Conclusion

In PEM fuel cells, water is present as vapor, in liquid form and dissolved in the ionomer. The effects of water in all three phases, basically pore flooding and ionomer dehydration, are investigated with a newly developed 1D transient model. The model accounts for the loss mechanisms in the cathode GDL, cathode CL and membrane.

The electrode structure is modeled as a network of spherical agglomerates. An

ex-6.4 Modeling Liquid Water and its Transient Effects in a PEMFC

cess of liquid water in the catalyst layer leads to coverage of these agglomerates, forming a water film which limits oxygen transport. Liquid water is modeled as sat-uration in the void space. Its transport properties depend strongly on the capillary pressure-saturation relationship in porous media, which in turn is a function of the wettability and pore structure. Based on ESEM images, immobile saturation is intro-duced due to the observed partly hydrophilic regions in the GDL. A continuous cap-illary pressure at the interface CL ↔ GDL is assumed, resulting in a discontinuous saturation distribution. Finite phase transition rates between the ionomer and pore space, namely adsorption/desorption and liquid water uptake/release, enable mem-brane dehydration in the case of dry operating conditions, resulting in an increased ohmic resistance.

The simulation results for dynamic current-voltage characteristics are in excellent agreement with measured data. The measured hysteresis loop in the limiting cur-rent density region is reproduced by the model and explained by pore flooding. The measured cell impedance during a voltage sweep, which is a measure for the time-dependent water content, is in agreement with the simulation over a wide range of operating conditions and current densities. Simulations of chronoamperometry ex-periments are performed with the validated parameter set. The model captures quali-tatively the current and impedance responses of measured chronoamperometry data.

The model forms a suitable basis for identifying the dominant loss mechanisms at dif-ferent operating points. Based on the simulation results, suggestions for a better choice of fuel cell components can be made, guidance for their physical properties like pore structure, wettability or thickness can be obtained or simply optimal operat-ing conditions can be found. The latter leads us to the topic of fuel cell control. A good understanding of the response on dynamic load changes is required to control a fuel cell within a stable operating point. This can be realized by implementing the model in a simplified form in a model-based control algorithm.

Parameter studies and a sensitivity analysis would be the next steps in ongoing work.

An upgrade to a multi-dimensional model is intended for the future.

6 Water Management in Polymer Electrolyte Membrane Fuel Cell

6.4.6 Nomenclature and Parameter List

Symbol Description Value / Eq. Unit Reference

Solving variables

F Faraday constant 96484 C mol⁻¹

R gas constant 8.314 J K⁻¹mol⁻¹

Structural values

L^CBP thickness of cathode bipolar plate

3·10⁻³ m

L^GDL GDL thickness 280·10⁻⁶ m

L^CL CL thickness 10·10⁻⁶ m

L^mem membrane thickness 35·10⁻⁶ m

L^ABP thickness of anode bipolar plate

3·10⁻³ m

Ra mean agglomerate radius 0.2·10⁻⁶ m [142]

_a volume fraction of primary pores in an agglomerate

0.4 − [117]

^CL_p volume fraction of secondary pores in CL

0.25 − [65, 58]

^CL_i volume fraction of ionomer in CL

0.3 −

^GDL_p volume fraction of open pores in GDL

0.7 − [143]

Λ agglomerate density Eq. 6.24 m⁻³

Ξ geometry factor 0.55 − calculated

Physical properties, local variables and boundary conditions

a_w water activity Eq. 6.41 −

6.4 Modeling Liquid Water and its Transient Effects in a PEMFC

Symbol Description Value / Eq. Unit Reference

c^d_O2,s dissolved oxygen concentra-tion at agglomerate surface c^∗_v vapor concentration at inlet Eq. 6.49 mol m⁻³

CDL double layer capacity 0 F m⁻³

d water film thickness Eq. 6.18 m

D_Oⁱ

Dv^g vapor diffusion coefficient in gas phase

Eq. 6.51 m²s⁻¹ Dv^{ef f,Ω} effective vapor diffusion

coef-ficient in gas phase

Eq. 6.51 m²s⁻¹ D_s^Ω water diffusion coefficient in

porous medium

Eq. 6.37 m²s⁻¹ D_λⁱ water diffusion coefficient in

ionomer

Eq. 6.26 m²s⁻¹ [132]

EW equivalent weight 1.1 kg [114]

h_gl heat of

vaporisa-tion/condensation

40.7·10³ J mol⁻¹ [144]

