Numerical study on cell performance and local transport phenomena
of PEM fuel cells with novel flow field designs
Wei-Mon Yan
a,∗, Hui-Chung Liu
a, Chyi-Yeou Soong
b, Falin Chen
c, C.H. Cheng
daDepartment of Mechatronic Engineering, Huafan University, Shih-Ting, Taipei 223, Taiwan, ROC bDepartment of Aerospace and Systems Engineering, Feng Chia University, Seatwen, Taichung 407, Taiwan, ROC
cInstitute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan, ROC dDepartment of Mechanical Engineering, Tatung University, Taipei 104, Taiwan, ROC Received 13 April 2006; received in revised form 2 May 2006; accepted 3 May 2006
Available online 13 June 2006
Abstract
In this work, a novel style of straight flow channel tapered in height or width is proposed to improve the efficiency of fuel utilization for PEM fuel cells. Fuel channels of various height and width taper ratios are numerically analyzed to understand their effects on fuel transport characteristics and cell performance. Influences of the liquid water formation on the transport phenomena and cell performance are included in the numerical model. The present results demonstrated that, with the tapered channel designs, the flow area contraction along the flow channel leads to increase in fuel velocity and thus enhances the fuel transport through porous layers, fuel utilization, and the capability of the liquid water removal. The results also reveal that the cell performance can be improved by either decreasing height taper ratio or increasing width taper ratio. If the power loss due to pressure drop is not considered, the performance of the fuel cell with the tapered flow channels is consistently improved with height taper ratios decreased and width taper ratio increased. With the pressure loss considered, however, the best performance can be obtained at the
height taper ratio (Λx) of 0.5 and the width taper ratio (Λz) of 1.8 among the taper ratios studied in the present work.
© 2006 Elsevier B.V. All rights reserved.
Keywords: PEM fuel cells; Novel flow field design; Electricity and mass transport
1. Introduction
In PEM fuel cells with conventional flow channels, reactant gases diffuse from channel inlet into catalyst layer through gas diffuser layer (GDL), and then take part in the reaction. Since the diffusion process is not helpful for removing heat and cath-ode water, various new styles of flow channel designs, such as serpentine, Z-type and interdigitated designs, are proposed to improve these matters.
A number of investigations were carried out on serpentine flow channel designs. Maharudrayya et al.[1]numerically ana-lyzed the effects of Reynolds number, aspect ratio and curvature ratio of flow channels on pressure drop, and found that the overall pressure drop reduces with the number of the serpen-tine channels. Also by numerical analysis of fuel cells with serpentine flow channels, Nguyen et al.[2] disclosed that the
∗Corresponding author. Tel.: +886 2 26632102; fax: +886 2 26632143.
E-mail address:wmyan@huafan.hfu.edu.tw(W.-M. Yan).
activation overpotential mainly occurs under the ribs, which implied that the Ohmic loss under the ribs is lower than that under the channels. In addition, it was indicated that the temper-ature at the interface between the channels and diffuser layer is 1–7◦C higher than the operating temperature. Using a commer-cial codes, FLUENT, Dutta et al.[3]studied three-dimensional mass transport process, fuel concentration variation and their effects on electrochemical reaction in PEM fuel cells with ser-pentine flow channels.
