# Optimization of Fuel Cell Stack Consistency Based on Multi-Model

Authors: Yijin Zeng; Jian Huang; Zhiliang Wang; Junxiong Li; Yahui Yi
Journal: Scientific Programming
 (2022)

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## Abstract

With the proposal of cloud computing, fog computing, and edge computing, various simulation operations are greatly guaranteed, which benefits the multi-model operations of Matlab and CFD. This paper established the 1-D flow network model and 12 cm ∗ 8 cm 3-steady-state PEMFC model. Based on the experiment, the intake flow distribution of the cathode anode of 80 cells is simulated to obtain the maximum and minimum intake flow cell. The 3-D and steady-state single-cell model is used to calculate the cell’s performance, and the performance difference between the two cells is improved by optimizing the size structure of the single cell. The results show that the best version of the cell was obtained when the values of the width and depth were 1.1  mm and 0.8  mm, and the power density difference between the two cells decreased from 5.7% to 2.1%. The voltage difference at 1000 mA·cm−2 current density decreases from 0.065 to 0.035 V after optimization. The intake flow extreme difference of the reactor improved significantly, and Cv was reduced by 48.7%.


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## Body

## 1. Introduction

Proton exchange membrane fuel cell (PEMFC) has become one of the ideal energy sources in the 21st century based on the advantages of high specific power, zero emission, and low operating noise. Due to the limited output power of individual PEMFC, fuel cells are usually connected in series to form fuel cell stacks to meet the practical power requirements. The reactants provided by the stack manifold flow through the fuel cell in multiple channels in a complex flow network in the fuel cell stack. The reactant flow and pressure distribution may differ between different cells, and a single cell's heat and water management strategy is challenging to achieve. This will cause the overall performance of the fuel cell stack to decrease [1]. Therefore, it is essential for the study of reactor equilibrium.Generally, the layout of the intake manifold of the fuel cell stack isZ-shaped and U-shaped. In the actual work process, no matter what kind of layout, there is a specific difference in the intake airflow reaching the entrance of every single cell due to the intake loss. What is worse, this difference intensifies as the power of the stack increases (the number of cells increases). Finally, the difference in the intake airflow between the monomers will affect their electrochemical performance. The durability and implementation of the stack will be directly related to the performance of the monomer, which is a typical “bucket effect” [2]. At present, to accelerate the commercialization of fuel cells, many domestic and foreign scholars have done a lot of research on the consistency of the stack. For the consistency of the stack, the industry generally uses the voltage difference coefficient (Cv) to express [3]. The factors that affect the consistency of the stack are usually gas pressure, gas mass flows [4], control methods such as purge mode [5, 6], cell voltage detection level [1, 7], and other factors.In summary, the research on the consistency of the stack is focused on how to improve its consistency through external factors. Because of this, this article will start from the optimization of the flow field size of the single cell and combine it with the data on the airflow distribution of the stack composed of 80 single cells. Take the highest air intake monomer and the lowest air intake monomer as a comparison, optimize the size of the flow field, and minimize the electrochemical performance differences between the two to improve the consistency of the stack. In addition, the industry’s approach to optimizing the size of a single unit mainly starts from the aspects of length [8, 9], depth [10, 11], width [12], and cross-sectional shape [13, 14]. Since the stack size of the article has been fixed and the cell adopts the cathode and anode straight flow field, the article will optimize the cell performance from the width and depth of the flow field.


## 2. Models and Parameters

The paper includes two models: 1-D fuel cell stack and 3-D and steady-state fuel cell monomer straight flow field model. The model and relevant parameters are as follows.


### 2.1. 1-D Fuel Cell Stack Model

#### 2.1.1. Computational Domain of 1-D Model

The computational domain of the one-dimensional model is mainly used to represent the flow distribution of individual units in a stack, which is a schematic diagram of simplified stack flow network configuration. Figure1 shows the current research situation of the fuel cell stack, including the inlet, outlet, manifold, and gas flow channel of the fuel cell stack. In this diagram, the reactants are supplied and transported at the reactor inlet of the top manifold. In this figure, the reactants are supplied at the stack inlet of the top manifold and transported along the top manifold while being assigned to the cell channel. The remaining reactants and products of the electrochemical reaction are discharged into the bottom manifold at the channel outlet and then removed from the fuel cell stack at the fuel cell stack outlet. Traffic network construction and analysis are based on controlling the volume, the i circuit shown in Figure 1. Each loop has six branches (control volume), and the top branch is a segment of the top manifold connecting adjacent units. The bottom branch is a segment of the base manifold. Each channel is divided into two branches of the same length. Branches in the circulation are numbered clockwise from the top manifold branches. Furthermore, branches in the circulation are numbered clockwise from the full manifold branches.Figure 1
Geometric model of flow channel.In this model, the pressure, velocity, and components are assumed to be uniform on each loop branch. The reaction points indicated by the symbol⊗ are located in the middle of the channel, where property parameters such as pressure and flow velocity are the mean of the anterior segment and terminal channel branches. Since the mass transfer of the electrochemical reaction is considered to occur in the reaction center, the interface connecting the various branches and the different branches is represented by nodes with 4 nodes per cycle. The parameters of the reactor model are shown in Table 1.Table 1
Stack model parameters.
ParameterUnitValueCell numberStretch80Intake manifold lengthcm12Intake manifold widthcm10Intake pressure of cathodeMPa0.2Intake pressure of anodeMPa0.2Air power viscosityPa·s−12.06e − 5Hydrodynamic viscosityPa·s−11.12e − 5Flow channel section lengthmm1Flow channel section widthmm1GDL thicknessum235Catalytic layer thicknessum6Membrane thicknessum18Channel lengthcm12Current densitymA·cm−11000Cathodic stoichiometric ratioInitial2.5Anodic stoichiometric ratio2.5The cathode flow channel formStraightThe anode flow channel formStraightIntake manifold structureZ