H Henry constant 0.0254 − [70]

j_O^g

2 gaseous oxygen flux Eq. 6.43 mol m⁻²s⁻¹

6 Water Management in Polymer Electrolyte Membrane Fuel Cell

Symbol Description Value / Eq. Unit Reference

jv vapor flux Eq. 6.48 mol m⁻²s⁻¹

js liquid water interstitial velocity Eq. 6.33 m s⁻¹

j_T heat flux Eq. 6.53 J m⁻²s⁻¹

jp,e charge flux Eq. 6.20 A m⁻²

j_λ dissolved water flux Eq. 6.25 mol m⁻²s⁻¹ j_gen^a current generation per

ag-glomerate

Eq. 6.12 A

k^a_ad adsorption/desorption rate on anode

Eq. 6.75 s⁻¹ assumed

k_ads adsorption rate 80 s⁻¹ assumed

k_des desorption rate 50 s⁻¹ assumed

k_eva evaporation rate 100 m s kg⁻¹ [137]

k_con condensation rate 100 s⁻¹ [137]

ku water uptake rate 0.1 mol s kg⁻¹m⁻² assumed

k_r water release rate 0.1 mol s kg⁻¹m⁻² assumed

k₀ reaction rate 0.001 s⁻¹ assumed

K_abs^GDL absolute permeability in GDL 8.7·10⁻¹² m² [127]

K_abs^CL absolute permeability in CL 1·10⁻¹³ m² [127]

K_rel relative permeability Eq. 6.38 n number of transfered

elec-trons

2 −

p^Ω_c capillary pressure in domain Ω

P a

p^sat saturation pressure Eq. 6.42 P a [1]

q_ORR source/sink term due to ORR Eq. 6.23 A m⁻³ qad source/sink term due to

ad-sorption/desorption

Eq. 6.29 mol m⁻³s⁻¹ q_ur source/sink term due to liquid

water uptake/release

Eq. 6.32 mol m⁻³s⁻¹ qec source/sink term due to

evap-oration/condensation

Eq. 6.40 mol m⁻³s⁻¹ qh source/sink term of the heat Eqs. 6.55-6.59 J m⁻³s⁻¹

RH relative humidity Eq. 6.41 −

s^GDL/CL_im immobile saturation 0.2/0 − assumed

α symmetry factor 0.45 −

α_drag electro-osmotic drag coeffi-cient

Eq.6.27 −

∆S enthalpy change 162.2 J mol⁻¹K⁻¹ [126]

Θ_m contact angle in ionomer channels

90.02 deg [37]

Θ^Ω contact angle in porous me-dia (GDL/CL)

105/95 deg

6.4 Modeling Liquid Water and its Transient Effects in a PEMFC

Symbol Description Value / Eq. Unit Reference

κGDL thermal conductivity of GDL 1.67 W m⁻¹K⁻¹ [126]

κCL thermal conductivity of CL 0.67 W m⁻¹K⁻¹ [126]

κ_mem thermal conductivity of mem-brane

0.67 W m⁻¹K⁻¹ [126]

κtit thermal conductivity of tita-nium

21.9 W m⁻¹K⁻¹ [144]

λ_eq equilibrated water content Eq. 6.30 − [1]

µ liquid water viscosity 0.001 kg m⁻¹s⁻¹ [96]

ν_g molar volume of ideal gas 2.2414·10⁻² m³mol⁻¹ ν_w molar volume of liquid water 1.8015·10⁻⁵ m³mol⁻¹

ρi ionomer density 1980 kg m⁻³ [114, 112]

σ_w surface tension of water 0.07 [96]

σ_contact unified conductivity of all electronic conductors normed to BP2

600/650 S m⁻¹ assumed

σ^Ω protonic conductivity in do-mainΩ

Ω^c_v vapor transfer coefficient cathode

2.4·10⁴ m⁻² assumed

Ω^c_s saturation transfer coefficient cathode

3·10² m⁻² assumed

Ω^a_w water transfer coefficient an-ode

1·10⁻⁵ m⁻² assumed

ΩT heat transfer coefficient 1150 J K⁻¹m⁻²s⁻¹ assumed Operating conditions

i_cell current density A cm⁻²

p_O2 oxygen partial pressure 0.21 atm

P total pressure 1 atm

T_coolant coolant temperature 313 K

T_DP^a anode dew point temperature various K T_DP^c cathode dew point

tempera-ture

6 Water Management in Polymer Electrolyte Membrane Fuel Cell

6.5 Enhancing Liquid Water Management by GDL

Im Dokument Investigation of dominant loss mechanisms in low-temperature polymer electrolyte membrane fuel cells (Seite 140-146)