K, Mani A, Groll M. Performance comparison of vapour jet refrigeration system with environment friendly working fluids. Appl Therm Eng 2001;21:585e98. [17] Khaliq A. Exergy analysis of gas turbine trigeneration system for combined production of power heat and refrigeration. Int J Refrig 2009;32:534e45.
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[18] Ghaebi H, Amidpour M. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011;35:697e709. [19] Vijayaraghavan S, Goswami DY. On evaluating efficiency of a combined power and cooling cycle. J Energy Resour Technol 2003;125:221e7. [20] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York, USA: John Wiley; 1996. [21] Kotas TJ. The exergy method of thermal plant analysis. Malabar, Florida,USA: Krieger Publishing Company; 1995. p. 328. [22] NIST Standard Reference Database 23. NIST thermodynamic and transport properties of refrigerants and refrigerant mixtures REFPROP. Version 8.0. Maryland,USA: Gaithersburg; 2007. [23] Elbel SW. Experimental and analytical investigation of a two-phase ejector used for expansion work recovery in a transcritical R744 air-conditioning system. Dissertation. Urbana,Illinois,USA: University of Illinois at UrbanaChampaign; 2007.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Energy and exergy analyses of a modified combined cooling, heating, and power system using supercritical CO2 Xiao Xiao Xu*, Chao Liu, Xiang Fu, Hong Gao, Yourong Li Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 May 2014 Received in revised form 10 April 2015 Accepted 11 April 2015 Available online xxx
In aim to reduce the greenhouse-gas emissions and improve the low-grade heat efficiency, a modified CCHP (combined cooling, heating, and power) system is proposed using supercritical CO2. This cycle combines a Brayton cycle and a transcritical ejector refrigeration cycle by adding an extraction turbine. A mathematical model is developed to simulate the modified CCHP system. Parametric analysis and exergy analysis are conducted to investigate the effects of key thermodynamic parameters on the performance and exergy destruction. Due to the difficulties in the thermal efficiency evaluation for CCHP system, a more practical performance metric is introduced in order to quantify system performance. The results indicate that both higher extraction rate and extraction pressure are helpful to gain more refrigeration. For the conditions considered, the exergy efficiency of the modified CCHP with the extraction turbine is higher than that of the CCHP with the no-extraction turbine from 10.4% to 22.5%. Furthermore, there is a large increase in the turbine power output and the exergy efficiency with increased turbine inlet temperature. It reveals that a rise of heat source quality benefits the system performance. © 2015 Elsevier Ltd. All rights reserved.
Keywords: CCHP CO2 Transcritical cycle Ejector Exergy Simulation
1. Introduction The advantages of the CCHP (combined cooling, heating, and power) are higher primary energy efficiency, more environmental benefits, and better economic feasibility [1]. CCHP is a suitable solution in the case of a medium- and small-scale basis (below 1 or 2 MWe) [2]. In particular, the application of CCHP in municipal energy systems and food industry demanding cold and heat simultaneously can be significant [3]. Recent studies revealed that the novel CCHP cycle combined a Rankine cycle or a Kalina cycle with an absorption refrigeration cycle or an ejector refrigeration cycle. Wang et al. [4] proposed a novel solar energy-driven CCHP system, which integrated an organic Rankine cycle and an ejector refrigeration cycle, and conducted a parameter optimization to obtain the best performance. Zhai et al. [5] proposed a hybrid solar heating, cooling, and power generation system based on helical screw expander and silica gel-water adsorption chiller. Al-Sulaiman et al. [6] presented performance assessment of a novel CCHP system combined an organic Rankine cycle and a single-effect absorption chiller. Li and Wu [7] constructed a novel micro CCHP
* Corresponding author. Tel./fax: þ86 023 65112469. E-mail address: [email protected] (X.X. Xu).