#### 2.1.2. Governing Equation of 1-D Model

The mathematical model of the 1-D model mainly includes the mass conservation model and the momentum conservation model, as detailed in the literature, and the specific equations are shown in Table2.Table 2
Mass conservation and energy conservation equations of 1-D model.
DescriptionEquationsInlet molar flow rateN˙H2,instack=SanNcellJAcell/2FN˙O2,instack=ScaNcellJAcell/4FTotal inlet molar qualityN˙in,anstack=N˙H2,instack⋅Pin,anstack/Pin,anstack−Psat,inN˙in,castack=N˙Air,instack⋅Pin,castack/Pin,castack−Psat,inPsat=e77.3450+0.0057⋅T−7325.0/T/T8.2Reaction consumptionΔN˙r=∑i=speciesΔN˙riTotal molar consumptionΔN˙rH2=−JAcell/2FΔN˙r=ΔN˙rH2+N˙dragH2OMolar fraction of waterYout,anH2O=Psat,out/Pout,anstackOutlet molar flow rateN˙H2,outstack=San−1NcellJAcell/2FN˙O2,outstack=Sca−1NcellJAcell/4FFlow rate of waterN˙H2O,instack=N˙in,anstack⋅Psat,in/Pin,anstackN˙H2O,outstack=Tout,anH2O⋅N˙H2,outstack/1−Yout,anH2OWater dragN˙H2O,dragstack=N˙H2O,instack−N˙H2O,outstackThe amount of water dragN˙dragH2O=N˙H2O,dragstack/NcellCathode water producedΔN˙rO2=−JAcell/4FΔN˙rH2O=JAcell/2FAmount of total molar mass changeΔN˙ca=ΔN˙rO2+ΔN˙rH2O+ΔN˙dragH2OThe flow directions and molar flow rates for each segmentN˙i−1,3=θi−1,2N˙i−1,2+ΔN˙i−1/θi−1,3N˙i,1=θi−1,1N˙i−1,1+N˙inletstack−θi−1,2N˙i−1,2/θi,1N˙i,4=θi−1,3N˙i−1,3−θi−1,4N˙i−1,4−N˙outletstack/θi,4Total pressure drop∑j=1Nbranchθi,jΔPi,j=0i=1,2,,…,NloopΔPi,j=ΔPf,i,j+ΔPm,i,jΔPf,i,j=Cf,i,jLi,j/Dj,i,jρi,jVi,j2/2The calculation of Reynolds numberCf,i,j=C1⋅Rei,j−1Rei,j≤2×1030.316Rei,j−1/44×103<Rei,j≤105Rei,j=ρi,jVi,jDh,i,j/μi,jThe molar flow representationΔPi=∑j=1Nbranchθi,jr1,i,jN˙i,jn1,i,j+r2,i,j+r3,i,jN˙i,jn2,i,j=0i=1,2,3,…,Nloop, r1,i,j=0.032Li,jμi,jRT/Dh,i,j4Pi,j1.3560×10−6Li,jμi,j0.25ρi,j0.75RT1.75/Dh,i,j4.75Pi,j1.75The meanings of the corresponding letters in Table2 are shown in Table 3.Table 3
Meanings of symbols.
SymbolMeaningSymbolMeaningN˙Molar flow rateinInlet of the stackN˙rReactant consumption rateoutOutlet of the stackNcellNumber of cellsanAnodeAcellActive cell areacaCathodeSStoichiometrysatSaturationJCurrent densitydragDragged moleculesPPressureH2HydrogenTTemperatureO2OxygenYMolar fractionH2OWaterCWall friction coefficientbranchNumber of segments in a loopρDensityμViscosityVFlow velocityrFlow resistance coefficientDhHydraulic diameterRUniversal gas constant


### 2.2. 3-D Fuel Cell CFD Model

#### 2.2.1. Computational Domain of 3-D Model

The physical model of the 3-D model is mainly a 12 cm ∗ 8 cm straight flow field PEMFC single cell model, as shown in Figure2, and model parameters are shown in Table 4.Figure 2
Geometric model of flow channel.Table 4
Parameters of the model.
SymbolParametersValueLFlow field length/m0.032W_chFlow field width/m0.032H_gdlGDL thickness/m3.80e − 04H_gdlGDL thickness/m3.80e − 04H_electrodePorous electrode thickness/m5.00e − 05H_membraneMembrane thickness/m1.00e − 04RHaRelative humidity of anode0.8RHcRelative humidity of cathode0.8P_satSaturated vapor pressure/PaAccording to calculateP_aAnode pressure/Pa2.5e5P_cCathode pressure/Pa2.5e5MH2Hydrogen molar mass/kg·mol−10.002MH2OWater molar mass/kg·mol−10.018MO2Oxygen molar mass/kg·mol−10.032MN2Nitrogen molar mass/kg·mol−10.028xH2Oa_inAnode water vapor pressure/PaRHa ∗ P_sat/P_axH2_inAnode hydrogen pressure/Pa1-xH2Oa_inxH2Oc_inCathode water vapor pressure/PaRHc ∗ P_sat/P_cxO2_inCathode oxygen pressure/Pa0.21 ∗ (1-xH2Oc_in)xN2_inCathode nitrogen pressure/Pa0.79 ∗ (1-xH2Oc_in)D_H2_H2OH2-H2O binary diffusion coefficient/m2·s−11.11e − 4 (calculated)D_N2_H2ON2-H2O binary diffusion coefficient/m2·s−13.09e − 5 (calculated)D_O2_N2O2-N2 binary diffusion coefficient/m2·s−12.89e − 5 (calculated)D_O2_H2OO2-H2O binary diffusion coefficient/m2·s−13.41e − 5 (calculated)mu_anodeAnode viscosity/Pa·s1.19e − 05mu_cathodeCathode viscosity/Pa·s2.46e − 05kappa_gdlGDL permeability/m21e − 12kappa_clPermeability (porous electrode)/m21e − 13sigma_gdlGDL electric conductivity/S·m−15000sigma_clCL electric conductivity/S·m−15000sigma_mMembrane electric conductivity/S·m−12eps_gdlGDL porosity0.3eps_clPorous electrodes porosity1-eps_gdl-eps_leps_lElectrolyte phase volume fraction0.2eps_iIonomer volume fraction0.27cH2_refHydrogen reference concentration/mol·m356.4cO2_refOxygen reference concentration/mol·m33.39stoich_aAnode stoichiometry1.5stoich_cCathode stoichiometry3TCell temperature/K343.15V_cellCell voltage/V0.9i_cellCurrent density/A·cm2According to calculateA_clCatalytic layer area/m2W_ch ∗L


#### 2.2.2. Assumptions of 3-D Model

This article model carries out the following assumptions:(1)
The PEMFC is operating at a steady state.(2)
The gas flow in the FF is regarded as the laminar of an ideal gas and the incompressible flow.(3)
All gases cannot pass through the proton exchange membrane.(4)
The gravity effect is neglected.(5)
Both the GDL and CL are assumed to be homogeneous and isotropic.(6)
The PEMFC model is applied in a fuel cell.