Though serpentine flow channel design promotes fuel cell performance, it has penalty of higher pressure loss as a result of too many bends. To solve this problem, Nguyen [4] pro-posed interdigitated flow channel, in which baffle plates/blocks are added to conventional channels, and then the channels are divided into two parts, inlet and outlet channels. Reactant gases from the inlet channels are forced into the outlet channels through the gas diffusion layer (GDL). With the assistance of the forced convection besides diffusion, gases are compelled to pass the domain under the ribs in a shortest way. Um and Wang
[5,6]dealt with the effects of oxygen and vapor distributions and
0378-7753/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2006.05.007
DH+ proton diffusivity in membrane
Dk,eff effective mass diffusivity for the kth species
(m2s−1)
dporous equivalent surface diameter of porous media
F Faraday constant (96,487 C mol−1)
H height of flow field (m) H+ hydrogen ion
H2O water
IY local current density in the Y-direction (A m−2)
i current density (A m−2)
ja current density at anode side (A m−2)
jc current density at cathode side (A m−2)
j0 reference current density
kc coefficient of water vapor condensation rate (s−1)
ke coefficient of water vapor evaporation rate
kp permeability (m2)
L length of flow field (m)
M mole
N number of baffles
P pressure (atm)
Psat saturated water vapor pressure (atm)
P perturbed variation of pressure in control volume Power power (W m−2)
q source term of variable (φ)
R universal gas constant (8.314 J mol−1K−1)
S surface area (m2)
Sc corrected source term of concentration equation
Sj source term of phase potential equation
SL source term of liquid water effect
Su source term of momentum equation in the
x-direction
Sv source term of momentum equation in the
y-direction
Sw source term of momentum equation in the
z-direction
s volume ratio occupied by liquid water
T temperature (K)
t time (s)
u velocity in the x-direction (m s−1)
V volume (m3)
Vcell operating cell pressure (V)
v velocity in the y-direction (m s−1)
ν kinematic viscosity (m s−1)
ρ density (kg m−3)
η over-potential (V)
σm electric conductivity in membrane
φ dependent variables
Γφ exchange coefficient
Φ phase potential function
Λx height tapered ratio
Λz width tapered ratio
Superscripts
ref reference value
turtuosity of the pore in the porous medium
Subscripts a anode CL catalyst layer c cathode channel channel eff effective
GDL gas diffuser layer H+ hydrogen ion H2 hydrogen
H2O water
inlet entrance
k the kth species of the mixture Mem membrane
O2 oxygen
outlet outlet
porous porous medium sat saturation total total
x in the x-direction
y in the y-direction
z in the z-direction
fuel transport on electrochemical reaction in three dimensional fuel cells with straight channels and interdigitated channels.
Kazim et al.[7]and Yi and Nguyen[8]analyzed the effects of various flow channel designs on PEM fuel cell performance, and concluded that interdigitated design is superior in accelerating chemical reaction and improving cell performance. Hu et al.
cell performance. Their results showed that, relative to straight flow channel, interdigitated design in the cathode side causes higher oxygen concentration and lower liquid water content in the diffuser layer, but its cell performance is worse if the cathode fuel gas supplied without humidification.
Two main reasons cause water molecules appearing within the membrane. One is the electro-osmotic drag by potential gra-dient and the other is the back diffusion by water concentration gradient across the cell. When these two kinds of movement have the same rate, the water in the membrane lies at the equilibrium state. Okada et al.[11]developed a simple model to investigate water transport in the membrane, and their computational results indicated that the water concentration profile is influenced by the thickness and humidity of the membrane and the current density of the cell. Bussel et al.[12]divided a MEA into tens of units to establish a two-dimensional dynamical model, and studied the water formation, electro-osmosis and diffusion process in the PEM, and their effects on cell performance under various operating conditions. Mazumder and Cole[13,14]demonstrated the differences between two-dimensional and three-dimensional numerical results, and employed a simplified model to discuss the effects of liquid water on cell performance. Recently, Yan and co-workers presented a series of experimental and numeri-cal studies about the flow field designs on the cell performance of PEM fuel cells[15–19].
As mentioned above, up to now the flow channel designs of PEM fuel cells appeared in the open literature are limited to straight, serpentine, Z-type and interdigitated designs. Basically, straight channel designs have lower capability in cell perfor-mance and liquid water removal, though their pressure drop is lower. Serpentine designs have too large pressure drop due to channel bends. Interdigitated designs also have very high pres-sure drop in the presence of channel blockage. Therefore, based on straight flow channels, a new style of flow field, i.e., tapered flow channel, is proposed to enhance fuel utilization efficiency at high current density. In this work, straight flow channels of taper ratio in height or width are proposed in order to improve the effi-ciency of fuel transport, fuel utilization, and cell performance in PEM fuel cells. For cells with this class of tapered channel designs, the effects of flow area variation along the flow channel on the fuel flow velocity, the fuel distribution, the fuel transport and utilization, the capability of the liquid water removal, and the cell performance are explored numerically.
