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Asymptotic analysis for the inlet relative humidity effects on the performance of proton exchange membrane fuel cell
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Asymptotic analysis for the inlet relative humidity effects on the performance of proton exchange membrane fuel cell ⁎
Yongfeng Liua, , Lei Fana, Pucheng Peib, Shengzhuo Yaoa, Fang Wanga a
Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, School of Mechanical-electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China b State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China
H I G H L I G H T S inlet humidification efficiency (IHE) model is proposed. • AThenovel model could carry out the dynamic inlet humidification efficiency. • The IHE of species distribution are shown to make up the experiments. • The contours • inlet humidification efficiency is 57% at 40% RH (70 °C operating temperature).
A R T I C L E I N F O
A B S T R A C T
Keywords: PEMFC Relative humidity Gas humidification Computational fluid dynamics Inlet humidification efficiency
In order to study the inlet relative humidity (RH) effects on the performance of proton exchange membrane fuel cell (PEMFC), the inlet humidification efficiency (IHE) model is proposed. The total water content of PEMFC is consisted of two parts including the internal electro-migration water content and the external water content of the humidified gas. The dynamic inlet humidification efficiency is derived. The current density of PEMFC is calculated by the incorporating parameters including inlet humidification efficiency and water content of the humidified gas in the IHE model. Firstly, the schedule diagram of calculation is given and the geometric model is established according to actual size of PEMFC. The computational meshes are partitioned by using the software (Gambit). The IHE model is imported into the computational fluid dynamics software (Fluent). Secondly, the experimental system is established and experiments have been done at the operating temperature of 70 °C and at 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. Finally, the contours of H2 O molar concentrations (both in anode channels and cathode channels), membrane water content (MWC) and polarization curves of the IHE model, the Fluent model and experimental are compared and analyzed at above experimental conditions. The results show that the species distribution uniformities of the IHE model such as H2 O molar concentrations (both in anode channels and cathode channels) and MWC are the best when the PEMFC at 100% RH. When the operating temperature is 70 °C (40% RH and 350 mA/cm2 ), the accuracy of the IHE model is improved by 79% compared with the Fluent model. When the operating temperature is 70 °C (40% RH and 350 mA/cm2 ), the inlet humidification efficiency reaches 57%.
1. Introduction In recent years, owing to the environmental pollution problems and major concerns on the depletion of petroleum based energy resources, the interests of the various types of clean power sources and renewable energies are more focused [1–6]. Among them, proton exchange membrane fuel cell (PEMFC) is a new kind of the renewable energyconversion device which directly converted the chemical energy of hydrogen and oxygen into electrical energy and heat through the
⁎
electrochemical reactions [6–15]. PEMFC has high energy conversion, high efficiency, low emissions, highly reliability, low operation temperature (20–90 °C) with the consequent quick start-up and other advantages [5,8,16–22]. However, there are several issues in commercialization of PEMFC [20]. Among them, one of the most important issues is water management problem, which is mainly managed two parts including both the water content of humidified gas and the electro-migration water content. The water content of the humidified gas is affected deeply by relative humidity (RH). Hence, many
Corresponding author. E-mail address: [email protected] (Y. Liu).
https://doi.org/10.1016/j.apenergy.2017.11.008 Received 11 June 2017; Received in revised form 4 October 2017; Accepted 2 November 2017 0306-2619/ © 2017 Published by Elsevier Ltd.
Please cite this article as: Liu, Y., Applied Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.11.008
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Nomenclature
ϕwh
nd I F λ α PWV Psat (T) ϕwih d Qm φ Ps P
Qm,H2 λ H2 N Qm,Air ϕw eih
water content produced by electrochemical reactions, mol/(cm2 ·s) electro migration coefficient current density, A/cm2 Faraday constant, 96,487 C/mol water content in proton exchange membranes water saturation water vapor pressure, Pa saturation pressure, Pa water content of the humidified gas, mol/(cm2 ·s) humidity ratio, g/kg mass flow, kg/s relative humidity, % water vapor saturation pressure, Pa atmospheric pressure, Pa
H2 mass flow, kg/s H2 excess coefficient series connection cell number air mass flow, kg/s total water content of PEMFC, mol/(cm2·s) inlet humidification efficiency
Abbreviation PEMFC RH IHE MWC MEA CFD PEM
proton exchange membrane fuel cell relative humidity inlet humidification efficiency membrane water content membrane electrode assembly computational fluid dynamics proton exchange membrane
Then they analyzed humidification problems of PEMFC and considered the internal and external humidification methods. The effects on humidification methods of membrane hydration were evaluated by its power loss rate and the performance of stacks. The external humidification was effective in most operating conditions. But the effects of external humidification were limited when the stacks had high temperature, low load or the membrane is in a dry state. Many researchers made valuable achievements in the field of RH for the performance of PEMFC through simulation and experiments, but they qualitatively studied the effects from the variation trend and did not have a quantitative analysis for the RH effects on the performance of PEMFC. In this paper, firstly, the inlet humidification efficiency (IHE) model is proposed. The inlet humidification efficiency is calculated by the internal electro-migration water content and the external water content of the humidified gas in the IHE model. Furthermore, the current density of PEMFC is calculated by the inlet humidification efficiency and the water content of the humidified gas. Secondly, the schedule diagram of calculation is given and the geometric model is established according to actual size of PEMFC. The computational meshes are partitioned by using the software (Gambit). The IHE model is imported into the computational fluid dynamics software (Fluent). The experimental system of PEMFC is established. The experiments are conducted at the operating temperature of 70 °C, at 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. Finally, the contours of H2 O molar concentrations (both in anode channels and cathode channels), membrane water content (MWC) and the polarization curves of the IHE model, the Fluent model and experimental are compared and analyzed at above experimental conditions.