#### 2.2.3. Governing Equation of 3-D Model

The 3-D model mainly includes mass conservation equation, momentum conservation equation, energy conservation equation, component conservation equation, electrochemical equation, diffusion equation of gas components in porous medium, and transport equation for liquid water. The specific equations are shown in Table5.Table 5
Conservation equations of 3-D model.
DescriptionEquationsMass conservation equation∂ρ/∂t+∇⋅ρu⟶=SmMomentum conservation equation∂ρu⟶/∂t+∇⋅ρu⟶u⟶=∇⋅μ∇u⟶+Su⟶Material conservation equation∂ρYi/∂t+∇⋅ρu⟶Y=∇⋅Di∇Yi+SYiEnergy conservation equation∂ρT/∂t+∇⋅ρu⟶T=∇⋅k/cp∇T+STProton conservation equation∇⋅σeff∇φH++SφH+=0SφH+=jaanode CLjccathode CLElectron conservation equation∇⋅κeff∇φe−+Sφe−=0Sφe−=−jaanode CL−jccathode CLja and jc[16]ja=ai0,aCH2/CH2,ref1/2αa+αc/RTFηjc=−ai0,cexp−164561/T−1/353.15CO2/CO2,refexp−αcF/RTηDiffusion equations of gas components in porous mediaDi=ε1.51−srsDi0P0/PγpT/T0rtTransmission equation for liquid water∂ερls/∂t+∇⋅ρlv¯ls=rwThe meanings of the corresponding source items and the letters in Table5 are shown in Tables 6 and 7, respectively.Table 6
Expressions for source terms.
Source itemsCLGDLMembraneBipolar plateFlow fieldSmSYH2/O2 + SYH2O0000Su⟶−μ/KGDLu⟶−μ/KCLu⟶000SYH2/O2−Misij/nF0000SYH2O−MH2Osij/nF−∇⋅nd/Fi⟶e0−∇⋅nd/Fi⟶e00STjη+TdU0/dT+i⟶e2/keeff+i⟶s2/σeeffi⟶s2/σeeffi⟶e2/keeffi⟶s2/σeeff0SφH+−j0—00Sφe−j—0——Table 7
Symbols and meanings.
SymbolMeaningSymbolMeaningρDensity/(kg·m−3)i0Exchange current density/(A·m2)ψSolving variablesCVolume molar concentration/(mol·dm−2)tTime/sCrefReference molar concentration/(mol·dm−2)u⟶Velocity vector/(m·s−1)αConversion rate of the electrochemical reactionsΓGeneralized diffusion coefficient/(m2·s−1)UActivation potential/VκThermal conductivity/(W·m−1 K−1)TTemperature/KσProton conduction rate/(S·m−1)DiCoefficient of diffusionkElectron conductivity/(S·m−1)ndProton number/electron numberμViscosity coefficient/(kg·m−1·s−1)εThe initial diffusion coefficient of the componentsKGDLThe permeability of the GDL/(m2·s)Di0The initial diffusion coefficient of thei componentsKCLPermeation of the catalytic layer (CL)/(m2·s)rsSaturation indexMiChemical expressionrpPressure factorSiStoichiometric coefficients of each componentrtTemperature exponentnThe number of electronsρlThe density of water (kg·m−3)FFaraday constant/96 485°C/molrwCondensation rate of wateraActive reaction area/m2sPhase saturation of water


### 2.3. Validation of the Model

#### 2.3.1. 1-D Model Validation

Figure3 shows the comparison of the pressure drop of the numerical analysis and experimental results [15] at the anode of the PEM fuel cell stack under the same operating conditions. In Figure 3, (a) and (b) are the contrasts of the stoichiometric ratios of 1.2 and 1.5, respectively. The results show that the pressure drop obtained by the numerical method is in good agreement with the experimental results in anodic stoichiometry. Consequently, the correctness of the model is demonstrated.Figure 3
1-D model verification.


#### 2.3.2. 3-D Model Validation

To ensure the accuracy and scientificity of the simulation results, it is necessary to verify the selected model mentally, and the comparison between the experiment and the simulated polarization curve is selected as the verification method. To ensure the accuracy of the trial validation effect of the selected model, the experiment is consistent with the critical parameters in the simulation. Figure2 shows the 16-channel straight flow field PEMFC used in the model simulation and experiment. Figure 4 shows the experimental schematic (the size parameters and operating parameters of the single cell in the experiment are shown in Table 8), and Figure 5 shows the polarization curve comparison of simulation and experiment. It can be seen from Figure 6 that the experimental results are consistent with the simulation results, and the experimental results can verify the accuracy and feasibility of numerical simulation.Figure 4
Experimental and simulation models. (a) Simulation cell. (b) Experimental cell.
(a)(b)Table 8
PEMFC experiment parameters.
ParameterValueGDL porosity0.4GDL thickness/m380e − 6Porous electrode thickness/m50e − 6Membrane thickness/m100e − 6Catalytic layer porosity0.3Gas back pressure/MPaAtmospheric pressureAnode transfer coefficient0.5Cathode transfer coefficient1Cell effective area/cm296O2 flow rate/ml·min−1889H2 flow rate/ml·min−1536Cell temperature/K343.15Gas temperature/K348.15Dewpoint temperature/K343.15Figure 5
Experimental schematic diagram.Figure 6
Experimental validation of the model.


## 2.1. 1-D Fuel Cell Stack Model

### 2.1.1. Computational Domain of 1-D Model

The computational domain of the one-dimensional model is mainly used to represent the flow distribution of individual units in a stack, which is a schematic diagram of simplified stack flow network configuration. Figure1 shows the current research situation of the fuel cell stack, including the inlet, outlet, manifold, and gas flow channel of the fuel cell stack. In this diagram, the reactants are supplied and transported at the reactor inlet of the top manifold. In this figure, the reactants are supplied at the stack inlet of the top manifold and transported along the top manifold while being assigned to the cell channel. The remaining reactants and products of the electrochemical reaction are discharged into the bottom manifold at the channel outlet and then removed from the fuel cell stack at the fuel cell stack outlet. Traffic network construction and analysis are based on controlling the volume, the i circuit shown in Figure 1. Each loop has six branches (control volume), and the top branch is a segment of the top manifold connecting adjacent units. The bottom branch is a segment of the base manifold. Each channel is divided into two branches of the same length. Branches in the circulation are numbered clockwise from the top manifold branches. Furthermore, branches in the circulation are numbered clockwise from the full manifold branches.Figure 1
Geometric model of flow channel.In this model, the pressure, velocity, and components are assumed to be uniform on each loop branch. The reaction points indicated by the symbol⊗ are located in the middle of the channel, where property parameters such as pressure and flow velocity are the mean of the anterior segment and terminal channel branches. Since the mass transfer of the electrochemical reaction is considered to occur in the reaction center, the interface connecting the various branches and the different branches is represented by nodes with 4 nodes per cycle. The parameters of the reactor model are shown in Table 1.Table 1
Stack model parameters.
ParameterUnitValueCell numberStretch80Intake manifold lengthcm12Intake manifold widthcm10Intake pressure of cathodeMPa0.2Intake pressure of anodeMPa0.2Air power viscosityPa·s−12.06e − 5Hydrodynamic viscosityPa·s−11.12e − 5Flow channel section lengthmm1Flow channel section widthmm1GDL thicknessum235Catalytic layer thicknessum6Membrane thicknessum18Channel lengthcm12Current densitymA·cm−11000Cathodic stoichiometric ratioInitial2.5Anodic stoichiometric ratio2.5The cathode flow channel formStraightThe anode flow channel formStraightIntake manifold structureZ


