Influences of feeding conditions and objective function on the optimal ...

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 9

Available online at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/he

Influences of feeding conditions and objective function on the optimal design of gas flow channel of a PEM fuel cell Javad Mahmoudimehr*, Amirhosein Daryadel Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran

article info

abstract

Article history:

Polymer electrolyte membrane fuel cell (PEMFC) is one of the promising electricity gener-

Received 6 May 2017

ating technologies with a wide range of applicability; however, it needs further improve-

Received in revised form

ments to be commercially viable. The design of a PEMFC plays a key role in its viability, and

13 July 2017

is often reduced to the design of gas flow channel (GFC) at the cathode side. In this study, it

Accepted 24 July 2017

is attempted to figure out the optimal dimensions (i.e., width and height) of the rectangular

Available online xxx

cross sectional area of the cathode GFC of a PEMFC via numerical examination of various sets of dimensions. The optimization procedure is carried out for two different objective

Keywords:

functions (the maximization of the maximum power and the maximization of the average

PEM fuel cell

power over a range of operating voltages) as well as for different sets of operating condi-

Channel design

tions (cell temperature, operating pressure, and stoichiometry and relative humidity of

Optimization

inlet gases). To the best of authors' knowledge, the following observations may be

Feeding conditions

considered to be the contributions of the present work to the subject: First, the influence of

Objective function

cross sectional dimensions on the PEMFC performance is considerable, and this considerable influence is not limited to a specific set of operating conditions. Second, the performance of the PEMFC may both deteriorate and improve with the channel width or height, depending on its operating conditions as well as on its current dimensions. Third, there exists no single optimal cross section for different sets of operating conditions. Fourth, the polarization curves of two different cross sections may intersect, and as a result, one cross section may have a greater maximum power but at the same time lower average power in comparison to the other one. And fifth, among all the operating parameters, the relative humidity of inlet gases has the greatest effect on the optimal cross sectional dimensions. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction The consumption of fossil fuels is the major cause of environmental pollution, and the fossil fuel resources will be

depleted in the coming decades. These problems necessitate paying special attention to the alternative sources of energy. Polymer electrolyte membrane fuel cell (PEMFC) is one of the promising technologies due to its several beneficial characteristics such as high efficiency, high power density, low

* Corresponding author. Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran. E-mail addresses: [email protected], [email protected] (J. Mahmoudimehr). http://dx.doi.org/10.1016/j.ijhydene.2017.07.196 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Mahmoudimehr J, Daryadel A, Influences of feeding conditions and objective function on the optimal design of gas flow channel of a PEM fuel cell, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.07.196

2


Nomenclature aw C CL cp Cw D Dw F GDL GFC I j k kp M Mm,dry nd P R RH S T U V X Y

Water activity Molar concentration, kmol m3 Catalyst layer Specific heat capacity, J kg1 k1 Mass concentration of water, kg m3 Diffusion coefficient, m2 s1 Water diffusivity, m2 s1 Faraday constant, 96,485C mol1 Gas diffusion layer Gas flow channel Current, A Transfer current density, A m3 Thermal conductivity, w m1 k1 Permeability, m2 Molecular weight, kg kmol1 Equivalent weight of a dry membrane, kg kmol1 Electro-osmotic drag coefficient Pressure, kPa Universal gas constant, 8.314 kj kmol1 k1 Relative humidity Source term in governing equation Temperature, K Velocity, m s1 Voltage, V Mole fraction Mass fraction

weight, quick startup, low operation temperature, and small (or zero) emission of pollutants [1]. However, this technology needs further improvement in order to be commercially viable. The design of a PEMFC plays a key role in its viability, and is often reduced to the design of its gas channel or bipolar geometry at the cathode side. This is because the rate of oxygen reduction at the cathode side is low, and the design of cathode gas channel is influential in transferring oxygen to reaction zone [2]. In recent years, various numerical and/or experimental research works have focused on the improvement in the design or performance of PEMFCs. A group of works has investigated the influence of various operating parameters on the performance of PEMFCs. Inaba et al. [3] carried out hydrogen gas crossover measurements and durability tests for a single PEMFC under open-circuit conditions to study membrane degradation. The results indicated that hydrogen peroxide formation, which is most probably formed by the gas crossover of oxygen and the resulting catalytic combustion at the anode side, is the primary reason for the membrane degradation. Moreover, it was observed that gas crossover increased with cell temperature, humidity and hydrogen gas pressure. Zhang et al. [4] experimentally and theoretically investigated liquid water transport and removal from the GDL and gas channel of a PEMFC. Liquid droplet formation from the GDL surface was characterized and two modes of liquid water removal were identified: one

Greek letters a Transfer coefficient g Concentration dependence ε Porosity h Overpotential l Water content m Viscosity, kg m1 s1 x Specific active surface area, m1 r Density, kg m3 rm,dry Density of dry membrane, kg m3 s Electrical conductivity, U1 m1 ∅ Phase potential, V 4 Stoichiometry Subscripts An Anode Ca Cathode I Gas species Mem Electrolyte phase Mix Mixture Oc Open circuit React Reaction Ref Reference Sat Saturate Sol Solid phase Superscripts Eff Effective Ref Reference

through droplet detachment by the shear force of the core gas flow followed by a mist flow in the channel, and the other by capillary wicking onto the more hydrophilic channel walls followed by the annular film flow and/or liquid slug flow in the channel. Moreover, a theory was developed to determine what operating parameters and channel surface contact angles lead to sufficient liquid drainage from the cell via corner flow. Qu et al. [5] presented a 2D dynamic model to study the effect of air stoichiometry on the performance of a single-channel PEMFC. The results showed that the oxygen is progressively depleted downstream along the gas channel during the load change, resulting in reactant gas dilution on the reaction zone. In the presence of large air dilution, the over-potential for the oxygen reduction within the catalyst layer (CL) significantly increased to sustain a specific operating current density, thus led to the cell voltage undershoot during load change. It was also shown that this undershoot could be reduced or eliminated by improving the air stoic change rate, or by increasing the initial air stoic flow ratio. Chen et al. [6] investigated the effects of dead-ended anode operation on the electrode carbon corrosion of a PEMFC by using a reduced order isothermal model. The results showed that the presence of oxygen in the anode channel creates a H2/O2 front as N2 and water accumulate at the end of the channel and hydrogen is depleted along the channel. It also results in a gradual drop of the membrane phase potential, promoting carbon corrosion in the cathode. Xing et al. [7] presented a 2D model to study

