Performance Analysis and Multi-Objective Optimization of an Irreversible Solid Oxide Fuel Cell-Stirling Heat Engine Hybrid System

Transcription

1 Int. J. Electroche. Sci., 8 (3) International Journal of ELECTROCHEMICAL SCIENCE erforance Analysis Multi-Objective Optiization of an Irreversible Solid Oxide Fuel Cell-Stirling Heat Engine Hybrid Syste Liwei Chen, Songhua Gao, Houcheng Zhang, Mechanic Electronic Engineering College, Saning University 365, Fujian rovince, China. Departent of hysics, Ningbo University, Ningbo 35, Zhejiang rovince, China E-ail: zhanghoucheng@nbu.edu.cn Received: 8 May 3 / Accepted: 3 June 3 / ublished: August 3 A new hybrid syste consists of a solid oxide fuel cell (SOFC) a Stirling heat engine is established, where the heat engine is driven by high-quality waste heat generated in the SOFC. Based on the electrocheistry non-equilibriu therodynaics, analytical expressions for the efficiency power output of the hybrid syste are derived by taking various irreversible losses into account. The curves of the equivalent efficiency power output varying with the electric current density are represented through nuerical calculations. It shows that the perforance of the solid oxide fuel cell can be greatly enhanced by coupling a Stirling heat engine to further convert the waste heat for power generation. The general perforance characteristics of the hybrid syste are revealed the optial regions of soe iportant perforance paraeters are deterined. By eploying the ulti-objective optiization ethod, the optial operating regions are further divided into ore detailed based on the priorities of the engineer. Moreover, it is pointed out that the investigation ethod in the present paper is valid for soe other siilar energy conversion electrocheistry systes as well. Keywords: Solid oxide fuel cell, Stirling heat engine, Hybrid syste, erforance analysis, Multiobjective optiization. INTRODUCTION The cobined effects of liited fossil fuel sources environental pollution have shown the requireent for innovative energy generation systes not only to increase the efficiency of energy

2 Int. J. Electroche. Sci., Vol. 8, conversion but also to reduce the harful eissions of energy conversion processes. A fuel cell is a device that can efficiently cleanly converts the cheical energy fro a fuel into electricity through a cheical reaction with oxygen or other oxidizing agents. In 839, the first fuel cell was invented by Welsh hysicist Willia Grove []. The first coercial use of fuel cells was in NASA space progras to generate power for probes, satellites space capsules. Since then, fuel cells have been used in any other applications. Fuel cells are used for priary backup power for coercial, industrial residential buildings in reote or inaccessible areas, because of their high conversion efficiencies low environental ipact. [-5]. There are any types of fuel cells, such as proton exchange ebrane fuel cells (EM), alkaline fuel cells (AFC), solid oxide fuel cells (SOFC), so on []. Aong the, SOFC is ade entirely of solid aterials, which is not liited to the flat plane configuration of other types of fuel cells is often designed as rolled tubes [8], it has been one of the ost proising fuel cells due to its fuel flexibility high efficiency. The high teperatures operating characteristics (8 to C) [9,, 5] provide the possibility of cogeneration with other types of power generators such as gas turbines [] or heat engines [3] for further power generation. Thus, it is a task deserving deeply investigation on how to availably utilize the waste heat produced in SOFC. In the present paper, we will construct a hybrid syste coposed of a SOFC a Stirling heat engine, in which not only the irreversible losses in the SOFC but also the heat-leak fro the fuel cell to the environent as well as heat transfer between the fuel cell the heat engine are considered. Based on the therodynaic-electrocheical analysis, new expressions for soe key paraeters of the hybrid syste such as efficiency power output are derived. By using nuerical calculations, the general perforance characteristics are revealed the the optial regions for soe iportant perforance paraeters are given. As a consequence, the perforance characteristics of the hybrid syste are optiized.. AN IRREVERSIBLE MODEL OF THE FUEL CELL-HEAT ENGINE HYBRID SYSTEM Figure shows the configuration of a SOFC-Stirling heat engine power generation syste, which ainly consists of a SOFC, a Stirling engine a regenerator. The SOFC in the hybrid syste plays a role of the high-teperature heat reservoir of a Stirling engine for a further use of the waste heat. The regenerator acts as a counter-flow heat exchanger, which econoically absorbs the heat in the high-teperature exhaust gas to preheat the reactants to attain the reaction teperature. In order to analyze the perforance of the whole hybrid syste, the following ajor assuptions are often adopted [6-]: () Both the SOFC the Stirling engine are operated under steady-state condition; () The regenerator is regarded as a perfect one; (3) Operating teperature pressure are unifor constant in the SOFC;