2. Analysis
This work establishes a three-dimensional PEM fuel cell model to analyze its electrochemical reaction and transport phe-nomena of reactants in anode catalyst layer, PEM, and cathode catalyst layer in the MEA, where the reaction occurs. In other regions such as the GDL, no chemical reaction takes place. Therefore, the governing equations of this model include mass, momentum, species and electrical potential conversation equa-tions. For simplicity, the following assumptions are made: (1) the cell system is three-dimensional and steady; (2) the inlet fuel is ideal gas;
Table 1
The parametric values used in this work
Length of flow channel (L) (mm) 141 Height of channel (Hchannel) (mm) 1
Width of channel (W) (mm) 1
Thickness of GDL (HGDL) (mm) 0.3
Thickness of CL (HCL) (mm) 0.01
Thickness of membrane (HMem) (mm) 0.035
Porosity of GDL (εGDL) 0.4
Porosity of CL (εCL) 0.4
Porosity of membrane (εMem) 0.28
Permeability of GDL (kp,GDL) (m2) 1.76× 10−11 Permeability of CL (kp,CL) (m2) 1.76× 10−11 Permeability of membran (kp,Mem) (m2) 1.8× 10−18 Electric conductivity of GDL ( −1m−1) 53 Electric conductivity of CL ( −1m−1) 53 Reference current density in anode side (Ajref0,a) (A m−3) 9.23× 108 Reference current density in cathode side (Ajref0,c) (A m−3) 1.05× 106
(3) the system is isothermal; (4) the flow is laminar; (5) the fluid is incompressible;
(6) the thermal properties are constant; and
(7) the porous layers such as GDL, catalyst layer and PEM are isotropic.
To reduce the time cost of three-dimensional cell computa-tion, small scale fuel cell models were adopted by most asso-ciated literature. However, due to their short flow channels, the results hardly agreed with the general performance of the cells at a large scale. This work aims to establish a relatively large fuel cell model with the area of 14.1× 14.1 cm2. The geometri-cal dimensions and physigeometri-cal properties of its flow channels are listed inTable 1. Considering the symmetry nature of the fuel cell configuration as shown inFig. 1, only the essential part of the fuel cell model is taken as the computational domain for saving the computational time. The schematic diagram of the three-dimensional tapered flow channel designs is depicted in
Fig. 2. Two parameters, height taper ratio Λx and width taper
ratio Λz,are defined as follows:
Λx= Houtlet
Hinlet , Λz= Woutlet
Winlet (1)
where Houtlet, Hinlet, Woutlet, and Winletare the outlet height, inlet
height, outlet width, and inlet width, respectively.
The governing equations under the assumptions mentioned above can be depicted as follows:
continuity equation: ∂u ∂x + ∂v ∂y+ ∂w ∂z = 0. (2) momentum equation (x): εeff u∂u ∂x + v ∂u ∂y + w ∂u ∂z = −εeff ρ ∂P ∂x + υεeff ∂2u ∂x2 + ∂2u ∂y2 + ∂2u ∂z2 + Su (3)
Fig. 1. Schematic diagram of the three dimensional model.
momentum equation (y):
εeff u∂v ∂x + v ∂v ∂y+ w ∂v ∂z = −εeff ρ ∂P ∂y + υεeff ∂2v ∂x2 + ∂2v ∂y2+ ∂2v ∂z2 + Sv (4) momentum equation (z): εeff u∂w ∂x + v ∂w ∂y + w ∂w ∂z = −εeff ρ ∂P ∂z + υεeff ∂2w ∂x2 + ∂2w ∂y2 + ∂2w ∂z2 + Sw (5)
In various layers, Su, Sv and Sw denote different source
terms, whose details are listed inTable 2. In PEM, Su, Svand
Swembody the proton transport and the liquid water dragged
by electro-osmosis. InTable 1, εeffis the effective porosity of
porous material, CF the quadratic drag factor, and Zf the ion
valence in PEM. In addition, Dk,eff is the effective diffusion
coefficient of the kth speices, which is calculated by the Brug-german equation [20], and kp is the permeability in porous
material, and its dependence of porosity can be described by
Blake–Kozeny equation[21], kp= dporous2 150 ε3 (1− ε)2 (6) where dporous is the equivalent area of porous material and
expressed in the from of
dporous=6V porous Sporous
Species equation (kth species):
εeff u∂Ck ∂x + v ∂Ck ∂y + w ∂Ck ∂z = Dk,eff ∂2Ck ∂x2 + ∂2Ck ∂y2 + ∂2Ck ∂z2 + Sc+ SL (7)
where Ckis the concentration of kth species, and Scis the source