### 2.1.2. Governing Equation of 1-D Model

The mathematical model of the 1-D model mainly includes the mass conservation model and the momentum conservation model, as detailed in the literature, and the specific equations are shown in Table2.Table 2
Mass conservation and energy conservation equations of 1-D model.
DescriptionEquationsInlet molar flow rateN˙H2,instack=SanNcellJAcell/2FN˙O2,instack=ScaNcellJAcell/4FTotal inlet molar qualityN˙in,anstack=N˙H2,instack⋅Pin,anstack/Pin,anstack−Psat,inN˙in,castack=N˙Air,instack⋅Pin,castack/Pin,castack−Psat,inPsat=e77.3450+0.0057⋅T−7325.0/T/T8.2Reaction consumptionΔN˙r=∑i=speciesΔN˙riTotal molar consumptionΔN˙rH2=−JAcell/2FΔN˙r=ΔN˙rH2+N˙dragH2OMolar fraction of waterYout,anH2O=Psat,out/Pout,anstackOutlet molar flow rateN˙H2,outstack=San−1NcellJAcell/2FN˙O2,outstack=Sca−1NcellJAcell/4FFlow rate of waterN˙H2O,instack=N˙in,anstack⋅Psat,in/Pin,anstackN˙H2O,outstack=Tout,anH2O⋅N˙H2,outstack/1−Yout,anH2OWater dragN˙H2O,dragstack=N˙H2O,instack−N˙H2O,outstackThe amount of water dragN˙dragH2O=N˙H2O,dragstack/NcellCathode water producedΔN˙rO2=−JAcell/4FΔN˙rH2O=JAcell/2FAmount of total molar mass changeΔN˙ca=ΔN˙rO2+ΔN˙rH2O+ΔN˙dragH2OThe flow directions and molar flow rates for each segmentN˙i−1,3=θi−1,2N˙i−1,2+ΔN˙i−1/θi−1,3N˙i,1=θi−1,1N˙i−1,1+N˙inletstack−θi−1,2N˙i−1,2/θi,1N˙i,4=θi−1,3N˙i−1,3−θi−1,4N˙i−1,4−N˙outletstack/θi,4Total pressure drop∑j=1Nbranchθi,jΔPi,j=0i=1,2,,…,NloopΔPi,j=ΔPf,i,j+ΔPm,i,jΔPf,i,j=Cf,i,jLi,j/Dj,i,jρi,jVi,j2/2The calculation of Reynolds numberCf,i,j=C1⋅Rei,j−1Rei,j≤2×1030.316Rei,j−1/44×103<Rei,j≤105Rei,j=ρi,jVi,jDh,i,j/μi,jThe molar flow representationΔPi=∑j=1Nbranchθi,jr1,i,jN˙i,jn1,i,j+r2,i,j+r3,i,jN˙i,jn2,i,j=0i=1,2,3,…,Nloop, r1,i,j=0.032Li,jμi,jRT/Dh,i,j4Pi,j1.3560×10−6Li,jμi,j0.25ρi,j0.75RT1.75/Dh,i,j4.75Pi,j1.75The meanings of the corresponding letters in Table2 are shown in Table 3.Table 3
Meanings of symbols.
SymbolMeaningSymbolMeaningN˙Molar flow rateinInlet of the stackN˙rReactant consumption rateoutOutlet of the stackNcellNumber of cellsanAnodeAcellActive cell areacaCathodeSStoichiometrysatSaturationJCurrent densitydragDragged moleculesPPressureH2HydrogenTTemperatureO2OxygenYMolar fractionH2OWaterCWall friction coefficientbranchNumber of segments in a loopρDensityμViscosityVFlow velocityrFlow resistance coefficientDhHydraulic diameterRUniversal gas constant


## 2.1.1. Computational Domain of 1-D Model

The computational domain of the one-dimensional model is mainly used to represent the flow distribution of individual units in a stack, which is a schematic diagram of simplified stack flow network configuration. Figure1 shows the current research situation of the fuel cell stack, including the inlet, outlet, manifold, and gas flow channel of the fuel cell stack. In this diagram, the reactants are supplied and transported at the reactor inlet of the top manifold. In this figure, the reactants are supplied at the stack inlet of the top manifold and transported along the top manifold while being assigned to the cell channel. The remaining reactants and products of the electrochemical reaction are discharged into the bottom manifold at the channel outlet and then removed from the fuel cell stack at the fuel cell stack outlet. Traffic network construction and analysis are based on controlling the volume, the i circuit shown in Figure 1. Each loop has six branches (control volume), and the top branch is a segment of the top manifold connecting adjacent units. The bottom branch is a segment of the base manifold. Each channel is divided into two branches of the same length. Branches in the circulation are numbered clockwise from the top manifold branches. Furthermore, branches in the circulation are numbered clockwise from the full manifold branches.Figure 1
Geometric model of flow channel.In this model, the pressure, velocity, and components are assumed to be uniform on each loop branch. The reaction points indicated by the symbol⊗ are located in the middle of the channel, where property parameters such as pressure and flow velocity are the mean of the anterior segment and terminal channel branches. Since the mass transfer of the electrochemical reaction is considered to occur in the reaction center, the interface connecting the various branches and the different branches is represented by nodes with 4 nodes per cycle. The parameters of the reactor model are shown in Table 1.Table 1
Stack model parameters.
ParameterUnitValueCell numberStretch80Intake manifold lengthcm12Intake manifold widthcm10Intake pressure of cathodeMPa0.2Intake pressure of anodeMPa0.2Air power viscosityPa·s−12.06e − 5Hydrodynamic viscosityPa·s−11.12e − 5Flow channel section lengthmm1Flow channel section widthmm1GDL thicknessum235Catalytic layer thicknessum6Membrane thicknessum18Channel lengthcm12Current densitymA·cm−11000Cathodic stoichiometric ratioInitial2.5Anodic stoichiometric ratio2.5The cathode flow channel formStraightThe anode flow channel formStraightIntake manifold structureZ