3 Int. J. Electroche. Sci., Vol. 8, (4) All gases involved are assued to be copressible ideal gases; (5) Copleted cheical reactions are considered no reactants are reained after the reactions. SOFC Q loss SOFC (T) Q h reactants in Regenerator water out Stirling Heat Engine H Q l T Figure. The scheatic diagra of an irreversible SOFC-Stirling heat engine hybrid syste. With the help of these assuptions, the expressions of the syste perforance can be investigated. Below, we will analyze each coponent in the hybrid syste respectively then study the perforance of the whole hybrid syste.. An irreversible SOFC odel

4 Int. J. Electroche. Sci., Vol. 8, Figure. rinciple of a solid oxide fuel cell. By using hydrogen as fuel air as oxidant [9, ], the basic principle of an SOFC is illustrated in Figure. At the cathode, oxygen is reduced by the incoing electrons to oxygen anions that are conducted through the electrolyte to the anode where they electrocheically cobine with the adsorbed hydrogen to for water heat as a by-product release electrons to the external circuit. The overall reaction in such a fuel cell can be suarized as H / O HO Heat Electricity. In order to quantificationally describe the electrocheical reactions in the SOFC, it is quite iportant to underst the therodynaic principles of the fuel cell operation. The basic therodynaic relationship can be given as H Q G T S () The total energy H Q is divided into two parts, which are electrical theral coponents. As long as the enthalpy change is ore negative than the Gibbs free energy change of the reaction, a part of the total energy, which cannot be converted to electrical energy, is released as heat. The enthalpy change Gibbs free energy change between the products the reactants of the global electrocheical reaction at teperature T for the steady-state fuel cell can be, respectively, expressed as [6, 9, -3] dn dn e k e j ia H hk( T) hj( T) h( T) () dt dt n F k j e dn dn e k e j ia G k( T) j( T) g( T, p) dt dt n F (3) k j e

5 Int. J. Electroche. Sci., Vol. 8, 3 776, g( T, p) kk ( T, p) j j ( T, p), n is the nuber of oles, h where h khk jhj k j k is the olar enthalpy of the species at teperature T, p is the partial pressure of the species, is the partial olar Gibbs free energy of species, subscripts k j represent the k th product the j th reactant of the reaction, respectively. Since the Gibbs free energy change of an electrocheical reaction is a easure of iu electrical energy obtainable as work fro the reaction, the iu power output generated by the reaction in the fuel cell can be deterined by ia rev G g( T, p) (4) nf e In practice, this part of energy is never copletely utilized because of the various therodynaic electrocheical irreversibilities [6,, ]. When the fuel cell works norally produce useful power through the external load, the total entropy production rate can be deterined by [9, ] S I R / T I R / T (5) tot int int leak leak where T is the abient teperature, I int is the electric current through the equivalent internal resistance R int entropy production, S tot, the I leak is the electric current through the leakage resistance R leak. Here the rate of j, is that of the fuel cell syste environent together it is never negative. By considering all the irreversibilities, the power output the efficiency of fuel cell can be deduced as [9, ] ia k cell G T Stot (6) nef RTd where cell k cell (7) H h RTd / p H p O g ( T) RT ln( ) RTd, k Rint p / Rleak, HO i i in L F E i i d n n. e el el esinh ( ) esinh ( ) exp( ) ln( ) ln( ) i, a i, c R RT il, a il, c.. A Stirling heat engine The Stirling cycle is one of the iportant stard air cycles for heat engines [4, 5], as shown in Figure 3. It is seen fro Fig. 3 that the Stirling cycle is coposed of two isotheral processes at teperatures T T, two constant-volue processes at volue V V,

