Integration of the detailed channel two-phase flow into three-dimensional multi-phase simulation of proton exchange membrane electrolyzer cell

ABSTRACT

In this study, we proposed a novel method that integrates the detailed channel two-phase flow into the 3D (three-dimensional) multi-phase full-cell model of PEMEC (proton exchange membrane electrolyzer cell), which makes it able to predict the effect of oxygen in anode channel on the transport phenomena in the porous electrode and cell performance. It is found that if neglecting the oxygen in anode channel, the simulation results of parallel and serpentine flow fields using 3D full-cell model will be almost the same, which is contrary to the experimental results. But if we add the oxygen volume fraction distribution at the interface of channel and L/GDL (liquid/gas diffusion layer) into the 3D full-cell model as the boundary condition of oxygen equation solved in the porous electrodes, the simulated polarization curves will fit the experimental data reasonably, indicating that the oxygen in anode channel cannot be neglected. In addition, the channel oxygen plays a vital role in the distributions of oxygen, current density, and temperature in the porous electrodes mainly because it largely hinders the oxygen removal process. Then, we extended it to the integration of modeling the detailed channel two-phase flow by VOF (volume of fluid) method into the 3D multi-phase model of PEMEC. Based on this integration method, the influence of oxygen in anode channel on the transport phenomena and cell performance can be investigated in detail.

KEYWORDS:

• PEMEC
• 3d multi-phase full-cell model
• VOF method
• two-phase flow
• model validation

Nomenclature

$A$	=	Area (m2)
$C_{\mathrm{p}}$	=	Specific heat (J kg−1 K−1)
$D$	=	Diffusion coefficient (m2 s−1)
$E_{\mathrm{r}\mathrm{e}\mathrm{v}}$	=	Thermodynamic voltage (V)
${E_{\mathrm{a}\mathrm{c}\mathrm{t}}}_{,\mathrm{a}}$	=	activation energy (J)
${E_{\mathrm{a}\mathrm{c}\mathrm{t}}}_{,\mathrm{c}}$	=	activation energy (J)
F	=	Faraday’s constant (96487 C mol−1)
Fs	=	The surface tension source term (N m−3)
g	=	Gravitational constant (m s−2)
h	=	Latent heat (J mol−1)
I	=	Current density (A m−2)
$J$	=	Volumetric reaction rate (A m−3)
$J_{0,\mathrm{a}}^{\mathrm{r}\mathrm{e}\mathrm{f}}$	=	Anode reference exchange current density(A m−3)
$J_{0,\mathrm{c}}^{\mathrm{r}\mathrm{e}\mathrm{f}}$	=	Anode reference exchange current density(A m−3)
K	=	Intrinsic permeability (m2)
$k$	=	Relative permeability or thermal conductivity (W m−1 K−1)
M	=	Molar mass (kg mol−1)
m	=	Mass flow rate (kg s−1)
$\vec{n}$	=	The unit normal vector on the interface
$n_{\mathrm{d}}$	=	EOD coefficient
${\vec{n}}_{\mathrm{w}}$	=	Unit vectors normal to the channel wall
P	=	Pressure (Pa)
Pc	=	Capillary pressure (Pa)
R	=	Universal gas constant (J mol−1 K−1)
S	=	Source term (kg m−3 s−1, mol m−3 s−1, A m−3 or W m−3)
$s$	=	Saturation
T	=	Temperature (K)
t	=	Time (s)
${\vec{t}}_{\mathrm{w}}$	=	Unit vectors tangential to the channel wall
$u$	=	Velocity (m s−1)
$Y_{\mathrm{i}}$	=	Gas species mass fraction
Greek letters	=
$\alpha$	=	Transfer coefficient
$\gamma$	=	Water condensation/evaporation rate (s−1)
${\delta }_{\hspace{0.17em}}$	=	Thickness (m)
$\epsilon$	=	Porosity
$\eta$	=	Overpotential (V)
$\theta$	=	Contact angle (°)
${\kappa }_{\mathrm{e}}$	=	Electric conductivity (S m−1)
${\kappa }_{\mathrm{i}\mathrm{o}\mathrm{n}}$	=	Ionic conductivity (S m−1)
$\lambda$	=	Membrane water content
$\mu$	=	Dynamic viscosity (kg m−1 s−1)
$\xi$	=	Stoichiometric ratio
$\rho$	=	Density (kg m−3)
$\sigma$	=	Surface tension coefficient (N m−1)
${\phi }_{\mathrm{e}}$	=	Electric potential (V)
${\phi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$	=	Ionic potential (V)
$\omega$	=	Electrolyte volume fraction
Subscripts and superscripts	=
a	=	Anode
c	=	Capillary or cathode
CH	=	Channel
CL	=	Catalyst layer
con	=	Consumed
drag	=	Electro-osmotic drag
e	=	Electrical
eff	=	Effective value
g	=	Gas phase
H2	=	Hydrogen
H2O	=	Water
i	=	Gas species
in	=	Inlet
ion	=	Ionic
l	=	Liquid phase
L/GDL	=	Liquid/gas diffusion layer
m	=	Mass or mixture
mem	=	Membrane
O2	=	Oxygen
Out	=	Outlet
ref	=	Reference value
sat	=	Saturation state
T	=	Temperature
u	=	Momentum
v-l	=	Vapor to liquid phase
w	=	Channel wall

Additional information

Funding

This work was supported by the China–UK International Cooperation and Exchange Project (Newton Advanced Fellowship) jointly supported by the National Natural Science Foundation of China [51861130359]; UK Royal Society [NAF\R1\180146]; National Natural Science Foundation of Tianjin (China) for Distinguished Young Scholars [18JCJQJC46700].