Please cite this article in press as: Mahmoudimehr J, Daryadel A, Influences of feeding conditions and objective function on the optimal design of gas flow channel of a PEM fuel cell, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.07.196


thermal transport within the MEA of a PEMFC. The results indicated that higher operating temperature improved the cell performance by increasing the kinetics, reducing the liquid water saturation on the cathode, and increasing the water carrying capacity of the anode gas. Moreover, applying higher temperature on the anode and enlarging the width ratio of the channel/rib could improve the cell performance. In contrast, higher cathode temperature caused the oxygen mole fraction to decrease, resulting in an insufficient oxygen supply and a limitation of the cell performance. Xing et al. [8] developed a two-dimensional, two-phase flow, non-isothermal, agglomerate model to study the distributions of liquid water and heat and CL effectiveness factors within the MEA and channels of a low temperature PEMFC. Results showed that low liquid water saturation is associated with large contact angle, low electrode porosity and platinum loading, and short and deep channel. Moreover, a novel channel design featured with multi-outlets and inlets along the channel was proposed to mitigate the effect of water flooding and improve the cell performance. Xing et al. [9] developed a two dimensional, non-isothermal, two-phase flow, anode partial flooding model to investigate the effects of relative humidity, stoichiometric flow ratio and channel length on the performance of a PEMFC. The results indicated that the liquid water transport through the electrode was mainly determined by the capillary diffusion mechanism. Moreover, higher anode relative humidity was required to the improved cell performance. It was observed that the optimal cathode relative humidity increased with the decrease in the anode relative humidity and increase in channel length. The initial increase in stoichiometric flow ratio improved the limiting current densities; however, the further increases led to limited contributions. Mahmoudimehr and Darbandi [10] illustrated the effects of air feeding conditions on the performance of a PEMFC on the Psychrometric chart. The results showed that the PEMFC performance improves as a result of increasing temperature at a constant relative humidity, increasing humidity at a constant temperature, and increasing pressure. However, it is observed that the PEMFC performance deteriorates with increasing temperature at a constant specific humidity due to the PEMFC dehydration. Other group of works has studied the influence of the design of PEMFC on its performance. Li and Sabir [11] reviews the works which have focused on the influence of the path shape (e.g., parallel, serpentine, and inter-digitated) of the flow of reactants through a PEM stack on various parameters such as the rates of reactions, the distribution of reactants throughout the stack, the capability of water removal, and pressure drop. The numerical study of Scholta et al. [12] showed that the small dimensions of gas channels are generally preferred in the case of high current densities, whereas big dimensions are better in the case of low current densities. Numerical investigations of Sun et al. [13] indicated that the size ratio of a PEMFC with a trapezoidal crosssectional shape has a significant effect on the flow crossover. Numerical comparison of PEMFCs with rectangular and trapezoidal channel shapes carried out by Ahmed and Sung [14] showed that although the rectangular channel led to greater power, the trapezoidal channel resulted in more uniform distributions of reactants and current densities, and

3

hence, it resulted in lower overpotential. Moreover, it was observed that the increase of shoulder width caused the ohmic loss to reduce, but it increased the concentration loss. Shimpalee and Van Zee [15] numerically studied the effect of rib size on the PEMFC performance. The results illustrated that a narrower channel, as a result of better heat conduction through bipolar plate, led to lower and more uniform temperature, higher membrane water content, and a better polarization curve. The experimental investigations of Hsieh and Chu [16] showed that the optimal channel size obtained when the pressure drop and generated power were considered simultaneously was different from that obtained when only generated power was taken into consideration. Secanell et al. [17] presented a comprehensive numerical framework for optimal cathode electrode design. The proposed design and optimization framework coupled an agglomerate cathode CL model to a numerical gradient-based optimization algorithm. The design parameters were the CL platinum loading, platinum to carbon ratio, amount of electrolyte in the agglomerate and the GDL porosity. The results showed that the optimal CL composition and GDL porosity depended on operating conditions. It was numerically shown by Wang et al. [18] that at high operating voltages (or low current densities), oxygen sufficiently reaches the reaction region, and therefore, channel design has negligible effect on the performance of a PEMFC. However, at low operating voltages (or high current densities), the performance of a PEMFC highly depends on the channel design, and smaller channel cross sectional area improves water removal, and consequently, the performance of the PEMFC. Kumar and Kolar [19] numerically studied the effects of channel dimensions on the performance of an air-breathing PEMFC. The results showed that an increase in each of the channel depth and width improved the PEMFC performance due to the increased buoyancy forces. Wang et al. [20] adopted a combined optimization procedure, including a simplified conjugategradient method and a three-dimensional, two-phase, nonisothermal model, to optimize the flow field design of a serpentine PEMFC with five channels. Channel heights constituted the design variables. The obtained optimal design had three tapered channels and a final diverging channel, and achieved an 11.9% increment in the power density as compared to the basic case (i.e., a cell with straight channels). A similar work was carried out by the same authors [21], except that channel widths were also included in the set of design variables in addition to channel heights. The resulted optimal design had a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5. In this case, the superiority of the optimal design in the power density over the basic case was about 22.5%. Wang et al. [22] numerically investigated the influence of sub-rib convection on the performances of PEMFCs with single and triple serpentine flow fields. The results illustrated that for the single serpentine flow field in which sub-rib convection presents under all ribs, changing channel aspect ratio has minimal effects on cell performance since the oxygen supply is sufficient. However, for the triple serpentine flow field or for the serpentine cell with poor external heat loss, owing to limited sub-rib convection or to low membrane moisture content, decrease in channel aspect ratio significantly


4


Table 1 e A brief review of the optimal cathode channel dimensions obtained in some of the previous studies. Reference Scholta et al. [12] Shimpalee and Van Zee [15] Hsieh and Chu [16] Wang et al. [18]

Kumar and Kolar [19]

Wang et al. [22] Wang et al. [24]

Manso et al. [26]

Liu et al. [30] Muthukumar et al. [32]

Variables and their domain of search

Optimum value of variables

Channel widths: 0.5e1.5 mm. Rib widths: 0.5e1.5 mm. Channel to rib width ratios (mm/mm): 0.9/0.9, 1/0.7, and 0.7/1. Channel-to rib width ratio: 0.5e2. Aspect ratio (channel height to width ratio): 0.5e2. Channel dimensions (mm2): 1.53 1.53, 1.21 1.21, 1 1, 0.74 0.74, 0.53 0.53, and 0.307 0.307.

