Journal of Power Sources 143 (2005) 179184

Short communication

Optimization of a combined heat and powei, A.g Depaan, Iran

8 Novery 2005

Abstract

In this pap olymeapplication h ugh thspace heatin ptimizshow that fo l cell tthe range of ratio s 2005 Else

Keywords: C

1. Introdu

Fuel cells are electrochemical devices that directly con-vert the chemical energy of a reaction into electrical energy.The basic structure or building block of a fuel cell consistsof an electcathode onfuel cells ielectrolytewhich corrsentation oion conducFig. 1.

From poseveral memost popul(CHP) [1,2low powerings for locfuel cell, wused for spa

CorresponE-mail ad

r is pasup and is used for the CHP application. There are previouspublications about energy and exergy analyses of PEFC fuelcell systems. These analyses have been published with vary-ing degrees of cogeneration in order to seek and develop fuel

0378-7753/$doi:10.1016/jrolyte layer in contact with a porous anode andeach side. One of the most popular types of

s the polymer electrolyte fuel cell (PEFC). Thein this fuel cell is an ion exchange membrane inosion problems are minimal. A schematic repre-f a PEFC with the reactant/product gases and thetion flow directions through the cell is shown in

int of view of thermodynamic design, there arethods to increase the efficiency of a fuel cell. Thear way using power and heat is combined cycles]. The polymer electrolyte fuel cell which has aand heat generation capacity may be used in build-al power distribution. For CHP application of thisater, which is a cooling media in the fuel cell, isce heating or water heating [3]. In these fuel cells,

ding author. Tel.: +98 21 8250506; fax: +98 21 6000021.dress: saman@sharif.edu (M.H. Saidi).

cells with better economic and energy saving characteris-tics than conventional power generating plants [4,5]. Severalhybrid system configurations have been suggested for effi-ciency improvement. In addition, performance predictionsunder part-load conditions have been made for the systems,for which power output is over 200 kW [68]. Magistri et al.[9] proposed a very small 5 kW gas turbine plant combinedwith a SOFC 31 kW, and evaluated its part-load performance.However, none of the previous works have done a completeexergy analysis of a CHP system, which considers the heattransfer and pressure drop in the reactant, product and coolingchannel.

2. Mathematical model

The proposed system under consideration is shown inFig. 1. The model consists of a PEFC fuel cell having 5 kWpower output with cogeneration application. In this system,

see front matter 2005 Elsevier B.V. All rights reserved..jpowsour.2004.11.061M.H. Saidi , M.A. EhyaeCenter of Excellence in Energy Conversion, Mechanical Engineerin

P.O. Box 11365-9567, Tehr

Received 24 October 2004; accepted 2Available online 26 Februa

er, design and exergy method optimization of a 5 kW power output pas been investigated. It is assumed that cooling water is passed thro

g applications. The performance of the proposed system has been or maximum system efficiency and minimum entropy generation, fueapplication. Also, the fuel cell pressure and stoichiometric air:fuelvier B.V. All rights reserved.

ogeneration; Efficiency; Exergy; Optimization; PEFC; Fuel cell

ction water PEFC by exergy analysisAbbasirtment, Sharif University of Technology,

mber 2004

r electrolyte fuel cell (PEFC) fuel cell with cogeneratione fuel cell cooling channel, warmed up and supplied fored by the second law based on exergy analysis. Resultsemperature and voltage should be as high as possible inhould be as low as possible in the range of application.

sed through the fuel cell cooling channel, warmed

180 M.H. Saidi et al. / Journal of Power Sources 143 (2005) 179184

Nomenclature

a air:fuel stoichiometric ratioCPDhe

fFh

hfkKLm

Mn

NuPPPcQRReTv

VWx

SubscripchffifoinKlo

outphs

totw

Greek sy

average specific heat (kJ (kg K)1hydraulic diameter (m)exergy (kJ kg1)friction coefficientFaraday constantconvection heat transfer coefficient(W (m2 C)1)enthalpy of formation (kJ kg1)heat conduction coefficient (W (m C)1)correction factor (Eq. (16))length of passage (m)mass flow rate (kg s1)atomic numbernumber of cellsNusselt numberpressure (kPa)pressure loss (kPa)perimeter of cooling channel (m)heat production (kW)universal gas constant (kJ (kmol K)1)Reynolds numbertemperature (K)velocity of fluid in channel (m s1)fuel cell voltage (V)power (kW)mole fraction

tschemicalfuel cellinlet water temperatureoutlet water temperatureinletlocalfrictionstandard conditionoutletphysicaldiffusion layertotalwater

mbolsviscosity coefficient (Pa s)density (kg m3)correction factorsystem efficiency

Fig. 1. Sche

cooling waup and suptake place i

H2 2H+

2H+ + 2e

Based on tthe mass fland steam

mH2,in = 2

mair,in = 4

mair,out =

msteam,out =matic of a PEFC fuel cell with proton exchange membranes.

ter is passed through a cooling channel, warmedplied for space heating. The following reactionsn the anode and cathode of the proposed fuel cell:

+ 2e (1)+ 12 O2 H2O (2)

he control volume, which is shown in Fig. 2, andow rates of inlet hydrogen, the inlet and outlet aircan be calculated as follows:W

FVMH2 (3)W

FV

1xO2

aMair (4)

W

4FV1xO2

(a 1)Mair (5)

W

2FVMH2O (6)

Fig. 2. Proposed control volume.