system based on two bed silica gel-water adsorption chillers. The working fluids of the novel CCHP cycles are concentrated on some organic working fluids and binary working pairs, such as ammonia/ water and water/lithium bromide. Few studies can be found in the open literatures using CO2 as the working fluid in the CCHP system. However, CO2 is a non-flammable natural refrigerant with zero ODP (Ozone Depression Potential) and a negligible GWP (Global Warming Potential). The lower critical temperature (31.1 C) of CO2 results in the transcritical cycle. It can take advantage of thermophysical properties of CO2 near the critical region, and allow better matching of the refrigerant temperature with the secondary fluid during the heat rejection process with a relatively small compressor pressure ratio. Therefore, studies on transcritical carbon dioxide refrigeration systems have been dramatically promoted in recent years. For the transcritical CO2 ejector system (shown in Fig. 1), a two-phase ejector is used as a substitute for an expansion valve to recover the expansion process losses and reduce the compression work. More attention has been paid to reduce the throttle losses by introducing CO2 ejector [8,9], but the fact may be ignored that the compressor outlet temperature could reach 80 Ce150 C in the transcritical CO2 ejector system. In general, the heat from the compressor outlet is cooled and discharged into the environment by the gas cooler, which leads to the waste of low-
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Nomenclature E gc I m h pf s sf Q mf m n p n1 T n2 u s x i
exergy (kW) gas cooler exergy destruction (kW) mixing section of ejector specific enthalpy (kJ kg1) primary flow specific entropy (kJ kg1 K1) secondary flow heat load (kW) mixed fluid mass flow rate (kg s1) nozzle pressure (MPa) inlet of nozzle temperature ( C) outlet of nozzle velocity (m s1) isentropic process vapor quality () component
grade heat as well being unfriendly to environment. An attractive alternative solution is to use low-grade heat sources (such as solar energy, geothermal energy and industrial waste heats, etc.) to further raise the temperature of the heat generated from the compressor outlet, thus the grade of heat is enhanced to produce cooling output, heating output, and power output simultaneously. For the innovation, Wang et al. [10] firstly propose a novel CCHP system using natural substance CO2 as the working fluid. The novel CCHP combines a Brayton cycle and a transcritical CO2 ejector refrigeration cycle. It not only takes advantage of the low-grade heat sources and the waste heat from the compressor outlet in trancritical CO2 compression system, but also produces high-grade energy for cooling, heating, and power. However, the turbine expands to a lower supercritical pressure as the primary pressure of the ejector, which leads to a relatively small amount of refrigeration output. So, the novel CCHP is not adaptable to the large refrigeration application. On basis of the above-mentioned review, a modified CCHP system using supercritical CO2 is proposed. This system combines the Brayton cycle and the transcritical ejector system cycle by
COP a,b
coefficient of performance () inlet/outlet state of point
Subscripts 0 environment state c compressor Q heating source g gas heater EJE ejector cycle e evaporator EUE energy utilization v valve Greek h x t m ej h d
heater ratio turbine entrainment ratio ejector efficiency diffuser section of ejector
adding an extraction turbine. The extraction turbine not only extracts a relatively high-pressure fluid as a primary stream of ejector for large refrigeration output, but the remaining fluid in the extraction turbine also continues to expander a lower pressure for more power output. The modified CCHP cycle presented in this paper has some parts in common with Wang et al. [10]. There are some differences are summarized as follows: (1) the present cycle adds an extraction turbine. One stream extracted from the extraction turbine expands to a low supercritical pressure as the ejector primary stream, and the remaining stream continues to expand until left the extraction turbine, then is drawn into the compressor directly. (2) The extraction turbine extracted a relatively high-pressure fluid as a primary stream of ejector is helpful to gain more refrigeration. This view has been confirmed by Elbel et al. [11]. Considering the present cycle combined the power cycle and vapor compression cycle, a more practical performance metric is introduced in order to quantify system performance. The thermal efficiency is defined separately by energy utilization efficiency (hEUE ) and refrigeration coefficient (COP). In addition, in order to prove the superiority of the modified CCHP system, the exergy efficiency between the modified CCHP cycle with the extraction turbine and the CCHP with the no-extraction turbine (the same as Wang et al. [10]’s cycle) is compared. Meanwhile, the COPs between the modified CCHP system and the transcritical CO2 ejector system is also compared. 2. System description
Fig. 1. Schematic diagram of transcritical CO2 ejector system.