6 Int. J. Electroche. Sci., Vol. 8, respectively. Its ain advantages are that the cycle ay be driven by a wide variety of fuels, it offers the opportunity for high efficiency power generation [4-6]. The Stirling cycle has been seriously considered for a variety of uses. For exaple, Stirling engines driven by fuel cell ay be used in obile applications. Generally, the analyses about the optial atch of the fuel cell the heat engine ay be a key issue for any hybrid syste [7]. T T Q T Q T V V V Figure 3. V-diagra of a Stirling heat engine. For a practical Stirling heat engine, there are invariably theral resistances between the working substance the external heat reservoirs. Hence, we will use a powerful tool which is finitetie therodynaics. The results obtained here have ore realistic instructive significance for the optial design of real fuel cell-driven systes than those derived fro traditional equilibriu therodynaics. The aounts of heat Q Q absorbed fro the heat reservoir at teperature T released to the heat source at teperature T per cycle ay be written as [4] Q k ( T T ) t (8) Q k ( T T ) t (9) respectively, where k k are the theral conductances between the working substance the heat reservoirs at teperatures T (the teperature of exhaust gas) T (abient teperature), t t are the ties spent on the two isotheral branches at teperatures T T, respectively. It should be pointed out that the regenerative processes are affected by internal theral resistances. One ay quantify these regenerative losses by [4]

7 Int. J. Electroche. Sci., Vol. 8, Q xc( T T ) () where x is the fractional deviation fro ideal regeneration, when x the Stirling cycle operators with ideal (coplete) regeneration, C is the heat capacity of the working substance per ole partaking in the regenerative processes. For the convenience of analysis, it is assued that the tie spent on the regenerative branches is proportional to that of the isotheral branches, i.e. t b( t t ) () re where b is a constant. The average rate of heat supply can be exped as Qh T ( T T ) qh, () t t t ( b) T / k ( T T ) T / k ( T T ) re h c where xc / Rln( V / V ) the Stirling engine can be attained is given by [4] qh / K ( ) T T Te engine T q / K ( ) T T T where, R is the universal gas constant. For a q h, the iu efficiency of h (.5 ) h / 4 ( ) e, (3) k Te T T q K TT, K. ( b)( k / k ) As illustrated in Figure, a part of the waste heat produced in the fuel cell is directly released as heat-leak to the environent, the aount of the heat can be given by [6, 7, 8] Q A ( T T ) (6) loss l where is the convective heat-leak coefficient, A l denotes the effective heat-transfer area. Cobining the previous analysis, the rate of waste heat fro SOFC to the Stirling heat engine is given by q H Q H A ( T T ) (7) h cell loss cell l By substituting Eq. (7) into Eq. (3), the optiu efficiency power output of the Stirling heat engine ay be expressed as ( ) T T i ( cell ) 3 ( T T ) Te engine (8) T ( ) T T i ( ) ( T T ) T cell 3 K i ( ) ( T T ) engine cell 3 ( ) Th T i ( cell ) 3 ( T T ) Te T ( ) T T i ( ) ( T T ) T cell 3 A A l where h 3. n FK K e e e (9).3. An ideal regenerative heat exchanger

8 Int. J. Electroche. Sci., Vol. 8, As illustrated in Figure, the regenerator working as a heat exchanger in the hybrid syste, heats the inlet reactants fro the abient teperature to the cell teperature by using the high teperature outlet gas of the fuel cell. For the sake of siplicity, the regeneration process is assued to be ideal. This assuption is reasonable, because the efficiency of regenerators with the values of 98 99% have already been reported [, 3, 9-3]. With the help of perfect regeneration, the fuel cell hence the whole hybrid syste can be ensured to work norally continually under the condition of steady-state..4. The efficiency power output of the hybrid syste Using equations (6), (7), (8) (9), one ay obtain the efficiency the power output of the entire SOFC-Stirling engine hybrid syste, i.e., hybrid cell engine hybrid Q H all 3 cell cell ( T T ) i ( ) T T i ( cell ) 3 ( T T ) Te T ( ) T T i ( ) ( T T ) T cell 3 hybrid cell engine 3 cell cell ( T T ) ia i h nf e ( ) T T i ( cell ) 3 ( T T ) Te T ( ) T T i ( cell ) 3 ( T T ) Te It is seen fro equations () () that the efficiency the power output of hybrid syste are closely dependent on the irreversible losses including the irreversibilities within the fuel cell itself originating fro the heat transfer between the SOFC Stirling heat engine. In the next section, the general perforance characteristics the optial criteria of the hybrid syste will be given. e () () 3. GENERAL ERFORMANCE CHARACTERISTICS AND OTIMAL CRITERIA Optial design analysis of the SOFC-Stirling heat engine hybrid syste require a thorough understing of its perforance liitations. Equations () () clearly show that the perforance of the hybrid syste depends on a set of therodynaic electrocheical paraeters such as the fuel cell teperature (T ), operating current density ( i ), the paraeters related to the heat transfer between the SOFC the Stirling heat engine the heat-leak to the surroundings, i.e.,

