Discussion Forum

Laura,

Yes, I believe the continuity equation must be fulfilled to get a consistent solution. Since the software is solving for the mass fraction of the ions, any non-conservation of the total mass should lead to non-conservation of the ion mass.

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Luke Gritter
AltaSim Technologies

What kind of equations do you have? Why can't you just keep this background gass a constant (or a constant function of time and space)?

To me it seems this kind of problem, that the background does not considerably change such that it's change has an influence on the dynamics. So you can set this field at an easily predictable value.

Thank you for the reply,
the gas density comes from gas dynamic simulation. The background gas density decreases towards the ends to about 0.05- 0.02 of the density at the injection in the middle of the tube. Therefore the velocity of the background gas also changes considerably. And it changes sign, as the gas flows to both ends of the tube. I tried a 2D plasma model. There I take the background gas density and velocity from a gas flow (transitioal flow) simulation. But I don't know, if I have to define any inlets/outlets for the background gas .
I get the error:
Detail: Undefined value found in the stiffness matrix.
There are 3864 equations giving NaN/Inf in the matrix rows for the variable comp2.Ne2
This comes only when taking the plasma density (or pressure) from the transitional flow simulation (tran.N) when I choose another distribution for the pressure the simulation runs.

I did simulation without a convective term, there everything works and results make sense. The problem is the convective term (from the background gas flow) that can not be ignored for the ion motion...

I attached the model file...

Laura,

For some reason, the software is initially seeing a zero or negative pressure when the solution process is begun. I'm not sure of the reason for this (it does not appear to be caused by the interpolation to the new mesh), but it can be easily remedied by using an expression such as max(1e-3,tran.N*1.381e-23[J/K]*30[K]) for the pressure. Make sure that the cutoff value (1e-3 in the example) is below the minimum value from the flow simulation so that the solution is not affected.

Also, in the "Values of variables not solved for", change the method from "Initial Expression" to "Solution".

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Luke Gritter
AltaSim Technologies

Thank you Luke,
now the model is running. But there still seems tobe a problem with the in- and outgoing fluxes. The incomming flux is the integrated T+ rate (respecting the recombination). The outgoing flux is the integrated (convective, diffusive and migrative) flux at each boundary in -1*normal direction. When comparing both fluxes, the incomming ammount of tritium is larger than the outgoing ammount although the solution has reached the stationary state. Do you know how this could be?
I tried the same problem in 1D, there I had the same problem with the not-matching fluxes. This came from the discontinuity of the velocity in the middle of the tube which seemed to work as an effective ion inlet.
But this should not be the case in my 2D simulation, as there is a "real" gas injection.

Laura,

How large is the difference between the net production and the outgoing flux? Could you upload the 2D model in which you see the discrepancy?

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Luke Gritter
AltaSim Technologies

Hello Luke,

in the model I attached the difference is up to four orders of magnitude. The flux that goes out is much larger than the created number of ions.
When I look at the 1D ion flux in y direction on the edges up and down, I can see that there is a large incoming flux in the middle of the tube (where the backround gas inlet is in the transitional flow). There should just be an tritium gas (backround gas) inlet in the middel of the tube and no ion inlet. Maybe this is the problem? But how can I change it?
The strange thing is that in my other attemps (witout including the transitional flow directly) the discrepancy was not that large and the rate of created number of ions was larger than the outgoing flux, the outgoing flux was ten times smaller than the creation rate.

Regards,
Laura

I changed the ion outflow BC at the side walls by an recombination surface reaction and used the T+ outflow BC only at both ends and in the middle of the tube(at the T-inlet).
Now the incomming rate and outgoing flux for the ions is sitll different, but its much closer (sum outgoing fluxes: 1.6e13 (ms)^-1, integrated rate: 2.1e13 (ms)^-1 ).
However there is still a difference between both fluxes. Do you know why?

The potential inside the tube is much larger than we expected (and then was found in the 1d-model). We expected the potential to be dominated by the left (tube end) potential . In this model this should result in a quasi zero potential. But the solution is far away... This is due to the ion density (and space charge) distribution that looks also kind of strange to me...

Regards Laura

Laura,

Both Inlet and Outlet boundary conditions should be defined for T+. The Inlet boundary condition for T is not actually being used because T is not being solved for. When I add an Inlet boundary condition for T+, I get a total outgoing flux of 2.2e13 and an integrated rate of 2.4e13. The 10 % discrepancy is still a bit high, but it could possibly be improved by means of a finer mesh.

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Luke Gritter
AltaSim Technologies

Hello Luke,

thanks for your helpful answear. I tried to implement th T+ inlet but somehow I cannot get a solution for the model. Either there are these strange potential values or the solver gives the error that it can't find appropriate initial conditions.
so can you maybe upload your model file that worked for you with the inlet?

Best regards,
Laura

It seems to work now...
Thank you for your help

Hello Luke, when looking at the creation rate of ions it is much higher in my solution than the 2.6e13 1/(ms) from your solutinn. I get 1.85e14 /(ms). this is again much higher than the outgoing fluxes. And I do not understand, why the electron rate from this model (-1.3e13) is much smaller than the ion rate (it should be the same). It is even negative. How could this be? Is this because of the Stabilization? And does this influence the solution?
Can you please upload your model that gave you the right solution?
Maybe I took a to coarse mesh size or something like that.

Regards
Laura

Laura,

I've attached the file (the solutions have been cleared). The high electric potential is due to the boundary conditions - the electrons are lost at the upper and lower boundaries, but the ions are not, leading to a large positive space charge.

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Luke Gritter
AltaSim Technologies