M.H. Saidi et al. / Journal of Power Sources 143 (2005) 179184 181

Fig. 3. Flo

Also, the hequations:

QW =

It should btions, whic

1. inlet a(To = 29

2. outlet ai

Mass flo

mw =CP(

The unknocalculatedThe specificonfiguratithe Reynol

Table 1Specification

W (w)V (V)A (cm2)

n

P (kPa)

4. The

1]:4mDh

7.53

onvec

f the c

k

DhNu

Tf

ional pnel of

Lwchart to calculate outlet temperature of the cooling water.

eat generation can be calculated by the following

mair,out( hf + CP(Tf To))air,out

+

msteam,out( hf + CP(Tf To))steam,out

mair,in( hf)air,in

mH2,in( hf)H2,in (7)

e noted that Eq. (7) is based on the two assump-h are given as follows:

ir and hydrogen are at standard condition8 K, Po = 1 atm);r and steam are at fuel cell temperature.

Fig.

[10,1

Re =

Nu =The cture o

h =

Tfo =

Frictchanw rate of cooling water is calculated as follows:

Q

Tfo Tfi )(8)

wn outlet temperature of the cooling water can bebased on the flowchart, which is shown in Fig. 3.cation of the system is summarized in Table 1. Theon of cooling channel is shown in Fig. 4. Also,ds and Nusselt numbers are calculated as follows

of the system

5000220250

2440300

Pl = fD

Also, fricti

f = 82Re

where this[10,11]:

f = 64Re

The value oLocal p

channel of

Pk = K

The value oetry and thconfiguration of the cooling, reactant and product channels.

w

n, Re 2300 (9)

(10)tion heat transfer coefficient h and outlet tempera-ooling water Tfo are calculated [12], respectively:

(11)

(Tf Tfi ) exp(pcnLmwCpw

h

)(12)

ressure loss in the cooling, reactant and productthe fuel cell is calculated as follows [10,11]:

hv2

2(13)

on coefficient in the cooling channel is [10,11]:(14)

coefficient in reactant and product channel is

(15)

f correction factor is equal to 0.85 [10,11].ressure loss in the cooling, reactant and productthe fuel cell is as follows [10,11]:v2

2(16)

f the multiplier K depends on the channel geom-e range of its variation is 1

182 M.H. Saidi et al. / Journal of Power Sources 143 (2005) 179184

The total pressure loss in the cooling channel can be cal-culated by the following equation [10,11]:

Pt = PAlso, pressfollows [13

Ps = 384

Finally, the[13]:

Pt = f LD

2.1. Exerg

Physicapressure ofsystem. Thenthalpy antions of temrespectivelstant specifi

eph = CPT

The chemichemical cment can b

ech =

x

The total e

etot = eph +As a resultculated as f

Sgen = 1To

The second

= minm

Considerinentropy gen

Sgen = f (WNoting thahave a constion of the

Sgen = f (W

Variation of entropy generation with fuel cell temperature at differentiometric fuel air ratios.

ming a constant number of cells be equal to 440 andt pow

ore sim

= f (V

esults

fect oel airhownis obvase ineraturrationis eff

ratione inc

ase in

. Variation of system efficiency with fuel cell temperature at differentiometric fuel air ratios.l +Pk +Ps (17)ure loss in the diffusion layer can be calculated as]:000n

m (18)

total pressure loss in the fuel cell is as follows

hv2

2+Kv

2

2+ 384000

nm (19)

y analysis

l exergy is associated with the temperature andthe reactants and the products in the fuel cell

e physical exergy is expressed in terms of the ofd entropy difference from those standard condi-perature and pressure To = 298 K and Po = 1 atm,

y. The physical exergy of an ideal gas with con-c heat CP can be written as follows:

o

[T

To 1 ln

(T

To

)]+ RTo ln

(P

Po

)(20)

cal exergy is associated with the departure of theomposition of a system from that of the environ-e calculated by equation below:

nech + RTo

xn ln xn (21)

xergy flow can be calculated:

ech (22), the entropy generation of the system can be cal-ollows:{

minetot,in

moutetot,out W}

(23)

law efficiency of the system is as follows:

wCP,w(Tfo Tfi )+Winetot,in

outmoutetot,out

(24)

g Eqs. (3)(23), the functional relationship of theeration of the system can be written as follows:

, V, a, Tf, , L, pc, P) (25)t the cooling and reactant and product channelstant geometry which is shown in Fig. 4, the func-entropy generation can be simplified as below:

, V, a, Tf, P, ) (26)

Fig. 5.stoich

Assuoutpube mSgen

3. R

Efof fuare s

Itincretempgeneon thgene

Thincre

Fig. 6stoicher of 5 kW. The entropy generation function canplified such as:

, a, Tf, P) (27)

and discussions

f the fuel cell temperature and stoichiometric ratioon the entropy generation and system efficiencyin Figs. 5 and 6.ious from the above-mentioned figures that thefuel cell temperature causes the increase in outlete of the cooling water, which is supplied for co-in this system (Eqs. (11) and (12)), so that basedect the system efficiency increases and entropydecreases.rease in stoichiometric air:fuel ratio causes theoutlet air mass flow rate, which is warmed up

M.H. Saidi et al. / Journal of Power Sources 143 (2005) 179184 183

Fig. 7. Variation of entropy generation with fuel cell temperature at differentvoltage.

in the fuel cell and is rejected to environment. Due to thisrejection of heat, entropy generation increases and systemefficiency d

As seeneffect on thconsider aiture from 321% but inof entropycell voltagespectively.220 V at coabout 71%shows theentropy genit is obviourate. This re

Fig. 8. Variatat different vo

Fig. 9. Variation of entropy generation with fuel cell temperature at differentpressure.

(13)(19), whereas this variation decreases entropy genera-tion and increases system efficiency.

gs. 9eraturency,ure inency.ase int of ththan thin theratione mosystemressuraxim

uel ceecreases.in Figs. 5 and 6, fuel cell temperature has a greatere system efficiency than entropy generation. Now,r:fuel ratio a= 1; the increase in fuel cell tempera-30 K to 550 K decreases entropy generation aboutcreases system efficiency about 79%. Variationgeneration and efficiency of the system with fuel

and temperature are shown in Figs. 7 and 8, re-The increase in fuel cell voltage from 140 V tonstant temperature decreases entropy generationand increases efficiency about 44%. This variationvital influence of fuel cell voltage on the systemeration and efficiency. Considering Eqs. (3)(6),

s that the increase in voltage, decreases mass flowduction decreases pressure loss according to Eqs.

Fitempefficipressefficiincreoutleinletergygene

Thand sthe pthe mthe fion of system efficiency generation with fuel cell temperatureltage.

Fig. 10. Variapressure.and 10 show the effect of fuel cell pressure ande on the entropy generation of the system andrespectively. As shown, the increase in fuel cellcreases entropy generation and decreases systemFocussing on Eq. (20), it is understandable that thepressure increases physical exergy at the inlet ande fuel cell, but this effect is greater at the fuel celle outlet, which causes increasing net physical ex-

fuel cell. According to Eqs. (23) and (24) entropyincreases and system efficiency decreases.t effective parameter affecting entropy generationefficiency according to Figs. 510 is voltage and

e has a lesser effect on system performance, so forum efficiency and minimum entropy generation,ll temperature and voltage should be as high astion of system efficiency with fuel cell temperature at different

184 M.H. Saidi et al. / Journal of Power Sources 143 (2005) 179184

possible; meanwhile, the pressure and stoichiometric air:fuelratio should be as low as possible.

4. Conclusions

A PEFC fuel cell with a 5 kW power output and a cogener-ation application has been thermodynamically designed andits optimized performance has been considered by exergyanalysis. The effect of variation in fuel cell temperature, sto-ichiometric air:fuel ratio, voltage and pressure on the sys-tem has been investigated. The following conclusions are ob-tained:

1. Exergy analysis is a suitable tool for system optimization.2. Increase in fuel cell temperature and voltage, decrease en-

tropy generation, and as a result the fuel cell efficiency in-creases, whereas an increase in the stoichiometric air:fuelratio and fuel cell pressure, increase entropy generation,and as a result, the system efficiency decreases.

3. The fuel cell voltage has the most influence on entropygeneration and system efficiency, whereas, fuel cell pres-sure has the weakest effect on entropy generation andsystem efficiency. So, fuel cell temperature and voltageshould be as high as possible. Also, the fuel cell pres-sure and stoichiometric air:fuel ratio should be as low aspossible.

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Optimization of a combined heat and power PEFC by exergy analysisIntroductionMathematical modelExergy analysis

Results and discussionsConclusionsReferences