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Problem modelling potential equations with addtional variables

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Old   October 2, 2013, 07:39
Default Problem modelling potential equations with addtional variables
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Tom Tranter
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Hi - I have a problem I'm hoping you can help with.

Short Version:
How do you solve a transport equation for a scalar additional variable that is not volumetric or specific e.g an electric potential. I know CFX has the electric potential functionality already but I need to define a new one to represent proton transport as well as electron transport. Converting units to get diffusivity in m^2/s incurs problems where additional variable is coupled to flow when it shouldn't be.


Long Version:
To give some context I am trying to model a fuel cell in CFX from scratch and this firstly requires solving two potential equations for electron transport through solid and porous domains and proton transport through a porous membrane.

The governing equations are div(grad(PhiS)) + Rs = 0 and div(grad(PhiM)) + Rm = 0. On either side of the cell Rs=-Rm and has different magnitudes on either side.

The equations are coupled to each other via the transfer current (Rs, Rm) source terms but at the moment not coupled to any fluid flow. Eventually the current transfer will be linked to species transport as hydrogen is split into protons and electrons on the anode side of the cell and recombines with oxygen on the cathode side of the cell to form water.

I have created two additional variables, PhiS and PhiM which at first I specified as volumetric and have now swithed to specific but still get problems. S stands for solid and M stands for membrane. The units for the potentials are volts and the sources are in A/m^3.

The fluid and solid models for the potentials in CFX are both poisson as the situation is not time-dependent. My first difficulty is that to solve the equations I must convert from Volts to density as if I am solving a species diffusion equation rather than an electric potential as CFX does not allow me to specify a general diffusivity in units of an electrical conductance (S/m) but rather requires the standard units of m^2/s. I have done this by multiplying the source terms by an expression called unitFactor = 1[kg V A^-1 s^-1].

Now when running the simulation to solve the equations I find that my potentials have become dependent on the fluid flow in the domain somehow when they should be independent. I have uploaded the ccl and an image of the problem which is a cross-section of the cell to dropbox.
https://www.dropbox.com/sh/adc8n4805hvcwir/QhEwZEx-eg?m
The values of the electric potential are set by boundary conditions at the top an bottom and should remain constant until the catalyst layers either side of the central membrane region where the transfer current source terms govern the membrane potential.

I'm sure this general type of problem has been encountered before and I feel I'm close to a solution but may have done something wrong along the way.
Thanks
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Old   October 2, 2013, 17:48
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Glenn Horrocks
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If you use an unspecified additional variable it can be in any units you like and you define with with a CEL expression. Will this do what you want?

I would also ask ANSYS support on this. They may well have an example of a similar simulation they can give you which will get you started. This is likely a better way to get started rather then doing it from scratch.
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Old   October 3, 2013, 05:27
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Tom Tranter
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Hi Glenn,

Thanks for the reply. Changing the variable to unspecified only leaves me with algebraic equation as the option to solve. How would I then implement the poisson equation I need to solve?

I have contacted Ansys as you suggest but as this is for my PhD I would like to start from scratch to gain the best understanding.

p.s for completeness I forgot to include the conductivity (sigma) in the governing equations

div(sigma*(grad(PhiS))) + Rs = 0
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Old   October 3, 2013, 05:33
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Actually, forget I asked that last question. On closer inspection it looks like I had an error in one of my source terms and re-running the simulation now produces reasonable results. Sorry to waste your time.
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Old   October 3, 2013, 08:20
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Glenn Horrocks
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Good to see you have some progress.

But a general comment - a PhD does not mean you do things ignoring what others have done. You do not get a PhD by repeating what somebody else has done.
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