Fig. 2 shows the schematic diagram of the modified CCHP system (Fig. 2a) and the processes of the corresponding cycle in a temperature-specific entropy diagram (Fig. 2b). As can be seen in Fig. 2, the system includes a compressor, a gas heater, an extraction turbine, a heater, a gas cooler, an ejector, a separator, an evaporator, and throttle valves. CO2 is used as the working refrigerant for the system. The compressor compresses the CO2 stream to its supercritical state. The temperature of the supercritical CO2 continues to increase at the gas heater by absorbing the heat from heat sources, and then enters the extraction turbine. The stream extracted from
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3
Fig. 2. A modified combined cooling, heating and power system (a) Schematic diagram, (b) Temperature-entropy chart.
the extraction turbine expands to a low supercritical pressure, and the remaining stream continues to expand until leaving the extraction turbine. Both types of streams flow into the heater to supply the heat for the user, and then reject heat in the gas cooler. The primary stream is utilized to entrain refrigerant exiting from the evaporator, and then both streams come into contact in the mixing chamber. The two-phase CO2 stream pressure continues to increase at the diffuser, then leaves the ejector and flows into the separator, where it is divided into saturated liquid and saturated vapor. The saturated liquid enters the evaporator through a throttle valve by absorbing heat to produce the cooling effect, and a part of the saturated vapor is fed back to the evaporator through a throttle valve. The other part of the saturated vapor stream is drawn into the compressor with the remaining stream from the extraction turbine. Compared with the transcritical CO2 ejector refrigeration system, the modified CCHP system has the following advantages: (1) The supercritical CO2 stream can be expanded through the extraction turbine to generate power. (2) The supercritical CO2 stream, exiting from the compressor, can be further heated by gas heater. It cannot only increase the turbine power output but also upgrade the heat quality. (3) Part of supercritical CO2 stream is extracted from the extraction turbine as the ejector primary flow, which is utilized to entrain refrigerant exiting from the evaporator. The ejector pre-compresses the mass flow rate of the evaporator, and the compressor work decreases.
3.1. Ejector model Following assumptions are made for the ejector model: (1) The primary stream and the entrained stream are not mixed until they reach the mixing chamber; (2) The working fluid flow is one-dimensional and uniform; (3) The kinetic energy at the inlets of the primary nozzle and the suction chamber and at the diffuser exit is negligible. Based on the above assumptions, the mass, momentum, and energy equations are applied to each section of the ejector. Three independent efficiencies of the motive nozzle, mixing section, and diffuser are defined by Eqs. (1)e(3). The efficiencies are assumed as 0.9 [14], 0.85 [15], and 0.85 [16]. The ratio of the mass flow of the entrained stream to the primary stream is defined as the entrainment ratio, which is characterized as the important parameters of the ejector performance, as demonstrated by Eq. (4)
hn ¼
hm ¼
hd ¼
hpf;n1 hpf;n2 hpf ;n1 hpf;n2;s u2mf;m u2mf;m;s hmf;d;s hmf;m hmf;d hmf;m
msf mpf
(1)
(2)
(3)
3. Mathematical model
m¼
The ejector is the key component in the combined cycle. The ejector mathematical model is calculated based on a onedimensional constant pressure flow model. The basic principle of the model is introduced by Keenan et al. [12]. Based on reference [13], the detailed descriptions of the ejector mathematical model are presented.
Fig. 3 illustrates the iterative structure of the ejector calculation routine and presents the governing equations involved. The iteration completes when the value of the entrainment ratio (m) could be obtained. The convergence condition is that the absolute errors of the actual outlet enthalpy of the mixed fluid (hmf;d ) in both equations are less than 104. One equation neglects the outlet velocity of
(4)
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X.X. Xu et al. / Energy xxx (2015) 1e9
(6) The compressor and the turbine have a given isentropic efficiency. The basic equations obtained from the conservation law for energy in the components are given as follows: For evaporator
Qe ¼ me ðh8b h8a Þ
(5)
For gas heater
Qg ¼ mg ðh2 h1 Þ
(6)
For heater user
Qh ¼ m3 ðh3a h3b Þ þ m4 ðh4a h4b Þ
(7)
For turbine
Wt ¼ m3 ðh2 h3a Þ þ m4 ðh2 h4a Þ
(8)
For compressor
Wc ¼ mc ðh1 h12 Þ
(9)
3.3. System performance
Fig. 3. Flowchart of iterative calculation routine for ejector.
the mixed fluid (umf;m;d ), and the other equation is based on the isentropic efficiency of the diffuser in the ejector (hd ).
