Fluid channel connected to "infinite" reservoir
 

Dear Foamers,

I am trying to solve the temperature distribution in liquid helium. One part of the fluid is contained in a narrow channel, one end of the channel is a dirichlet condition with a fixed temperature of T=2.17K, the other end is the one that is giving me a hard time. The channel is connected to an "infinite" reservoir of liquid helium (no physical discontinuity between the channel and the reservoir) where T and P are assumed constant.
At first, I tried to simulate this using a modified version of the chtmultiregionfoam solver, where I split two regions, one being the channel with fluid = liquid helium, the second region being the reservoir also with fluid = liquid helium. At the interface, heat transfer takes place according to temperature differences. In the second region, I managed to modify the solver so that T would remain constant through every time step of the calculation. However, I am not sure how much this physically makes sense.
So my question is, how would you tackle such a case, meaning how would you split the domain, what boundary conditions would you set ?

Thank you !

Hi,
You wrote that you are interested in temperature distribution.
If the reservoir is at fixed temperature, why do you want to solve any equations there at all? You already know the temperature.

Hi, thank you for your reply.
Yes I am indeed solving for temperature, but I said the reservoir was kept at constant temperature T=2.17K, however at the "junction", meaning the area where the channel end coincides with the neck of the reservoir, there must be a temperature gradient, and this is what I am trying to model. Like I said in my first simulations I imposed a constant temperature in the whole region, but it comes down to solving a simple laplacian inside the channel, which does not make sense, I agree. Hence my problem !

Could you make a sketch of this? It's not completely clear to me... Is there any flow involved or just the stationary fluid? Also, what about the wall of the channel?

I attached a basic drawing of the problem. There is no flow involved, only the stationary fluid. I am getting the temperature profile from which I compute the heat flux. The problem is simple in definition, but I can't figure out what boundary condition I should set at the junction.

Thanks again for the help.

Yes this comes down to a simple laplacian :D
You can use your calculator to solve this, no need for openFoam...

You need to specify what effect you want to account for additionally. Otherwise I would actually use the calculator.

To clear any misunderstanding, I drew the dashed line only to symbolize the junction, like I said there is no discontinuity, no physical boundary.

It would be a laplacian problem if the entire fluid region in the reservoir was at constant temperature, but that is not what happens in theory. There will be a temperature gradient around the "bottleneck".

If you want to see that, you need to put a boundary of constant temperature somewhere in the reservoir - with some distance to the bottleneck.
Now do a second simulation where this boundary has a larger distance to the bottleneck and see if the result changes in your region of interest. If it doesn't, the result is independent of the boundary conditions. If if does you need to put the boundary even more far away. Do this until you get independence of b.c.

Yes that is also the idea I had, I just figured there would be a proper way to do it without having to play with the geometry parameters. But I will be working on solving it this way, meanwhile if anyone has some input to share I am still very open to suggestions.
Thank you Philipp for your help !

I know this is not very satisfying, but I don't think there is any good way to determine the best place for such thermal b.c.

No worries, I could not think of anything better. But maybe someone already modelled such a phenomenon and has a trick for it.