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Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
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Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes Mengmeng Wu a, Houcheng Zhang a,*, Tianjun Liao b,** a b
Department of Microelectronic Science and Engineering, Ningbo University, Ningbo 315211, China Department of Physics, Xiamen University, Xiamen 361005, China
article info
abstract
Article history:
In order to recover the waste heat produced in molten carbonate fuel cells (MCFCs), a new
Received 17 August 2017
hybrid system mainly consisting of an MCFC, a thermoelectric generator, and a thermo-
Received in revised form
electric cooler is integrated for performance enhancement. The irreversible losses in each
15 October 2017
subsystem are fully considered. The relationship between the dimensionless electric cur-
Accepted 17 October 2017
rent of the thermoelectric element and the electric current density of the MCFC is dis-
Available online xxx
cussed in detail. Based on non-equilibrium thermodynamics, the analytical formulas for power density and efficiency of the hybrid system are specified under different operation
Keywords:
conditions. The general performance characteristics of the hybrid system are revealed and
Molten carbonate fuel cell
the optimum regions for several parameters are given. Numerical calculations show that
Thermoelectric generator
the power density and efficiency of the hybrid system are 3.4% and 4.0% larger than that of
Thermoelectric cooler
the stand-alone MCFC, respectively. The effects of some main operating and design pa-
Hybrid system
rameters on the performance of the proposed system are discussed through parametric
Performance assessment
analyses. Abundant numerical calculation examples are provided to show how to improve the system performance. The results obtained may provide some theoretical bases for the MCFC performance improvement through heat management method. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction With the rising energy demands and the increasing depletion of fossil fuels, it is urgent to find alternative energy sources such as solar energy, wind turbine, fuel cell, etc. Fuel cells enable to directly and efficiently convert chemical energy of a fuel into electricity without pollutants, which are regarded as one of the most promising technologies [1e6]. Among various fuel cells, MCFCs have attracted considerable interests
because of many advantages such as low emissions, fuel flexibility, possibility for CO2 capture and storage and etc [7e10]. To now, a number of investigations on MCFCs have focused attention on aspects such as fabrication of cathode and anode materials [11e13], stack modeling and dynamic simulation [14,15], and theoretical modeling of a single MCFC [16,17]. The high-grade waste heat generated in MCFCs provides the opportunity for additional power generation or for combined heat and power (CHP) cogeneration [18e21]. Recently,
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (H. Zhang), [email protected] (T. Liao). https://doi.org/10.1016/j.ijhydene.2017.10.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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many researchers have employed various thermal devices to recover the waste heat from MCFCs for various applications using various analysis approaches [22e33]. Wu et al. [22] proposed a hybrid system coupling a TEG to an MCFC to recover the waste heat produced in the MCFC. They evaluated the performance of the system by considering the thermoelectrochemical losses within the system and discussed the effects of some designing and operating parameters on the hybrid system performance. Yang et al. [23] introduced an MCFC-based hybrid system that bottomed with a thermophotovoltaic cell. They systematically evaluated the performance characteristics of the MCFC-thermophotovoltaic cell hybrid system and demonstrated the superiority of the introduced system over other similar hybrid systems. Huang et al. [24] performed the thermodynamic analyses of an MCFCthermionic generator (TIG) hybrid system which includes a reforming MCFC and a TIG. They considered the effects of irreversible losses in the reforming and electrochemical reaction processes and then revealed the generic performance characteristics and obtained the optimal regions of the proposed system. The results showed that the maximum power density of the MCFC-TIG system is about 22% larger than a stand-alone MCFC. Ac¸ıkkalp performed the ecologic and sustainable objective thermodynamic analyses of an MCFCsupercritical CO2 Brayton cycle hybrid system [25] and an MCFC-heat engine hybrid system [26]. The results obtained are helpful to design more environmental-friendly MCFCbased hybrid systems. Mehrpooya et al. [27] introduced and analyzed a hybrid system composed of an MCFC and a supercritical carbon dioxide Brayton cycle for additional power production. This kind of hybrid system not only improved the efficiency and reduced the cost but also enabled to reduce the harmful emissions and negative impact on the environment. Duan et al. [28] used Aspen Plus to investigate a coal-fired power plant that captures CO2 by integrating a molten carbonate fuel cell, and showed that the total efficiency the proposed system is increased by 4.05% compared with that of the coal-fired power plant without CO2 capture system. Zhang et al. [29] used an absorption refrigerator to recover the waste heat from an MCFC for combined power and cooling applications. It is found that the maximum power density and efficiency of the proposed system are increased by 3.2% and 3.8% compared with that of the sole MCFC. Thermoelectric devices are kinds of energy conversion devices that convert waste heat directly into electricity (i.e., thermoelectric generator, TEG) or convert electrical energy into thermal energy for cooling (i.e., thermoelectric cooler, TEC) or heating (i.e., thermoelectric heat pump, THP) [34]. Thermoelectric devices can be used in a significant of amount of fields such as aerospace, military, industrial, and vehicle applications as they are structure-compacted, quiet, environmentalfriendly, highly reliable and flexible to various heat sources [35]. To improve thermoelectric devices performance, a number of studies have done on aspects including geometric configuration design [36e38], advanced materials fabrication [39,40], and system integration and optimization [41e43]. Alternatively, the TEG, TEC and THP could be readily connected in a multistage way to enhance their performance [44e46]. Furthermore, different kinds of thermoelectric devices can be cascaded to achieve specific purposes such as heat to cooling, power/cooling
cogeneration, and power/heating cogeneration [47,48]. The combination of TEGs and TECs offers the possibility to convert the heat to cooling using electricity as agent [49]. Obviously, the thermoelectric devices TEG-TEC can be used to recover the waste heat in MCFCs for additional cooling production, and thus the performance of MCFCs can be improved. In this study, a new hybrid system that integrates a thermoelectric generator and a thermoelectric cooler with an MCFC to simultaneously produce electricity and cooling is proposed. Based on the theories of electrochemistry and nonequilibrium thermodynamics, the multi-irreversible losses in each component are described. The problem how to design and operate the cascading thermoelectric devices will be solved. Expressions for equivalent power output and efficiency of the MCFC, thermoelectric devices and hybrid system are derived, from which the generic performance characteristics of the proposed system will be revealed. Finally, parametric studies will be used to discuss the effects of some designing parameters and operating conditions on the proposed system performance.
Description of the hybrid system Fig. 1 shows the schematic diagram of the proposed hybrid system that mainly consists of an MCFC, a TEG, a TEC, and a regenerator. Fuel and air are supplied to the fuel cell and participate in electrochemical reactions to produce electric power PMCFC and waste heat. A part of the waste heat, QH (J s1), is transferred from the MCFC at temperature T to the TEG for electricity generation via Seebeck effect. The generated electrical current Ig is flowed to TEC for extracting heat QC (J s1) from the cooled space at temperature TC via Peltier effect. Another part of the produced waste heat, QL (J s1), is directly leaked from the MCFC to the environment at temperature T0 via convection or conduction heat-transfer. The rest part of waste heat, QR (J s1), is used to compensate the regenerative loss in the regenerator. The regenerator utilizes the heat in high-temperature exhaust products to preheat the reactants from T0 to T. Q1 (J s1) and Q2 (J s1) are, respectively, heat-transfer rates between the environment and the TEG and the TEC.