## 2.1.2. Governing Equation of 1-D Model

The mathematical model of the 1-D model mainly includes the mass conservation model and the momentum conservation model, as detailed in the literature, and the specific equations are shown in Table2.Table 2
Mass conservation and energy conservation equations of 1-D model.
DescriptionEquationsInlet molar flow rateN˙H2,instack=SanNcellJAcell/2FN˙O2,instack=ScaNcellJAcell/4FTotal inlet molar qualityN˙in,anstack=N˙H2,instack⋅Pin,anstack/Pin,anstack−Psat,inN˙in,castack=N˙Air,instack⋅Pin,castack/Pin,castack−Psat,inPsat=e77.3450+0.0057⋅T−7325.0/T/T8.2Reaction consumptionΔN˙r=∑i=speciesΔN˙riTotal molar consumptionΔN˙rH2=−JAcell/2FΔN˙r=ΔN˙rH2+N˙dragH2OMolar fraction of waterYout,anH2O=Psat,out/Pout,anstackOutlet molar flow rateN˙H2,outstack=San−1NcellJAcell/2FN˙O2,outstack=Sca−1NcellJAcell/4FFlow rate of waterN˙H2O,instack=N˙in,anstack⋅Psat,in/Pin,anstackN˙H2O,outstack=Tout,anH2O⋅N˙H2,outstack/1−Yout,anH2OWater dragN˙H2O,dragstack=N˙H2O,instack−N˙H2O,outstackThe amount of water dragN˙dragH2O=N˙H2O,dragstack/NcellCathode water producedΔN˙rO2=−JAcell/4FΔN˙rH2O=JAcell/2FAmount of total molar mass changeΔN˙ca=ΔN˙rO2+ΔN˙rH2O+ΔN˙dragH2OThe flow directions and molar flow rates for each segmentN˙i−1,3=θi−1,2N˙i−1,2+ΔN˙i−1/θi−1,3N˙i,1=θi−1,1N˙i−1,1+N˙inletstack−θi−1,2N˙i−1,2/θi,1N˙i,4=θi−1,3N˙i−1,3−θi−1,4N˙i−1,4−N˙outletstack/θi,4Total pressure drop∑j=1Nbranchθi,jΔPi,j=0i=1,2,,…,NloopΔPi,j=ΔPf,i,j+ΔPm,i,jΔPf,i,j=Cf,i,jLi,j/Dj,i,jρi,jVi,j2/2The calculation of Reynolds numberCf,i,j=C1⋅Rei,j−1Rei,j≤2×1030.316Rei,j−1/44×103<Rei,j≤105Rei,j=ρi,jVi,jDh,i,j/μi,jThe molar flow representationΔPi=∑j=1Nbranchθi,jr1,i,jN˙i,jn1,i,j+r2,i,j+r3,i,jN˙i,jn2,i,j=0i=1,2,3,…,Nloop, r1,i,j=0.032Li,jμi,jRT/Dh,i,j4Pi,j1.3560×10−6Li,jμi,j0.25ρi,j0.75RT1.75/Dh,i,j4.75Pi,j1.75The meanings of the corresponding letters in Table2 are shown in Table 3.Table 3
Meanings of symbols.
SymbolMeaningSymbolMeaningN˙Molar flow rateinInlet of the stackN˙rReactant consumption rateoutOutlet of the stackNcellNumber of cellsanAnodeAcellActive cell areacaCathodeSStoichiometrysatSaturationJCurrent densitydragDragged moleculesPPressureH2HydrogenTTemperatureO2OxygenYMolar fractionH2OWaterCWall friction coefficientbranchNumber of segments in a loopρDensityμViscosityVFlow velocityrFlow resistance coefficientDhHydraulic diameterRUniversal gas constant


## 2.2. 3-D Fuel Cell CFD Model

### 2.2.1. Computational Domain of 3-D Model

The physical model of the 3-D model is mainly a 12 cm ∗ 8 cm straight flow field PEMFC single cell model, as shown in Figure2, and model parameters are shown in Table 4.Figure 2
Geometric model of flow channel.Table 4
Parameters of the model.
SymbolParametersValueLFlow field length/m0.032W_chFlow field width/m0.032H_gdlGDL thickness/m3.80e − 04H_gdlGDL thickness/m3.80e − 04H_electrodePorous electrode thickness/m5.00e − 05H_membraneMembrane thickness/m1.00e − 04RHaRelative humidity of anode0.8RHcRelative humidity of cathode0.8P_satSaturated vapor pressure/PaAccording to calculateP_aAnode pressure/Pa2.5e5P_cCathode pressure/Pa2.5e5MH2Hydrogen molar mass/kg·mol−10.002MH2OWater molar mass/kg·mol−10.018MO2Oxygen molar mass/kg·mol−10.032MN2Nitrogen molar mass/kg·mol−10.028xH2Oa_inAnode water vapor pressure/PaRHa ∗ P_sat/P_axH2_inAnode hydrogen pressure/Pa1-xH2Oa_inxH2Oc_inCathode water vapor pressure/PaRHc ∗ P_sat/P_cxO2_inCathode oxygen pressure/Pa0.21 ∗ (1-xH2Oc_in)xN2_inCathode nitrogen pressure/Pa0.79 ∗ (1-xH2Oc_in)D_H2_H2OH2-H2O binary diffusion coefficient/m2·s−11.11e − 4 (calculated)D_N2_H2ON2-H2O binary diffusion coefficient/m2·s−13.09e − 5 (calculated)D_O2_N2O2-N2 binary diffusion coefficient/m2·s−12.89e − 5 (calculated)D_O2_H2OO2-H2O binary diffusion coefficient/m2·s−13.41e − 5 (calculated)mu_anodeAnode viscosity/Pa·s1.19e − 05mu_cathodeCathode viscosity/Pa·s2.46e − 05kappa_gdlGDL permeability/m21e − 12kappa_clPermeability (porous electrode)/m21e − 13sigma_gdlGDL electric conductivity/S·m−15000sigma_clCL electric conductivity/S·m−15000sigma_mMembrane electric conductivity/S·m−12eps_gdlGDL porosity0.3eps_clPorous electrodes porosity1-eps_gdl-eps_leps_lElectrolyte phase volume fraction0.2eps_iIonomer volume fraction0.27cH2_refHydrogen reference concentration/mol·m356.4cO2_refOxygen reference concentration/mol·m33.39stoich_aAnode stoichiometry1.5stoich_cCathode stoichiometry3TCell temperature/K343.15V_cellCell voltage/V0.9i_cellCurrent density/A·cm2According to calculateA_clCatalytic layer area/m2W_ch ∗L


### 2.2.2. Assumptions of 3-D Model

This article model carries out the following assumptions:(1)
The PEMFC is operating at a steady state.(2)
The gas flow in the FF is regarded as the laminar of an ideal gas and the incompressible flow.(3)
All gases cannot pass through the proton exchange membrane.(4)
The gravity effect is neglected.(5)
Both the GDL and CL are assumed to be homogeneous and isotropic.(6)
The PEMFC model is applied in a fuel cell.


