HARTMANN PROBLEM

Numerical methods and mathematical models of Elmer
Andrea_P
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HARTMANN PROBLEM

Post by Andrea_P »

Hi,
I want to simulate the "Hartmann Problem." I have an electrically conducting, viscous, incompressible fluid between two parallel plates with an applied transverse magnetic field. The pressure varies only in the x-direction. The channel extent in the z-direction is much greater than that in the y-direction so that no variations occur whit z. The electrodes are assumed to be perfect conductors. I have attached the case.sif, themes, and a figure to explain the problem. I have tried to simulate this problem but without convergence. I thank you for any suggestions.
Regards,
Andrea
Attachments
Immagine 2021-05-09 201236.jpg
Immagine 2021-05-09 201236.jpg (20.5 KiB) Viewed 2345 times
case.sif
(4.04 KiB) Downloaded 141 times
beam_step.step
(16.72 KiB) Downloaded 139 times
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
kevinarden
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Re: HARTMANN PROBLEM

Post by kevinarden »

You might start with units, your constants and materials appear to be SI units, so your beam is 1000 meters by 50 meters. Large domains tend not to converge well. If this was supposed to be 1 meter by .05 meter then there is a scaling command that can be used in the sif file, in the Simulation Section.


Coordinate Scaling = 0.001
Andrea_P
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Re: HARTMANN PROBLEM

Post by Andrea_P »

Hi,
I have proved, but it does not converge. Is there any example already developed of this kind of problem?
Regards,
Andrea
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
kevinarden
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Re: HARTMANN PROBLEM

Post by kevinarden »

Not that I know of, but since you have the mag and the stokes solvers, it is best to specify the boundary conditions for both solvers at every boundary. IS it diverging on the stokes or the mag? I would guess stokes, especially if the velocity is too high.

Boundary Condition 1
Target Boundaries(1) = 4
Name = "potencial wall"
AV {e} 3 = 0.01
AV {e} = 0
End

Boundary Condition 2
Target Boundaries(1) = 2
Name = "wall"
AV {e} = 0
AV = 0
AV {e} 3 = 0
End

Boundary Condition 3
Target Boundaries(1) = 6
Name = "outlet"
External Pressure = 3.97
End

Boundary Condition 4
Target Boundaries(1) = 3
Name = "top"
Noslip wall BC = True
End

Boundary Condition 5
Target Boundaries(1) = 1
Name = "bottom"
Noslip wall BC = True
End
Andrea_P
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Re: HARTMANN PROBLEM

Post by Andrea_P »

Yes, it is diverging in stokes solver. I put the boundary conditions like yours.
Andrea
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
Andrea_P
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Re: HARTMANN PROBLEM

Post by Andrea_P »

How can I impose an external magnetic field in Elmer?
Andrea
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
kevinarden
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Re: HARTMANN PROBLEM

Post by kevinarden »

I just reiterated your BC as an example, what I meant was you need stoke's BCs on all 6 boundaries. Also the pressure is to high for laminar flow. Non-laminar flow often will not have a steady state condition, meaning it will never converge in steady state. This example converges
beam3d.grd
(743 Bytes) Downloaded 139 times
ycase.sif
(4.28 KiB) Downloaded 140 times
You can turn beam3d.grd into a mesh with
ElmerGrid 1 2 beam3d.grd
Andrea_P
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Re: HARTMANN PROBLEM

Post by Andrea_P »

Thanks for your answer and help. I have run your case but it does not converge. I attached the output file. I didn't understand this:
You can turn beam3d.grd into a mesh with
ElmerGrid 1 2 beam3d.grd
.
Andrea
Attachments
output.txt
(18.33 KiB) Downloaded 133 times
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kevinarden
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Re: HARTMANN PROBLEM

Post by kevinarden »

Convergence can be mesh sensitive as well. The program ElmerGrid converts various formats in an elmer, including and elmer grid file.
To execute the program you use a terminal window or command prompt window and type

ElmerGrid 1 2 beam3d.grd

the program creates a mesh in a folder called beam3d

If you type ElmerGrid with no arguments it lists all of the options.

If you ran my sif with your mesh it may not match up, the type of elements, and boundary numbers were different.
Andrea_P
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Re: HARTMANN PROBLEM

Post by Andrea_P »

Hi Kevin,
Is it possible applying an external electric field like the magnetic one in Elmer?
Regards,
Andrea
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
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