Fig. 1 e Schematic diagram of an MCFC/thermoelectric devices hybrid system.
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
For simplification, the following assumptions are summarized [49e52]: (1) Both the MCFC and the thermoelectric devices are operated at steady-state conditions; (2) Operating temperature and pressure in the MCFC are uniform and constant; (3) Reactants are ideal gases and have constant electrochemical and thermodynamic properties; (4) Chemical reaction is complete and there is no residue of reactants after the reactions; (5) Thermoelectric elements in TEG and TEC are identical; (6) Geometrical configuration of a thermoelectric element is under the optimum form; (7) Thermoelectric elements are insulated both electrically and thermally from their surroundings except at the reservoir-junction contacts; (8) Seebeck coefficient, thermal conductance, electrical resistance, and figure of merit of the thermoelectric devices are temperature-independent; (9) Thompson effects in the thermoelectric devices are neglected.
The MCFC MCFCs use carbonate salts of alkali metals (e.g. Li, Na, and K) as electrolytes with an operating temperature about 650 C. The overall chemical reaction in the MCFC can be summarized as: H2 þ 12O2 þ CO2;cat /H2 O þ CO2;ano þ Electricity þ Heat, where subscripts “ano” and “cat” denote anode and cathode of the MCFC. Generally, the measured circuit voltage Ucell of a practical MCFC is always lower than the equilibrium potential U0 determined by Nernst equation [53], because there are some inevitably irreversible losses resulting from the anode overpotential Uano , cathode overpotential Ucat , and ohmic overpotential Uohm . According to the semi-empirical model developed by Yuh and Selmam [50], the power output PMCFC and efficiency hMCFC of an MCFC can be, respectively, expressed as [33]: PMCFC ¼ Ucell I ¼ jAðU0 Uano Ucat Uohm Þ
(1)
and hMCFC ¼
PMCFC
DH
jA
¼
DH
ðU0 Uano Ucat Uohm Þ
(2)
where I and j are, respectively, the electrical current and operating current density of the MCFC, A is the effective electrode area, DH ¼ jADh=ðne FÞ is the total energy released per unit time, Dh denotes the mole enthalpy change of the electrochemical reaction, F is Faraday's constant, ne is the number of electrons transferred in reaction, U0 , Uano , Ucat and Uohm can be further explicitly calculated by the following equations [29,33]: " pffiffiffiffiffiffiffiffiffiffiffiffiffi# pCO2 ;cat pH2 ;ano pO2 ;cat 2:42 105 45:8T RT þ ln U0 ¼ pH2 O;ano pCO2 ;ano ne F ne F 9
Uano ¼ 2:27 10
Eact;ano 0:42 0:17 1:0 PH2 ;ano PCO2 ;ano PH j exp 2 O;ano RT
Eact;cat 0:43 0:09 PO2 ;cat PCO2 ;cat Ucat ¼ 7:505 1010 j exp RT
(3)
The thermoelectric devices As shown in Fig. 1, the cascading thermoelectric devices composed of a TEG and a TEC, and the work output produced by the TEG is directly used to power the TEC for cooling. The TEG composed of m pairs thermoelectric elements is operated between the heat reservoir (i.e., the MCFC) and the heat sink (i.e., the ambient). The TEC composed of n pairs thermoelectric elements is operated between the heat sink and the cooled space. Each element in TEG and TEC consists of a P-type semiconductor leg and an N-type semiconductor leg which are connected thermally in parallel and electrically in series. The irreversible losses inside a thermoelectric element involve the Joule heat and the Fourier heat losses. Neglecting the external heat-transfer irreversibilities between the thermoelectric devices and the heat reservoirs, the heat balance equations can be expressed as [54]: QH ¼ amIg T 0:5mI2g Rte þ mKðT T0 Þ
(7)
Q1 ¼ amIg T0 þ 0:5mI2g Rte þ mKðT T0 Þ
(8)
Q2 ¼ anIg T0 þ 0:5nI2g Rte nKðT0 TC Þ
(9)
and QC ¼ anIg TC 0:5nI2g Rte nKðT0 TC Þ
(10)
where a, Rte and K are the Seebeck coefficient, equivalent electric resistance and the thermal conductance of a thermoelectric element. Based on Eqs. (7)e(10), we can define an internal structure parameter x for the thermoelectric devices to describe the number of thermoelectric elements among the top and bottom stages: x¼
m 1 t2 þ i=ðZT0 Þ ¼ n 1=t1 1 i=ðZT0 Þ
(11)
where t1 ¼ T0 =T, t2 ¼ TC =T0 , i ¼ aIg =K is the dimensionless electric current and Z ¼ a2 =ðKRte Þ is the figure of merit of a thermoelectric element. Based on Eqs. (7)e(11), the coefficient of performance j and the cooling rate 4 of the thermoelectric devices can be, respectively, derived as: QC ½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ ¼ ½i i2 =ð2ZT0 Þ þ 1 t1 ½1 t2 þ i=ðZT0 Þ QH
(12)
and f ¼ QC
(5)
and Uohm ¼ 0:5 104 j exp½3016ð1=T 1=923Þ
where pH2 , pO2 , pH2 O , pCO2 are, respectively, the partial pressures of H2, O2, H2O and CO2, R is the universal gas constant, Eact is the activation energy of an electrode. The above semiempirical electrochemical model had been validated in Ref. [24], and it was found that the simulation results were in good agreement with the experimental data in Ref. [53].
j¼ (4)
3
(6)
¼
ð1 þ 1=xÞKmT0 it2 i2 ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ 1t (13)
where t ¼ t1 t2 ¼ TC =T.
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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When the thermoelectric devices exert their functions, both the coefficient of performance and the cooling rate are larger than zero, i.e., j > 0 and 4 > 0. According to these two inequalities, the effective dimensionless current density range should locate in i1 < i < i2
(14)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where i1 ¼ ZT0 t2 ½1 1 2ð1 t2 Þ=ðZT0 t22 Þ and i2 ¼ ZT0 ð1=t1 1Þ. Substituting i1 and i2 into Eq. (11), one can obtain the corresponding internal structure parameters pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x1 ¼½t1 t 12ð1t2 Þ=ðZT0 t22 Þ=½1t1 ð1 12ð1t2 Þ=ðZT0 t22 ÞÞt and x2 /∞, respectively. Thus, the thermoelectric devices can generate power output only when x locates in the region of x>x1 . Taking the exergy content difference between the cooling load and the electric power into account [55], the equivalent power output Ptd and efficiency htd for the thermoelectric devices can be expressed as: Ptd ¼ QC j1 T0 =TC j ¼ KT0 mð1 þ 1=xÞj1 T0 =TC j
½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ 1t
(15)
and htd ¼
Ptd QH
¼ KT0 m ð1 þ 1=xÞj1 T0 =TC j
½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ ð1 tÞQH
(16)
(17)
where Kre , Are and b are the heat-transfer coefficient, heattransfer area, and efficiency of the regenerator, respectively.