term in the catalyst layers with the correction by chemical reac-tion. It is of the form−ja/2FCtotal,afor hydrogen,−jc/4FCtotal,c
for oxygen, and−jc/2FCtotal,cfor vapor. In these expressions, ja and jc, respectively, denote the current densities on anode
T able 2 Source terms appeared in the go v erning equations Su Sv Sw Sc Channel 000-GDL − υε ef f 2 kp u − ε eCeff F ρu k p u 2+ v 2+ w 2 − υε 2 eff kp v − ε 3Ceff F ρv k p u 2+ v 2+ w 2 − υε 2 eff kp w − ε 3Ceff F ρw k p u 2+ v 2+ w 2 0 Catalyst layer − υε 2 eff kp u − ε 3Ceff F ρu k p u 2+ v 2+ w 2 − υε 2 eff kp v − ε 3Ceff F ρv k p u 2+ v 2+ w 2 − υε 2 eff kp w − ε 3Ceff F ρw k p u 2+ v 2+ w 2 H2 :− 1 2FC a ja O2 :− 1 4FC c jc H2 O: 1 2FC c jc Membrane − υε ef f 2 kp u − εef f 3C F ρu k p u 2+ v 2+ w 2+ kp Z υ f CH + F ·∇ Φ ·ux − υε ef f 2 kp v − εef f 3C F ρv k p u 2+ v 2+ w 2+ kp Z υ f CH + F ·∇ Φ ·vy − υε ef f 2 kp w − εef f 3C F ρw k p u 2+ v 2+ w 2+ kp Z υ f CH + F ·∇ Φ ·wz ZF RT Dk, ef f, H + CH + ∂ 2Φ 2∂x + ∂ 2Φ 2∂y + ∂ 2Φ 2∂z equations: ja= Ajref0 CH2 CrefH2 e(αaF/RT )η− 1 e(αcF/RT )η (8) jc= Ajref0 CO2 CrefO2 e(αaF/RT )η− 1 e(αcF/RT )η (9) Besides the continuity, momentum, and energy equations, the phase potential equation for potential and current profile is
∂ ∂x σm∂Φ ∂x + ∂ ∂y σm∂Φ ∂y + ∂ ∂z σm∂Φ ∂z = Sj (10)
where Φ is the phase potential function, and σmis the
mem-brane conductivity and is expressed as below according to Springer et al.[22]and Nguyen and White[23].
σm(T ) = σmrefexp 1268 1 303 − 1 T , (11)
where σmref is the reference conductivity of membrane, and is
expressed as follows:
σmref= 0.005139λ − 0.00326 (12) λ =
0.043 + 17.81a − 39.85a2+ 36.0a3 0≤ a ≤ 1
14+ 1.4(a − 1) 1 < a ≤ 3 (13) in which a denotes the vapor activity and λ the water content in PEM, Sjin Eq.(10)is the electricity source, which is zero in
the PEM without electrochemical reaction and is−jaor−jcon
the cathode or anode side. The relationship between the phase potential Φ and the current density i is expressed as below:
ix= −σm∂Φ ∂x (14) iy= −σm∂Φ ∂y (15) iz= −σm∂Φ ∂y (16)
Thereby, the phase potential equation can be reduced to the fol-lowing equation: ∂ix ∂x + ∂iy ∂y + ∂iz ∂z = Sj (17)
As another important issue of this model, the effects of liq-uid water are simplified. Although there is no two-phase flow behavior included in the model, the blockage effects with the presence of liquid water in the pores of porous layers such as the GDL, catalyst layer and PEM, are taken into account. The source term SLin the species equations is expressed to be the
water amount of condensation or evaporation, and is evaluated as: SL= ⎧ ⎨ ⎩ MH2OkcεeffCH2O
ρRT (PH2O− Psat), if PH2O> Psat keεeffs(Psat− PH2O), if PH2O< Psat
Fig. 2. Schematic diagrams of the tapered channel designs: (a) flow channel tapered in height; (b) flow channel tapered in width.
where M is the molar weight, kcand kethe vapor condensation
and evaporation constant, and Psatthe vapor saturated pressure,
which is calculated as follows[16–18]:
Psat= 10−2.1794+0.02953T −9.1837×10−5T2+1.4454×10−7T3 (19) where s denotes the volume ratio of liquid water to pore of the porous material, and that is,
s = volume of liquid water
volume of pore . (20)
Liquid water affects the effective porosity of porous layers, which is expressed as below:
εeff= ε(1 − s) (21)
2.1. Boundary conditions
The boundary conditions of the present computational model contain those at inlet, outlet, wall, and interfaces between differ-ent layers. For comparison with the experimdiffer-ents, the inlet flow rates in cathode and anode flow fields are, respectively, specified to be 2000 and 4000 cm3min−1, and the other specifications are listed inTable 3. At the outlet, fully developed flow is assumed and the boundary conditions of velocity and concentration can be expressed as:
u = ∂v ∂y = w =
∂Ck
∂y = 0 (22)
At the interface between the flow channels and bipolar plates, the velocity and mass flux are zero.