9 Int. J. Electroche. Sci., Vol. 8, 3 78, 3. It is necessary to point out the physical significance of the three paraeters, 3. is a paraeter to easure the irreversibility of finite-rate heat transfer in the heat engine. The paraeter is a colligation easureent for the systeic structure, which ay be ainly used to discuss the influence of the irreversible heat transfer between the heat engine the fuel cell []. The paraeter 3 is used to discuss the influence of the heat-leak irreversibility fro the fuel cell to the surroundings. In the following calculation, the paraeters.4, KA, Table. Operating conditions perforance-related paraeters. araeter Value Operating pressure, p (at) Fuel coposition, Air coposition, Nuber of electrons, H ; O (at); fuel H O (at).97;.3 (at).;.79 H O n e re-factor for anode exchange current density, (A - ) 8 a 5.5 Activation energy of anode, E act, a (J ol - ) 5. re-factor for cathode exchange current density, (A - ) 8 c 7. Activation energy of cathode, E act, c (J ol - ) 5 Electrolyte thickness, Activation energy of re-factor of L el (μ) O, O, (S - ) E el (J ol - ) Ratio of the internal resistance to the leakage resistance, k / Anode liiting current density, i La, (A - ) 4.99 Cathode liiting current density, i Lc, (A - ) 4.6 Faraday constant, F (C ol - ) Universal gas constant, R (J ol - K - ) 834 Table. Molar enthalpy change Gibbs free energy change values at p at of the hydrogenoxygen reaction for different teperatures. Teperature(K) T=73K T=3K T=73K T=3K T=73K h (J/ol)

10 Int. J. Electroche. Sci., Vol. 8, 3 78 g (J/ol) are chosen. Below, nuerical calculations are carried out to quantitatively investigate the influence of these paraeters on the perforance of the hybrid syste. The results are based on the paraeters suarized in Table Table, these paraeters are kept constant unless entioned specifically. The fuel coposition is taken as 97% H 3% HO, the typical oxygen coposition in the abient air, i.e., % O 79%N, is used as oxidant. By using Eqs. () (), the efficiency power density of the hybrid syste operating at different current density are presented in Figure 4, where the separate efficiencies in the hybrid syste are given / A. It can be clearly seen fro Figure 4 that the efficiency power density of the hybrid syste first increase then decrease as the current density increases. The values of the efficiency of the single syste are lower than that of the hybrid syste. Through the way of coupling syste, the utilization rate of energy can be greatly iproved. In addition, there exist a iu power density a iu efficiency, which will be ade a detailed discussion in the following. Figure 5 shows the efficiency versus the power density at different operating teperatures, where are the power density at the iu efficiency the efficiency at the iu power output, respectively. According to Figure 5, one can obtain the optially operating regions, which has a negative slope in the part of the ~ curve. When the hybrid syste operates in this region, the efficiency will decrease as the power density increase, vice versa. Thus, the optial ranges of the efficiency power density should be given as () (3) The above results show that,, are the four iportant paraeters which are related to a set of therodynaic electrocheical paraeters. deterine the allowable optiu values of the lower bounds of the power density efficiency, while deterine the upper bounds. It is significant to note that the four iportant paraeters closely depend on the therodynaic electrocheical paraeters of the hybrid syste can be calculated nuerically for the given values of other paraeters. According to Eqs. () (), one can further generate the curves of efficiency power density varying with current density for different teperatures, as shown in Figure 6, where i i are, respectively, the current densities at the iu efficiency the iu power density. Figure 7 can also explain the optial region of the current density i i i (4) Both the efficiency the power density increase with the increase of current density when i i, while they decrease with current density increase when i i. It is obvious that the regions of i i