The power output and efficiency of the hybrid system The part of waste heat directly leaked into the environment can be expressed as [29]: (18)
where KL is the heat-leakage coefficient and AL is the corresponding heat-transfer area. According to the first law of thermodynamics, the heat flow transferred from the MCFC to the thermoelectric devices can be expressed as:
QH ¼ DH PMCFC QR QL ADh 2Fc1 ðT T0 Þ 2Fc2 ðT T0 Þ ð1 hMCFC Þj ¼ 2F Dh Dh
(20) Based on Eqs. (2)e(20) and the parameters in Table 1 [33,49,50,54], one can obtain the curves of i j for different T, T0 and ZT0 , as shown in Fig. 2. It is found that i increases from i1 to i2 as j increases from j1 to j2 , where j1 and j2 are the startup and cut-off current densities corresponding to i1 and i2 , respectively. The values of j1 and j2 can be determined by using Eqs. (20) and (14). Fig. 2 shows that i increases as T decreases or T0 and Z increases, the thermoelectric devices cannot simultaneously work accompanying with the MCFC but only work in the region of j1
h¼
The regenerator in the proposed system functions as a heat exchanger that utilizes the heat in the high-temperature exhaust products to preheat the inlet reactants. The regenerative loss in the regenerator due to the thermal resistances is expressed as [56]:
QL ¼ KL AL ðT T0 Þ
i ¼ ZT sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZA Dh ðhMCFC 1Þj 2ðc1 þ c2 ÞðT T0 Þ ðZTÞ2 þ 2ZðT T0 Þ mK F
(21)
and
The regenerator
QR ¼ Kre Are ð1 bÞðT T0 Þ
Combining Eq. (7) with Eq. (19) gives the numerical relationship between the dimensionless electric current of the thermoelectric devices i and the operating current density of MCFC j as follows:
(19)
where c1 ¼ Kre Are ð1 bÞ=A and c2 ¼ KL AL =A are two temperature-independent parameters that are related to the regenerative losses and the heat-leakage, respectively.
PMCFC þ Ptd
(22)
DH
Table 1 e Parameters used in the modeling [33,49,50,54]. Parameter
Value
Faraday constant, F (C mol1) Number of electrons, ne Universal gas constant, R (J mol1 K1) Operating temperature, T (K) Operating pressure, p (atm) Partial pressure of H2 in the anode, pH2 O;ano (atm) Partial pressure of CO2 in the anode, pCO2 ;ano (atm) Partial pressure of H2O in the anode, pH2 O;ano (atm) Partial pressure of O2 in the cathode, pO2 ;cat (atm) Partial pressure of N2 in the cathode, pN2 ;cat (atm) Partial pressure of CO2 in the cathode, pCO2 ;cat (atm) Partial pressure of H2O in the cathode, pH2 O;cat (atm) Activation energy in the anode, Eact,ano (J mol1) Activation energy in the cathode, Eact,cat (J mol1) Heat conductivity of a thermoelectric element, K (W K1 m1) Figure of merit of the thermoelectric materials, ZT0 The number of thermoelectric elements in TEG, m Constants, c1 (W m2 K1) Constants, c2 (W m2 K1) Temperature of the ambience, T0 (K) Temperature of cooled space, TC (K)
96,485 2 8.314 893 1.0 0.60 0.15 0.25 0.08 0.59 0.08 0.25 53,500 77,300 0.03 1.0 8 0.1 0.1 298 273
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
Fig. 2 e Curves of i j for different (a) T and T0 , and (b) ZT0 , where j1 and j2 are the start-up and cut-off current densities corresponding to i1 and i2 , respectively.
General performance characteristics The curves of the power densities and efficiencies of the MCFC, the thermoelectric devices and the hybrid system are shown in Fig. 3, where P* ¼ P=A and P*MCFC ¼ PMCFC =A are, respectively, the power densities of the hybrid system and the MCFC, Pmax and PMCFC;max are, respectively, maximum power densities of the hybrid system and the MCFC, jP and hP are, respectively, the operating current density and efficiency at Pmax , jMCFC;P , jtd;P , and jtd;h are operating current densities at PMCFC;max , Ptd;max , and htd;max , respectively. Fig. 3 show that P*MCFC , Ptd and P* first increase and then decrease as j increases. hMCFC and h are the monotonically decreasing functions of j, while htd first increases and then decreases in the region of j1 < j < j2 . Fig. 3 also show that P* ¼ P*MCFC and h ¼ hMCFC when j < j1 or j > j2 . Apparently, P* and h are larger than that of P*MCFC and hMCFC when current density j is situated in the region of j1 < j < j2 . Numerical calculations show that Pmax is about 3.4% larger than PMCFC;max and hP is about 4.0% larger than hMCFC;P .
5
Fig. 3 e (a) power densities, and (b) efficiencies of the MCFC, thermoelectric devices and hybrid system varying with the operating current density of the MCFC, where P* ¼ P=A and P*MCFC ¼ PMCFC =A are the power densities of the hybrid system and the MCFC, Pmax and PMCFC;max are maximum power densities of the hybrid system and the MCFC, jP and hP are the operating current density and efficiency at Pmax , jMCFC;P , jtd;P , and jtd;h are operating current densities at PMCFC;max , Ptd;max , and htd;max , respectively.
Taking P* and h two performance parameters into consideration simultaneously, the optimum operating ranges for current density, power density and efficiency are, respectively, suggested to situate in j1 < j jP
(23)
P* Pmax
(24)
and h hP
(25)
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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Effect of T
Results and discussion As shown by Eqs. (21) and (22), the performance of the MCFCthermoelectric devices hybrid system depends on a set of designing parameters and operating conditions such as operating temperature, operating pressure, thermal conductance, the number of thermoelectric elements in TEG and etc. In the following sections, we will discuss the effects of these parameters on the performance of the hybrid system.
Fig. 4 displays that the increasing T can improve both P* and h, where jS is the stagnation current density from which the MCFC could not deliver electricity any more. A higher operating temperature T would increase the equilibrium potential and reduces the anode, the cathode and ohmic overpotentials and then improve the performance of MCFC. In addition, a higher operating temperature T leads to a larger temperature difference ðT T0 Þ that would also improve the thermoelectric devices performance. Meanwhile, larger thermodynamic losses would be also caused by a higher T, as showed by Eqs. (17) and (18). Since the performance improvements in the MCFC and thermoelectric devices are more pronounced than the performance deterioration resulting from the thermodynamic losses, a higher T is always preferable for the whole system performance. P*max and jS increase while hP decreases with the increasing of T, the effects of T on the proposed system performance occur in the whole region of j and become more and more significant as j increases. Extensive numerical calculation examples summarized in Table 2 show that jP , j1 , j2 , Dj ¼ ðj2 j1 Þ and xP increase with increasing T.
Effect of p Operating pressure p is an important operating condition of MCFC that affects the equilibrium potential, anode overpotential and cathode overpotential. In addition, operating
Fig. 4 e Effects of the operating temperature T on the hybrid system performance.