### 2.2.3. Governing Equation of 3-D Model

The 3-D model mainly includes mass conservation equation, momentum conservation equation, energy conservation equation, component conservation equation, electrochemical equation, diffusion equation of gas components in porous medium, and transport equation for liquid water. The specific equations are shown in Table5.Table 5
Conservation equations of 3-D model.
DescriptionEquationsMass conservation equation∂ρ/∂t+∇⋅ρu⟶=SmMomentum conservation equation∂ρu⟶/∂t+∇⋅ρu⟶u⟶=∇⋅μ∇u⟶+Su⟶Material conservation equation∂ρYi/∂t+∇⋅ρu⟶Y=∇⋅Di∇Yi+SYiEnergy conservation equation∂ρT/∂t+∇⋅ρu⟶T=∇⋅k/cp∇T+STProton conservation equation∇⋅σeff∇φH++SφH+=0SφH+=jaanode CLjccathode CLElectron conservation equation∇⋅κeff∇φe−+Sφe−=0Sφe−=−jaanode CL−jccathode CLja and jc[16]ja=ai0,aCH2/CH2,ref1/2αa+αc/RTFηjc=−ai0,cexp−164561/T−1/353.15CO2/CO2,refexp−αcF/RTηDiffusion equations of gas components in porous mediaDi=ε1.51−srsDi0P0/PγpT/T0rtTransmission equation for liquid water∂ερls/∂t+∇⋅ρlv¯ls=rwThe meanings of the corresponding source items and the letters in Table5 are shown in Tables 6 and 7, respectively.Table 6
Expressions for source terms.
Source itemsCLGDLMembraneBipolar plateFlow fieldSmSYH2/O2 + SYH2O0000Su⟶−μ/KGDLu⟶−μ/KCLu⟶000SYH2/O2−Misij/nF0000SYH2O−MH2Osij/nF−∇⋅nd/Fi⟶e0−∇⋅nd/Fi⟶e00STjη+TdU0/dT+i⟶e2/keeff+i⟶s2/σeeffi⟶s2/σeeffi⟶e2/keeffi⟶s2/σeeff0SφH+−j0—00Sφe−j—0——Table 7
Symbols and meanings.
SymbolMeaningSymbolMeaningρDensity/(kg·m−3)i0Exchange current density/(A·m2)ψSolving variablesCVolume molar concentration/(mol·dm−2)tTime/sCrefReference molar concentration/(mol·dm−2)u⟶Velocity vector/(m·s−1)αConversion rate of the electrochemical reactionsΓGeneralized diffusion coefficient/(m2·s−1)UActivation potential/VκThermal conductivity/(W·m−1 K−1)TTemperature/KσProton conduction rate/(S·m−1)DiCoefficient of diffusionkElectron conductivity/(S·m−1)ndProton number/electron numberμViscosity coefficient/(kg·m−1·s−1)εThe initial diffusion coefficient of the componentsKGDLThe permeability of the GDL/(m2·s)Di0The initial diffusion coefficient of thei componentsKCLPermeation of the catalytic layer (CL)/(m2·s)rsSaturation indexMiChemical expressionrpPressure factorSiStoichiometric coefficients of each componentrtTemperature exponentnThe number of electronsρlThe density of water (kg·m−3)FFaraday constant/96 485°C/molrwCondensation rate of wateraActive reaction area/m2sPhase saturation of water


## 2.2.1. Computational Domain of 3-D Model

The physical model of the 3-D model is mainly a 12 cm ∗ 8 cm straight flow field PEMFC single cell model, as shown in Figure2, and model parameters are shown in Table 4.Figure 2
Geometric model of flow channel.Table 4
Parameters of the model.
SymbolParametersValueLFlow field length/m0.032W_chFlow field width/m0.032H_gdlGDL thickness/m3.80e − 04H_gdlGDL thickness/m3.80e − 04H_electrodePorous electrode thickness/m5.00e − 05H_membraneMembrane thickness/m1.00e − 04RHaRelative humidity of anode0.8RHcRelative humidity of cathode0.8P_satSaturated vapor pressure/PaAccording to calculateP_aAnode pressure/Pa2.5e5P_cCathode pressure/Pa2.5e5MH2Hydrogen molar mass/kg·mol−10.002MH2OWater molar mass/kg·mol−10.018MO2Oxygen molar mass/kg·mol−10.032MN2Nitrogen molar mass/kg·mol−10.028xH2Oa_inAnode water vapor pressure/PaRHa ∗ P_sat/P_axH2_inAnode hydrogen pressure/Pa1-xH2Oa_inxH2Oc_inCathode water vapor pressure/PaRHc ∗ P_sat/P_cxO2_inCathode oxygen pressure/Pa0.21 ∗ (1-xH2Oc_in)xN2_inCathode nitrogen pressure/Pa0.79 ∗ (1-xH2Oc_in)D_H2_H2OH2-H2O binary diffusion coefficient/m2·s−11.11e − 4 (calculated)D_N2_H2ON2-H2O binary diffusion coefficient/m2·s−13.09e − 5 (calculated)D_O2_N2O2-N2 binary diffusion coefficient/m2·s−12.89e − 5 (calculated)D_O2_H2OO2-H2O binary diffusion coefficient/m2·s−13.41e − 5 (calculated)mu_anodeAnode viscosity/Pa·s1.19e − 05mu_cathodeCathode viscosity/Pa·s2.46e − 05kappa_gdlGDL permeability/m21e − 12kappa_clPermeability (porous electrode)/m21e − 13sigma_gdlGDL electric conductivity/S·m−15000sigma_clCL electric conductivity/S·m−15000sigma_mMembrane electric conductivity/S·m−12eps_gdlGDL porosity0.3eps_clPorous electrodes porosity1-eps_gdl-eps_leps_lElectrolyte phase volume fraction0.2eps_iIonomer volume fraction0.27cH2_refHydrogen reference concentration/mol·m356.4cO2_refOxygen reference concentration/mol·m33.39stoich_aAnode stoichiometry1.5stoich_cCathode stoichiometry3TCell temperature/K343.15V_cellCell voltage/V0.9i_cellCurrent density/A·cm2According to calculateA_clCatalytic layer area/m2W_ch ∗L


## 2.2.2. Assumptions of 3-D Model

This article model carries out the following assumptions:(1)
The PEMFC is operating at a steady state.(2)
The gas flow in the FF is regarded as the laminar of an ideal gas and the incompressible flow.(3)
All gases cannot pass through the proton exchange membrane.(4)
The gravity effect is neglected.(5)
Both the GDL and CL are assumed to be homogeneous and isotropic.(6)
The PEMFC model is applied in a fuel cell.


