Angular momentum flux between regions
 

Hi.
I am trying to simulate a steady flow tumble measurement rig for cylinder head.
I soon realised that there is a problem with the angular momentum conservation (which is in fact a problem of all the finite volume CFD codes).
In order to understand what is happening, I switched to a much simpler geometry: just a cylinder with a swirling flow entering.
The tube has a total length 500mm and it is divided in 3 regions: region 1 and 3 are just 10mm short segments in the start and the end of the geometry. Region 2 is the middle part. The velocity fieled is set by file (solid body rotation in the normal to the axis plane and constant axial velocity). Steady state, laminar flow, slip walls, etc, to keep it simple. Ideally the angular momentum should be conserved until the exit of the tube, in the absence of any torque acting on the fluid. In reallity I would expect a reasonable decline (depending on the mesh refinement), due to the known issues mentioned above. But the angular momentum flux from region 1 to region 2 (just a very short length from inlet, 1 or 2 cells distance) is 30% lower than the theoritical !. That is too much and made me wonder if there is a problem in the inter-region angular momentum flux calculation in the dynamic output files, or the inter-region surface recreation, where the integration takes place.
Does anybody has come to something like that?

Any suggestion would be much appreciated.

Andreas

P.S. It would be a good featrure for CONVERGE to allow such quantities like the inter-region angular momentum fluxes, to be also calculated for bounday surfaces (inlets, outlets, etc.)

Update: It is not caused by some error in the flux calculation. Tangential velocities actually decay rapidly after inlet (1st axial cell after inlet). Then with an expected lower rate.
That is caused by the slip wall conditions in the cylinder's sidewall.
Replacing with "SYMMETRY" conditions solves the issue.

Hi, it is glad to know the issue was resolved. As you figured out, the wall boundary condition plays an important role in the conservation of momentum and angular momentum. But it is surprising the the slip wall caused a big change, since there is no friction there. It should perform the same as the SYMMETRIC for your case (according to your description). It would be great if you can send the case to us at support@convergecfd.com for a further check.

Another thing to keep in mind is that the numerical viscosity can also affect the conservation, especially when you use a coarse mesh, large CFL, and upwind scheme. It would be useful to have some sensitivity tests on the mesh size and numerical schemes you use.

I hope it helps.

Dear Shengbai,

Thank you for your reply.
I have done many tests for this case. Grid resolution surely plays a role. Central schemes also improve the results. The slip velocity and the symmetry BCs give different results.
My point with angular momentum conservation is the following (which is not only CONVERGE's issue):
Linear momentum in conservative finite volume formulation CFD codes, is inherently conserved (fluxes from each cell face is positive for one cell, negative for the adjacent cell). So when momentum residuals are low enough, what comes in, goes out (in steady state incompressible flows). Irrespectively of viscosity or mesh resolution.
That is not the case with angular momentum. Angular momentum is not conserved very well in CFD codes, and there are some publications pointing to that fact.
I have tested the exact same geometry with a different commercial CFD code (with body fitted unstructured mesh, similar grid density) and still got angular momentum loss (though lower).
With CONVERGE and the grid I used (with some embedding) I managed to get at the exit 74% of the incoming angular momentum. And that without any torque acting on the fluid (symmetry BCs at the outer wall).
As I stated in my first message that is an effect I am aware of (I just tried to get a measure of the extend of the angular momentum loss).
What initially got my attention was the rapid reduction of angular momentum after inlet, when slip wall BC is used.
I am sending you this simple case, with a small description and a reference to you.

Regards.
Andreas

Thank you. We will have some support engineers work on it once we receive the case.