Table 2 e The values of j1 , j2 , Dj, jP , P*max , hP and xP for different values of T, m and K, where xP is the internal parameter for the thermoelectric devices at P*max and the unmentioned parameters are given in Table 1. T (K)
m
K (W K1 m1)
j1 (A m2)
j2 (A m2)
Dj (A m2)
jP (A m2)
P*max (W m2)
hP
xP
893
6
0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04
1669 2289 2655 1973 2705 3134 2247 3077 3562 1845 2552 2972 2191 3030 3523 2505 3457 4015 2010 2806 3279 2399 3345 3903 2752 3828 4460
2839 3874 4475 3350 4558 5257 3805 5164 5949 3183 4374 5067 3771 5162 5969 4295 5861 6767 3519 4869 5656 4184 5764 6681 4779 6559 7590
1170 1585 1820 1377 1853 2123 1558 2087 2387 1338 1822 2095 1580 2132 2446 1790 2404 2752 1509 2063 2377 1785 2419 2778 2027 2731 3130
2942 2872 3017 2826 3049 3332 2860 3287 2942 3724 3584 3663 3649 3687 3918 3581 3884 4257 4623 4432 4439 4623 4461 4625 4460 4587 4927
1484 1519 1530 1498 1530 1505 1516 1511 1484 1864 1888 1914 1865 1916 1922 1884 1924 1887 2281 2290 2322 2281 2327 2354 2287 2352 2352
0.394 0.413 0.396 0.414 0.392 0.353 0.414 0.359 0.394 0.391 0.411 0.408 0.399 0.406 0.383 0.411 0.386 0.346 0.385 0.403 0.408 0.385 0.407 0.397 0.399 0.399 0.372
e 0.392 0.226 0.853 0.215 0.150 0.424 0.154 e e 0.673 0.330 2.735 0.308 0.187 0.749 0.199 0.139 e 1.30 0.502 e 0.464 0.251 1.611 0.266 0.170
8
10
923
6
8
10
953
6
8
10
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
7
when the reactants are supplied at a larger p. Nevertheless, a larger p also consumes more additional electricity to compress the inlet reactants and brings a higher cost in balance of plant. Therefore, the ambient operating pressure, i.e., 1:0 atm, is usually chosen for p.
Effect of m
Fig. 5 e Effects of the operating pressure p on the hybrid system performance.
pressure affects the amount of heat transferred to the TEG for electricity generation. Fig. 5 shows that both P* and h increase as p increases, and Pmax , jP , jS , j1 , j2 , and Dj increase with increasing p. Moreover, the effects of p on the performance of the hybrid system become more dramatically as p increases. Generally, the hybrid system present a better performance
Fig. 6 e Effects of the number of thermoelectric elements in TEG m on the performance of the (a) thermoelectric devices and (b) hybrid system.
Fig. 6(a) depicts that Ptd;max , jtd;h , jtd;P , j1 , j2 , and Dj increase as m increases, while htd;max nearly keeps constant with increasing m, and both the curves of Ptd j and htd j are moved rightward as m increases. As shown in Fig. 6(b), the effect of m on the hybrid system only occurs in the region of j1 < j < j2 , and Pmax first increases and then decrease as m increases. It implies that we can optimize the m to obtain the maximum power density Pmax . This lies in the fact that the improvement in Ptd is less than the reduction in PMCFC for a larger m when jtd;P > jMCFC;P . Based on the parameters in Table 1, the optimum value of m locates between 6 and 10. More numerical calculation cases about m for the proposed system can be found in Table 2.
Effect of K It is seen from Eqs. (15), (16) and (20) that the thermal conductance K of a thermoelectric element significantly affects the performance of thermoelectric devices. As shown in Fig. 7(a), Ptd;max , jtd;h , jtd;P , j1 , j2 , and Dj increase as K increases, while
Fig. 7 e Effects of the thermal conductance of a thermoelectric element K on the performance of the (a) thermoelectric devices and (b) hybrid system.
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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Fig. 8 e Effects of the thermodynamic losses related parameters c1 and c2 on the hybrid system performance. htd;max changes negligibly with increasing K, and the curves of Ptd j and htd j move rightward as K increases. Fig. 7(b) shows that jP continuously increases with increasing K, and the increase in Ptd is less significantly than the decrease in PMCFC as K increases when jtd;P > jMCFC;P . As a result, Pmax first increases and then decrease as K increases, and there exists an optimum value of K to maximizePmax . For the parameters given in Table 1, the optimum value for K is found to be located between 0.02 and 0.04. More numerical calculation cases about K for the proposed system can be found in Table 2.
Effect of c1 and c2 As shown by Eqs. (17)e(19), besides temperature difference ðT T0 Þ, the thermodynamic losses are also associated with the integrated parameters c1 and c2 . It is observed from Fig. 8 that Pmax changes negligibly when two small parameters c1 and c2 are selected, Pmax evidently decreases as c1 and c2 increase, and j1 , j2 and jP increase with increasing c1 and c2 . By numerical calculations, it is found that the value of Dj slightly decreases with increasing c1 and c2 . The black solid lines in Fig. 8 indicate that the influences of regenerative losses QR and the heat leakage QL are neglected. In this case, Eqs. (19) and (20) can be, respectively, rewritten as: jADh ð1 hMCFC Þ QH ¼ 2F
(26)
Fig. 9 e Effects of the dimensionless thermoelectric figure of merit ZT0 on the hybrid system performance. coefficient, small electrical resistance as well as small thermal conductivity.
Conclusions We have proposed a new MCFC-based hybrid system to harvest the waste heat from MCFC for additional cooling production. The electrochemical and thermodynamic irreversible losses existing in the system are fully taken into account, and the relationship for the electric currents of the MCFC and the cascading thermoelectric devices is derived. The effective operating current density region permits the thermoelectric devices to work is determined, and the mathematical expressions for the performance of the hybrid system are specified under different operation conditions. For given typical operation conditions, it is found that the power density and efficiency of the proposed system is effectively increased by 3.4% and 4.0% comparing with the stand-alone MCFC. The optimization criteria for some performance parameters of the hybrid system are given. Comprehensive parametric studies are conducted to discuss the effects of some operating and design parameters on the performance of the hybrid system. Detailed numerical examples are derived and which may provide some useful information for the optimum design and performance improvement for the proposed MCFC-based system.
and i ¼ ZT
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ZA Dh ð1 hMCFC Þj Z2 T2 þ 2ZðT T0 Þ þ mK F
Acknowledgement (27)
Effect of ZT0 The dimensionless thermoelectric figure of merit ZT0 dramatically affects the performance of the thermoelectric devices, and numerous efforts have been initiated on improving it [57,58]. As shown in Fig. 9, both P* and h increase as ZT0 increases in the region of j1 < j < j2 . P*max , jP , j2 and Dj increase as ZT0 increases, while j1 and jS are kept as constants with the increasing ZT0 . The difficulty in improving ZT0 is that how to fabricate a thermoelectric element with large Seebeck
This research is supported by the National Natural Science Foundation of China (Grant No. 51406091), Natural Science Foundation of Zhejiang Province (Grant No. LQ14E060001) and K. C. Wong Magna Fund in Ningbo University.