researchers took active steps to research the effects of RH on the performance of PEMFC and improve the performance of PEMFC. Owing to a lot of difficulties in measuring species movement and distribution inside PEMFC, numerical simulation has become an effective research method to solve above problems at a certain extent. Several researchers conducted some researches mainly through numerical simulation, which could be categorized as one-dimensional model, two-dimensional model and three-dimensional model. For onedimensional model, Karpenko-Jereb et al. [23] described the dependence of diffusion and electro-osmotic coefficient using linear functions through establishing a model for development describing charge transport and water in the fuel cell. This model considered three driving forces including electrical potential, concentration and pressure gradients. For two-dimensional model, Lei et al. [24] described the liquid water profiles inside the membrane electrode assembly (MEA) through a two-phase flow, along-the-channel, non-isothermal model, which was taken into account all the major transports and electro-chemical processes except for the reactant species crossover through the membrane. For three-dimensional model, Houreh and Afshari [25] developed a model which was consisted of a set of coupled equations including conservations of mass, momentum, species and energy to study and compare the performance of humidifiers with counter-flow and parallel-flow configurations. The results revealed that at dry side, an increase in temperature and a decrease in mass flow rate resulted in a better humidification performance. Iranzo et al. [26] presented a CFD 50 cm2 fuel cell model to predict the liquid water distributions inside the fuel cell. The model was validated against a piece of experimental data. The results revealed the model values matched well the experimental values. They also compared the local liquid water distributions predicted by the model with the liquid water distributions of the real cell. The qualitative results showed a good agreement between them. However, the numerical simulation on the PEMFC may not be sufficient and accurate, experimental study can be complimentary to the simulation. Several researchers also did experimental researches from two aspects: single fuel cell and fuel cell stack. For single fuel cell, Zhang et al. [27] studied three operational parameters including back pressure, RH and air stoichiometry had influences on the performance of PEMFC. Their results showed that the performance of PEMFC was better with the increase of the RH, but the stability sustained. For fuel cell stack, Nandjou et al. [28] conducted the durability test to study and quantify effects on automotive application. In the test, they investigated the local performance by in situ measurement of a printed circuit board. They found that local deposits in the cell were caused by water evaporation and the probability of the bipolar plate corrosion increased largely with accumulated water condensation. F. Migliardini et al. [29] conducted the experiments on PEMFC stacks of three different sizes.
2. IHE model The IHE model introduces the item of electro-migration water content in Springer [30] model ϕwh , which is water content produced by electrochemical reactions. This item is related to the current density of PEMFC. The water content of electro-migration in the proton exchange membrane is:
ϕwh = nd
I F
(1)
where ϕwh is the water content produced by electrochemical reactions (mol/(cm2 ·s) ), I the current density (A/cm2 ), F Faraday constant (96,487 C/mol ), nd electro migration coefficient [31] namely the number of water molecules per proton transfer and λ is water content in proton exchange membranes namely the number of water molecules per sulfonic acid group. 2
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3.2. Geometric model
According to the measurements of Springer and so on, we know:
nd =
2.5λ 22
Fig. 2 shows the geometric model of PEMFC. The regions of PEMFC geometric model are shown in Fig. 2(a) and the straight flow channels are shown in Fig. 2(b). The PEMFC geometric model is established by Gambit and constituted of 9 parts including anode current collector, anode channels, anode diffusion layer, anode catalyst layer, proton exchange membrane, cathode catalyst layer, cathode diffusion layer, cathode channels and cathode current collector. It has 56 straight channels consisted of both 28 anode channels (hydrogen) and 28 cathode channels (air). The sizes of PEMFC geometric model are shown in Table 1. Among them, the ridge width in Table 1 is defined the gap of neighbor channels along the direction of width.
(2)
The relationship between λ and water saturation α is [32]:
λ = 0.043 + 17.81α−39.85α 2 + 36.0α3 λ = 14.0 + 1.4(α−1) 1 ⩽ α ⩽ 3 λ = 16.8 α > 3
α<1 (3)
PWV Psat
is water saturation, PWV the water vapor pressure (Pa) , where α = and Psat (T) is saturation pressure (Pa ) [33]. The water content of the humidified gas is:
ϕwih = dQm
(4)
d = 622φPs /(P−φPs )
(5)
Qm = Qm,H2 + Qm,Air
(6)
Qm,H2 =
Iλ H2 N Iλ H2 N MH2 = × 10−3 2F F
(7)
Qm,Air =
IλAir N 1 Iλ N × × MAir = Air × 34.52 × 10−3 4F 0.21 F
(8)
3.3. Computational meshes The computational meshes are shown in Fig. 3. Each part of the geometric model is partitioned according to the order from line to face to volume. For multi body meshes generation, the topological relationship among them should be considered. Otherwise, when the ahead meshes partition are completed, the back meshes partition maybe occur errors. In this work, non-conformal meshes are employed to reduce the meshes partition workload and improve the meshes quality. The computational meshes amounts of each part are shown in Table 2.
where ϕwih is the water content of the humidified gas (mol/(cm2 ·s) ), d humidity ratio (g/kg ), Qm mass flow (kg/s ), φ relative humidity (%), Ps water vapor saturation pressure (Pa), P atmospheric pressure (Pa), Qm,H2 H2 mass flow (kg/s ), λ H2 H2 excess coefficient, N series connection cell number, F Faraday constant (96,487 C/mol ) and Qm,Air is air mass flow (kg/s ). The total water content of PEMFC is:
ϕw = ϕwh + ϕwih
4. Experimental Fig. 4 shows the schematic of the experimental system used in this work. Pure hydrogen (dry or humidified) as fuel and air (dry or
(9)
Start
The inlet humidification efficiency is:
eih =
ϕwih ϕwih = ϕw ϕwh + ϕwih
Modelling
(10)
From Eq. (1), we know:
I=
ϕwh F nd
Partitioning Meshes
(11)
From Eq. (10), we know:
ϕwh =
ϕwih (1−eih) eih
Importing IHE Model (12)
From Eqs. (11) and (12), we get:
I=
ϕwih (1−eih) F × eih nd
Setting up parameters (13)
Calculating
3. Calculation 3.1. Schedule diagram of calculation
N.
Satisfied
Fig. 1 shows the schedule diagram of the calculation. The geometric model is established according to actual size of PEMFC and conducted the mesh partition. The mesh quality is checked by Fluent. If the mesh quality is qualified, the IHE model is imported into Fluent and relevant parameters including material parameters and boundary conditions are set up. Then the numerical model is initialized and then calculated. The function curve convergence in the calculation process is paid attention and adjusted the relevant parameters to make the function curve converge. Finally, the calculated results are output. Otherwise, the meshes are re-divide until the mesh quality is qualified and then calculated according to the above steps.
Y. Output
End Fig. 1. Schedule diagram of calculation.
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Anode channels Anode current collector
Anode diffusion layer Anode catalyst layer Membrane Cathode catalyst layer
Cathode current collector Cathode channels
Cathode diffusion layer
(a)
(b) Fig. 2. Geometric model: (a) schematic of PEMFC model regions and (b) schematic of straight flow channels.
