Problem with fluid dynamics of a heat exchanger

[Unisa]

Dear Moderator,

I'm studing a model to simulate a heat exchanger with concentrical tubes.
The problem is that the system works well only with a particular lenght (L=20*Ree) of the exchanger.
I need to increase the lenght (ie L=50*Ree) but the response of the model in this case is not correct as before.
I also tried to icrease the lenght using the function "staged" but it doesn't help me.

What can i try to do?

I post the .pde file here.
Thank you in advance,
best regards!

[moderator]

I do not think this has anything to do with the length. I believe your penalty factor of 1e7 in your pressure equation is too severe. 1e4 is the value that professor Backstrom uses in his examples and that value works when I try it.

Once this change is made the solution shows signs that your boundary conditions on the left end are not consistent with your equations (there is a VR component at that end). I would suggest re-checking your BCs.

[Unisa]

Hello,
i'm still studying this kind of problem. Some days ago I bought professor Backstrom's ebook: "Simple Fields of Physics by Finite Element Analysis" and i have to say it has helped me.
I also changed the boundary conditions as you suggested me, including the velocity vr at the outlet.

Now i have another great problem: the time of computing!
Could I reduce this time? Seems that i'm not able to reduce the nodes below the minimum number that FlexPDE calculates at the begining. Is It correct?

Another consideration is that the value 10^4 used by Prof. Backstrom in his simple example (Uniform Velocity of Injection at Re>>1: "sim241.pde") in my case isn't the best choice for each stage. I mean that in some case div(v) seems to be different from zero (i saw a decrease of velocity, in particular in the external tube).

Thank you in advance to everyone who will answer.
Best regards.

[moderator]

The reason this problem runs a long time is that FlexPDE is unable to converge on a solution.
If you look at the output plots, you will see that the trial solutions are producing velocities and pressures in the range of 1e6 or greater, in spite of your programmed input velocities significantly less than 1.
The usual cause of this kind of behavior is an incorrectly posed PDE system, especially in the imposition of boundary conditions that are inconsistent or in conflict with the meaning of the PDE.
In order for FlexPDE to find a solution, the solution must actually exist. Behavior of the kind you are seeing usually means that it does not.

I suggest you start with a simpler problem, perhaps a single tube, and see if you can get that one to work correctly before adding complications.

[Unisa]

[quote="moderator"]you will see that the trial solutions are producing velocities and pressures in the range of 1e6 or greater[/quote]
I'm sorry, but i didn't see any of this. When the problem converges the values seem to be good. (the problem is "when")

As you suggested me, I re-checked my boundary conditions(BC) and I think that they are correct! (In my trials i have also used the same BC used by prof. Backstrom and... we should trust in him).
The program starts and gives (good) results for the low velocities (until the 4th step in the "complete configuration" using FlexPDE 5 Pro), then, doesn't converge anymore! If the problem are the wrong BC we would obtain nothing in any case.

However I applied your advice before to reply : i splitted the problem considering one tube per time, with the same BC of the "complete version".
Using "FlexPDE6 Trial" I obtained good results until the 11th step, using "FlexPDE5 Student" until the 4th step, then in both cases, only errors.
I can't understand! Why it diverges?

A little good news to conclude: I partly resolved the problem of computing time adding "SELECT THREADS = 2".
This command allow to use (i know, only partially with FlexPDE 5) the second processor.
Best regards and thank you for your time