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Available online at www.sciencedirect.com
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Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes Mengmeng Wu a, Houcheng Zhang a,*, Tianjun Liao b,** a b
Department of Microelectronic Science and Engineering, Ningbo University, Ningbo 315211, China Department of Physics, Xiamen University, Xiamen 361005, China
article info
abstract
Article history:
In order to recover the waste heat produced in molten carbonate fuel cells (MCFCs), a new
Received 17 August 2017
hybrid system mainly consisting of an MCFC, a thermoelectric generator, and a thermo-
Received in revised form
electric cooler is integrated for performance enhancement. The irreversible losses in each
15 October 2017
subsystem are fully considered. The relationship between the dimensionless electric cur-
Accepted 17 October 2017
rent of the thermoelectric element and the electric current density of the MCFC is dis-
Available online xxx
cussed in detail. Based on non-equilibrium thermodynamics, the analytical formulas for power density and efficiency of the hybrid system are specified under different operation
Keywords:
conditions. The general performance characteristics of the hybrid system are revealed and
Molten carbonate fuel cell
the optimum regions for several parameters are given. Numerical calculations show that
Thermoelectric generator
the power density and efficiency of the hybrid system are 3.4% and 4.0% larger than that of
Thermoelectric cooler
the stand-alone MCFC, respectively. The effects of some main operating and design pa-
Hybrid system
rameters on the performance of the proposed system are discussed through parametric
Performance assessment
analyses. Abundant numerical calculation examples are provided to show how to improve the system performance. The results obtained may provide some theoretical bases for the MCFC performance improvement through heat management method. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction With the rising energy demands and the increasing depletion of fossil fuels, it is urgent to find alternative energy sources such as solar energy, wind turbine, fuel cell, etc. Fuel cells enable to directly and efficiently convert chemical energy of a fuel into electricity without pollutants, which are regarded as one of the most promising technologies [1e6]. Among various fuel cells, MCFCs have attracted considerable interests
because of many advantages such as low emissions, fuel flexibility, possibility for CO2 capture and storage and etc [7e10]. To now, a number of investigations on MCFCs have focused attention on aspects such as fabrication of cathode and anode materials [11e13], stack modeling and dynamic simulation [14,15], and theoretical modeling of a single MCFC [16,17]. The high-grade waste heat generated in MCFCs provides the opportunity for additional power generation or for combined heat and power (CHP) cogeneration [18e21]. Recently,
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (H. Zhang), [email protected] (T. Liao). https://doi.org/10.1016/j.ijhydene.2017.10.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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many researchers have employed various thermal devices to recover the waste heat from MCFCs for various applications using various analysis approaches [22e33]. Wu et al. [22] proposed a hybrid system coupling a TEG to an MCFC to recover the waste heat produced in the MCFC. They evaluated the performance of the system by considering the thermoelectrochemical losses within the system and discussed the effects of some designing and operating parameters on the hybrid system performance. Yang et al. [23] introduced an MCFC-based hybrid system that bottomed with a thermophotovoltaic cell. They systematically evaluated the performance characteristics of the MCFC-thermophotovoltaic cell hybrid system and demonstrated the superiority of the introduced system over other similar hybrid systems. Huang et al. [24] performed the thermodynamic analyses of an MCFCthermionic generator (TIG) hybrid system which includes a reforming MCFC and a TIG. They considered the effects of irreversible losses in the reforming and electrochemical reaction processes and then revealed the generic performance characteristics and obtained the optimal regions of the proposed system. The results showed that the maximum power density of the MCFC-TIG system is about 22% larger than a stand-alone MCFC. Ac¸ıkkalp performed the ecologic and sustainable objective thermodynamic analyses of an MCFCsupercritical CO2 Brayton cycle hybrid system [25] and an MCFC-heat engine hybrid system [26]. The results obtained are helpful to design more environmental-friendly MCFCbased hybrid systems. Mehrpooya et al. [27] introduced and analyzed a hybrid system composed of an MCFC and a supercritical carbon dioxide Brayton cycle for additional power production. This kind of hybrid system not only improved the efficiency and reduced the cost but also enabled to reduce the harmful emissions and negative impact on the environment. Duan et al. [28] used Aspen Plus to investigate a coal-fired power plant that captures CO2 by integrating a molten carbonate fuel cell, and showed that the total efficiency the proposed system is increased by 4.05% compared with that of the coal-fired power plant without CO2 capture system. Zhang et al. [29] used an absorption refrigerator to recover the waste heat from an MCFC for combined power and cooling applications. It is found that the maximum power density and efficiency of the proposed system are increased by 3.2% and 3.8% compared with that of the sole MCFC. Thermoelectric devices are kinds of energy conversion devices that convert waste heat directly into electricity (i.e., thermoelectric generator, TEG) or convert electrical energy into thermal energy for cooling (i.e., thermoelectric cooler, TEC) or heating (i.e., thermoelectric heat pump, THP) [34]. Thermoelectric devices can be used in a significant of amount of fields such as aerospace, military, industrial, and vehicle applications as they are structure-compacted, quiet, environmentalfriendly, highly reliable and flexible to various heat sources [35]. To improve thermoelectric devices performance, a number of studies have done on aspects including geometric configuration design [36e38], advanced materials fabrication [39,40], and system integration and optimization [41e43]. Alternatively, the TEG, TEC and THP could be readily connected in a multistage way to enhance their performance [44e46]. Furthermore, different kinds of thermoelectric devices can be cascaded to achieve specific purposes such as heat to cooling, power/cooling
cogeneration, and power/heating cogeneration [47,48]. The combination of TEGs and TECs offers the possibility to convert the heat to cooling using electricity as agent [49]. Obviously, the thermoelectric devices TEG-TEC can be used to recover the waste heat in MCFCs for additional cooling production, and thus the performance of MCFCs can be improved. In this study, a new hybrid system that integrates a thermoelectric generator and a thermoelectric cooler with an MCFC to simultaneously produce electricity and cooling is proposed. Based on the theories of electrochemistry and nonequilibrium thermodynamics, the multi-irreversible losses in each component are described. The problem how to design and operate the cascading thermoelectric devices will be solved. Expressions for equivalent power output and efficiency of the MCFC, thermoelectric devices and hybrid system are derived, from which the generic performance characteristics of the proposed system will be revealed. Finally, parametric studies will be used to discuss the effects of some designing parameters and operating conditions on the proposed system performance.
Description of the hybrid system Fig. 1 shows the schematic diagram of the proposed hybrid system that mainly consists of an MCFC, a TEG, a TEC, and a regenerator. Fuel and air are supplied to the fuel cell and participate in electrochemical reactions to produce electric power PMCFC and waste heat. A part of the waste heat, QH (J s1), is transferred from the MCFC at temperature T to the TEG for electricity generation via Seebeck effect. The generated electrical current Ig is flowed to TEC for extracting heat QC (J s1) from the cooled space at temperature TC via Peltier effect. Another part of the produced waste heat, QL (J s1), is directly leaked from the MCFC to the environment at temperature T0 via convection or conduction heat-transfer. The rest part of waste heat, QR (J s1), is used to compensate the regenerative loss in the regenerator. The regenerator utilizes the heat in high-temperature exhaust products to preheat the reactants from T0 to T. Q1 (J s1) and Q2 (J s1) are, respectively, heat-transfer rates between the environment and the TEG and the TEC.
Fig. 1 e Schematic diagram of an MCFC/thermoelectric devices hybrid system.