It is difficult to evaluating the efficiency of the CCHP cycle. The reason is that there are different quality outputs, such as cooling, heating, and power outputs. Khaliq [17] defined as the ratio of all the useful energy extracted from the system (electricity, process heat, and cold) to the energy of fuel input for the first law efficiency of gas turbine trigeneration system. Ghaeb et al. [18] also defined as the ratio of useful energies produced by the system (cold, heat and power) to the input energy of fuel for evaluating the thermal efficiency of a CCHP system with gas turbine prime mover. The first law efficiency counted different kinds of outputs together is not a satisfactory criterion. Vijayaraghavan et al. [19] pointed that the thermal efficiency of the combined cycle approaches that of Carnot cycle or even exceeds them using this definition in some cases. In contrast with the other CCHP, the energy input of the modified CCHP system includes not only the heat from heat source, but also the work from the compressor. The thermal efficiency of the overall system cannot be defined exactly by the first thermodynamic law or the energy conservation law. Considering the modified cycle combined with the power cycle and vapor compression cycle, the thermal efficiency is defined separately by energy utilization efficiency (hEUE ) and refrigeration coefficient COP. Meanwhile, the ratio of COP (x) between the modified combined cycle and the ejector cycle is developed to describe the improvement of the system refrigeration performance.
hEUE ¼
Qh þ Wt Wc Qg
(10)
COP ¼
Qe Wc Wt
(11)
Qe; EJE Wc; EJE
(12)
3.2. System model Based on the mass, momentum, and energy conservations, the modified CCHP system is presented. To simplify the theoretical model, the following assumptions are made: (1) The system runs in a steady state; (2) The pressure drops in the gas heater, the heater, the gas cooler, the separator, the evaporator, and the connection tubes are neglected; (3) The vapor stream from the separator is saturated vapor, and the liquid stream from the separator is saturated liquid; (4) The stream at the evaporator outlet is saturated vapor; (5) The flows across the throttle valves are isenthalpic;
COPEJE ¼
x¼
COP COPEJE
(13)
where,
Qe;EJE ¼ me;EJE ðh4 h11 Þ
(14)
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X.X. Xu et al. / Energy xxx (2015) 1e9
Wc;EJE ¼ mc;EJE ðh2 h1 Þ
(15)
Qe,EJE is the refrigeration output and Wc,EJE is the compressor work of the transcritical CO2 ejector refrigeration cycle. Refer to Fig. 1 for the subscripts of Eqs (14) and (15). Exergy efficiency, based on the second law of thermodynamics, is used to calculate the efficiency of CCHP system, taking into account the different thermodynamic values of different energy forms and quantities. Therefore, the exergy efficiency (hEXG ) is chosen to be the criterion for the cycle performance evaluation.