Between 0.7 and 1 mm for either channel or rib widths

Channel width: 2,4, 6 mm; Channel height: 2, 6, and 10 mm. (For the constant rib width of 1 mm). Channel height: 0.75, 1.00, 1.25, 1.50, and 2.00 mm (For the constant channel and rib widths of 1 mm) Channel dimensions (mm2)- number of channels/ number of ribs: 1.53 1.538/7, 1.21 1.2110/9, 1 112/11, 0.74 0.7416/15, 0.53 0.5322/21, and 0.307 0.30738/37. (all cells have the same active area of 23 23 mm2) Aspect ratio (mm/mm): 2/30, 3/20, 4/15, 5/12, 6/10, 10/6, 12/5, 15/4, 20/3 and 30/2. (All cells have the same channel cross section area, 1.06 mm2, and the same total effective reactive area, 256 mm2). Width: 1.8 mme8 mm. Rib-to-channel width ratio: 0.2e0.8. Landing-to-channel width ratio (mm/mm): 0.5/0.5, 1/1, 1.5/1.5, and 2/2.

enhances cell performance. Wang et al. [23] employed a three-dimensional, two-phase transport model to investigate the effect of flow channel aspect ratio on the performance of PEMFCs with single and triple serpentine flow fields. The predictions showed that for both flow fields, the cell performance improved with decreasing aspect ratio. Moreover, the aspect ratio had less effect on the cell performance for the triple serpentine flow field than for the single serpentine flow field due to the weaker under-rib convection. The influence of channel size on the performance of PEMFCs with serpentine flow fields was numerically studied by Wang et al. [24]. It was observed that the decrease of channel size increased the reactant velocity, which enhanced liquid water removal as well as oxygen transfer into the reaction zone; hence, it improved the cell performance; on the other hand, it caused the pressure drop to increase. Finally, a trade-off channel cross section of 0.535 0.535 mm2 was proposed in this work. Secanell et al. [25] presented a computational framework for fuel cell analysis and optimization. The framework was based on a two-dimensional, isothermal, and single phase MEA model. The model input parameters were: platinum loading, platinum to carbon ratio, electrolyte content and GDL porosity. To solve the optimization problem a gradient-based optimization algorithm was used in conjunction with analytical sensitivities. The results showed that the proposed framework is capable of solving a complete MEA optimization problem in approximately 30 min, making it viable for solving large-scale fuel cell problems. With the assumption of a constant channel cross sectional area, the influence of cross section aspect ratio on the performance of a PEMFC was

Channel to rib width ratio: 0.7/1. Channel to rib width ratio: 0.67 For parallel design: Aspect ratio ¼ 0.5; channel dimensions (mm2): 0.307 0.307. For interdigitated design: Aspect ratio ¼ 1; channel dimensions (mm2): 1 1. Channel width: 4 mm Channel depth: 6 mm Height: 0.75 mm. Channel dimensions (mm2)- number of channels/number of ribs: 0.53 0.5322/21

Aspect ratio: 10/6 and 12/5.

Width: 1.8 mm. Rib-to-channel width ratio: 0.2. Landing-to-channel width ratio (mm/mm): 0.5/0.5

numerically studied by Manso et al. [26]. The results indicated that greater aspect ratios led to more uniform temperature and current density distributions as well as higher values of membrane water content. Shimpalee et al. [27] numerically studied the influence of draft angle of channel's trapezoidal cross section on the performance of a PEMFC. The results indicated that a zero draft angle (resulting in a rectangular cross section) resulted in the optimal performance. This was because a higher draft angle led to a less heat conduction through the land, and hence, to the more dehydration of water content, which in turn resulted in the lower membrane ionic conductivity. Wang et al. [28] numerically compared the performances of PEMFCs with triangular, semicircular, trapezoidal, and rectangular cross sections. Results indicated that for a constant flow rate, non-rectangular cross sections showed better performances than the rectangular one as a result of their increased velocity within the gas channels, and accordingly, their greater capability of water removal. Moreover, among the studied cross sections, triangular one showed the best performance. Wang et al. [29] attempted to improve the performance of a PEMFC through the contraction of the outlet cross sectional area of gas flow channel. Numerical simulation results indicated that this modification increased the gas velocity near the outlet region, which in turn, enhanced reactant transport and utilization, and liquid water removal, and improved the polarization curve. Numerical and experimental studies of Liu et al. [30] showed that relatively small widths of flow channels and ribs as well as the small ratios of rib-to-channel width ratio are preferred for obtaining high power densities. Xing et al. [31] employed a



5

Fig. 1 e A schematic view of a PEMFC.

multiple surrogate model in conjunction with a twodimensional, isothermal agglomerate framework for the optimal design of cathode CL. Platinum loading, platinum mass ratio, electrolyte volume fraction, thickness of CL and agglomerate radius, constituted the design parameters. Two optimization strategies, maximizing the current density at a fix cell voltage and during a specific range, are implemented for the optima prediction. The results showed that the optimal catalyst composition depended on operating cell voltages. Moreover, high platinum loading and small agglomerate radius could improve current density at all cell voltages. Among various sizes of channel cross section with square shape, numerically studied by Muthukumar et al. [32], the smallest one (0.5 0.5 mm2) showed the best water management and the best polarization curve as a result. The superiority of a tapered PEMFC over a conventional one due to its increased capability of the water removal was numerically shown by Mancusi et al. [33]. Table 1presents a brief review of the optimal cathode channel dimensions achieved by a number of previous studies. As shown in Table 1, the provided literature suggest a variety of optimal channel dimensions from narrow to wide but not a single set of optimal dimensions. This is because each research work corresponds to a specific set of operating conditions (cell temperature, operating pressure, and stoichiometry and relative humidity of inlet gases), and PEMFC thermo-electro-chemical characteristics. The present work attempts to figure out the influence of operating conditions as well as objective function on the optimal cross sectional dimensions of the GFC of a PEMFC, that have not been previously addressed in literature to the best of authors' knowledge. To this end, polarization curve is obtained for the different sets of cross sectional dimensions, and then the cross sections

are compared on the basis of their maximum power and average power as two different objective functions. Moreover, this procedure is repeated for the different sets of operating conditions.

Modeling and governing equations As schematically shown in Fig. 1, a PEMFC is composed of current collector (CC), gas flow channel (GFC), gas diffusion layer (GDL), and catalyst layer (CL) at each anode and cathode side, and a membrane in the middle. At the anode side, hydrogen molecules flow through the GFC, penetrate into the GDL, and react when they reach the CL. As a result, as shown in Eq. (1), they are decomposed into electrons and hydrogen protons. The resultant electrons and protons are then transmitted to the cathode side through an external circuit and the membrane, respectively. On the other hand, at the cathode side, oxygen molecules flow through the GFC, pass through the GDL, and reach the CL where they react with the electrons and protons received from the anode side, as shown in Eq. (2). Eq. (3) shows the overall reaction occurring in a PEMFC. The chemical energy released is either converted to the electrical power or wasted as heat [10]. H2 /2Hþ þ 2e

(1)

1 O2 þ 2Hþ þ 2e /H2 O 2

(2)

1 H2 þ O2 /H2 O 2

(3)

In this study, PEMFC is simulated through solving its three dimensional, non-isothermal, single-phase and steady state


6


governing equations via finite volume approach by using Fluent© and Gambit (mesh generating) software. It is worth mentioning that at high current densities (or low cell voltages), more liquid water is formed due to the accelerated chemical reaction. The formation of liquid water within the void spaces (pores) of the porous layers, especially if the excess liquid is not properly removed, decreases the oxygen transport and the cell performance. Therefore, the single-phase model employed in this study is a simplification which neglects the influences of liquid water, and to achieve more accurate solutions at high current densities, two-phase models should be employed [7e9,21,22, and 24]. The physical and electrochemical phenomena occurring inside a PEMFC are governed by the following equations. Mass Conservation [10,34e36]: Eq. (4) shows the continuity equation. The mixture density, observed in Eq. (4), is calculated as shown in Eq. (5). Moreover, the source term for the consumption of hydrogen, which is applicable at the anode CL, is obtained from Eq. (6), and the source terms for the consumption of oxygen and the creation of water, which are applicable at the cathode CL, are obtained from Eqs. (7) and (8), respectively. ! ! V $ðr u Þ ¼ SH2 þ SO2 þ SH2 O rmix ¼