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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For simplification, the following assumptions are summarized [49e52]: (1) Both the MCFC and the thermoelectric devices are operated at steady-state conditions; (2) Operating temperature and pressure in the MCFC are uniform and constant; (3) Reactants are ideal gases and have constant electrochemical and thermodynamic properties; (4) Chemical reaction is complete and there is no residue of reactants after the reactions; (5) Thermoelectric elements in TEG and TEC are identical; (6) Geometrical configuration of a thermoelectric element is under the optimum form; (7) Thermoelectric elements are insulated both electrically and thermally from their surroundings except at the reservoir-junction contacts; (8) Seebeck coefficient, thermal conductance, electrical resistance, and figure of merit of the thermoelectric devices are temperature-independent; (9) Thompson effects in the thermoelectric devices are neglected.
The MCFC MCFCs use carbonate salts of alkali metals (e.g. Li, Na, and K) as electrolytes with an operating temperature about 650 C. The overall chemical reaction in the MCFC can be summarized as: H2 þ 12O2 þ CO2;cat /H2 O þ CO2;ano þ Electricity þ Heat, where subscripts “ano” and “cat” denote anode and cathode of the MCFC. Generally, the measured circuit voltage Ucell of a practical MCFC is always lower than the equilibrium potential U0 determined by Nernst equation [53], because there are some inevitably irreversible losses resulting from the anode overpotential Uano , cathode overpotential Ucat , and ohmic overpotential Uohm . According to the semi-empirical model developed by Yuh and Selmam [50], the power output PMCFC and efficiency hMCFC of an MCFC can be, respectively, expressed as [33]: PMCFC ¼ Ucell I ¼ jAðU0 Uano Ucat Uohm Þ
(1)
and hMCFC ¼
PMCFC
DH
jA
¼
DH
ðU0 Uano Ucat Uohm Þ
(2)
where I and j are, respectively, the electrical current and operating current density of the MCFC, A is the effective electrode area, DH ¼ jADh=ðne FÞ is the total energy released per unit time, Dh denotes the mole enthalpy change of the electrochemical reaction, F is Faraday's constant, ne is the number of electrons transferred in reaction, U0 , Uano , Ucat and Uohm can be further explicitly calculated by the following equations [29,33]: " pffiffiffiffiffiffiffiffiffiffiffiffiffi# pCO2 ;cat pH2 ;ano pO2 ;cat 2:42 105 45:8T RT þ ln U0 ¼ pH2 O;ano pCO2 ;ano ne F ne F 9
Uano ¼ 2:27 10
Eact;ano 0:42 0:17 1:0 PH2 ;ano PCO2 ;ano PH j exp 2 O;ano RT
Eact;cat 0:43 0:09 PO2 ;cat PCO2 ;cat Ucat ¼ 7:505 1010 j exp RT
(3)
The thermoelectric devices As shown in Fig. 1, the cascading thermoelectric devices composed of a TEG and a TEC, and the work output produced by the TEG is directly used to power the TEC for cooling. The TEG composed of m pairs thermoelectric elements is operated between the heat reservoir (i.e., the MCFC) and the heat sink (i.e., the ambient). The TEC composed of n pairs thermoelectric elements is operated between the heat sink and the cooled space. Each element in TEG and TEC consists of a P-type semiconductor leg and an N-type semiconductor leg which are connected thermally in parallel and electrically in series. The irreversible losses inside a thermoelectric element involve the Joule heat and the Fourier heat losses. Neglecting the external heat-transfer irreversibilities between the thermoelectric devices and the heat reservoirs, the heat balance equations can be expressed as [54]: QH ¼ amIg T 0:5mI2g Rte þ mKðT T0 Þ
(7)
Q1 ¼ amIg T0 þ 0:5mI2g Rte þ mKðT T0 Þ
(8)
Q2 ¼ anIg T0 þ 0:5nI2g Rte nKðT0 TC Þ
(9)
and QC ¼ anIg TC 0:5nI2g Rte nKðT0 TC Þ
(10)
where a, Rte and K are the Seebeck coefficient, equivalent electric resistance and the thermal conductance of a thermoelectric element. Based on Eqs. (7)e(10), we can define an internal structure parameter x for the thermoelectric devices to describe the number of thermoelectric elements among the top and bottom stages: x¼
m 1 t2 þ i=ðZT0 Þ ¼ n 1=t1 1 i=ðZT0 Þ
(11)
where t1 ¼ T0 =T, t2 ¼ TC =T0 , i ¼ aIg =K is the dimensionless electric current and Z ¼ a2 =ðKRte Þ is the figure of merit of a thermoelectric element. Based on Eqs. (7)e(11), the coefficient of performance j and the cooling rate 4 of the thermoelectric devices can be, respectively, derived as: QC ½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ ¼ ½i i2 =ð2ZT0 Þ þ 1 t1 ½1 t2 þ i=ðZT0 Þ QH
(12)
and f ¼ QC
(5)
and Uohm ¼ 0:5 104 j exp½3016ð1=T 1=923Þ
where pH2 , pO2 , pH2 O , pCO2 are, respectively, the partial pressures of H2, O2, H2O and CO2, R is the universal gas constant, Eact is the activation energy of an electrode. The above semiempirical electrochemical model had been validated in Ref. [24], and it was found that the simulation results were in good agreement with the experimental data in Ref. [53].
j¼ (4)
3
(6)
¼
ð1 þ 1=xÞKmT0 it2 i2 ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ 1t (13)
where t ¼ t1 t2 ¼ TC =T.
Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114
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When the thermoelectric devices exert their functions, both the coefficient of performance and the cooling rate are larger than zero, i.e., j > 0 and 4 > 0. According to these two inequalities, the effective dimensionless current density range should locate in i1 < i < i2
(14)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where i1 ¼ ZT0 t2 ½1 1 2ð1 t2 Þ=ðZT0 t22 Þ and i2 ¼ ZT0 ð1=t1 1Þ. Substituting i1 and i2 into Eq. (11), one can obtain the corresponding internal structure parameters pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x1 ¼½t1 t 12ð1t2 Þ=ðZT0 t22 Þ=½1t1 ð1 12ð1t2 Þ=ðZT0 t22 ÞÞt and x2 /∞, respectively. Thus, the thermoelectric devices can generate power output only when x locates in the region of x>x1 . Taking the exergy content difference between the cooling load and the electric power into account [55], the equivalent power output Ptd and efficiency htd for the thermoelectric devices can be expressed as: Ptd ¼ QC j1 T0 =TC j ¼ KT0 mð1 þ 1=xÞj1 T0 =TC j
½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ 1t
(15)
and htd ¼
Ptd QH
¼ KT0 m ð1 þ 1=xÞj1 T0 =TC j
½it2 i2 =ð2ZT0 Þ 1 þ t2 ½1 t1 it1 =ðZT0 Þ ð1 tÞQH
(16)
(17)
where Kre , Are and b are the heat-transfer coefficient, heattransfer area, and efficiency of the regenerator, respectively.