hEXG ¼
EQ ;e þ EQ ;h þ Wt Wc EQ ;g
(16)
The exergy inputs to the gas heater and the evaporator from low-grade heat source and refrigeration room, correspondingly. The exergy outputs to the heater and the gas cooler from heater user and cooling water, correspondingly. The equation can be expressed as follows:
EQ ;i ¼ Qi
T 1 0 TQ ;i
! (17)
Exergy analysis of a complex system can be performed by analyzing each component of the system, which will have a potential suggestion to improve the system efficiency from main exergy destruction. The definitions of the exergy destructions are referred to the literatures [20,21]. The exergy of each state point can be considered as
Ei ¼ mi ½ðhi h0 Þ T0 ðsi s0 Þ
(18)
For the combined cycle, the exergy destruction of each component can be expressed as follows:
Ii ¼
X i
" Qi 1
# X X T0 Ein;i Eout;i Wi þ TQ ;i i
(19)
i
The exergy destruction in the gas heater can be estimated by
Ig ¼ Ein;g Eout;g þ EQ ;g
(20)
The exergy destruction in the turbine can be given as
It ¼ Ein;t Eout1;t Eout2;t Wt
(21)
5
Igc ¼ Ein1;gc Eout1;gc EQ ;gc1 þ Ein2;gc Eout2;gc EQ ;gc2
(27)
3.4. Simulation conditions Table 1 lists the detailed conditions for the simulations of the modified CCHP cycle. The proposed system with a level of 200 kW low-grade heats is simulated to validate the system feasibility and performance improvement. Parts of parameter selections are based on the reference [10]. The thermodynamic properties of CO2 were calculated by REFPROP [22]. Li [13] pointed out that it is difficult to control a real transcritical CO2 ejector refrigeration system working in its steady-state, which satisfied the mass conservation constraint x ¼ 1=ð1 þ mÞ. He modifies the cycle by feeding back part of the vapor in the separator to the evaporator inlet through a throttle valve, which relaxes the constraints between the entrainment ratio of the ejector and the quality of the ejector outlet stream. In this work, the extraction turbine and the gas heater are introduced into the Li's modified cycle. Therefore, it should be noted that the entrainment ratio of the ejector and the ejector outlet quality must satisfy x > 1=ð1 þ mÞ in order to realize the cycle. 4. Results and discussion Based on the above model and conditions, a simulation program is developed. Table 2 and Table 3 show the thermodynamic state of each point and system performance for the modified CCHP system. Exergy analysis is performed to evaluate the exergy destruction for each component in the system as shown in Table 4. According to the percentage of the exergy destruction, most exergy destruction occurs in the heater, gas heater, and gas cooler. It means that the exergy destruction could be decreased by reducing the heat transfer temperature difference in those heat exchangers. It is found that the exergy destruction of compressor is up to 17.19%. It is partly due to the remaining stream (4c, Fig 2a) with relatively high temperature. The remaining stream is drawn into the compressor that leads to an increase of the compressor inlet temperature, thus causing the compressor efficiency to decrease and the exergy destruction to increase. In addition, using high-efficiency turbine and compressor could reduce the exergy destruction in the turbine and compressor. Fig. 4 shows the effect of extraction rate on the system performance. As the extraction rate increases, more supercritical fluid CO2 is extracted from turbine to ejector as the driving force, which
The exergy destruction in the evaporator can be given as
Ie ¼ Ein;e Eout;e þ EQ ;e
(22)
The exergy destruction in the compressor can be given as
Ic ¼ Ein;c Eout;c þ Wc
(23)
The exergy destruction in the ejector can be given as
Ic ¼ Ein1;EJE þ Ein2;EJE Eout;EJE
(24)
The exergy destruction in throttle valve is given as
Iv ¼ Ein;v1 Eout;v1 þ Ein;v2 Eout;v2
(25)
The exergy destruction in heater is given as
Ih ¼ Ein1;h Eout1;h EQ ;h1 þ Ein2;h Eout2;h EQ ;h2 The exergy destruction in gas cooler is given as
(26)
Table 1 The simulation conditions of the modified CCHP cycle. Parameters
Amount
Mass flow rate of working fluid Environment temperature Environment pressure Turbine inlet temperature Turbine inlet pressure Turbine extraction pressure Turbine extraction rate Ejector inlet temperature Ejector back pressure Heater outlet temperature Gas cooler outlet temperature Evaporation temperature Cooling room temperature Turbine isentropic efficiency Compressor isentropic efficiency Mass flow rate of flue Approach temperature difference of heat exchanger
1.4 kg/s 15 C 0.1013 MPa 220 C 12 MPa 8.4 MPa 0.55 36 C 4.6 MPa 70 C 36 C 5 C 10 C 0.85 0.8 5 kg/s 10 C