u = v = w = ∂Ck
∂z = 0 (23)
At the interface between the flow fields and the GDLs, the velocity, mass flux, species concentration and species flux are all continuous. εeff,GDL∂v ∂x x=XGDL = ∂v ∂x x=Xchannel , εeff,GDL∂w ∂x x=XGDL = ∂w ∂x x=Xchannel , vx=XGDL = vx=Xchannel (24) εeff,GDL∂Ck ∂x x=XGDL = ∂Ck ∂x x=Xchannel , Ck,x=XGDL = Ck,x=Xchannel (25) Table 3
The inlet conditions of fuel gases used in this work
Anode side Cathode side
Inlet velocity (m s−1) 0.475 0.95
Fuel H2, H2O O2, H2O, N2
Relative humidity (%) 100 100
At the interface between the GDLs and the catalyst layers, the velocity and concentration conditions are similar to those at the interface between the flow fields and the GDLs.
εeff,CL∂v ∂x x=XCL = εeff,GDL∂v ∂x x=XGDL , εeff,CL∂w ∂x x=XCL = εeff,GDL∂w ∂x x=XGDL , vx=XCL = vx=XGDL, wx=XCL = wx=XGDL (26) εeff,CL∂Ck ∂x x=XCL = εeff,GDL∂Ck ∂x x=XGDL , Ck,x=XCL = Ck,x=XGDL (27)
Also, at the interfaces between the catalyst layers and PEM, as gases cannot permeate PEM, their velocity, mass flux, species concentration and species flux are all zero.
εeff,CL∂v ∂x x=XCL = 0, εeff,CL∂w ∂x x=XCL = 0, vx=XCL = 0 (28) εeff,CL∂Ck ∂x x=XCL = 0, Ck,x=XCL = 0 (29)
Since liquid water can transport through the PEM as a result of the influences of proton transport and electro-osmosis, its velocity, mass flux, liquid water saturation degree Cs and its
flux is continuous at the interfaces between the catalyst layers and the PEM.
εeff,Mem∂v ∂x x=XMem = εeff,CL∂v ∂x x=XCL , εeff,Mem∂w ∂x x=XMem = εeff,CL∂w ∂x x=XCL , vx=XMem = vx=XCL, wx=XMem= wx=XCL (30) εeff,Mem∂Cs ∂x x=XMem = εeff,CL∂Cs ∂x x=XCL , Cs,x=XMem= Cs,x=XCL (31)
The boundary conditions of potential at the interface between the anode catalyst layers and the PEM is Φ = 0, and that at the interface between the cathode catalyst layer and the PEM can be expressed as ∂Φ/∂x = ∂Φ/∂z = 0.
The general convection–diffusion equation can be expressed in a conservative form as follows:
∂
∂t(ρφ) + ∇ · (ρuφ − Ξφ∇φ) = Sφ (32)
where t is the time, φ general dependent variable, such as veloc-ity components, concentration, Ξφexchange coefficient such as
viscosity, diffusion coefficient, Sφsource term such as pressure gradient,u velocity vector and ρ is the density.
When Eq.(32)is integrated over a control volume, a finite-volume equation can be resulted in as
apφp= aEφE+ aWφW+ aNφN+ aSφS+ aHφH+ aLφL+ b
(33) where φpis the value of variable φ at node P of control volume, φE, . . . , φLvalue of variable at node of neighboring control vol-ume, aP, . . . , aL coefficients in discretized equations and b is the expression of source for the discretized equation of variable
φ.
The Semi Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm, developed by Patankar[24], is employed to solve the governing equations.
3. Results and discussion
The validation of the numerical results is performed by comparing the present predictions with previous experimental results.Fig. 3shows the comparison of the numerical and experi-mental results of the cell performance, i.e., the operation voltage
Vcell versus the current density of fuel cells I (A m−2), at the operating conditions of fully humidified fuel gases with flow rate of 4000 cm3min−1, pressure of 1 atm, and humidifying and operating temperatures of 50◦C. The solid circles denote the experimental results of Cheng[25]and the curve is the present numerical prediction. The numerical results show a few devi-ations from the measurements at low and high current density regimes. Since in the numerical model the presence of the liquid water is assumed to cause only the effects of blocking pores and hindering fuel transport. This is different from the complicated two-phase transport phenomena in a real case. At high current, the numerical analysis with a simplified model underestimates the liquid water effects and the model is not appropriate to simu-late the real dead-zone condition. Nevertheless, the discrepancy of the cell performance between the numerical predictions and
Fig. 4. Effects of tapered channel design in 2-D and 3-D models on the I–V curves.
the experimental results lies within a reasonable range. Thereby it can be deduced that the present numerical method is appro-priately valid in simulation of the three-dimensional fuel cells with the presence of liquid water.