11 Efficiency Efficiency Int. J. Electroche. Sci., Vol. 8, 3 78 i i are not optial fro the therodynaic point of view although the hybrid syste ay work in these regions. Thus, i i are, respectively, the upper lower bounds of the optiized current density. Specifically, the iu efficiency the iu power density will increase when T is increased, accordingly, the optial current density i i will also be changed. In the practical operation of the hybrid syste, engineers should choose soe reasonable paraeters in order to iprove the syste perforance...8 Hybrid Syste Stirling Engine Fuel Cell ower Density (W/ ) Current Density (A/ ) 4 Figure 4. The curves of the efficiency the power density varying with the current density, where the power density / A. hybrid hybrid T = 73 K T = 73 K T = 73 K ower Density (W/ )

12 % (?Y) Efficiency Int. J. Electroche. Sci., Vol. 8, Figure 5. The curves of the efficiency varying with the power density for different teperatures, where are, respectively, the iu efficiency power density of hybrid syste. Thus, how to give a consideration to both the efficiency the power output in the optial region will becoe an iportant proble in practical optiu design operation. For this reason, we ay introduce a ulti-objective function which is defined as the product of the efficiency with a weighting factor power output [4], i.e., Z (5) where is a weighting factor, whose value is deterined by the engineer s requireents for the power output the efficiency. In other words, the ulti-objective function is a concrete value of the hybrid syste,. a % (?X) T=73K T=3K T=73K T=3K T=73K. i Current Density (A/ )

13 Efficiency ower Density (W/ ), Z (W/ ) Int. J. Electroche. Sci., Vol. 8, b 4 ower Density (W/ ) T=73K T=3K T=73K T=3K T=73K i Current Density (A/ ) Figure 6. The curves of (a) efficiency (b) power density varying with current density for different teperatures, where i i are, respectively, the current density at the iu efficiency the iu power density Z, 6. i i Z, i Current Density (A/ ) Figure 7. The curves of the efficiency, power density, Z varying with the current density, where Z Z / A, i is the current density corresponding to Z Z,. 4

14 Efficiency Int. J. Electroche. Sci., Vol. 8, D << D D.6.4. z, << Z, Figure 8. The where Z, Z,. ower Density (W/ ) curve used to expound the physical eaning of the ulti-objective function, are, respectively, the efficiency power density corresponding to Z, If one focus ore on the efficiency than power output, the weighting factor can be let as. When, the ulti-objective function ay be rewritten as a new for, i.e. / / Z, which is efficiency. If one takes ore attention to the power output, the weighting factor can be let as. When, the ulti-objective function ay becoe one objective function, i.e., Z. If engineer gives the sae attention to the power output the efficiency, the weighting factor can be chosen as, which has been shown in Figure 7. In order to discuss the choice proble of the optial current density, we will ark soe divided points in Figure 8, which illustrates ore clearly how to select the optial operating region, using Eqs. (), () (5). Where D, D D on the curve correspond to the state that attains its iu when,. oint D represents any point on the Z ~ curve between D D. The horizontal vertical coordinates corresponding to D ay for a rectangle, whose area is equal to Z. In Figure 8, the area of the shaded part is Z,. It is clearly seen fro Figure 8 that the weighting factor plays an iportant role in the ultiobjective function. The optial operation region i i i can be subdivided according to the different requireents for both the efficiency the power output. If one ephasizes ore on the efficiency than on the power output, e.g. SOFC hybrid stationary plant for power generation [3], the optial operation region of the current density, power output the efficiency, respectively, should be