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Table 2 Results of simulation for the modified CCHP cycle. State
t( C)
p(MPa)
x
h(kJ kg1)
s(kJ kg1 K1)
m(kg s1)
1 2 3a 3b 3c 4a 4b 4c 5a 6 7 8a 8b 9 10 11 12 13
103.5 220 188 70 36 138.7 70 36 10.87 10.87 5 5 5 5 5 10.87 20.35 10.87
12 12 8.4 8.4 8.4 4.6 4.6 4.6 4.6 4.6 3.969 3.969 3.969 3.969 3.969 4.6 4.6 4.6
1 1 1 1 1 1 1 1 0.6769 0 0.07266 0.1011 1 1 0.9742 1 1 1
13.28 142.6 117.6 35.55 181.6 79.64 3.399 39.82 147.5 278.6 278.6 272.5 79.29 79.29 84.84 84.84 64.58 84.84
0.8625 0.4993 0.4897 0.8769 1.335 0.472 0.6748 0.8076 1.181 1.643 1.639 1.617 0.9227 0.9227 0.9426 0.9602 0.8899 0.9602
1.4 1.4 0.77 0.77 0.77 0.63 0.63 0.63 1.156 0.3734 0.3734 0.3855 0.3855 0.3855 0.01215 0.7821 1.4 0.01215
Table 3 The performance of the modified CCHP cycle. Parameters
Amount
Turbine power Refrigeration output Heating output Heat absorption from heat source Compressor power COP Energy utilization efficiency Exergy efficiency
58.88 kW 74.51 kW 166 kW 218.2 kW 71.82 kW 5.755 0.7013 0.2567
Table 4 The exergy destructions of the modified CCHP cycle. Component
Amount (kW)
Percentage (%)
Compressor Ejector Evaporator Gas cooler Gas heater Heater Turbine Throttle
11.08 5.58 1.36 13.94 15.93 9.12 7.09 0.40
17.19 8.65 2.11 21.61 24.70 14.14 11.00 0.62
drives the entrained flow into the suction chamber, thus the flow rate of entrained flow and refrigeration output increase. At the same time, the increase of the supercritical fluid CO2 extracted leads to the decrease of the turbine power output. Comparatively, the decrease of the turbine power output far outpaces the increase of the refrigeration output. Therefore, the COP decreases. It can be seen that the heat output increases with increasing extraction rate, mainly because of the high temperature of the working fluid extracted, resulting in an increase in energy utilization efficiency. It is found that the system exergy efficiency decreases with increasing extraction rate. Table 5 shows the trends of the exergy destructions of components with variable extraction rate. It can be observed that the high heat transfer temperature difference in the gas heater and the gas cooler contribute to the decrease of the exergy efficiency. In addition, more working fluid CO2 extracted from the turbine further reduces the power output, which also causes the decrease of the exergy efficiency. Fig. 5 shows the effect of turbine inlet temperature on the system performance. There is a large increase in the turbine power output and the exergy efficiency with the increase of turbine inlet temperature. It reveals that a rise of heat source quality benefits the system performance. Increasing in turbine power output leads to decreasing in the net power input of the system, when the compressor power input keeps almost unchanged, thus the COP increase. It is also found that the energy utilization efficiency keeps rising. This could be explained by the higher turbine exhausting temperature, which could generate more heat output from the heater as the turbine inlet temperature increases. Fig. 6 shows the effect of the compressor outlet pressure on the system performance. It can be clearly seen that, as the compressor outlet pressure increases, both turbine power output and compressor power input increase correspondingly owing to the increasing pressure ratio across the turbine and the compressor. The exergy destructions of the turbine and the compressor, however, increase along with the compressor outlet pressure increases, and the proportion of the exergy destruction in the turbine and the compressor is relatively large. Therefore, the exergy efficiency decreases. It is found that the heat output decreases as the compressor outlet pressure increases. The reason mainly is that the turbine exhausting temperature can be reduced with the increase of the compressor outlet pressure. On the other hand, the compressor outlet temperature increases with the increase of the compressor outlet pressure increases. With constant turbine inlet temperature, the heat absorption from heat source decreases. From the reasons presented above, the energy utilization efficiency decreases. It is also found that the COP increases first and then decreases, which indicates that the system exists an optimum highside pressure to get high system performance. Fig. 7 shows the effect of extraction pressure on the system performance. It is obvious that the power output of the expander decreases as the extraction pressure increases. As the extraction
Table 5 Trend of exergy destructions with variable extraction rate.