RT

P P Yi

(18)

(8)

jca ¼ xca jref ca

CO2

!gca

ref

CO2

aan F aca F han exp han exp RT RT

aca F aca F hca þ exp hca exp RT RT

(9)

(10)

The overpotential at the anode or cathode side is obtained from Eq. (11). The reference voltage (Vref) in this equation is considered to be equal to 0 and open circuit voltage with negative sign at the anode and cathode sides, respectively. h ¼ ∅sol ∅mem Vref

The ionic conductivity of the membrane is considered to be a function of water content and temperature, as shown in Eq. (16). Moreover, Eqs. (17) and (18) shows the relations between the source terms of phase potential equations and the transfer current densities.

Smem ¼ jan;ca

!gan

ref CH2

(15)

(5)

The volumetric transfer current densities at the anode and cathode sides are obtained on the basis of Buttler-Volmer model as shown in Eqs. (9) and (10), respectively. jan ¼

V$ðsmem $V∅mem Þ þ Smem ¼ 0

(17)

(7)

CH2

(14)

Ssol ¼ jan;ca

jca SO2 ¼ MO2 4F

xan jref an

V$ðssol $V∅sol Þ þ Ssol ¼ 0

(4)

(6)

SH2 O

Phase potential [36,38, and 39]: The driving force behind the electrochemical reaction is the surface over potential, representing the difference between the phase potentials of the solid (electron conductor) and electrolyte (proton conductor). The phase potential equations for the solid and electrolyte are shown in Eqs. (14) and (15), respectively.

(16)

Mi

jca ¼ þ MH2 O 2F

(13)

1 1 smem ¼ ½0:514l 0:326exp 1268 303 T

jan ¼ MH2 2F

SH2

eff

Di ¼ ε1:5 Di

(11)

Energy [10]: The energy equation and its source term are shown in Eqs. (19) and (20), respectively. u T ¼ V$ðkVTÞ þ Sh V$ rcp !

(19)

Sh ¼ I2 Rohm þ hreact jan;ca han;ca

(20)

Momentum [10,35]: Eq. (21) shows the momentum equation. The source term of the momentum equation, which is defined in Eq. (22), is applicable within the GDL and CL. ! !! ! ! ! V $ðr u u Þ ¼ V P þ V $ V m! u þ Su

(21)

m Su ¼ ε ! u kp

(22)

Water transport through the membrane [12,19, and 30]: Electro-osmotic drag, water concentration gradient, and pressure gradient (omitted here) are the causes of water transport through the membrane. These phenomena are governed by Eq. (23). ! nd $MH2 O ! ! V$ I DW V C w ¼ 0 F

(23)

Species transport [10,34, and 37]: The species transport equation is shown in Eq. (12). In this equation, the effective gas species diffusivity is approximated as shown in Eq. (13). It is worth mentioning that the source term of this equation is only applicable at CL layers.

Electro-osmotic drag coefficient, water diffusivity, and water mass concentration are calculated as shown in Eqs. (24)e(26), respectively. Moreover, membrane water content is obtained from Eq. (27), the water activity in this equation is calculated as shown in Eq. (28).

! eff ! ! ! V $ðr u Yi Þ ¼ V $ rDi V Yi þ Si

nd ¼ 2:5

(12)

l 22

(24)



Table 2 e Specification of the reference case study.

Verification

Reference current density at the anode side (A/m2) [41]

7.17

Reference hydrogen concentration (mol/m3) [41] Reference current density at the cathode side (A/m2) [41] Reference oxygen concentration (mol/m3) [41] Channel length (mm) [40] Channel width (mm) [40] Channel height (mm) [40] Type of gas diffusion layer

0.8814 7.17 105 0.8814 70 1 1 Carbon fiber paper 0.254 5000 0.5 1 1012 Platinum 0.014 5000 0.4 1 1012 Nafion- 1100

Gas diffusion layer thickness (mm) [10] Gas diffusion layer conductivity (U m)1 [42] Gas diffusion layer porosity [18] Gas diffusion layer permeability (m2) [14] Type of catalyst layer Catalyst layer thickness (mm) [10] Catalyst layer conductivity (U m)1 [42] Catalyst layer porosity [18] Catalyst layer permeability (m2) [14] Membrane type-equivalent weight (kg/kmol) [10] Density of dry membrane (kg m3 ) [20] Membrane thickness (mm) [10] Reference pressure (Pa) [40] Open circuit voltage (v)

1980 0.051 101,325 1.09

8 2346 > 7 > 3:1 10 l3 l½expð0:28lÞ 1exp > < T Dw ¼ > 2346 > > : 4:17 108 l½1 þ 161 expðlÞexp l>3 T rm;dry l CW ¼ Mm;dry

0:043 þ 17:81aw 39:85a2w þ 36a3w l¼ 14 þ 1:4ðaw 1Þ XH2 O P aw ¼ Psat

(25)

(26) for 0 < aw 1 for 1 aw 3

(27) (28)

Table 3 e Detailed information about the meshes considered for mesh independency analysis. Mesh 1 Mesh 2 Mesh 3 Mesh 4 Number of divisions of CL in the y-direction Number of divisions of CC in the y-direction Number of divisions of GDL in the y-direction Number of divisions of membrane in the y-direction Number of divisions of each component in the xdirection Number of divisions of each component in the z-direction Total number of computational cells

2

3

4

5

6

9

15

18

3

5

7

9

3

4

5

6

7

8

12

20

24

39

48

70

120

7800

21,888

79,800 201,600

To verify the present modeling, the modeling results are compared to the experimental data existing in Ref. [40] for the same case study. The case study is a 70 mm-long PEMFC with the square channels cross section of 1 1 mm2. Moreover, stoichiometry of 2, temperature of 70C, pressure of 1 atm, and relative humidity of 100% are the operating conditions at both the anode and cathode sides. Other physical and electrochemical specifications of the case study are gathered in Table 2. For the mesh independency analysis, four different meshes with 7800, 21,882, 79,800, and 201,600 hexahedral cells are generated. The detailed specifications and front views of the meshes are shown in Table 3 and Fig. 2, respectively. The polarization curves of the meshes are compared in Fig. 3. The results show that the maximum differences between the polarization curves of meshes 1 and 2, meshes 2 and 3, and meshes 3 and 4 are approximately 5.5%, 2.4% and 0.4%, respectively. Therefore, mesh 3, consisting of 79,800 hexahedral computational cells, is considered to be sufficiently fine. It is worth mentioning that the average run time on an Intel (R) Core (TM) i5 2.66 GHz processor was approximately 6 min (with a tolerance of about ±20%). Fig. 4 indicates an acceptable agreement between the present modeling and the experimental data with an average difference of about 1.9%.

