[TemC]

Hi foamers, I Hope you're all doing well...

I'am simulating the flow of a Bingham fluid through a single cylinder, with a constant circular section. (The dimensions of this cylinder are Radius = 0.25 cm and Length = 2.5 cm). So I have one inlet, one outlet, and some lateral walls.

For the velocity field: I set 'zeroGradient' boundary condition at both inlet and outlet; for the lateral walls I set a 'noSlip' BCs, and the initial field is set to (0 0 0).

For the pressure field: I impose a fixed pressure difference between the inlet and the outlet, and a 'zeroGradient' BC for the lateral walls.

The fluid parameters are the yield stress 'tau0', and the fluid consistancy 'k'. I have chosen some values for those parameters. Now I apply a well chosen pressure gradient, so that I obtain a plugged zone with 0.18 cm of radius.
Basicaly the 'plugged zone' is a zone where the fluid velocity is constant.

So far so good.

Now I'am trying to conduct a mesh independence study, to make sure that my simulation results will not depend of the mesh coarsement anymore.

attachment1 is my tolerances, attachment2 is my discretization schemes, and attachment3 shows how my velocity profiles evolve when I refine my mesh.
- When monitoring the residuals, my criteria are reached (both for U and p);
- When checking some probe points for the pressure, they all reach a steady state;
- And about the domain imbalance, the volumetric flow rate at the inlet is exactly the opposite of the one at the outlet.

Now what bothers me is that the extension of this so called 'plugged zone' is increasing when I refine the mesh. I was expecting this extension to remain the same. May it be linked to my discretization Schemes? My tolerances? (It is a steadyState, laminar flow with Re < 0.1)

And secondly, my velocity profile doesn't seem to converge towards a 'limit' profile. Do you think I need to refine the mesh a lot more?

I hope you will find some time to share your point of view, or even some suggestions... Thanks in advance, and have a good day.

Regards.

[PanPeter]

Hi Térence,

How did you mesh your geometry? Did you add a boundary layer?

If not:
If you're interested in the velocity profile in a pipe you must take extra care to finely resolve the steep velocity gradients towards the no-slip wall.

Increase the resolution towards the pipe wall by adding boundary layers, while keeping a fine bulk resolution. Now make your mesh independence study first on the boundary layers and then on the bulk mesh.

cheers,
Fynn

[TemC]

Hi Fynn,

Thank you very much for your reply. You are really ringing a bell when talking about boundary layer. I've never thought about that... In attachment is the type of geometry I'm currently working with. I do those with Gmsh.

As you guessed, I'am interested in the velocity profile in a pipe. Can you suggest me some threads, links, or whatever where I could find more details about meshing boundary layers?

Thanks in advance, and have a good week.

Regards.

[PanPeter]

Hi,

I'm not experienced in gmsh. I like salome for meshing but you could also write a script for a blockMesh.

cheers,
Fynn

[zyliao]

Originally Posted by TemC

Hi foamers, I Hope you're all doing well...

I'am simulating the flow of a Bingham fluid through a single cylinder, with a constant circular section. (The dimensions of this cylinder are Radius = 0.25 cm and Length = 2.5 cm). So I have one inlet, one outlet, and some lateral walls.

For the velocity field: I set 'zeroGradient' boundary condition at both inlet and outlet; for the lateral walls I set a 'noSlip' BCs, and the initial field is set to (0 0 0).

For the pressure field: I impose a fixed pressure difference between the inlet and the outlet, and a 'zeroGradient' BC for the lateral walls.

The fluid parameters are the yield stress 'tau0', and the fluid consistancy 'k'. I have chosen some values for those parameters. Now I apply a well chosen pressure gradient, so that I obtain a plugged zone with 0.18 cm of radius.
Basicaly the 'plugged zone' is a zone where the fluid velocity is constant.

So far so good.

Now I'am trying to conduct a mesh independence study, to make sure that my simulation results will not depend of the mesh coarsement anymore.

attachment1 is my tolerances, attachment2 is my discretization schemes, and attachment3 shows how my velocity profiles evolve when I refine my mesh.
- When monitoring the residuals, my criteria are reached (both for U and p);
- When checking some probe points for the pressure, they all reach a steady state;
- And about the domain imbalance, the volumetric flow rate at the inlet is exactly the opposite of the one at the outlet.

Now what bothers me is that the extension of this so called 'plugged zone' is increasing when I refine the mesh. I was expecting this extension to remain the same. May it be linked to my discretization Schemes? My tolerances? (It is a steadyState, laminar flow with Re < 0.1)

And secondly, my velocity profile doesn't seem to converge towards a 'limit' profile. Do you think I need to refine the mesh a lot more?

I hope you will find some time to share your point of view, or even some suggestions... Thanks in advance, and have a good day.

Regards.

Hi Emery,
These days I met the same mesh independence problem when I simulated the plane-Poiseuille flow, i.e., when the cells incerase, the outlet flux decreases and the value didn't seem to converge to a stable value. I wonder have you solve this problem?