15 Int. J. Electroche. Sci., Vol. 8, i i i Z, (6) (7) Z, (8) Z, If ore attention is paid on the power output than on the efficiency, i.e. start-up for SOFC hybrid vehicles [33], the optial operation regions of the paraeters entioned above are, respectively, deterined by i i i (9) Z, Z, (3). (3) Z, 4. CONCLUSIONS The iportance of present paper lies in a new cycle odel which can describe the general characteristic of SOFC-Stirling heat engine hybrid syste. The various irreversible therodynaic electrocheical losses are described. The iu efficiency, power output the optial operating region are deterined to iprove the whole syste perforance through nuerical siulations. The proble how to give consideration to the efficiency power output in the optial region of the current density is discussed in detail. The results obtained here ay provide soe theoretical basis for the optial design operation of practical SOFC-Stirling heat engine. This ethod ay be easily extended to other fuel cell hybrid syste to develop irreversible odels suitable for the optial energy-anageent strategies of fuel cell hybrids. ACKNOWLEDGEMENTS This work was supported by the Natural Science Foundation of Fujian rovince (No. J6), Foundation of Zhejiang Educational Coission (Y36937), Natural Science Foundation of Saning University (No. B/G), eople s Republic of China. References. S.C. Singhal, K. Kendal, High Teperature Solid Oxide Fuel Cell: Fundaentals Design Applications, Elsevier Ltd., Oxford, S. Kakac, A. rauanjaroenkij, X. Zhou, Int. J. Hydrogen Energy 3 (7) 76.

16 Int. J. Electroche. Sci., Vol. 8, G. Nahar, K. Kendall, Fuel rocessing Technology 9 () H. Zhang, J. Wang, S. Su, J. Chen, Int. J. Hydrogen Energy 3 8 (3) S.H. Chan, H.K. Ho, Y. Tian, Int. J. Hydrogen Energy 8 (3) M. Ghasei, M. Isail, S. K. Kaarudin, K. Saeedfar, etc., Applied Energy (3) W.J. Yang, S.K. ark, T.S. Kia, J.H. Kib, etc., J. ower Sources, 6 (6) C. Haynes,J. ower Sources, 9 () 99. Y. Zhao, N. Shah, N. Bron, J. ower Sources, () 8.. Hill, Michael. Ceraic Industry, Septeber, 5.. Y. Zhao, J. Chen, J. ower Sources, 86 (9) 96.. Y. Zhao, C. Ou, J. Chen, Int. J. hydrogen energy 33 (8) M.S. Isail, K.J. Hughes, D.B. Ingha, L. Ma, M. ourkashanian, Applied Energy 95 () Stabouli, A. Boudghene. Renewable Sustainable Energy Reviews, 6() D.A. Noren, M.A. Hoffan, J. ower Sources 5 (5) S.T. Ro, J.L. Sohn, J. ower Sources 67 (7) Y. Qi, B. Huang, K.T. Chuang, J. ower Sources 5 (5) Y. Zhao, C. Ou, J. Chen, Int. J. Hydrogen Energy 33 (8) Yingru Zhao, Jincan Chen, Journal of ower Sources 86 (9) 96.. F. Calise, A. alobo, L. Vanoli, J. ower Sources 58 (6) 5.. S.J.Watowich, R.S. Berry, J. hys. Che. 9 (986) C.Wang, M.H.Nehrir, S.R. Shaw, IEEE Trans. Energy Convers. (5) J. Chen, Z. Yan, L. Chen, B. Andresen, Int. J. Energy Res.,, (998) M. W. Zeansky, (968). Heat therodynaics, 5th edn, McGraw-Hill, New York. 5. Ayres, R. U. R.. Mckenna, Alternatives to the Internal Cobustion Engines, The Johns Hopkins University ress, Baltiore, MD D. Sanchez, A. Mu noz, T. Sanchez, J. ower Sources 69 (7) G. Bavarsad, Int. J. Hydrogen Energy 3 (7) D.A. Blank, G.W. Davis, C.Wu, Energy 9 (994) S. Bhattacharyya, D.A. Blank, Int. J. Energy Res. 4 () D.A. Blanka, J. Appl. hys. 84 (998) H.Y. Kwak, H.S. Lee, J.Y. Jung, J.S. Jeon, D.R. ark, Fuel 83(4) M. De Francesco, E. Arato, J. ower Sources 8()4. 3 by ESG (