Using this numerical model, the tapered flow channel design is analyzed with the emphasis on the effects of the height taper ratio and width taper ratio on cell performance.Fig. 4presents the effects of height taper ratio on the two-dimensional (2-D) and three-dimensional (3-D) predictions of the cell performance.
Fig. 5. Effects of height taper ratio Λxon the cell performance. (a) I–V curves;
(b) I–P curves.
Fig. 6. Effects of width taper ratio Λzon the cell performance. (a) I–V curves;
(b) I–P curves.
The solid and dashed lines, respectively, denote the results of 3-D and 2-3-D models. It is disclosed inFig. 4that, for the voltage less than 0.6 V, the current density predicted using the 2-D model is about two times of that using the 3-D model, because the com-putational domain of the 2-D model is equivalently the central section of the 3-D model or section A inFig. 1, where the cur-rent density is the maximum in the 3-D model. The diffusion path of the fuel under the ribs is longer than that under the flow channels, and part of fuel under the flow channels has partici-pated in the reaction, so the concentration of the fuel under the ribs is lower. Since the concentration of the fuel under the ribs is low and the liquid water is difficult to be removed, the current density lowers down, and thus the current density calculated by the 3-D model are less than that by the 2-D model.
Figs. 5 and 6present the effects of the height taper ratio Λx
and the width taper ratio Λzon cell performance, andFig. 5(a
and b) denotes the results of I–Vcell (current density–voltage)
and I–P (current density–power), respectively. At high voltage (Vcell> 0.7 V), the tapered channel design has little effects on
current density for low electrochemical reaction rate. As the voltage decreases and the current density increases, the fuel amount needed rises up for more active electrochemical reac-tion, and the limiting condition due to lack of fuel occurs as the voltage lies at about 0.5 V. For the lower height taper ratios in
Fig. 5(a), fuel transport into GDL can be enhanced in the region near the end or the downstream portion of the flow channels, so
Fig. 7. Effects of height taper ratio Λxon the local current density distributions
at various cross sections of the membrane. (a) Vcell= 0.7 V and (b) Vcell= 0.3 V.
the fuel amount increases and the occurrence of the fuel mass transport limit can be delayed. In addition, at a lower current density (I < 4000 A m−2), the height taper ratio has little effects on the output power for slow electrochemical reaction, while at higher current density (I > 4000 A m−2), a lower height taper ratio results in a higher output power. With increasing width taper ratio, the contact area between fuel and GDL rises for the area increment of the flow channels, then the content of fuel in the GDL becomes higher and, subsequently, the current den-sity also rises.Fig. 6(b) shows the growth of the output power with the increasing width taper ratio corresponding to the cases presented inFig. 6(a).
Figs. 7 and 8present the effects of the height and width taper ratios on local current distributions at various sections. Along the fuel channels, the fuel amount drops due to consumption in reaction, while the liquid water as a product of the reaction accumulates. As a result, at the end of the flow channels, the fuel transport rate lowers down, and the local current density decreases along the channel (Y) direction. The data inFig. 7(a) show that the local current density increases with the height taper ratio in the inlet region (Y < 0.02 m), because the liquid water accumulates in this region and increases the resistance of fuel diffusion. Along the channel length, more fuel in the flow channels diffuses to the GDL and catalyst layer. This enhance-ment is caused by the contraction of the flow area of the fuel channels with its height tapered along the channel length. As a
Fig. 8. Effects of width taper ratio Λzon the local current density distributions
at various cross sections of the membrane. (a) Vcell= 0.7 V and (b) Vcell= 0.3 V.
result, the lower Λxgenerates better current density distribution
in the region of Y > 0.02 m. In the inlet region of the flow chan-nels of Λx= 0.1, the fuel diffusion to the GDL is enhanced due
to the channel taper effect, which not only increase the current density and fuel flux but also benefit the liquid water removal. At the voltage of 0.3 V inFig. 7(b), the current density distribution is similar to that at 0.7 V. However, since the electrochemical reaction at 0.3 V is very drastic, a large amount of fuel reacts in the region beneath the flow channels. It leads to very low current density under the ribs, so the effects of height taper ratio are not evident under the ribs.