## 2.2.3. Governing Equation of 3-D Model

The 3-D model mainly includes mass conservation equation, momentum conservation equation, energy conservation equation, component conservation equation, electrochemical equation, diffusion equation of gas components in porous medium, and transport equation for liquid water. The specific equations are shown in Table5.Table 5
Conservation equations of 3-D model.
DescriptionEquationsMass conservation equation∂ρ/∂t+∇⋅ρu⟶=SmMomentum conservation equation∂ρu⟶/∂t+∇⋅ρu⟶u⟶=∇⋅μ∇u⟶+Su⟶Material conservation equation∂ρYi/∂t+∇⋅ρu⟶Y=∇⋅Di∇Yi+SYiEnergy conservation equation∂ρT/∂t+∇⋅ρu⟶T=∇⋅k/cp∇T+STProton conservation equation∇⋅σeff∇φH++SφH+=0SφH+=jaanode CLjccathode CLElectron conservation equation∇⋅κeff∇φe−+Sφe−=0Sφe−=−jaanode CL−jccathode CLja and jc[16]ja=ai0,aCH2/CH2,ref1/2αa+αc/RTFηjc=−ai0,cexp−164561/T−1/353.15CO2/CO2,refexp−αcF/RTηDiffusion equations of gas components in porous mediaDi=ε1.51−srsDi0P0/PγpT/T0rtTransmission equation for liquid water∂ερls/∂t+∇⋅ρlv¯ls=rwThe meanings of the corresponding source items and the letters in Table5 are shown in Tables 6 and 7, respectively.Table 6
Expressions for source terms.
Source itemsCLGDLMembraneBipolar plateFlow fieldSmSYH2/O2 + SYH2O0000Su⟶−μ/KGDLu⟶−μ/KCLu⟶000SYH2/O2−Misij/nF0000SYH2O−MH2Osij/nF−∇⋅nd/Fi⟶e0−∇⋅nd/Fi⟶e00STjη+TdU0/dT+i⟶e2/keeff+i⟶s2/σeeffi⟶s2/σeeffi⟶e2/keeffi⟶s2/σeeff0SφH+−j0—00Sφe−j—0——Table 7
Symbols and meanings.
SymbolMeaningSymbolMeaningρDensity/(kg·m−3)i0Exchange current density/(A·m2)ψSolving variablesCVolume molar concentration/(mol·dm−2)tTime/sCrefReference molar concentration/(mol·dm−2)u⟶Velocity vector/(m·s−1)αConversion rate of the electrochemical reactionsΓGeneralized diffusion coefficient/(m2·s−1)UActivation potential/VκThermal conductivity/(W·m−1 K−1)TTemperature/KσProton conduction rate/(S·m−1)DiCoefficient of diffusionkElectron conductivity/(S·m−1)ndProton number/electron numberμViscosity coefficient/(kg·m−1·s−1)εThe initial diffusion coefficient of the componentsKGDLThe permeability of the GDL/(m2·s)Di0The initial diffusion coefficient of thei componentsKCLPermeation of the catalytic layer (CL)/(m2·s)rsSaturation indexMiChemical expressionrpPressure factorSiStoichiometric coefficients of each componentrtTemperature exponentnThe number of electronsρlThe density of water (kg·m−3)FFaraday constant/96 485°C/molrwCondensation rate of wateraActive reaction area/m2sPhase saturation of water


## 2.3. Validation of the Model

### 2.3.1. 1-D Model Validation

Figure3 shows the comparison of the pressure drop of the numerical analysis and experimental results [15] at the anode of the PEM fuel cell stack under the same operating conditions. In Figure 3, (a) and (b) are the contrasts of the stoichiometric ratios of 1.2 and 1.5, respectively. The results show that the pressure drop obtained by the numerical method is in good agreement with the experimental results in anodic stoichiometry. Consequently, the correctness of the model is demonstrated.Figure 3
1-D model verification.


### 2.3.2. 3-D Model Validation

To ensure the accuracy and scientificity of the simulation results, it is necessary to verify the selected model mentally, and the comparison between the experiment and the simulated polarization curve is selected as the verification method. To ensure the accuracy of the trial validation effect of the selected model, the experiment is consistent with the critical parameters in the simulation. Figure2 shows the 16-channel straight flow field PEMFC used in the model simulation and experiment. Figure 4 shows the experimental schematic (the size parameters and operating parameters of the single cell in the experiment are shown in Table 8), and Figure 5 shows the polarization curve comparison of simulation and experiment. It can be seen from Figure 6 that the experimental results are consistent with the simulation results, and the experimental results can verify the accuracy and feasibility of numerical simulation.Figure 4
Experimental and simulation models. (a) Simulation cell. (b) Experimental cell.
(a)(b)Table 8
PEMFC experiment parameters.
ParameterValueGDL porosity0.4GDL thickness/m380e − 6Porous electrode thickness/m50e − 6Membrane thickness/m100e − 6Catalytic layer porosity0.3Gas back pressure/MPaAtmospheric pressureAnode transfer coefficient0.5Cathode transfer coefficient1Cell effective area/cm296O2 flow rate/ml·min−1889H2 flow rate/ml·min−1536Cell temperature/K343.15Gas temperature/K348.15Dewpoint temperature/K343.15Figure 5
Experimental schematic diagram.Figure 6
Experimental validation of the model.


## 2.3.1. 1-D Model Validation

Figure3 shows the comparison of the pressure drop of the numerical analysis and experimental results [15] at the anode of the PEM fuel cell stack under the same operating conditions. In Figure 3, (a) and (b) are the contrasts of the stoichiometric ratios of 1.2 and 1.5, respectively. The results show that the pressure drop obtained by the numerical method is in good agreement with the experimental results in anodic stoichiometry. Consequently, the correctness of the model is demonstrated.Figure 3
1-D model verification.