Table 1 PEMFC geometric model sizes. Quantity (units)
Anode
Cathode
Length of channels (mm) Width of channels (mm) Ridge width of channels (mm) Depth of channels (mm) Thickness of collector plate (mm)
250 1.2 0.8 0.6 2
250 1.2 0.8 0.8 2
humidified) as oxidant are used. The pressures of the hydrogen and air are controlled by the electromagnetic valves. And the flow rates of them are measured by the flowmeters. The humidity and temperature of reaction gases are controlled by the humidifiers. The humidification of hydrogen and air is conducted in humidifier by a simple bubbling process. In order to control the import and export of reaction gases, the personal computer (PC) controls the opening and closing of each valve. To realize inlet humidification, PC controls the humidifiers of experimental system. In order to avoid the interference of the operating temperature fluctuation on the performance of PEMFC, the operating temperature of PEMFC is maintained 70 °C. The reaction gases are passed into PEMFC (hydrogen from the anode channels and air from the cathode channels). The reaction gases supplied by hydrogen cylinder and air compressor are provided through respective intake devices including filter, electromagnetic valve, flowmeter and so on. The 40% RH, 55% RH, 70% RH, 85% RH and 100% RH are respectively controlled through humidifying and temperature control devices including humidifier, filter, deionizing water storage tank and so on. The reaction
Fig. 3. Computational meshes.
gases enter the PEMFC and fully react to generate water. The discharged mixture is conducted the water vapor separation. When the water produced by the reactions reaches the specified amount, the electromagnetic valve is opened to drainage. The experimental data are 4
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(70 °C).
Table 2 Computational meshes amounts of each PEMFC element. Parameters
Amounts
Anode current collector Anode channels Anode diffusion layer Anode catalyst layer Proton exchange membrane Cathode catalyst layer Cathode diffusion layer Cathode channels Cathode current collector
833,581 222,892 288,000 288,000 288,000 288,000 288,000 274,464 949,116
5.1.2. Contours of H2 O molar concentrations in cathode channels In Fig. 6, the molar concentrations of H2 O in cathode channels under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 6(a)–(e) show the molar concentrations of H2 O in cathode 5.97 × 10−3− 4.34 × 10−3−8.84 × 10−3 kmol/m3, channels are − 3 − 2 3 − 3 3 9.22 × 7.59 × 10 −1.15 × 10 kmol/m , 9.47 × 10 kmol/m , 10−3−1.51 × 10−2 kmol/m3 and 1.08 × 10−2−1.93 × 10−2 kmol/m3. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the H2 O molar concentrations in cathode 3.50 × 10−3 kmol/m3, 4.50 × 10−3 kmol/m3 , channels are − 3 3 − 3 3 3.91 × 10 kmol/m , 5.88 × 10 kmol/m and 8.50 × 10−3 kmol/m3 , respectively. The working condition of minimum difference is 55% RH (70 °C).
collected and processed through the data processing system. Finally, the polarization curves of every operating condition are obtained. In addition, the system is equipped with safety protection device. When the errors or problems of the system is emerged, the system will automatically switch the hydrogen replaced by nitrogen. The anode channels are swept by nitrogen according to non-humidification route.
5.1.3. Contours of membrane water content In Fig. 7, the membrane water content under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 7(a)–(e) reveal the membrane water content is respectively 3.05%–11.2%, 3.78%–11.5%, 5.83%–12.9%, 9.46%–14.6% and 9.78%–14.9%. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the membrane water content are 8.15%, 7.72%, 7.07%, 5.14% and 5.12%, respectively. The working condition of minimum difference is 100% RH (70 °C).
5. Results and discussion 5.1. Contours 5.1.1. Contours of H2 O molar concentrations in anode channels In Fig. 5, the molar concentrations of H2 O in anode channels under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 5(a)–(e) show the molar concentrations of H2 O in anode 6.11 × 10−3− 4.45 × 10−3−7.47 × 10−3 kmol/m3 , channels are 9.41 × 7.78 × 10−3−9.84 × 10−3 kmol/m3, 7.99 × 10−3 kmol/m3 , 10−3−1.06 × 10−2 kmol/m3 and 6.82 × 10−3−1.09 × 10−2 kmol/m3. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the H2 O molar concentrations in anode 1.88 × 10−3 kmol/m3 , 3.02 × 10−3 kmol/m3, channels are 2.06 × 10−3 kmol/m3 , 1.19 × 10−3 kmol/m3 and 4.08 × 10−3 kmol/m3, respectively. The working condition of minimum difference is 85% RH Pressure Gauge Filter
5.2. Polarization curves 5.2.1. 40% relative humidity Fig. 8 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 40% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be
Electromagnetic Valve Data Processing System
Humidifier
Reducing Valve Hydrogen
Hydrogen outlet Air outlet
Nitrogen
Anode PEMFC
Electronic Load
Cathode
Thermometer
Flowmeter Air Compressor Deionizing Water Storage Tank
Water Storage Tank
Waste Water Collector
Fig. 4. Schematic of the experimental system.
5
Legend
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 5. Contours of H2 O molar concentrations (kmol/m3 ) in anode channels.
experimental is 2.8 × 10−3 V/(mA/cm2) , 3.0 × 10−3 V/(mA/cm2) and 2.8 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.67 V, 0.89 V to 0.70 V and 0.84 V to 0.65 V, respectively. And the average decline of the IHE model, the Fluent model and
divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.99 V to 0.85 V, 1.04 V to 0.89 V and 0.98 V to 0.84 V, respectively. And the average decline of the IHE model, the Fluent model and 6
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 6. Contours of H2 O molar concentrations (kmol/m3 ) in cathode channels.
experimental is 6.0 × 10−4 V/(mA/cm2) , 6.3 × 10−4 V/(mA/cm2) and 6.3 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 79% compared with the Fluent model. At the whole state of voltage drop, the difference of the IHE
model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water 7
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 7. Contours of membrane water content (%).
(0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the
content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density 8
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PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is far away from the experimental. Because when the inlet RH is 55%, the inlet humidification efficiency is 52%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 40% RH. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 235 mW/cm2 , 242 mW/cm2 and 225 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.67 mW/mA , 0.69 mW/mA and 0.65 mW/mA , respectively.
Fig. 8. Polarization curves of experimental, the IHE model and the Fluent model at 40% RH (70 °C).
hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is very close to experimental. Because when the inlet RH is 40%, the inlet humidification efficiency is 57%. It means that the influences of the inlet humidification on the performance of PEMFC are great. The IHE model exactly takes account of these influences. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 235 mW/cm2 , 245 mW/cm2 and 230 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.67 mW/mA , 0.70 mW/mA and 0.66 mW/mA , respectively.