The power output and efficiency of the hybrid system The part of waste heat directly leaked into the environment can be expressed as [29]: (18)
where KL is the heat-leakage coefficient and AL is the corresponding heat-transfer area. According to the first law of thermodynamics, the heat flow transferred from the MCFC to the thermoelectric devices can be expressed as:
QH ¼ DH PMCFC QR QL ADh 2Fc1 ðT T0 Þ 2Fc2 ðT T0 Þ ð1 hMCFC Þj ¼ 2F Dh Dh
(20) Based on Eqs. (2)e(20) and the parameters in Table 1 [33,49,50,54], one can obtain the curves of i j for different T, T0 and ZT0 , as shown in Fig. 2. It is found that i increases from i1 to i2 as j increases from j1 to j2 , where j1 and j2 are the startup and cut-off current densities corresponding to i1 and i2 , respectively. The values of j1 and j2 can be determined by using Eqs. (20) and (14). Fig. 2 shows that i increases as T decreases or T0 and Z increases, the thermoelectric devices cannot simultaneously work accompanying with the MCFC but only work in the region of j1
h¼
The regenerator in the proposed system functions as a heat exchanger that utilizes the heat in the high-temperature exhaust products to preheat the inlet reactants. The regenerative loss in the regenerator due to the thermal resistances is expressed as [56]:
QL ¼ KL AL ðT T0 Þ
i ¼ ZT sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZA Dh ðhMCFC 1Þj 2ðc1 þ c2 ÞðT T0 Þ ðZTÞ2 þ 2ZðT T0 Þ mK F
(21)
and
The regenerator
QR ¼ Kre Are ð1 bÞðT T0 Þ
Combining Eq. (7) with Eq. (19) gives the numerical relationship between the dimensionless electric current of the thermoelectric devices i and the operating current density of MCFC j as follows:
(19)
where c1 ¼ Kre Are ð1 bÞ=A and c2 ¼ KL AL =A are two temperature-independent parameters that are related to the regenerative losses and the heat-leakage, respectively.
PMCFC þ Ptd
(22)
DH
Table 1 e Parameters used in the modeling [33,49,50,54]. Parameter
Value
Faraday constant, F (C mol1) Number of electrons, ne Universal gas constant, R (J mol1 K1) Operating temperature, T (K) Operating pressure, p (atm) Partial pressure of H2 in the anode, pH2 O;ano (atm) Partial pressure of CO2 in the anode, pCO2 ;ano (atm) Partial pressure of H2O in the anode, pH2 O;ano (atm) Partial pressure of O2 in the cathode, pO2 ;cat (atm) Partial pressure of N2 in the cathode, pN2 ;cat (atm) Partial pressure of CO2 in the cathode, pCO2 ;cat (atm) Partial pressure of H2O in the cathode, pH2 O;cat (atm) Activation energy in the anode, Eact,ano (J mol1) Activation energy in the cathode, Eact,cat (J mol1) Heat conductivity of a thermoelectric element, K (W K1 m1) Figure of merit of the thermoelectric materials, ZT0 The number of thermoelectric elements in TEG, m Constants, c1 (W m2 K1) Constants, c2 (W m2 K1) Temperature of the ambience, T0 (K) Temperature of cooled space, TC (K)
96,485 2 8.314 893 1.0 0.60 0.15 0.25 0.08 0.59 0.08 0.25 53,500 77,300 0.03 1.0 8 0.1 0.1 298 273
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
Fig. 2 e Curves of i j for different (a) T and T0 , and (b) ZT0 , where j1 and j2 are the start-up and cut-off current densities corresponding to i1 and i2 , respectively.
General performance characteristics The curves of the power densities and efficiencies of the MCFC, the thermoelectric devices and the hybrid system are shown in Fig. 3, where P* ¼ P=A and P*MCFC ¼ PMCFC =A are, respectively, the power densities of the hybrid system and the MCFC, Pmax and PMCFC;max are, respectively, maximum power densities of the hybrid system and the MCFC, jP and hP are, respectively, the operating current density and efficiency at Pmax , jMCFC;P , jtd;P , and jtd;h are operating current densities at PMCFC;max , Ptd;max , and htd;max , respectively. Fig. 3 show that P*MCFC , Ptd and P* first increase and then decrease as j increases. hMCFC and h are the monotonically decreasing functions of j, while htd first increases and then decreases in the region of j1 < j < j2 . Fig. 3 also show that P* ¼ P*MCFC and h ¼ hMCFC when j < j1 or j > j2 . Apparently, P* and h are larger than that of P*MCFC and hMCFC when current density j is situated in the region of j1 < j < j2 . Numerical calculations show that Pmax is about 3.4% larger than PMCFC;max and hP is about 4.0% larger than hMCFC;P .
5
Fig. 3 e (a) power densities, and (b) efficiencies of the MCFC, thermoelectric devices and hybrid system varying with the operating current density of the MCFC, where P* ¼ P=A and P*MCFC ¼ PMCFC =A are the power densities of the hybrid system and the MCFC, Pmax and PMCFC;max are maximum power densities of the hybrid system and the MCFC, jP and hP are the operating current density and efficiency at Pmax , jMCFC;P , jtd;P , and jtd;h are operating current densities at PMCFC;max , Ptd;max , and htd;max , respectively.
Taking P* and h two performance parameters into consideration simultaneously, the optimum operating ranges for current density, power density and efficiency are, respectively, suggested to situate in j1 < j jP
(23)
P* Pmax
(24)
and h hP
(25)
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
Effect of T
Results and discussion As shown by Eqs. (21) and (22), the performance of the MCFCthermoelectric devices hybrid system depends on a set of designing parameters and operating conditions such as operating temperature, operating pressure, thermal conductance, the number of thermoelectric elements in TEG and etc. In the following sections, we will discuss the effects of these parameters on the performance of the hybrid system.
Fig. 4 displays that the increasing T can improve both P* and h, where jS is the stagnation current density from which the MCFC could not deliver electricity any more. A higher operating temperature T would increase the equilibrium potential and reduces the anode, the cathode and ohmic overpotentials and then improve the performance of MCFC. In addition, a higher operating temperature T leads to a larger temperature difference ðT T0 Þ that would also improve the thermoelectric devices performance. Meanwhile, larger thermodynamic losses would be also caused by a higher T, as showed by Eqs. (17) and (18). Since the performance improvements in the MCFC and thermoelectric devices are more pronounced than the performance deterioration resulting from the thermodynamic losses, a higher T is always preferable for the whole system performance. P*max and jS increase while hP decreases with the increasing of T, the effects of T on the proposed system performance occur in the whole region of j and become more and more significant as j increases. Extensive numerical calculation examples summarized in Table 2 show that jP , j1 , j2 , Dj ¼ ðj2 j1 Þ and xP increase with increasing T.
Effect of p Operating pressure p is an important operating condition of MCFC that affects the equilibrium potential, anode overpotential and cathode overpotential. In addition, operating
Fig. 4 e Effects of the operating temperature T on the hybrid system performance.