## 2.3.2. 3-D Model Validation

To ensure the accuracy and scientificity of the simulation results, it is necessary to verify the selected model mentally, and the comparison between the experiment and the simulated polarization curve is selected as the verification method. To ensure the accuracy of the trial validation effect of the selected model, the experiment is consistent with the critical parameters in the simulation. Figure2 shows the 16-channel straight flow field PEMFC used in the model simulation and experiment. Figure 4 shows the experimental schematic (the size parameters and operating parameters of the single cell in the experiment are shown in Table 8), and Figure 5 shows the polarization curve comparison of simulation and experiment. It can be seen from Figure 6 that the experimental results are consistent with the simulation results, and the experimental results can verify the accuracy and feasibility of numerical simulation.Figure 4
Experimental and simulation models. (a) Simulation cell. (b) Experimental cell.
(a)(b)Table 8
PEMFC experiment parameters.
ParameterValueGDL porosity0.4GDL thickness/m380e − 6Porous electrode thickness/m50e − 6Membrane thickness/m100e − 6Catalytic layer porosity0.3Gas back pressure/MPaAtmospheric pressureAnode transfer coefficient0.5Cathode transfer coefficient1Cell effective area/cm296O2 flow rate/ml·min−1889H2 flow rate/ml·min−1536Cell temperature/K343.15Gas temperature/K348.15Dewpoint temperature/K343.15Figure 5
Experimental schematic diagram.Figure 6
Experimental validation of the model.


## 3. Analysis of the Consistence of Intake Flow Rate

Figures7(a) and 7(b) are, respectively, the iterative situations of the model during the calculation of the 1-D model. It can be seen from this figure that the cathode and anode converge within the 10000th step, which shows that the calculation model has good convergence and effectiveness. Figure 8 shows the distribution of intake airflow of every single cathode and anode. The uneven intake flow distribution of each monomer is both cathode and anode. Among them, the maximum monomer intake flow rate at the anode is 2.87 ∗ 10−5m3·s−1, the minimum is 2.35 ∗ 10−5m3·s−1, and the difference in intake flow rate is 0.52 ∗ 10−5m3·s−1. The maximum monomer intake flow rate of the cathode is 6.87 ∗ 10−5m3·s−1, the minimum is 5.51 ∗ 10−5m3·s−1, and the difference in intake flow rate is 1.27 ∗ 10−5m3·s−1. The difference in the intake flow rate of the single cell will cause a difference in the performance of the single cell, which will eventually affect the overall performance of the stack. Based on this, the article further optimizes the size of the flow channel to improve the performance of the minimum intake flow rate monomer, thereby enhancing the consistency of the stack.Figure 7
Model iteration times. (a) Anode. (b) Cathode.
(a)(b)Figure 8
Air intake flow distribution. (a) Anode. (b) Cathode.
(a)(b)


## 4. Size Optimization of Monomer Cell

The molecules of the above inlet flow conditions were substituted into the 3D model as boundary conditions for further numerical analysis, and the polarization curves at the highest and lowest inlet flows were obtained, as shown in Figure9. As shown in Figure 9, the performance difference between the two monomers is noticeable due to the difference in intake flow rate. Moreover, the maximum power density of the maximum intake flow rate monomer is 5.7% higher than that of the minimum intake flow rate monomer. At a current density of 1000 mA·cm−2, the voltage difference between the two is 0.065 V.Figure 9
Performance comparison.Figure10 shows the optimization results of channel depth and width. In order to improve the performance of monomer under the minimum intake flow, the width and depth of the channel are optimized in this section, and the width (0.8, 0.85, …, 1.15,1.2 mm) and depth (0.8, 0.85, …, 1.15, 1.2 mm) are selected with different size combination; the current density under 0.2V voltage changes with size parameters. The result shows that the current density changes accordingly with the width and depth size, and the current density reaches the maximum when the width and depth are 1.1 mm and 0.8 mm, respectively.Figure 10
Width-depth optimization.Figure11 shows the performance comparison between the lowest intake flow rate monomer and the highest intake flow rate monomer after the channel size optimization. As can be seen from the figure, the power density difference between the two monomers is reduced from 5.7% to 2.1%, and the voltage difference is reduced from 0.065 V to 0.035 V at a current density of 1000 mA·cm−2 after optimization.Figure 11
Performance comparison.According to the optimization of the channel size, the channel size is substituted into the 1-D model, and the distribution diagram of the cathode and anode intake flow rate is obtained. Compared with Figures12 and 8, it is evident that the intake flow equilibrium of the 80 monomers is significantly improved after the channel size optimization. Specifically speaking, the range of anode flow rate decreased from 0.52 ∗ 10−5m3·s−1 to 0.27 ∗ 10−5m3·s−1 and that of cathode flow rate decreased from 1.27 ∗ 10−5m3·s−1 to 0.58 ∗ 10−5m3·s−1. The improvement of the consistency of intake flow rate will improve the voltage consistency of the stack.Figure 12
Optimized air intake flow distribution. (a) Anode. (b) Cathode.
(a)(b)The 80-stack intake flow data before and after the channel size optimization are replaced into the 3-D model to obtain the voltage of each monomer in the stack at 1000 mA·cm−2. As shown in Figure 13, after the optimization of channel size, the voltage consistency of the stack has been significantly improved.Figure 13
Voltage consistency comparison.The voltage difference coefficient is further used to analyze the performance of the stack, the voltage difference coefficientCv represents the consistency of the cell voltage of the stack, and the calculation formula is(1)Cv=100×∑i=1NVi−V¯/V¯2n,where Vi is the cell voltage, V¯ is the average output voltage of the stack, and n is the number of cells.According to formula (1), Cv changes from 7.21 to 3.70 after optimizing channel size, and Cv is reduced by 48.7%.


## 5. Conclusion

The article establishes a 1-D flow network model of 80 cell stacks and a three-dimensional steady-state model of a 12 cm ∗ 8 cm PEMFC cell, the performance of the fuel cell is optimized, and the conclusions are as follows.Experiments were used to verify the accuracy of the 1-D flow network model and the 3-D steady-state model. The convergence of the 1-D model is good. Both the cathode and anode reach confluence within 10,000 steps.The flow rate distribution of the anode and cathode of the stack is uneven, and the maximum monomer airflow of the anode is 2.87 ∗ 10−5m3·s−1. The minimum is 2.35 ∗ 10−5m3·s−1, and the intake flow rate difference is 0.52 ∗ 10−5m3·s−1. The maximum monomer intake flow rate of the cathode is 6.87 ∗ 10−5m3·s−1, the minimum is 5.51 ∗ 10−5m3·s−1, and the difference in air intake flow is 1.27 ∗ 10−5m3·s−1.The maximum and minimum intake flow rates obtained from the 1-D model are used as the 3-D model’s boundary conditions to calculate the single-cell performance under different intake flow rate conditions. Optimize its performance by changing the minimum intake flow rate monomer’s width, depth, and other size parameters. When the width and depth are 1.1 mm and 0.8 mm, respectively, the monomer performance is the best, and the electrochemical performance is improved.After the optimization, the extreme difference in the intake flow rate between anode and anode of the stack has been significantly reduced. The consistency of the stack voltage has been considerably improved, andCv has been reduced by 48.7%.



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