5.2.3. 70% relative humidity Fig. 10 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 70% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.02 V to 0.85 V, 1.05 V to 0.87 V and 0.99 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3 V/(mA/cm2) , 3.6 × 10−3 V/(mA/cm2) and 3.4 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the
5.2.2. 55% relative humidity Fig. 9 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 55% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.00 V to 0.85 V, 1.04 V to 0.88 V and 0.98 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.0 × 10−3 V/(mA/cm2) , 3.2 × 10−3 V/(mA/cm2) and 3.2 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.67 V, 0.88 V to 0.69 V and 0.82 V to 0.65 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 6.0 × 10−4 V/(mA/cm2) , 6.3 × 10−4 V/(mA/cm2) and 5.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 51% compared with the Fluent model. At the state of voltage decrease, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of
Fig. 9. Polarization curves of experimental, the IHE model and the Fluent model at 55% RH (70 °C).
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Fig. 10. Polarization curves of experimental, the IHE model and the Fluent model at 70% RH (70 °C).
Fig. 11. Polarization curves of experimental, the IHE model and the Fluent model at 85% RH (70 °C).
voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.70 V, 0.87 V to 0.71 V and 0.82 V to 0.66 V, respectively. And the average decline of the IHE model, the Fluent 5.0 × 10−4 V/(mA/cm2) , model and experimental is − 4 2 − 4 5.3 × 10 V/(mA/cm ) and 5.3 × 10 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 25% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is further from experimental and closer to the Fluent model than at 55% RH. Because when the inlet RH is 70%, the inlet humidification efficiency is 43%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 55% RH. So the polarization curve of the IHE model is further from experimental and closer to the Fluent model. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 244 mW/cm2 , 247 mW/cm2 and 231 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.70 mW/mA , 0.71 mW/mA and 0.67 mW/mA , respectively.
5.2.4. 85% relative humidity Fig. 11 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 85% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.04 V to 0.87 V, 1.06 V to 0.88 V and 1.00 V to 0.83 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3V/(mA/cm2) , 3.6 × 10−3V/(mA/cm2) and 3.4 × 10−3V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.87 V to 0.73 V, 0.88 V to 0.73 V and 0.83 V to 0.69 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 4.7 × 10−4 V/(mA/cm2) , 5.0 × 10−4 V/(mA/cm2) and 4.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 10% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density.
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density variation trend shows that the power density is approximately linear with the current density. The power density slope of the IHE model, the Fluent model and experimental are 0.73 mW/mA , 0.73 mW/mA and 0.68 mW/mA , respectively.
The polarization curve of the IHE model is very close to the Fluent model. Because when the inlet RH is 85%, the inlet humidification efficiency is 36%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 70% RH. So the polarization curve of the IHE model is very close to the Fluent model. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 253 mW/cm2 , 255 mW/cm2 and 238 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.73 mW/mA , 0.73 mW/mA and 0.69 mW/mA , respectively.
6. Conclusions In the present study, the IHE model for PEMFC is established. It provides several contours of H2 O molar concentrations (both in anode channels and cathode channels) and membrane water content (MWC). The species distributions inside PEMFC and the polarization curves of the IHE model, the Fluent model and experimental at different RH (40%, 55%, 70%, 85% and 100%) are compared and analyzed. For real applications, the IHE model has two aspects: on one hand, the appropriate relative humidity (RH) of PEMFC under the different RH is provided by analyzing the inlet gas humidification efficiency and the performance of PEMFC. On the other hand, a new approach for the calculation of the current density of PEMFC is provided. This approach could forecast the current density of PEMFC through the inlet humidification efficiency and water content of the humidified gas without conducting the experiments. The conclusions are as follows:
5.2.5. 100% relative humidity Fig. 12 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 100% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.04 V to 0.87 V, 1.06 V to 0.89 V and 0.99 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3V/(mA/cm2) , 3.4 × 10−3V/(mA/cm2) and 3.4 × 10−3V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.87 V to 0.73 V, 0.89 V to 0.73 V and 0.82 V to 0.68 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 4.7 × 10−4 V/(mA/cm2) , 5.3 × 10−4 V/(mA/cm2) and 4.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 4% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is very close to the Fluent model. Because when the inlet RH is 100%, the inlet humidification efficiency is 22%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 85% RH. So the polarization curve of the IHE model is very close to the Fluent model. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 254 mW/cm2 , 256 mW/cm2 and 235 mW/cm2 when the current density is 350 mA/cm2 . The power
(1) When the PEMFC at low RH, the IHE model distribution uniformities of indices such as H2 O molar concentrations (in anode channels and cathode channels) and MWC are good. (2) With the increase of the RH of PEMFC, the accuracy of the IHE model decreases. When the inlet RH is 40%, 55%, 70%, 85% and 100% (70 °C and 350 mA/cm2 ), the accuracy of the IHE model is improved by 79%, 51%, 25%, 10% and 4% compared with the Fluent model. (3) With the increase of the RH of PEMFC, the inlet humidification efficiency decreases. When the inlet RH is 40%, 55%, 70%, 85% and 100% (70 °C and 350 mA/cm2 ), the inlet humidification efficiency is 57%, 52%, 43%, 36% and 22%, respectively.
Acknowledgment This work was supported by the National Key Research and Development Program (2016YFB0101305), National Natural Science Foundation of China (Nos. 21376138, 21676158), Beijing Municipal Natural Science Foundation (KZ201510016019), the Scientific Research Project of Beijing Educational Committee (KM201510016011) and State Key Laboratory of Engines, Tianjin University (K2017-07).
Fig. 12. Polarization curves of experimental, the IHE model and the Fluent model at 100% RH (70 °C).
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Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Asymptotic analysis for the inlet relative humidity effects on the performance of proton exchange membrane fuel cell ⁎
Yongfeng Liua, , Lei Fana, Pucheng Peib, Shengzhuo Yaoa, Fang Wanga a
Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, School of Mechanical-electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China b State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China
H I G H L I G H T S inlet humidification efficiency (IHE) model is proposed. • AThenovel model could carry out the dynamic inlet humidification efficiency. • The IHE of species distribution are shown to make up the experiments. • The contours • inlet humidification efficiency is 57% at 40% RH (70 °C operating temperature).
A R T I C L E I N F O
A B S T R A C T
Keywords: PEMFC Relative humidity Gas humidification Computational fluid dynamics Inlet humidification efficiency
In order to study the inlet relative humidity (RH) effects on the performance of proton exchange membrane fuel cell (PEMFC), the inlet humidification efficiency (IHE) model is proposed. The total water content of PEMFC is consisted of two parts including the internal electro-migration water content and the external water content of the humidified gas. The dynamic inlet humidification efficiency is derived. The current density of PEMFC is calculated by the incorporating parameters including inlet humidification efficiency and water content of the humidified gas in the IHE model. Firstly, the schedule diagram of calculation is given and the geometric model is established according to actual size of PEMFC. The computational meshes are partitioned by using the software (Gambit). The IHE model is imported into the computational fluid dynamics software (Fluent). Secondly, the experimental system is established and experiments have been done at the operating temperature of 70 °C and at 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. Finally, the contours of H2 O molar concentrations (both in anode channels and cathode channels), membrane water content (MWC) and polarization curves of the IHE model, the Fluent model and experimental are compared and analyzed at above experimental conditions. The results show that the species distribution uniformities of the IHE model such as H2 O molar concentrations (both in anode channels and cathode channels) and MWC are the best when the PEMFC at 100% RH. When the operating temperature is 70 °C (40% RH and 350 mA/cm2 ), the accuracy of the IHE model is improved by 79% compared with the Fluent model. When the operating temperature is 70 °C (40% RH and 350 mA/cm2 ), the inlet humidification efficiency reaches 57%.
