Dear Georg,
when you set Dirichlet boundary conditions the equation gets replaced by
the Dirichlet boundary condition. I think that's what's clear.
When you set Neumann boundary conditions in Dumux you set a value for
the entire flux term (advective + diffusive part). So when you set a
"no-flow" flow condition meaning
you set the values in the neumann boundary function to zero you really
get no flow over the boundary -> F(advective + diffusive)*n = 0. If you
set it to a value, you set the whole flux to that value.
If I understood correctly, this is NOT what you want to do in your
example. You want to set either the diffusive (something like grad c * n
= 0) or the advective (something like grad p * n = 0) part to zero and
keep the other part.
This is unfortunately not possible conveniently. What you have to do is
to use the function solDependentNeumann(). In that function (you
probably know the function) you have the current element volume
variables at hand.
So, if you want to set the diffusive flux to zero, you calculate the
advective flux in the solDependentNeumann function -> the total flux
gets replaced by the advective flux. The same works of course the other
way around.
You basically calculate the local residual inside the
solDependentNeumann function, leaving out either the advective or the
diffusive flux.
Note that the values obtained from the solDependentNeumann function get
multiplied with the face area during assembly, so you don't have to /
shouldn't do that in the function already.
I hope this works out for you.
Timo
On 08/11/2015 02:50 PM, georg.fut...@dlr.de wrote:
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 (S_g =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 à no diffusion, perfect mixing
4.Grad(p_g) = grad(p_l ) = grad(p), this means grad(S_g ) = grad(S_l ) = 0
With that, the molar flux out of the system of species kappa will read:
(1)
The flux of Oxygen out of the system can be calculated via Faradays law:
(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):
(3)
Inserting (3) in (1) gives the flux of an arbitrary species at the outlet:
(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/>
_______________________________________________
Dumux mailing list
Dumux@listserv.uni-stuttgart.de
https://listserv.uni-stuttgart.de/mailman/listinfo/dumux
--
____________________________________________________________________
Timo Koch phone: +49 711 685 64676
IWS, Universität Stuttgart fax: +49 711 685 60430
Pfaffenwaldring 61 email: timo.k...@iws.uni-stuttgart.de
D-70569 Stuttgart url: www.hydrosys.uni-stuttgart.de
____________________________________________________________________
_______________________________________________
Dumux mailing list
Dumux@listserv.uni-stuttgart.de
https://listserv.uni-stuttgart.de/mailman/listinfo/dumux