InFig. 8(a), the effects of the width taper ratio at the operat-ing voltage of 0.3 V are quite obvious. At Λz> 1, for its larger
area of the flow channels, the fuel velocity is lower than that at
Λz≤ 1. With an increase in the channel width, the fuel has more
time to diffuse, and its diffusion path under the ribs decreases, so the difference between the current density distributions in the regions under the ribs and the channels becomes smaller. At the largest taper ratio Λz= 1.8, the local current density at the
outlet is almost equal to that under the flow channels. At the operating voltage of 0.3 V, the results shown inFig. 8(b) reveal that the local current density drops very quickly along the chan-nel because most of the fuel takes part in the electrochemical reaction. For low width taper ratio, the fuel and the associated reaction concentrate in the central region. As a result, with a reduction in width taper ratio, the local current density under the flow channels rises, while under the ribs it decreases for
Fig. 9. Effects of tapered channel design on the velocity distributions along the cathode flow channels: (a) tapered in height; (b) tapered in width.
the effects of diffusion path. In the case of the flow channels with smaller area, the local current density under the flow chan-nels is generally higher, while under the ribs the current density is relatively lower for the concentrated reaction under the flow channels, so larger width taper ratio produces higher current density.
The fuel velocity in the flow channels affects the liquid water removal in fuel cells.Fig. 9presents the effects of tapered chan-nel on the fuel velocity at the center of the chanchan-nel. The effects of height and width tapered channels are shown inFig. 9(a and b), in which the continuous and dotted lines denote the results at 0.7 and 0.3 V, respectively. In the inlet region of the flow chan-nels, the flow develops approaching fully developed condition, and the center-line velocity usually has a significant increment. In the baseline case of Λx= 1, the velocity changes little and
slightly increases along the channel for the consumption of the fuel and the decrease of the fuel density on the cathode side. For the design of height tapered flow channels, as shown in
Fig. 9(a), the reduction in cross section area accelerates the fuel flow along the channels like the flow in a nozzle. This channel tapered effect becomes more remarkable as Λxdecreases. In the
width tapered flow channels of Λz< 1, due to nozzle effect and
the fuel consumption, the fuel velocity increases along the chan-nel, and the acceleration is more evident for lower Λx. For the
flow channels of Λz> 1, the center-line velocity drops along the
Fig. 10. Effects of tapered channel design on the oxygen distributions along the cathode flow channels: (a) tapered in height; (b) tapered in width.
flow for the increasing cross-sectional area, although the fuel consumption has somewhat influences in increasing the veloc-ity. In the case of a lower fuel velocity, the liquid water removal caused by electrochemical reaction is difficult, but the fuel can have enough time for diffusion towards the catalyst layer. At low voltage, most oxygen participates the reaction, which results in low fuel density. Therefore, the local velocity is higher than that at a higher voltage. Moreover, this situation is more obvious as
Λxdecreases.
Because the tapered flow channels are of a reduction in the channel cross sectional area, the fuel in it can be more easily to diffuse to the porous layers.Fig. 10shows the effects of the tapered channels on fuel distributions (weight concentration of oxygen) on the cathode. Fig. 10(a and b) displays the results of the height and width tapered flow channels, respectively. At operating potential of 0.7 V, for height tapered channels, the results inFig. 10(a) disclose that the fuel continuously diffuses to the GDL and catalyst layer and, then, takes part in the reaction in the catalyst layer and the oxygen concentration decreases along the channel. Whereas Λxhas only little effects on the oxygen
concentration for the slow electrochemical reaction. However, at a low voltage, 0.3 V, the current density gets higher and more oxygen is consumed. Besides, the taper effects are more obvi-ous. A smaller Λxshows more evident taper effects and forces
Fig. 11. Effects of tapered channel design on the liquid water distributions along the cathode flow channels: (a) tapered in height; (b) tapered in width.
the tapered channels increase the fuel utilization efficiency. For flow channels with large Λz, as shown inFig. 10(b), the
aver-age oxygen concentration reduces due to high utilization of the fuel oxygen. It is also observed that at a high current density, the drastic electrochemical reaction consumes more oxygen, but some oxygen in the flow channels cannot transport to the catalyst layer. Since a flow channel of a large width taper ratio have rela-tively larger flow area, which is beneficial to the fuel utilization efficiency.