1. Introduction In recent years, owing to the environmental pollution problems and major concerns on the depletion of petroleum based energy resources, the interests of the various types of clean power sources and renewable energies are more focused [1–6]. Among them, proton exchange membrane fuel cell (PEMFC) is a new kind of the renewable energyconversion device which directly converted the chemical energy of hydrogen and oxygen into electrical energy and heat through the
⁎
electrochemical reactions [6–15]. PEMFC has high energy conversion, high efficiency, low emissions, highly reliability, low operation temperature (20–90 °C) with the consequent quick start-up and other advantages [5,8,16–22]. However, there are several issues in commercialization of PEMFC [20]. Among them, one of the most important issues is water management problem, which is mainly managed two parts including both the water content of humidified gas and the electro-migration water content. The water content of the humidified gas is affected deeply by relative humidity (RH). Hence, many
Corresponding author. E-mail address: [email protected] (Y. Liu).
https://doi.org/10.1016/j.apenergy.2017.11.008 Received 11 June 2017; Received in revised form 4 October 2017; Accepted 2 November 2017 0306-2619/ © 2017 Published by Elsevier Ltd.
Please cite this article as: Liu, Y., Applied Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.11.008
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Nomenclature
ϕwh
nd I F λ α PWV Psat (T) ϕwih d Qm φ Ps P
Qm,H2 λ H2 N Qm,Air ϕw eih
water content produced by electrochemical reactions, mol/(cm2 ·s) electro migration coefficient current density, A/cm2 Faraday constant, 96,487 C/mol water content in proton exchange membranes water saturation water vapor pressure, Pa saturation pressure, Pa water content of the humidified gas, mol/(cm2 ·s) humidity ratio, g/kg mass flow, kg/s relative humidity, % water vapor saturation pressure, Pa atmospheric pressure, Pa
H2 mass flow, kg/s H2 excess coefficient series connection cell number air mass flow, kg/s total water content of PEMFC, mol/(cm2·s) inlet humidification efficiency
Abbreviation PEMFC RH IHE MWC MEA CFD PEM
proton exchange membrane fuel cell relative humidity inlet humidification efficiency membrane water content membrane electrode assembly computational fluid dynamics proton exchange membrane
Then they analyzed humidification problems of PEMFC and considered the internal and external humidification methods. The effects on humidification methods of membrane hydration were evaluated by its power loss rate and the performance of stacks. The external humidification was effective in most operating conditions. But the effects of external humidification were limited when the stacks had high temperature, low load or the membrane is in a dry state. Many researchers made valuable achievements in the field of RH for the performance of PEMFC through simulation and experiments, but they qualitatively studied the effects from the variation trend and did not have a quantitative analysis for the RH effects on the performance of PEMFC. In this paper, firstly, the inlet humidification efficiency (IHE) model is proposed. The inlet humidification efficiency is calculated by the internal electro-migration water content and the external water content of the humidified gas in the IHE model. Furthermore, the current density of PEMFC is calculated by the inlet humidification efficiency and the water content of the humidified gas. Secondly, the schedule diagram of calculation is given and the geometric model is established according to actual size of PEMFC. The computational meshes are partitioned by using the software (Gambit). The IHE model is imported into the computational fluid dynamics software (Fluent). The experimental system of PEMFC is established. The experiments are conducted at the operating temperature of 70 °C, at 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. Finally, the contours of H2 O molar concentrations (both in anode channels and cathode channels), membrane water content (MWC) and the polarization curves of the IHE model, the Fluent model and experimental are compared and analyzed at above experimental conditions.
researchers took active steps to research the effects of RH on the performance of PEMFC and improve the performance of PEMFC. Owing to a lot of difficulties in measuring species movement and distribution inside PEMFC, numerical simulation has become an effective research method to solve above problems at a certain extent. Several researchers conducted some researches mainly through numerical simulation, which could be categorized as one-dimensional model, two-dimensional model and three-dimensional model. For onedimensional model, Karpenko-Jereb et al. [23] described the dependence of diffusion and electro-osmotic coefficient using linear functions through establishing a model for development describing charge transport and water in the fuel cell. This model considered three driving forces including electrical potential, concentration and pressure gradients. For two-dimensional model, Lei et al. [24] described the liquid water profiles inside the membrane electrode assembly (MEA) through a two-phase flow, along-the-channel, non-isothermal model, which was taken into account all the major transports and electro-chemical processes except for the reactant species crossover through the membrane. For three-dimensional model, Houreh and Afshari [25] developed a model which was consisted of a set of coupled equations including conservations of mass, momentum, species and energy to study and compare the performance of humidifiers with counter-flow and parallel-flow configurations. The results revealed that at dry side, an increase in temperature and a decrease in mass flow rate resulted in a better humidification performance. Iranzo et al. [26] presented a CFD 50 cm2 fuel cell model to predict the liquid water distributions inside the fuel cell. The model was validated against a piece of experimental data. The results revealed the model values matched well the experimental values. They also compared the local liquid water distributions predicted by the model with the liquid water distributions of the real cell. The qualitative results showed a good agreement between them. However, the numerical simulation on the PEMFC may not be sufficient and accurate, experimental study can be complimentary to the simulation. Several researchers also did experimental researches from two aspects: single fuel cell and fuel cell stack. For single fuel cell, Zhang et al. [27] studied three operational parameters including back pressure, RH and air stoichiometry had influences on the performance of PEMFC. Their results showed that the performance of PEMFC was better with the increase of the RH, but the stability sustained. For fuel cell stack, Nandjou et al. [28] conducted the durability test to study and quantify effects on automotive application. In the test, they investigated the local performance by in situ measurement of a printed circuit board. They found that local deposits in the cell were caused by water evaporation and the probability of the bipolar plate corrosion increased largely with accumulated water condensation. F. Migliardini et al. [29] conducted the experiments on PEMFC stacks of three different sizes.
