Polymer electrolyte membrane
fuel cells (PEMFCs) are the most promising type of fuel
cells for automotive applications. The humidification of
the gas flows to the PEMFC plays an important role to improve
durability and to increase power densities. One way to
achieve this is the selective transfer of water vapor from
the output gas flows to the input gas flows. Different
membrane materials like ionomers (Nafion) or porous polymers
can be used.
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Fig. 1: Normalized mass transfer between
wet and dry side plotted against dry side inlet
temperature.
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Fig. 2:
Normalized wet side outlet temperatures plotted
against normalized dry inlet temperatures. At the
lowest dry side inlet temperature water vapor condensation
occurs leading to a higher wet side outlet temperature
compared to the trend. |
Gas humification units
Commercially available humification devices are available as cylinders filled
with tubes. Inside the tubes, dry gas is flowing to the stack. The water
content of this gas flow must be increased. Wet gas from the stack is flowing
around the tubes. Due to the difference in partial pressure of water vapor
this species is exchanged through the tube walls that are made out of the
membrane material.
Asymmetric porous membrane materials consist of a thin dense layer with pore
sizes less than 0.5 nm. The thickness of this layer is less than 1 µm
and is supported by a carrier layer, which is usually thicker by two orders
of magnitude [1]. Due to the small pore size, capillary condensation of water
vapor, occurs in the thin layer. The permeation of other gases is therefore
blocked. Thus, the thin layer is responsible for the selectivity to water
vapor transfer.
Meshing and model strategy
To avoid large meshes, the cylinder volume where heat and mass transfer occurs
(contact volume) is approximated by a porous medium. This method is also
used in the simulation of heat exchangers. To separate dry and wet gas in
the contact volume, the cells are duplicated and assigned to different fluids.
Thus, the gas streams do not interact with each other.
This approach makes it necessary to implement heat and mass transfer in user
subroutines. The models for mass transfer are based upon a convection/diffusion
transport mechanism under consideration of capillary condensation in the
thin layer. Heat is transferred by enthalpy exchange and conduction through
the tube wall.
Furthermore, the influence of water vapor condensation on the tube walls
must be considered. Due to heat conduction and enthalpy transfer, the wet
side cools down. If the local saturation pressure on the wet gas side is
lower than the water vapor partial pressure, condensation takes place. In
this situation, the heat transfer is governed by the Nusselt water skin theory.
Mass transfer will be enhanced because the porous wall material is saturated
with liquid water. Condensation is supported by a considerable difference
between dry and wet side inlet temperature with a lower temperature on the
dry side.
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| Fig. 3:
Distribution of water vapor mass fraction on wet
and dry side at the highest dry side inlet temperature.
The arrows depict the position of the inlets and
outlets on either side. |
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Fig. 4:
Distribution of volumetric mass transfer rate on
wet and dry side at the highest dry side inlet
temperature. The arrows depict the position of the inlets and outlets
on either side. |
Comparison with experiments
After the implementation of the heat and mass transfer mechanisms ,unknown
material parameters (e.g. porosity, tortuosity, heat conductivity of membrane
material) must be determined by fitting mass transfer rates and outlet temperatures
of wet and dry side to experimental results. As test geometry a single cylinder
was taken. Due to the position of the inlets and outlets, only a 60° slice
of the cylinder with appropriate symmetric boundary conditions was necessary
to consider.
Fig. 1 shows a comparison of the calculated normalized mass transfer rates
with experiments after parameter fitting. The normalized mass transfer is
plotted against the normalized inlet temperature of the dry side. The deviation
between CFD results and experimental data is less than 5 %.
A comparison of the outlet temperature on the wet side with experimental
data is shown in Fig. 2. The deviation is larger but the trend at lowest
dry side inlet temperature is represented correctly. The decrease of the
wet side outlet temperature is slowed down due to water vapor condensation.
The heat released by condensation is an additional energy source heating
both dry and wet gas.
Figs. 3 and 4 show the distribution of water vapor mass fraction and volumetric
heat and mass transfer rate at the highest dry inlet temperature. It can
be seen that the water vapor mass fraction increases continually in axial
direction from inlet to outlet on the dry side. This is due to the axial
flow within the tubes. A radial layering of water vapor mass fraction can
be seen on the wet side following the radial injection of the wet gas.
The volumetric heat and mass transfer rates have a similar spatial distribution
showing that enthalpy transfer from wet to dry side dominates heat transfer.
The highest volumetric heat and mass transfer rates are located near the
inlets and outlets of the wet side. At the inlet, the velocity of the injected
wet gas perpendicular to the tube axis is highest leading to the biggest
Sherwood numbers. At the outlet, which is located near the dry inlet, the
difference of water vapor and the difference of partial pressure is highest.
Both effects lead to the observed distribution of the volumetric heat and
mass transfer rates.
By comparing the CFD results with experimental data, we could show that we
have a sound physical description of heat and mass transfer inside the cylinder
of a gas humification device. The model is now ready to optimize such devices
on a very short timescale.
Technical paper:
Predicting water and current distributions in a commercial-size
PEMFC
S.Shimpalee, S.Greenway, D.Spuckler. J.W Van Zee
Literature [1] Schendel, R.L. (1984): Gas separation membranes and the gas
industry. PCGA Transmission Conference.
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