Results and discussion The influence of dimensions (width and height) of cathode channel cross section on the PEMFC performance is discussed in this section. The case study is similar to that introduced in Section 3, except that it is considered to be 20 mm long instead of 70 mm in order to reduce computation time since the current study needs a large number of computer simulations. In this regard, for a fixed set of operating conditions (cell temperature, operating pressure, and stoichiometry and relative humidity of inlet gases), the polarization curve is obtained for various cross sectional dimensions, and the best cross section is then identified for each objective function. In the current work, the maximum power and the average power, each calculated over the entire range of operating voltages, are to be maximized as two separate objectives. As shown in Eq (29), the average power of a polarization curve is calculated by dividing the sum of power values obtained at different operating voltages by the number of different operating voltages, denoted by n.

n P

Poweravg ¼

j¼1

ðV$IÞj n

(29)

Furthermore, to investigate the influence of operating conditions as well as to avoid achieving some raw general conclusions, the aforementioned procedure is repeated for various sets of operating conditions. In this study, seven different widths of [0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6 (all in mm)], and


8


Fig. 2 e Front views of (a) mesh 1 with 7800 cells (b) mesh 2 with 21,888 cells (c) mesh 3 with 79,800 cells (d) mesh 4 with 201,600 cells.

six different heights of [0.4, 0.6, 0.8, 1, 1.2, 1.4 (all in mm)] were considered, making 42 (¼7 6) possible different cross sections. The polarization curve of each cross section is obtained through numerical modeling of that cross section for seven different operating voltages [1.09 (¼Voc), 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 (all in V)]. And finally, the procedure of figuring out the optimal cross section is repeated for five different sets of operating conditions shown in Table 4. The set of operating conditions at the first row of Table 4 is considered as the reference set, and the ones introduced from rows 2 to 5, have different inlet gases stoichiometry (4), cell temperature (T), operating pressure (P), and inlet gases relative humidity (RH) as compared to the reference case, respectively. To summarize, the whole investigation of this study requires 1470 numerical simulations (¼42 cross sections 7 operating voltages 5 sets of operating conditions). In the following subsections, at first, the results are presented in general terms, and then, they are discussed in more detail.

The influence of cathode channel cross sectional dimensions: general view

Fig. 3 e Mesh independency analysis.

Fig. 4 e Modeling verification.

Each of Fig. 5ae5e shows the polarization curves of 42 different cross sections under a fixed set of operating conditions. These figures are mainly presented to provide an overview of the influence of cross sectional dimensions on the performance of the PEMFC, and hence, the curves on these figures are not numbered or labeled. The noticeable differences between the polarization curves in each of Fig. 5ae5e implies the substantial influence of cross sectional dimensions on the PEMFC performance, and that this substantial influence is not limited to a specific set of operating conditions. Moreover, this group of figures shows that the influence of cross sectional dimensions becomes more important at lower operating voltages (or higher current densities), as mentioned by literature [18,26]. The maximum and average power (the two objectives considered separately in this study) of each of cross sections are shown in Figs. 6e10 for the different sets of operating conditions. In this figures W and H denote the width and height of cross section, respectively. Moreover, dashed bars distinguish the optimal



Table 4 e Different sets of operating conditions. Set number

1

2

3

4

5

Operating pressure Cell temperature Relative humidity Stoichiometry

1 atm 60 C 100% 2

1 atm 60 C 100% 1.5

1 atm 70 C 100% 2

2 atm 60 C 100% 2

1 atm 60 C 50% 2

solutions from other ones. The specifications of the optimal solutions are shown over the dashed bars. Some points may be deduced from Figs. 6e10. First, the performance of the PEMFC may both deteriorate and improve with the channel width or height. As an illustration, as shown in Fig. 7, for the second set of operating conditions, both the maximum power and average power invariably increase with the channel width and decrease with

9

the channel height. However, as shown in Fig. 10, this monotonic behavior does not happen for the fifth set of operating conditions under which the PEMFC performance (both of average power and maximum power) deteriorates with the channel height when the channel width is greater than 1 mm, but this trend is reversed when the channel width is lower than 1 mm. Moreover, under the same (i.e., fifth) set of operating conditions, the PEMFC performance improves by increasing the channel width from 0.4 to 1 mm, but it deteriorates by increasing the channel width from 1 mm to 1.6 mm. Second, Figs. 6e10 indicate that the optimal cross sectional dimensions is not the same for all sets of operating conditions. For example, regarding Figs. 6 and 10, when the maximum power is being considered, the channel dimensions of 1.4 0.4 mm2 is the optimal choice for the first set of operating conditions, while the channel dimensions of 1 0.8 mm2 is

Fig. 5 e A general view of the influence of cross section design on polarization curve under a) first b) second c) third d) fourth e) fifth set of operating conditions. Please cite this article in press as: Mahmoudimehr J, Daryadel A, Influences of feeding conditions and objective function on the optimal design of gas flow channel of a PEM fuel cell, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.07.196

10


Fig. 6 e (a) Average and (b) Maximum power under first set of operating conditions.

Fig. 7 e (a) Average and (b) Maximum power under second set of operating conditions.

Fig. 8 e (a) Average and (b) Maximum power under third set of operating conditions.

optimal for the fifth set of operating conditions, which are noticeably different. Third point may be deduced from Figs. 6e10 is that the optimal channel dimensions may depend on the objective function being considered in addition to the operating conditions. For instance, as shown in Fig. 10, under the fifth set of operating conditions, the cross sectional dimensions of 1 0.8 mm2 is the optimal choice when the maximum power

is to be maximized, but it changes to 1 1 mm2 when the average power is to be maximized. This observation is due to the fact that the polarization curves (or power curves) of the two different cross sections intersects, as shown in Fig. 11a. As shown in Fig. 11a, the polarization curve of cross section of 1 1 mm2 lies above that of 1 0.8 mm2 for voltages from VOC to about 0.4 V, but this trend is reversed for the remaining range of voltages. To avoid attributing this observation to the numerical



11

Fig. 9 e (a) Average and (b) Maximum power under fourth set of operating conditions. uncertainties, it is worth noting that more obvious or noticeable intersections are observed for some other pairs of cross sections under the same operating conditions, and as an illustration, the polarization curves of the cross sections of 0.4 1.4 mm2, and 1.6 0.4 mm2 under the fifth operating conditions, presenting a more obvious intersection, are shown in Fig. 11b.