Fig. 4. Effect of extraction ratio on the system performance.
e
Ic(kW)
Ie(kW)
Iej(kW)
Ig(kW)
Igc(kW)
Ih(kW)
It(kW)
Iv(kW)
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
11.4 11.29 11.19 11.08 10.97 10.85 10.74 10.62 10.5 10.39
0.991 1.115 1.239 1.363 1.487 1.611 1.735 1.859 1.982 2.106
4.06 4.567 5.075 5.582 6.09 6.597 7.105 7.612 8.12 8.627
15.49 16.07 16.67 17.28 17.9 18.52 19.16 19.81 20.47 21.13
12.02 12.66 13.30 13.94 14.57 15.21 15.85 16.49 17.13 17.77
8.465 8.683 8.901 9.12 9.338 9.556 9.774 9.992 10.21 10.43
8.159 7.801 7.444 7.087 6.729 6.372 6.014 5.657 5.3 4.942
0.2915 0.328 0.3644 0.4009 0.4373 0.4737 0.5102 0.5466 0.5831 0.6195
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X.X. Xu et al. / Energy xxx (2015) 1e9
Fig. 5. Effect of turbine inlet temperature on the system performance.
Fig. 6. Effect of compressor outlet pressure on the system performance.
pressure increases, the refrigeration output increases more quickly. It is because the higher the extraction pressure, the lower the quality of the ejector outlet at a given entrainment ratio. The decrease of the quality of the ejector outlet leads to an increase of the liquid stream from the separator to evaporator and a decrease of the gas stream from the separator fed back to evaporator, then it
Fig. 7. Effect of extraction pressure on the system performance.
7
results in the refrigeration output increasing. It can be observed that the increase in the energy utilization efficiency, exergy efficiency, and the COP of the system follows the increasing extraction pressure. In general, the vapor extracted from the expander reduces the net power output of the expander, which decreases the system performance. However, the modified system of this work not only takes advantage of the remaining heat output, but also produces more refrigeration output, when it works in the higher extraction pressure. Therefore, the gain from refrigeration and heat output is the main factor, making the improvement in both the thermal efficiency and the exergy efficiency of the system. Compared to the no-extraction turbine, the extraction turbine extracted a relatively high-pressure fluid as a primary stream of ejector is helpful to gain more refrigeration. Fig. 8 shows the effect of compressor outlet pressure on the COPs of the modified CCHP system and the transcritical CO2 ejector system. The result is based on the same conditions, including the evaporation temperature, the ejector isentropic efficiency, the compressor isentropic efficiency, and the turbine isentropic efficiency. It can be seen that in the modified CCHP system there exists an optimal high-side pressure that gives a maximum COP. For a conventional transcritical CO2 system with expansion valve, Elbel [23] explained that the increasing of the high-side pressure increases the cooling capacity at the expense of the incremental increase in compressor power. A COP maximum exists when the incremental capacity increase equals the incremental increase in compressor power. This method of finding the COP maximizing high-side pressure can also apply to the transcritical CO2 ejector system and the modified CCHP cycle. The COP maximizing highside pressure of the modified CCHP system of approximately 12 MPa is higher than that of the transcritical CO2 ejector system. The difference of the COP maximizing high-side pressure in the modified CCHP cycle and the transcritical CO2 ejector system is that the net work equals compressor work subtract turbine power output, not equals compressor work. It can be also seen that the ratio of COPs between the modified CCHP cycle and the transcritical CO2 ejector cycle increases from 1.29 to 2.43 with the increasing of the compressor outlet pressure. Fig. 9 shows the exergy efficiency of the modified CCHP system and Wang et al. [10]’s CCHP system as a function of the compressor outlet pressure, one is the modified CCHP system with extraction turbine, the other is Wang et al. [10]’s CCHP system with noextraction turbine. For the case of the extraction turbine, it has higher exergy efficiency in comparison to the no-extraction
Fig. 8. Performance comparison of the modified CCHP system and the transcritical CO2 ejector system.