2. IHE model The IHE model introduces the item of electro-migration water content in Springer [30] model ϕwh , which is water content produced by electrochemical reactions. This item is related to the current density of PEMFC. The water content of electro-migration in the proton exchange membrane is:
ϕwh = nd
I F
(1)
where ϕwh is the water content produced by electrochemical reactions (mol/(cm2 ·s) ), I the current density (A/cm2 ), F Faraday constant (96,487 C/mol ), nd electro migration coefficient [31] namely the number of water molecules per proton transfer and λ is water content in proton exchange membranes namely the number of water molecules per sulfonic acid group. 2
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3.2. Geometric model
According to the measurements of Springer and so on, we know:
nd =
2.5λ 22
Fig. 2 shows the geometric model of PEMFC. The regions of PEMFC geometric model are shown in Fig. 2(a) and the straight flow channels are shown in Fig. 2(b). The PEMFC geometric model is established by Gambit and constituted of 9 parts including anode current collector, anode channels, anode diffusion layer, anode catalyst layer, proton exchange membrane, cathode catalyst layer, cathode diffusion layer, cathode channels and cathode current collector. It has 56 straight channels consisted of both 28 anode channels (hydrogen) and 28 cathode channels (air). The sizes of PEMFC geometric model are shown in Table 1. Among them, the ridge width in Table 1 is defined the gap of neighbor channels along the direction of width.
(2)
The relationship between λ and water saturation α is [32]:
λ = 0.043 + 17.81α−39.85α 2 + 36.0α3 λ = 14.0 + 1.4(α−1) 1 ⩽ α ⩽ 3 λ = 16.8 α > 3
α<1 (3)
PWV Psat
is water saturation, PWV the water vapor pressure (Pa) , where α = and Psat (T) is saturation pressure (Pa ) [33]. The water content of the humidified gas is:
ϕwih = dQm
(4)
d = 622φPs /(P−φPs )
(5)
Qm = Qm,H2 + Qm,Air
(6)
Qm,H2 =
Iλ H2 N Iλ H2 N MH2 = × 10−3 2F F
(7)
Qm,Air =
IλAir N 1 Iλ N × × MAir = Air × 34.52 × 10−3 4F 0.21 F
(8)
3.3. Computational meshes The computational meshes are shown in Fig. 3. Each part of the geometric model is partitioned according to the order from line to face to volume. For multi body meshes generation, the topological relationship among them should be considered. Otherwise, when the ahead meshes partition are completed, the back meshes partition maybe occur errors. In this work, non-conformal meshes are employed to reduce the meshes partition workload and improve the meshes quality. The computational meshes amounts of each part are shown in Table 2.
where ϕwih is the water content of the humidified gas (mol/(cm2 ·s) ), d humidity ratio (g/kg ), Qm mass flow (kg/s ), φ relative humidity (%), Ps water vapor saturation pressure (Pa), P atmospheric pressure (Pa), Qm,H2 H2 mass flow (kg/s ), λ H2 H2 excess coefficient, N series connection cell number, F Faraday constant (96,487 C/mol ) and Qm,Air is air mass flow (kg/s ). The total water content of PEMFC is:
ϕw = ϕwh + ϕwih
4. Experimental Fig. 4 shows the schematic of the experimental system used in this work. Pure hydrogen (dry or humidified) as fuel and air (dry or
(9)
Start
The inlet humidification efficiency is:
eih =
ϕwih ϕwih = ϕw ϕwh + ϕwih
Modelling
(10)
From Eq. (1), we know:
I=
ϕwh F nd
Partitioning Meshes
(11)
From Eq. (10), we know:
ϕwh =
ϕwih (1−eih) eih
Importing IHE Model (12)
From Eqs. (11) and (12), we get:
I=
ϕwih (1−eih) F × eih nd
Setting up parameters (13)
Calculating
3. Calculation 3.1. Schedule diagram of calculation
N.
Satisfied
Fig. 1 shows the schedule diagram of the calculation. The geometric model is established according to actual size of PEMFC and conducted the mesh partition. The mesh quality is checked by Fluent. If the mesh quality is qualified, the IHE model is imported into Fluent and relevant parameters including material parameters and boundary conditions are set up. Then the numerical model is initialized and then calculated. The function curve convergence in the calculation process is paid attention and adjusted the relevant parameters to make the function curve converge. Finally, the calculated results are output. Otherwise, the meshes are re-divide until the mesh quality is qualified and then calculated according to the above steps.
Y. Output
End Fig. 1. Schedule diagram of calculation.
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Anode channels Anode current collector
Anode diffusion layer Anode catalyst layer Membrane Cathode catalyst layer
Cathode current collector Cathode channels
Cathode diffusion layer
(a)
(b) Fig. 2. Geometric model: (a) schematic of PEMFC model regions and (b) schematic of straight flow channels.
Table 1 PEMFC geometric model sizes. Quantity (units)
Anode
Cathode
Length of channels (mm) Width of channels (mm) Ridge width of channels (mm) Depth of channels (mm) Thickness of collector plate (mm)
250 1.2 0.8 0.6 2
250 1.2 0.8 0.8 2
humidified) as oxidant are used. The pressures of the hydrogen and air are controlled by the electromagnetic valves. And the flow rates of them are measured by the flowmeters. The humidity and temperature of reaction gases are controlled by the humidifiers. The humidification of hydrogen and air is conducted in humidifier by a simple bubbling process. In order to control the import and export of reaction gases, the personal computer (PC) controls the opening and closing of each valve. To realize inlet humidification, PC controls the humidifiers of experimental system. In order to avoid the interference of the operating temperature fluctuation on the performance of PEMFC, the operating temperature of PEMFC is maintained 70 °C. The reaction gases are passed into PEMFC (hydrogen from the anode channels and air from the cathode channels). The reaction gases supplied by hydrogen cylinder and air compressor are provided through respective intake devices including filter, electromagnetic valve, flowmeter and so on. The 40% RH, 55% RH, 70% RH, 85% RH and 100% RH are respectively controlled through humidifying and temperature control devices including humidifier, filter, deionizing water storage tank and so on. The reaction
Fig. 3. Computational meshes.
gases enter the PEMFC and fully react to generate water. The discharged mixture is conducted the water vapor separation. When the water produced by the reactions reaches the specified amount, the electromagnetic valve is opened to drainage. The experimental data are 4
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(70 °C).