The influence of cathode channel cross sectional dimensions: detailed view This section discusses the results by pointing out simulation details. Looking at Figs. 6e10, one would observe that the channels with large widths (1.4 mm or 1.6 mm) and short heights (0.4 mm or 0.6 mm) are optimal for the operating conditions numbered 1 to 4; however, the fifth set of operating conditions, which is the only case with the feeding humidity of 50% (while it is 100% for the other cases), led to around square optimal cross section (1 1 mm2 when the objective is the maximization of maximum power, and 1 0.8 mm2 when the objective is the maximization of average power) which is substantially different from that of other cases. On the basis of this explanation, and to avoid a lengthy discussion, the detailed analyses are presented in the following form. First, the first set of operating conditions is considered as the representative of the operating conditions 1 to 4, since they all almost led to the same trends as shown in Figs. 6e9, and under the selected operating conditions the best and the worst channel designs are compared in detail to explain why the optimal design is superior. Second, it is attempted to answer why the optimal choice under the fifth set of operating conditions is noticeably different from those obtained for the other sets of operating conditions. This is done by comparing the simulation results of the optimal design obtained for the first set of operating conditions (as the representative of the optimal designs of operating conditions 1 to 4) and the optimal design obtained for the fifth set of operating conditions, both under the fifth set of operating conditions.

Comparison of the best and the worst channel dimensions under the reference operating conditions Under the first (or reference) operating conditions, the channel dimensions of 1.4 0.4 mm2 and 0.4 1.4 mm2 were

obtained as the best and worst cases, respectively. Fig. 12 shows the contours of oxygen concentration within the PEMFC for each of the best and the worst cases. Regarding Fig. 12, the superiority of the best case may be primarily attributed to its wider width, which in turn resulted in more oxygen transfer from the GFC to the GDL and then from the GDL to the reaction zone (or CL). As shown in Fig. 13, the best case led to greater current densities compared to the worst case. The higher water generation of the best case due to its greater current density (or reaction rate) is confirmed by comparing the water concentration at the outlet of cathode GFC of the best and the worst cases, as shown in Fig. 14. Although more water is generated in the best case, Fig. 14 shows that there exists more concentration of water within the GDL, CL, and membrane of the worst case. This is because in the best case more oxygen penetrates into the mentioned parts, resulting in lower concentration of water. The higher water content within the membrane of the worst case led to its higher ionic conductivity in comparison to the best case, as shown in Fig. 15. Fig. 16 illustrates the contours of temperature within the PEMFCs of the best and the worst designs under the first (or reference) set of operating conditions. This figure generally shows higher internal temperature for the best design, as compared to the worst one. This observation is consistent with the higher heat release of the best design as a result of its higher current densities. Moreover, as shown in Fig. 16, the hot core of the PEMFC of each design shows a shift toward the cathode side, where the exothermic reactions take place. Contours of velocity within the PEMFCs of the two designs are shown in Fig. 17. This figure indicates that at each (anode or cathode) side, the channel gas velocity magnitudes of the two cases are close. This closeness is due to the fact that the two designs pass the same rate of flow as well as they have the same cross sectional area (although at the cathode side, the channel shape of the best design is horizontal and that of the worst design is vertical). Contours of pressure within the best and the worst PEMFCs are shown in Fig. 18. As a result of the equality between the cross sectional areas as well as the similarity between the flow rates of the two designs, which has just been discussed, the


12


Fig. 10 e (a) Average and (b) Maximum power under fifth set of operating conditions.

Fig. 11 e Comparison of polarization curves of (a) 1 £ 0.8 and 1 £ 1 (b) 1.6 £ 0.4 and 0.4 £ 1.4 under fifth set of operating conditions.

Fig. 12 e Contours of oxygen concentration for the best and worst cases under first (reference) set of operating conditions. Please cite this article in press as: Mahmoudimehr J, Daryadel A, Influences of feeding conditions and objective function on the optimal design of gas flow channel of a PEM fuel cell, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.07.196


13

Fig. 13 e Contours of current density distribution for the best and worst cases under first (reference) set of operating conditions.

Fig. 14 e Contours of water concentration for the best and worst cases under first (reference) set of operating conditions.

reaction zone but lower water content within the membrane (and hence lower membrane ionic conductivity) as compared to the worst design. Keeping in mind that the PEMFC performance improves with reactants concentrations as well as membrane ionic conductivity, it is concluded that the positive influence of the greater oxygen concentration within the reaction zone of the best case dominated the negative influence of its lower membrane conductivity, resulting in the superiority of the performance of the best case over the worst case.

Fig. 15 e Membrane ionic conductivity of the best channel (1.4 £ 0.4) and worst channel (0.4 £ 1.4) in flow direction.

two designs show similar rates of pressure drop in the flow direction. To summarize, under the first set of operating conditions, the best design led to higher amounts of oxygen within the

Comparison of the optimal designs of the fifth set to the other sets of operating conditions To explain why the optimal design obtained for the fifth set of operating conditions (i.e., 1 1 mm2 or 1 0.8 mm2, depending on the objective function) is different from that obtained for the first set of operating conditions (i.e., 1.4 0.4 mm2), the performances of the two designs, both under the fifth set of operating conditions, are compared here. It is worth noting that between optimal channel designs of


14


Fig. 16 e Contours of temperature for the best and worst cases under first (reference) set of operating conditions.

Fig. 17 e Contours of velocity for the best and worst cases under first (reference) set of operating conditions.

Fig. 18 e Contours of pressure for the best and worst cases under first (reference) set of operating conditions.



15

Fig. 19 e Contours of oxygen concentration for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4) both under fifth set of operating conditions.

Fig. 20 e Contours of water concentration for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4) both under fifth set of operating conditions.

Fig. 21 e Membrane ionic conductivity of the optimal channel (1 £ 1) and non-optimal channel (1.4 £ 0.4) in flow direction operating conditions.

1 1 mm2 and 1 0.8 mm2 obtained for the two objectives under fifth set of operating conditions, only one of them (i.e., 1 1 mm2) is taken into consideration to be compared to the channel design of 1.4 0.4 mm2. Fig. 19 shows contours of oxygen concentration for the channel designs of 1.4 0.4 mm2 and 1 1 mm2. This figure shows that the optimal design (1 1 mm2) led to less penetration of oxygen into the reaction zone, as compared to the non-optimal design (1.4 0.4 mm2). On the other hand, Fig. 20 shows greater water concentration within the PEMFC components of the optimal design in comparison to the nonoptimal one. The higher water concentrations of the optimal design may be attributed to its higher water generation and its lower oxygen penetration from the cathode channel into the reaction zone. As shown in Fig. 21, the higher water content of the optimal design resulted in its greater membrane ionic


16


Fig. 22 e Contours of current density distribution for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4), both under fifth set of operating conditions.