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8
X.X. Xu et al. / Energy xxx (2015) 1e9 Table 7 Trend of exergy destructions with variable turbine inlet pressure (Wang et al. [10]’s CCHP cycle with no-extraction turbine).
Fig. 9. Exergy efficiency comparison of the modified CCHP system and Wang et al. [10]’s CCHP system.
turbine. The range of an increase in the exergy efficiency values of the two cases is about 10.4%e22.5%. A higher ejector primary inlet pressure in the case of the no-extraction turbine results in a lower turbine power output, which is accounted as low exergy efficiency of this cycle. In order to clearly understand how the exergy efficiency is sensitive to the specific component for the two cases, the exergy destructions of all components are listed in Table 6 and Table 7. Both the exergy destructions of the compressor and turbine in the case of the extraction turbine are higher than that of the noextraction turbine, but all heat exchangers in the case of the extraction turbine have lower exergy destructions in comparison to the no-extraction turbine. It is also observed that the exergy destructions of the ejector in the case of the extraction turbine are lower than that of the no-extraction turbine. The increased flow rate to the ejector results in the higher exergy destructions of the ejector in the case of the no-extraction turbine.
5. Conclusion A modified combined cooling, heating, and power system using supercritical CO2 is proposed. From thermodynamic points of view, it is provable that the combination of the Brayton cycle and the transcritical ejector refrigeration cycle by adding an extraction turbine is highly efficient. Using low-grade heat source to further increase the temperature of the heat generated from the compressor outlet enhances the heat source quality, which benefits the system performance. The following conclusions can be drawn from this work:
Table 6 Trend of exergy destructions with variable turbine inlet pressure (The modified CCHP cycle with extraction turbine). P2(MPa) Ic(kW)
Ie(kW) Iej(kW) Ig(kW) Igc(kW) Ih(kW) It(kW) Iv(kW)
9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363 1.363
8.594 9.147 9.669 10.16 10.63 11.08 11.5 11.91 12.3 12.68
5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582
22.34 20.84 19.47 18.2 17.02 15.93 14.92 13.97 13.1 12.28
13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94 13.94
10.37 10.11 9.85 9.601 9.357 9.12 8.887 8.658 8.434 8.213
4.455 5.031 5.58 6.104 6.606 7.087 7.548 7.991 8.417 8.827
0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009 0.4009
P2(MPa) Ic(kW)
Ie(kW) Iej(kW) Ig(kW) Igc(kW) Ih(kW) It(kW) Iv(kW)
9.5 10 10.5 11 11.5 12 12.5 13 13.5 14
2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478 2.478
7.746 8.25 8.726 9.178 9.608 10.02 10.41 10.79 11.15 11.5
10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15 10.15
28.99 27.28 25.69 24.22 22.85 21.58 20.39 19.28 18.24 17.27
19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68 19.68
12.11 11.9 11.69 11.48 11.28 11.08 10.89 10.7 10.51 10.32
1.329 1.885 2.415 2.921 3.406 3.87 4.316 4.744 5.157 5.554
0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288 0.7288
(1) The modified CCHP system exists an optimal high-side pressure that gives a maximum COP, and the COP maximizing high-side pressure of the modified CCHP system is higher than that of the transcritical CO2 ejector system. (2) The ratio of COPs between the modified CCHP cycle and the transcritical CO2 ejector cycle increases from 1.29 to 2.43. (3) The range of an increase in the exergy efficiency of the modified CCHP system with extraction turbine is about 10.4%e22.5% compared to Wang et al. [10]’s CCHP system with no-extraction turbine. (4) Although the extraction turbine extracted relatively highpressure fluid results in a decrease in the exergy destruction of the turbine, the gains from refrigeration and heat output are the main factors making the improvement of the thermal efficiency and the exergy efficiency of the system.
Acknowledgment This work is supported by National Natural Science Foundation of China (Project No. 51206197), National Basic Research Program of China (973 Program, Project No. 2011CB710701), Fundamental Research Funds for the Central Universities (Project No. cdjzr12140032) and Chongqing Natural Science Foundation (Project No. CSTC2011BB6094).
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