Table 2 Computational meshes amounts of each PEMFC element. Parameters
Amounts
Anode current collector Anode channels Anode diffusion layer Anode catalyst layer Proton exchange membrane Cathode catalyst layer Cathode diffusion layer Cathode channels Cathode current collector
833,581 222,892 288,000 288,000 288,000 288,000 288,000 274,464 949,116
5.1.2. Contours of H2 O molar concentrations in cathode channels In Fig. 6, the molar concentrations of H2 O in cathode channels under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 6(a)–(e) show the molar concentrations of H2 O in cathode 5.97 × 10−3− 4.34 × 10−3−8.84 × 10−3 kmol/m3, channels are − 3 − 2 3 − 3 3 9.22 × 7.59 × 10 −1.15 × 10 kmol/m , 9.47 × 10 kmol/m , 10−3−1.51 × 10−2 kmol/m3 and 1.08 × 10−2−1.93 × 10−2 kmol/m3. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the H2 O molar concentrations in cathode 3.50 × 10−3 kmol/m3, 4.50 × 10−3 kmol/m3 , channels are − 3 3 − 3 3 3.91 × 10 kmol/m , 5.88 × 10 kmol/m and 8.50 × 10−3 kmol/m3 , respectively. The working condition of minimum difference is 55% RH (70 °C).
collected and processed through the data processing system. Finally, the polarization curves of every operating condition are obtained. In addition, the system is equipped with safety protection device. When the errors or problems of the system is emerged, the system will automatically switch the hydrogen replaced by nitrogen. The anode channels are swept by nitrogen according to non-humidification route.
5.1.3. Contours of membrane water content In Fig. 7, the membrane water content under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 7(a)–(e) reveal the membrane water content is respectively 3.05%–11.2%, 3.78%–11.5%, 5.83%–12.9%, 9.46%–14.6% and 9.78%–14.9%. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the membrane water content are 8.15%, 7.72%, 7.07%, 5.14% and 5.12%, respectively. The working condition of minimum difference is 100% RH (70 °C).
5. Results and discussion 5.1. Contours 5.1.1. Contours of H2 O molar concentrations in anode channels In Fig. 5, the molar concentrations of H2 O in anode channels under different RH are compared to evaluate the influences of RH on the performance of PEMFC. The operating conditions of PEMFC are 70 °C operating temperature and 40% RH, 55% RH, 70% RH, 85% RH and 100% RH, respectively. The excess coefficients of anode and cathode are 1.2 and 2.0, respectively. Fig. 5(a)–(e) show the molar concentrations of H2 O in anode 6.11 × 10−3− 4.45 × 10−3−7.47 × 10−3 kmol/m3 , channels are 9.41 × 7.78 × 10−3−9.84 × 10−3 kmol/m3, 7.99 × 10−3 kmol/m3 , 10−3−1.06 × 10−2 kmol/m3 and 6.82 × 10−3−1.09 × 10−2 kmol/m3. They are generally expanded with the increase of RH ranged from 40% to 100%. The differences of the H2 O molar concentrations in anode 1.88 × 10−3 kmol/m3 , 3.02 × 10−3 kmol/m3, channels are 2.06 × 10−3 kmol/m3 , 1.19 × 10−3 kmol/m3 and 4.08 × 10−3 kmol/m3, respectively. The working condition of minimum difference is 85% RH Pressure Gauge Filter
5.2. Polarization curves 5.2.1. 40% relative humidity Fig. 8 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 40% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be
Electromagnetic Valve Data Processing System
Humidifier
Reducing Valve Hydrogen
Hydrogen outlet Air outlet
Nitrogen
Anode PEMFC
Electronic Load
Cathode
Thermometer
Flowmeter Air Compressor Deionizing Water Storage Tank
Water Storage Tank
Waste Water Collector
Fig. 4. Schematic of the experimental system.
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 5. Contours of H2 O molar concentrations (kmol/m3 ) in anode channels.
experimental is 2.8 × 10−3 V/(mA/cm2) , 3.0 × 10−3 V/(mA/cm2) and 2.8 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.67 V, 0.89 V to 0.70 V and 0.84 V to 0.65 V, respectively. And the average decline of the IHE model, the Fluent model and
divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.99 V to 0.85 V, 1.04 V to 0.89 V and 0.98 V to 0.84 V, respectively. And the average decline of the IHE model, the Fluent model and 6
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 6. Contours of H2 O molar concentrations (kmol/m3 ) in cathode channels.
experimental is 6.0 × 10−4 V/(mA/cm2) , 6.3 × 10−4 V/(mA/cm2) and 6.3 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 79% compared with the Fluent model. At the whole state of voltage drop, the difference of the IHE
model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water 7
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(a) 40%RH
(c) 70%RH
(b) 55%RH
(d) 85%RH
(e) 100%RH Fig. 7. Contours of membrane water content (%).
(0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the
content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density 8
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PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is far away from the experimental. Because when the inlet RH is 55%, the inlet humidification efficiency is 52%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 40% RH. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 235 mW/cm2 , 242 mW/cm2 and 225 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.67 mW/mA , 0.69 mW/mA and 0.65 mW/mA , respectively.
Fig. 8. Polarization curves of experimental, the IHE model and the Fluent model at 40% RH (70 °C).
hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is very close to experimental. Because when the inlet RH is 40%, the inlet humidification efficiency is 57%. It means that the influences of the inlet humidification on the performance of PEMFC are great. The IHE model exactly takes account of these influences. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 235 mW/cm2 , 245 mW/cm2 and 230 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.67 mW/mA , 0.70 mW/mA and 0.66 mW/mA , respectively.
5.2.3. 70% relative humidity Fig. 10 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 70% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.02 V to 0.85 V, 1.05 V to 0.87 V and 0.99 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3 V/(mA/cm2) , 3.6 × 10−3 V/(mA/cm2) and 3.4 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the
5.2.2. 55% relative humidity Fig. 9 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 55% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.00 V to 0.85 V, 1.04 V to 0.88 V and 0.98 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.0 × 10−3 V/(mA/cm2) , 3.2 × 10−3 V/(mA/cm2) and 3.2 × 10−3 V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.67 V, 0.88 V to 0.69 V and 0.82 V to 0.65 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 6.0 × 10−4 V/(mA/cm2) , 6.3 × 10−4 V/(mA/cm2) and 5.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 51% compared with the Fluent model. At the state of voltage decrease, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of
Fig. 9. Polarization curves of experimental, the IHE model and the Fluent model at 55% RH (70 °C).
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Fig. 10. Polarization curves of experimental, the IHE model and the Fluent model at 70% RH (70 °C).
Fig. 11. Polarization curves of experimental, the IHE model and the Fluent model at 85% RH (70 °C).
voltages of the IHE model, the Fluent model and experimental are reduced from 0.85 V to 0.70 V, 0.87 V to 0.71 V and 0.82 V to 0.66 V, respectively. And the average decline of the IHE model, the Fluent 5.0 × 10−4 V/(mA/cm2) , model and experimental is − 4 2 − 4 5.3 × 10 V/(mA/cm ) and 5.3 × 10 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 25% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is further from experimental and closer to the Fluent model than at 55% RH. Because when the inlet RH is 70%, the inlet humidification efficiency is 43%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 55% RH. So the polarization curve of the IHE model is further from experimental and closer to the Fluent model. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 244 mW/cm2 , 247 mW/cm2 and 231 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.70 mW/mA , 0.71 mW/mA and 0.67 mW/mA , respectively.