Fig. 23 e Contours of temperature for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4) both under fifth set of operating conditions.

conductivity, as compared to the non-optimal design. Comparing Figs. 15 and 21, one would observe that the differences between the curves of Fig. 21 are more noticeable than those of Fig. 15. This may be because the fifth set of operating conditions has a humidity of 50% while the other cases are well humidified (i.e., with the humidity of 100%), and hence, the membrane ionic conductivity under the fifth operating conditions is more sensible to any change in the water content. The other point may be noted is that the optimal design has wider ribs than non-optimal case, resulting in its lower ohmic resistance against the current flow. Finally, as shown in Fig. 22, the optimal design led to greater current densities. Fig. 23 illustrates the contours of temperature within the PEMFCs of the optimal and the non-optimal designs under the

fifth set of operating conditions. Although the optimal design led to higher heat release as a result of its greater current density, it did not result in obvious dominancy in temperature over the non-optimal design. Moreover, the optimal design even partly shows lower temperature values, as compared to the non-optimal design. This observation can be attributed to the wider rib of the optimal design allowing for the higher heat transfer through the PEMFC shoulder. As mentioned for the first set of operating conditions in Section 4.2.1, the hot core of the PEMFC of each design shows a shift toward the cathode side. Fig. 24 shows the contours of gas velocity within the PEMFCs of the optimal and non-optimal designs. At the anode side, as a result of the equality between the cross sectional areas as well as the similarity between the flow rates of the two designs, the gas velocities of the two designs are close. However, at the cathode side, as a result of the difference in



17

Fig. 24 e Contours of velocity for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4) both under fifth set of operating conditions.

Fig. 25 e Contours of pressure for the optimal channel (1 £ 1) and a non-optimal channel (1.4 £ 0.4) both under fifth set of operating conditions.

the cross sectional areas of the two designs, the non-optimal design shows greater gas velocities. Greater gas velocity can result in greater gas diffusion into GDL and, hence, higher performance. However, it is worth mentioning that the gas velocity is not the only difference between the two designs. Indeed, as mentioned previously in this section, the higher ohmic loss of the non-optimal design as a result of its narrower shoulder width was another factor that caused the nonoptimal PEMFC performance to deteriorate. The noticeable higher rate of pressure drop in the flow direction of the cathode gas channel of the non-optimal design, as shown in Fig. 25, resulted from its higher gas velocities and smaller hydraulic diameter. In brief, the optimal design led to more ionic conductivity due to its higher membrane water content as well as less ohmic loss due to its wider ribs (as two positive factors); however, it caused lower penetration of oxygen into the reaction zone (as a negative factor), as compared to the non-optimal case. The

result of the mentioned contradictory factors was the superiority of the optimal case over the non-optimal one.

Conclusions In the present work, it was attempted to figure out the optimal cross sectional dimensions of the cathode flow gas channel of a PEMFC through numerical examination of various sets of dimensions. The optimization procedure was carried out for two different objective functions (maximization of the maximum power, and maximization of the average power) as well as for five different sets of operating conditions. In summary: The results illustrated the substantial influence of cross sectional dimensions on the PEMFC performance. This substantial influence was not limited to a specific set of operating conditions.


18


There is no monotonous variation of the PEMFC performance with width or height. In other words, the performance of the PEMFC may both deteriorate and improve with channel width or height, depending on its operating conditions as well as on its current dimensions. There exists no single optimal cross section for different sets of operating conditions. The polarization curves of the two different sets of cross sectional dimensions may intersect. In this case, one cross section may be superior in average power but at the same time worse in maximum power in comparison to the other one. Channels with wider widths and shorter heights resulted in a better oxygen transfer into the reaction zone, but it led to lower water content within the membrane and greater ohmic loss due to its narrower ribs. The optimal solution in each case results from the competition of the mentioned contradictory effects. Among various operating parameters (cell temperature, operating pressure, and stoichiometry and relative humidity of inlet gases), relative humidity of the inlet gases had the greatest effects on the optimal cross sectional dimensions. For instance, a cross section with a wide width and short height was optimal when the inlet gases were well humidified, but an optimal cross section with a square shape was obtained when the inlet gases had the relative humidity of 50%.

[10]

[11] [12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

references

[1] Willamson ZR, Chun D, Kwon K, Lee T, Squibb CW, Kim D. Evaluation of fin structure effects on a heated air-breathing polymer electrolyte membrane (PEM) fuel cell. Appl Therm Eng 2013;56:54e61. [2] Perng SW, Wu HW, Jue TC, Cheng KH. Numerical predictions of a PEM fuel cell performance enhancement by a rectangular cylinder installed transversely in the flow channel. Appl Energy 2009;86:1541e54. [3] Inaba M, Kinumoto T, Kiriake M, Umebayashi R, Tasaka A, Ogumi Z. Gas crossover and membrane degradation in polymer electrolyte fuel cells. Electrochim Acta 2006;51:5746e53. [4] Zhang FY, Yang XG, Wang CY. Liquid water removal from a polymer electrolyte fuel cell. J Electrochem Soc 2006;153:A225e32. [5] Qu S, Li X, Hou M, Shao Z, Yi B. The effect of air stoichiometry change on the dynamic behavior of a proton exchange membrane fuel cell. J Power Sources 2008;185:302e10. [6] Chen J, Siegel JB, Matsuura T, Stefanopoulou AG. Carbon corrosion in PEM fuel cell dead-ended anode operation. J Electrochem Soc 2011;158:B1164e74. [7] Xing L, Liu X, Alaje T, Kumar R, Mamlouk M, Scott K. A twophase flow and non-isothermal agglomerate model for a proton exchange membrane (PEM) fuel cell. Energy 2014;73:618e34. [8] Xing L, Cai Q, Liu X, Liu C, Scott K, Yan Y. Anode partial flooding modelling of proton exchange membrane fuel cells: optimisation of electrode properties and channel geometries. Chem Eng Sci 2016;146:88e103. [9] Xing L, Cai Q, Xu C, Liu C, Scott K, Yan Y. Numerical study of the effect of relative humidity and stoichiometric flow ratio