Table 2 e The values of j1 , j2 , Dj, jP , P*max , hP and xP for different values of T, m and K, where xP is the internal parameter for the thermoelectric devices at P*max and the unmentioned parameters are given in Table 1. T (K)
m
K (W K1 m1)
j1 (A m2)
j2 (A m2)
Dj (A m2)
jP (A m2)
P*max (W m2)
hP
xP
893
6
0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04 0.02 0.03 0.04
1669 2289 2655 1973 2705 3134 2247 3077 3562 1845 2552 2972 2191 3030 3523 2505 3457 4015 2010 2806 3279 2399 3345 3903 2752 3828 4460
2839 3874 4475 3350 4558 5257 3805 5164 5949 3183 4374 5067 3771 5162 5969 4295 5861 6767 3519 4869 5656 4184 5764 6681 4779 6559 7590
1170 1585 1820 1377 1853 2123 1558 2087 2387 1338 1822 2095 1580 2132 2446 1790 2404 2752 1509 2063 2377 1785 2419 2778 2027 2731 3130
2942 2872 3017 2826 3049 3332 2860 3287 2942 3724 3584 3663 3649 3687 3918 3581 3884 4257 4623 4432 4439 4623 4461 4625 4460 4587 4927
1484 1519 1530 1498 1530 1505 1516 1511 1484 1864 1888 1914 1865 1916 1922 1884 1924 1887 2281 2290 2322 2281 2327 2354 2287 2352 2352
0.394 0.413 0.396 0.414 0.392 0.353 0.414 0.359 0.394 0.391 0.411 0.408 0.399 0.406 0.383 0.411 0.386 0.346 0.385 0.403 0.408 0.385 0.407 0.397 0.399 0.399 0.372
e 0.392 0.226 0.853 0.215 0.150 0.424 0.154 e e 0.673 0.330 2.735 0.308 0.187 0.749 0.199 0.139 e 1.30 0.502 e 0.464 0.251 1.611 0.266 0.170
8
10
923
6
8
10
953
6
8
10
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
7
when the reactants are supplied at a larger p. Nevertheless, a larger p also consumes more additional electricity to compress the inlet reactants and brings a higher cost in balance of plant. Therefore, the ambient operating pressure, i.e., 1:0 atm, is usually chosen for p.
Effect of m
Fig. 5 e Effects of the operating pressure p on the hybrid system performance.
pressure affects the amount of heat transferred to the TEG for electricity generation. Fig. 5 shows that both P* and h increase as p increases, and Pmax , jP , jS , j1 , j2 , and Dj increase with increasing p. Moreover, the effects of p on the performance of the hybrid system become more dramatically as p increases. Generally, the hybrid system present a better performance
Fig. 6 e Effects of the number of thermoelectric elements in TEG m on the performance of the (a) thermoelectric devices and (b) hybrid system.
Fig. 6(a) depicts that Ptd;max , jtd;h , jtd;P , j1 , j2 , and Dj increase as m increases, while htd;max nearly keeps constant with increasing m, and both the curves of Ptd j and htd j are moved rightward as m increases. As shown in Fig. 6(b), the effect of m on the hybrid system only occurs in the region of j1 < j < j2 , and Pmax first increases and then decrease as m increases. It implies that we can optimize the m to obtain the maximum power density Pmax . This lies in the fact that the improvement in Ptd is less than the reduction in PMCFC for a larger m when jtd;P > jMCFC;P . Based on the parameters in Table 1, the optimum value of m locates between 6 and 10. More numerical calculation cases about m for the proposed system can be found in Table 2.
Effect of K It is seen from Eqs. (15), (16) and (20) that the thermal conductance K of a thermoelectric element significantly affects the performance of thermoelectric devices. As shown in Fig. 7(a), Ptd;max , jtd;h , jtd;P , j1 , j2 , and Dj increase as K increases, while
Fig. 7 e Effects of the thermal conductance of a thermoelectric element K on the performance of the (a) thermoelectric devices and (b) hybrid system.
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8
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
Fig. 8 e Effects of the thermodynamic losses related parameters c1 and c2 on the hybrid system performance. htd;max changes negligibly with increasing K, and the curves of Ptd j and htd j move rightward as K increases. Fig. 7(b) shows that jP continuously increases with increasing K, and the increase in Ptd is less significantly than the decrease in PMCFC as K increases when jtd;P > jMCFC;P . As a result, Pmax first increases and then decrease as K increases, and there exists an optimum value of K to maximizePmax . For the parameters given in Table 1, the optimum value for K is found to be located between 0.02 and 0.04. More numerical calculation cases about K for the proposed system can be found in Table 2.
Effect of c1 and c2 As shown by Eqs. (17)e(19), besides temperature difference ðT T0 Þ, the thermodynamic losses are also associated with the integrated parameters c1 and c2 . It is observed from Fig. 8 that Pmax changes negligibly when two small parameters c1 and c2 are selected, Pmax evidently decreases as c1 and c2 increase, and j1 , j2 and jP increase with increasing c1 and c2 . By numerical calculations, it is found that the value of Dj slightly decreases with increasing c1 and c2 . The black solid lines in Fig. 8 indicate that the influences of regenerative losses QR and the heat leakage QL are neglected. In this case, Eqs. (19) and (20) can be, respectively, rewritten as: jADh ð1 hMCFC Þ QH ¼ 2F
(26)
Fig. 9 e Effects of the dimensionless thermoelectric figure of merit ZT0 on the hybrid system performance. coefficient, small electrical resistance as well as small thermal conductivity.
Conclusions We have proposed a new MCFC-based hybrid system to harvest the waste heat from MCFC for additional cooling production. The electrochemical and thermodynamic irreversible losses existing in the system are fully taken into account, and the relationship for the electric currents of the MCFC and the cascading thermoelectric devices is derived. The effective operating current density region permits the thermoelectric devices to work is determined, and the mathematical expressions for the performance of the hybrid system are specified under different operation conditions. For given typical operation conditions, it is found that the power density and efficiency of the proposed system is effectively increased by 3.4% and 4.0% comparing with the stand-alone MCFC. The optimization criteria for some performance parameters of the hybrid system are given. Comprehensive parametric studies are conducted to discuss the effects of some operating and design parameters on the performance of the hybrid system. Detailed numerical examples are derived and which may provide some useful information for the optimum design and performance improvement for the proposed MCFC-based system.
and i ¼ ZT
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ZA Dh ð1 hMCFC Þj Z2 T2 þ 2ZðT T0 Þ þ mK F
Acknowledgement (27)
Effect of ZT0 The dimensionless thermoelectric figure of merit ZT0 dramatically affects the performance of the thermoelectric devices, and numerous efforts have been initiated on improving it [57,58]. As shown in Fig. 9, both P* and h increase as ZT0 increases in the region of j1 < j < j2 . P*max , jP , j2 and Dj increase as ZT0 increases, while j1 and jS are kept as constants with the increasing ZT0 . The difficulty in improving ZT0 is that how to fabricate a thermoelectric element with large Seebeck
This research is supported by the National Natural Science Foundation of China (Grant No. 51406091), Natural Science Foundation of Zhejiang Province (Grant No. LQ14E060001) and K. C. Wong Magna Fund in Ningbo University.
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Please cite this article in press as: Wu M, et al., Performance assessment of an integrated molten carbonate fuel cell-thermoelectric devices hybrid system for combined power and cooling purposes, International Journal of Hydrogen Energy (2017), https://doi.org/ 10.1016/j.ijhydene.2017.10.114