Hello Dumux, I am still struggling with the boundary conditions for my system. What I want to do for the cathode side of my fuel cell model is depicted in Figure1.jpg. I want to simulate a fuel cell along one gas channel. I use the mpnc model with a 2p3c-fluidsystem. On the inlet, gas is fed to the fuel cell which may react along the channel. In the electrochemical reaction, O2 of the feed gas is consumed and H2O is produced. If the current that is produced in the cell is high enough, liquid water will be formed and transported to the outlet.
What I know is:
1. the total gas flux that goes into the system (depends on the current)
2. The gas phase composition at the inlet ( all mole fractions)
3. The saturation at the inlet (Sg=1)
4. the total flux that goes out of the system (I can calculate that
because I know the sources and sinks for H2O and O2 (see below))
5. the gas pressure at the outlet
What I want to determine from the Simulation:
1. the gas pressure at the inlet
2. the saturation at the outlet
For the boundary conditions at the outlet, I assume the following:
1. No gravity
2. Pure advection
3. Grad(x_alpha^kappa) = 0 --> no diffusion, perfect mixing
4. Grad(pg) = grad(pl) = grad(p), this means grad(Sg) = grad(Sl) = 0
With that, the molar flux out of the system of species kappa will read:
[cid:image002.png@01D0D43E.26B5E4A0]
(1)
The flux of Oxygen out of the system can be calculated via Faradays law:
[cid:image004.png@01D0D43E.B1464E20]
(2)
Where lambda is the stoichiometry factor for the fuel cell operation. A value
of lambda = 2 means that twice as much oxygen is fed to the cell as is needed
to draw the desired current and (labda-1) represents the amount of O2 that is
not consumed in the reaction (the amount that goes out). Further, I is the cell
current, 4 is the number of electrons which is transferred in the reaction, F
is Faradays constant, A is the Area of the Channel outlet and n is the normal
vector.
With that, the pressure gradient at the outlet can be calculated from (1) and
(2):
[cid:image006.png@01D0D440.38C822A0]
(3)
Inserting (3) in (1) gives the flux of an arbitrary species at the outlet:
[cid:image008.png@01D0D441.1279CF80]
(4)
Now I want to set these fluxes as Neumann conditions on the outlet for the
component conservation equations. Any comments/objections on that?
Additionally, I want to set the pressure at the outlet using a Dirichlet
condition.
For the saturation at the outlet I don't know which type of boundary condition
I can use. I don't know the value of the saturation at the outlet so Dirichlet
is not an option. Will setting a Neumann condition (values[s0Idx] = 0.0) mean
that the gradient of saturation is 0? Or what will happen if I use
values.setOutflow(s0Idx)?
Also, I don't know what to do with the pressure at the inlet. Its value should
be determined by the simulation so again, Dirichlet is not an option. Would
setting a Neumann condition (values[p0Idx] = molarGasFluxIn) mean I set the
corresponding pressure gradient?
Or could one also use an outflow condition for the pressure?
Thanks for your help
Georg
--------------------------
German Aerospace Center (DLR)
Institute of Engineering Thermodynamics | Computational Electrochemistry |
Pfaffenwaldring 38-40 | 70569 Stuttgart
Dipl.-Ing. Georg Futter | Ph.D. student
Telefon 0711/6862-8135 | georg.fut...@dlr.de<mailto:georg.fut...@dlr.de>
www.DLR.de<http://www.dlr.de/>
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