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

on PEM fuel cell performance with various channel lengths: an anode partial flooding modelling. Energy 2016;106:631e45. Mahmoudimehr J, Darbandi A. Technical study of a PEM fuel cell on the psychrometric chart. Int J Hydrogen Energy 2016;41:607e13. Li X, Sabir I. Review of bipolar plates in PEM fuel cells: flowfield designs. Int J Hydrogen Energy 2005;30:359e71. Scholta J, Escher G, Zhang W, Kuppers L, Jorissen L, Lehnert W. Investigation on the influence of channel geometries on PEMFC performance. J Power Sources 2006;155:66e71. Sun L, Oosthuizen PH, McAuley KB. A numerical study of channel-to-channel flow cross-over through the gas diffusion layer in a PEM-fuel-cell flow system using a serpentine channel with a trapezoidal cross-sectional shape. Int J Therm Sci 2006;45:1021e6. Ahmed DH, Sung HJ. Effects of channel geometrical configuration and shoulder width on PEMFC performance at high current density. J Power Sources 2006;162:327e39. Shimpalee S, Van Zee JW. Numerical studies on rib&channel dimension of flow-field on PEMFC performance. Int J Hydrogen Energy 2007;32:842e56. Hsieh SS, Chu KM. Channel and rib geometric scale effects of flow field plates on the performance and transient thermal behavior of a micro-PEM fuel cell. J Power Sources 2007;173:222e32. Secanell M, Karan K, Suleman A, Djilali N. Multi-variable optimisation of PEMFC cathodes using an agglomerate model. Electrochim Acta 2007;52:6318e37. Wang XD, Duan YY, Yan WM, Peng XF. Effects of flow channel geometry on cell performance for PEM fuel cells with parallel and interdigitated flow fields. Electrochim Acta 2008;53:5334e43. Kumar PM, Kolar AK. Effect of cathode channel dimensions on the performance of an air-breathing PEM fuel cell. Int J Therm Sci 2010;49:844e57. Wang XD, Huang YX, Cheng CH, Jang JY, Lee DJ, Yan WM, et al. An inverse geometry design problem for optimization of single serpentine flow field of PEM fuel cell. Int J Hydrogen Energy 2010;35:4247e57. Wang XD, Huang YX, Cheng CH, Jang JY, Lee DJ, Yan WM, et al. Flow field optimization for proton exchange membrane fuel cells with varying channel heights and widths. Electrochim Acta 2009;54:5522e30. Wang XD, Duan YY, Yan WM, Lee DJ, Su A, Chi PH. Channel aspect ratio effect for serpentine proton exchange membrane fuel cell: role of sub-rib convection. J Power Sources 2009;193:684e90. Wang XD, Zhang XX, Liu T, Duan YY, Yan WM, Lee DJ. Channel geometry effect for proton exchange membrane fuel cell with serpentine flow field using a three-dimensional two-phase model. J Fuel Cell Sci Technol 2010;7, 051019. Wang XD, Yan WM, Duan YY, Weng FB, Jung GB, Lee CY. Numerical study on channel size effect for proton exchange membrane fuel cell with serpentine flow field. Energy Convers Manag 2010;51:959e68. Secanell M, Songprakorp R, Djilali N, Suleman A. Optimization of a proton exchange membrane fuel cell membrane electrode assembly. Struct Multidiscip Optim 2010;40:563e83. Manso AP, Marzo FF, Garmendia Mujika M, Barranco J, Lorenzo A. Numerical analysis of the influence of the channel cross-section aspect ratio on the performance of a PEM fuel cell with serpentine flow field design. Int J Hydrogen Energy 2011;36:6795e808. Shimpalee S, Lilavivat V, Van Zee JW, McCrabb H, LozanoMorales A. Understanding the effect of channel tolerances on performance of PEMFCs. Int J Hydrogen Energy 2011;36:12512e23.



[28] Wang XD, Lu G, Duan YY, Lee DJ. Numerical analysis on performances of polymer electrolyte membrane fuel cells with various cathode flow channel geometries. Int J Hydrogen Energy 2012;37:15778e86. [29] Wang XD, Yan WM, Won WC, Lee DJ. Effects of operating parameters on transport phenomena and cell performance of PEM fuel cells with conventional and contracted flow field designs. Int J Hydrogen Energy 2012;37:15808e19. [30] Liu H, Li P, Wang K. Optimization of PEM fuel cell flow channel dimensions Mathematic modeling analysis and experimental verification. Int J Hydrogen Energy 2013;38:9835e46. [31] Xing L, Song X, Scott K, Pickert V, Cao W. Multi-variable optimisation of PEMFC cathodes based on surrogate modelling. Int J Hydrogen Energy 2013;38:14295e313. [32] Muthukumar M, Karthikeyan P, Vairavel M, Loganathan C, Praveenkumar S, Senthil Kumar AP. Numerical studies on PEM fuel cell with different landing to channel width of flow channel. Procedia Eng 2014;97:1534e42. [33] Mancusi E, Fontana E, Mariani VC, Ulson de Souza AA, Ulson de Souza SMAG. Numerical study of two-phase flow patterns in the gas channel of PEM fuel cells with tapered flow field design. Int J Hydrogen Energy 2014;39:2261e73. [34] Bilgili M, Bosomoiu M, Tsotridis G. Gas flow field with obstacles for PEM fuel cells at different operating conditions. Int J Hydrogen Energy 2015;40:2303e11.

19

[35] Akbari MH, Rismanchi B. Numerical investigation of flow field configuration and contact resistance for PEM fuel cell performance. Renew Energy 2008;33:1775e83. [36] Kuo JK, Yen TH, Chen CK. Three-dimensional numerical analysis of PEM fuel cells with straight and wave-like gas flow fields channels. J Power Sources 2008;177:96e103. [37] Fontana E, Mancusi E, da Silva A, Mariani VC, Ulson de Souza AA, Ulson de Souza SMAG. Study of the effects of flow channel with non-uniform cross-sectional area on PEMFC species and heat transfer. Int J Heat Mass Transf 2011;54:4462e72. [38] ANSYS FLUENT. Fuel cell modules manual. ANSYS Inc; 2011. [39] Guvelioglu GH, Stenger HG. Computational fluid dynamics modeling of polymer electrolyte membrane fuel cells. J Power Sources 2005;147:95e106. [40] Wang L, Husar A, Zhou T, Liu H. A parametric study of PEM fuel cell performances. Int J Hydrogen Energy 2003;28:1263e72. [41] Limjeerajarus N, Charoen-amornkitt P. Effect of different flow field designs and number of channels on performance of a small PEFC. Int J Hydrogen Energy 2015;40:7144e58. [42] Meng H. Numerical studies of liquid water behaviors in PEM fuel cell cathode considering transport across different porous layers. Int J Hydrogen Energy 2010;35:5569e79.


Influences of feeding conditions and objective function on the optimal ...

Influences of feeding conditions and objective function on the optimal ...

Suggest Documents

impact of objective function selection on optimal

Influences of ocean conditions and feeding ... - Wiley Online Library

Optimal objective function in high-dimensional regression

Optimal objective function in high-dimensional regression

A Novel Objective Function and Algorithm for Optimal ... - IEEE Xplore

influences of changing bioclimatic conditions on ...

Genetic Influences on Mosquito Feeding Behavior and the Emergence ...

externalities, monopoly and the objective function of

Influences of Environmental Conditions on the Cracking Tendency of ...

observations on the selection of objective function for the optimisation

A new plan quality objective function for determining optimal ... - PLOS

OPTIMAL MULTI-OBJECTIVE MULTIVARIABLE

On the generality of optimal versus objective classifier ... - Springer Link

Local Habitat Influences on Feeding and Respiration ...

Lime Wax Influences Feeding Behavior of Cryptotermes brevis and the ...

An Objective Function based on Fuzzy

Objective: biochemical function - Core

The Case of a Linear Objective Function

Feeding and infant development Breast-feeding and immune function

Affluence and Objective Environmental Conditions - Semantic Scholar

Affluence and Objective Environmental Conditions - Semantic Scholar

The Influences of Hydrodynamic Conditions and Nozzle ... - Core

externalities, monopoly and the objective function of the firm - Queen's ...

On the Optimal Estimation of the Cumulative Distribution Function in ...