Effects of the tapered channel on the liquid water distribution in the cathode are shown inFig. 11, in which the parameter S is an index denoting the degree of the liquid water saturation. The liq-uid water content increases along the channel as a consequence of the electrochemical reaction.Fig. 11(a and b) illustrates the effects of height taper ratio and width taper ratio, respectively. At the voltage of 0.7 V and the position of Y < 0.05 m, the liq-uid water distribution is similar for the small taper effect. In the downstream portion of the channel, as shown inFig. 9(a), the velocity rises in the tapered channel and more liquid water can thus be removed. As a result, in the downstream part of the channels (Y > 0.05 m), the liquid water distribution of a tapered channel is lower than that of the regular straight channel with
Λx= 1. As Λx= 0.1 and Y > 0.075 m, the liquid water removal is
performed well for the velocity increasing with Y as a result of the large taper effect. It is shown that in this region the liquid water
content rises with the increase in Λx. At 0.3 V, the more drastic
electrochemical reaction produces more liquid water than that at 0.7 V, and the region with evident tapered effect expands from
Y > 0.05 m to Y > 0.025 m. Near the outlet, the taper effects are
stronger, and the difference of liquid water distribution is more obvious. InFig. 11(b), at 0.7 V and in the region of Y < 0.05 m, the width of the flow channels changes little, and the liquid water produced in the catalyst layer has not permeate back to the flow channels, so the width taper ratio effects on liquid water distri-bution are not apparent. However, along the channel, the liquid water continuously flows in the channel and accumulates in the downstream region. For a tapered channel of Λz≤ 1, the flow
velocity increases along the channel, and the liquid water is not easy to accumulate in the channel; while in a divergent channel,
Λz> 1, more fuel takes part in reaction and more liquid water
forms. The flow velocity, as illustrated in Fig. 9(b), decreases along the channel, so the liquid water distribution increases with the increasing width taper ratio of the flow channel. These phe-nomena are more obvious at 0.3 V, in which the liquid water distribution significantly increases for the high reaction rate, and it rises by 1–2 times of that at 0.7 V. Therefore, a smaller width taper ratio leads to better capability of liquid water removal.
The tapered channel design is beneficial to the improvement in fuel diffusion and cell performance, and it also alters the resis-tance of the fuel flow. In order to explore the pressure loss caused
Fig. 12. Effects of tapered channel design on the pressure distributions along the cathode flow channels: (a) tapered in height; (b) tapered in width.
formance of liquid water removal, but the resistance of fuel flow also increases; the design with larger width taper ratio Λz> 1
increases the diffusion area of fuel, but there accumulates more liquid water in the flow channels.
4. Conclusions
In the present paper, the relatively novel channel design of variable cross-section has proposed and the effects of the taper ratio, either in height or width, have been analyzed in details. With this class of fuel channels, the present numerical analysis has demonstrated that the flow area variation along the flow channel leads to noticeable influences on the fuel velocity in flow channel, the capability of the liquid water removal, the fuel transport and utilization, and the cell performance. Based on the present predictions and analysis, the conclusions can be derived as follows:
1. For the cathode channels tapered in height, the reduction in outlet height is beneficial to the fuel utilization efficiency and the improvement in the cell performance.
2. For the tapered channel with the width of flow channel enlarged along the flow, the contact area of the interface between channels and GDL increases, which in turn, results in an increase in the transport rate of fuel in the outlet. There-fore, the cell performance is improved.
3. The flow channels tapered in height can enhance the fuel velocity along the flow channel, and improve the liquid water removal, whose rate increases with the decrease in height taper ratio. For the design of width tapered flow channels, the rise of the width decelerates the flow and weakens the capa-bility of liquid water removal, while it increases the reaction efficiency and cell performance.
4. At the height taper ratio Λxof 0.1, the design with a large
width tapered ratio weakens the taper effect. Therefore, the cell performance, the fuel velocity and the efficiency of liq-uid water removal are all reduced as the width taper ratio increases.
5. If the power loss due to pressure drop is not considered, the performance of the fuel cell with the tapered flow channels is consistently improved with height taper ratios decreased and width taper ratio increased. With the pressure loss con-sidered, however, the best performance can be obtained at the height taper ratio (Λx) of 0.5 and the width taper ratio
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