5.2.4. 85% relative humidity Fig. 11 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 85% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.04 V to 0.87 V, 1.06 V to 0.88 V and 1.00 V to 0.83 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3V/(mA/cm2) , 3.6 × 10−3V/(mA/cm2) and 3.4 × 10−3V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.87 V to 0.73 V, 0.88 V to 0.73 V and 0.83 V to 0.69 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 4.7 × 10−4 V/(mA/cm2) , 5.0 × 10−4 V/(mA/cm2) and 4.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 10% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density.
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density variation trend shows that the power density is approximately linear with the current density. The power density slope of the IHE model, the Fluent model and experimental are 0.73 mW/mA , 0.73 mW/mA and 0.68 mW/mA , respectively.
The polarization curve of the IHE model is very close to the Fluent model. Because when the inlet RH is 85%, the inlet humidification efficiency is 36%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 70% RH. So the polarization curve of the IHE model is very close to the Fluent model. The power density variation trend shows that the power density is approximately linear with the current density. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 253 mW/cm2 , 255 mW/cm2 and 238 mW/cm2 when the current density is 350 mA/cm2 . The power density slopes of the IHE model, the Fluent model and experimental are 0.73 mW/mA , 0.73 mW/mA and 0.69 mW/mA , respectively.
6. Conclusions In the present study, the IHE model for PEMFC is established. It provides several contours of H2 O molar concentrations (both in anode channels and cathode channels) and membrane water content (MWC). The species distributions inside PEMFC and the polarization curves of the IHE model, the Fluent model and experimental at different RH (40%, 55%, 70%, 85% and 100%) are compared and analyzed. For real applications, the IHE model has two aspects: on one hand, the appropriate relative humidity (RH) of PEMFC under the different RH is provided by analyzing the inlet gas humidification efficiency and the performance of PEMFC. On the other hand, a new approach for the calculation of the current density of PEMFC is provided. This approach could forecast the current density of PEMFC through the inlet humidification efficiency and water content of the humidified gas without conducting the experiments. The conclusions are as follows:
5.2.5. 100% relative humidity Fig. 12 shows the polarization curves of the IHE model, the Fluent model and experimental for the PEMFC at 100% RH (70 °C). It can be seen from the voltage variation that three groups of voltage drop trends are similar in the whole voltage drop stage. The voltage drop can be divided into two stages: (a) the voltage drop rapidly stage (0−50 mA/cm2 ) and (b) the voltage drop linearly stage (50−350 mA/cm2 ). When the current density is 0−50 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 1.04 V to 0.87 V, 1.06 V to 0.89 V and 0.99 V to 0.82 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 3.4 × 10−3V/(mA/cm2) , 3.4 × 10−3V/(mA/cm2) and 3.4 × 10−3V/(mA/cm2) , respectively. This stage corresponds to activation losses [34]. When the current density is 50−350 mA/cm2 , the voltages of the IHE model, the Fluent model and experimental are reduced from 0.87 V to 0.73 V, 0.89 V to 0.73 V and 0.82 V to 0.68 V, respectively. And the average decline of the IHE model, the Fluent model and experimental is 4.7 × 10−4 V/(mA/cm2) , 5.3 × 10−4 V/(mA/cm2) and 4.7 × 10−4 V/(mA/cm2) , respectively. This stage corresponds to ohmic polarization losses [35]. When the current density is 350 mA/cm2 , the IHE model accuracy is improved by 4% compared with the Fluent model. At the state of voltage drop, the difference of the IHE model and the Fluent model is decreasing with the increase of current density. Because voltage drop of PEMFC depends on the internal resistance of PEM, while the internal resistance of PEM is affected deeply by the hydration of PEM, which is affected by the water content of PEM. The water content of PEM comes from two parts including the water content of humidified gas and the water content by the electrochemical reactions inside PEMFC. When the current density is low (0−50 mA/cm2 ), the water content of humidified gas plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are large at low current density (0−50 mA/cm2 ). With the increase of the current density, the electrochemical reactions inside PEMFC are gradually increasing and the role of the water content of humidified gas is gradually reducing. When the current density is high (50−350 mA/cm2 ), the water content by the electrochemical reactions inside PEMFC plays a major role in the hydration of PEM. So the effects of the water content of humidified gas on the performance of PEMFC are small at high current density (50−350 mA/cm2 ). The IHE model considers that the role of the water content of humidified gas on the performance of PEMFC under the different RH is variable, while the Fluent model considers that it is stationary. With the increase of current density, the role of the water content of humidified gas on the performance of PEMFC is gradually fading. So the difference of the IHE model and the Fluent model is decreasing with the increase of current density. The polarization curve of the IHE model is very close to the Fluent model. Because when the inlet RH is 100%, the inlet humidification efficiency is 22%. It means that the influences of the inlet humidification on the performance of PEMFC are less than at 85% RH. So the polarization curve of the IHE model is very close to the Fluent model. The maximum power densities of the IHE model, the Fluent model and experimental are respectively 254 mW/cm2 , 256 mW/cm2 and 235 mW/cm2 when the current density is 350 mA/cm2 . The power
(1) When the PEMFC at low RH, the IHE model distribution uniformities of indices such as H2 O molar concentrations (in anode channels and cathode channels) and MWC are good. (2) With the increase of the RH of PEMFC, the accuracy of the IHE model decreases. When the inlet RH is 40%, 55%, 70%, 85% and 100% (70 °C and 350 mA/cm2 ), the accuracy of the IHE model is improved by 79%, 51%, 25%, 10% and 4% compared with the Fluent model. (3) With the increase of the RH of PEMFC, the inlet humidification efficiency decreases. When the inlet RH is 40%, 55%, 70%, 85% and 100% (70 °C and 350 mA/cm2 ), the inlet humidification efficiency is 57%, 52%, 43%, 36% and 22%, respectively.
Acknowledgment This work was supported by the National Key Research and Development Program (2016YFB0101305), National Natural Science Foundation of China (Nos. 21376138, 21676158), Beijing Municipal Natural Science Foundation (KZ201510016019), the Scientific Research Project of Beijing Educational Committee (KM201510016011) and State Key Laboratory of Engines, Tianjin University (K2017-07).
Fig. 12. Polarization curves of experimental, the IHE model and the Fluent model at 100% RH (70 °C).
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