Magnetic field induced by current in a cylindrical wire

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asandip
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

Thank you!

Multiplying the volume with the Elmer joule heating does bring Elmer joule heating close (if not, the same) to theoretical joule heating for the given dimensions.

I modified the radius (radius = 0.002 m) in the wire.grd file, length stayed the same (0.01 m), and solved for joule heating. Here are the results:
Elmer joule heating: 1.70E3 (max. joule heating e) X 1.256E-7 (volume) = 2.126E-4
Theoretical joule heating: 1.336E-05

I modified the length (0.02 m) in the wire.grd file, the radius stayed the same (0.001 m), and solved for joule heating. Here are the results:
Elmer joule heating: 4.2510E2 (max. joule heating e) X 6.283E-8 (volume) = 2.6709E-5
Theoretical joule heating: 0.000106

In the wire.grd file, I changed the value of radius, 'R', and length 'L, to modify the geometry.
***** ElmerGrid input file for structured grid generation *****
Version = 210903
Coordinate System = Cartesian 2D
Subcell Divisions in 2D = 3 1
Subcell Limits 1 = 0 0.5 R 5.0
Subcell Limits 2 = 0 L
Material Structure in 2D
1 1 2
End
Materials Interval = 1 2
Boundary Definitions
! type out int double of the boundaries
1 -1 1 1
2 -2 1 1
3 -3 1 1
4 -1 2 1
5 -2 2 1
6 -3 2 1
End
Numbering = Horizontal
Element Ratios 1 = 1 0.2 10.0
Element Ratios 2 = 1
Element Divisions 1 = 4 8 8
Element Divisions 2 = 10
Revolve Blocks = 4
Revolve Improve = 0.0


How should I proceed? Thanks for your help!
Attachments
wire.grd
(764 Bytes) Downloaded 254 times
case.sif
(4.71 KiB) Downloaded 254 times
annier
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Re: Magnetic field induced by current in a cylindrical wire

Post by annier »

asandip wrote: 03 Apr 2020, 03:00

What is the relation between length of the wire, radius of the wire and joule heating? I looked for the equation in Elmer Modes Manual (chapter 16) but couldn't find one. Thank you for any information you can provide.
Dear Ilaj,
If you look closely at Eq. 16.9 of the Elmer model manual,
the unit of h is [(V/m)*(1/(ohm *m))* (V/m)] , which is equal to [W/m^3].
Hence, the joule heating power is P (W) = integration of h over volume.

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
asandip
Posts: 92
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

Thanks, Anil.

Multiplying the volume with the Elmer joule heating does bring Elmer joule heating close (if not, the same) to theoretical joule heating for the given dimensions.

I modified the radius (radius = 0.002 m) in the wire.grd file, length stayed the same (0.01 m), and solved for joule heating. Here are the results:
Elmer joule heating: 1.70E3 (max. joule heating e) X 1.256E-7 (volume) = 2.126E-4
Theoretical joule heating: 1.336E-05

I modified the length (0.02 m) in the wire.grd file, the radius stayed the same (0.001 m), and solved for joule heating. Here are the results:
Elmer joule heating: 4.2510E2 (max. joule heating e) X 6.283E-8 (volume) = 2.6709E-5
Theoretical joule heating: 0.000106


In the wire.grd file, I changed the value of radius, 'R', and length 'L, to modify the geometry.
***** ElmerGrid input file for structured grid generation *****
Version = 210903
Coordinate System = Cartesian 2D
Subcell Divisions in 2D = 3 1
Subcell Limits 1 = 0 0.5 R 5.0
Subcell Limits 2 = 0 L
Material Structure in 2D
1 1 2
End
Materials Interval = 1 2
Boundary Definitions
! type out int double of the boundaries
1 -1 1 1
2 -2 1 1
3 -3 1 1
4 -1 2 1
5 -2 2 1
6 -3 2 1
End
Numbering = Horizontal
Element Ratios 1 = 1 0.2 10.0
Element Ratios 2 = 1
Element Divisions 1 = 4 8 8
Element Divisions 2 = 10
Revolve Blocks = 4
Revolve Improve = 0.0


How should I proceed? Thanks for your help!
Attachments
wire.grd
(764 Bytes) Downloaded 243 times
case.sif
(4.71 KiB) Downloaded 245 times
raback
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Re: Magnetic field induced by current in a cylindrical wire

Post by raback »

Hi

You cannot just change one value in the "subcell limits 1". Probably you entangle the mesh. The other values should be in proportion.

I just tested the scaling by altering

Code: Select all

  Coordinate Scaling(3) = 1.0e-4 1.0e-4 1.0e-3

i.e. scaling (x,y) differently than z. The "joule heating e" does not depend on the scaling of radius. Scaling by length shows inversely quadratic dependence as it should.

So unfortunately I cannot find anything wrong here.

-Peter
asandip
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

Hi Peter,

Thank you for your suggestions. I modified my case.sif file (attached). I continue to get the same numbers for max. joule heating that do not match with the theoretical numbers.

I modified the radius (radius = 0.002 m) in the wire.grd file, length stayed the same (0.01 m), and solved for joule heating. Here are the results:
Elmer joule heating: 1.70E3 (max. joule heating e) X 1.256E-7 (volume) = 2.126E-4
Theoretical joule heating: 1.336E-05

I modified the length (0.02 m) in the wire.grd file, the radius stayed the same (0.001 m), and solved for joule heating. Here are the results:
Elmer joule heating: 4.2510E2 (max. joule heating e) X 6.283E-8 (volume) = 2.6709E-5
Theoretical joule heating: 0.000106

How do I modify the radius and the length in the wire.grd file and keep all other values in proportion?

Thanks,
Anjali
Attachments
wire.grd
(764 Bytes) Downloaded 220 times
case.sif
(4.72 KiB) Downloaded 235 times
annier
Posts: 1168
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Re: Magnetic field induced by current in a cylindrical wire

Post by annier »

Dear Anjali,
The analytical equation [Eq. 3 in https://asmedigitalcollection.asme.org/ ... m=fulltext) for the joule heating in a regular cylinder of base area (A) and height (l) is given by:
P (W) = j^2 * resistivity* A *l(please note the volume is a regular one).

In a finite element mesh of 2D (for example, for a coarse mesh, a circle will be represented by a polygon of n sides , where n is a finite number), whereas a regular circle has n equal to infinity. The joule heating computed by FEM is obtained different than that of analytical one.
Can you make the mesh finer so that n tends to be near to infinity, and the curved surface area of cylinder is near to a regular cylinder?. In other words, can you increase the mesh density and see if this produces the difference in joule heating?

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
asandip
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

Anil,

Thank you for your response. I understand that numerical approximation and analytical solution may not be the same, but they should be close. I tried to refine the mesh based on your suggestions (modified max. H), but for whatever reason, it wouldn't go through.

Please find the wire.grd and the associate mesh files attached. Thank you for any information you can provide.

Anjali
Attachments
mesh.header
(35 Bytes) Downloaded 259 times
mesh.elements
(285.69 KiB) Downloaded 230 times
mesh.boundary
(64.29 KiB) Downloaded 240 times
Last edited by asandip on 08 Apr 2020, 01:00, edited 1 time in total.
asandip
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

Additional files.
Attachments
wire.grd
(764 Bytes) Downloaded 225 times
mesh.nodes
(174.25 KiB) Downloaded 231 times
annier
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Re: Magnetic field induced by current in a cylindrical wire

Post by annier »

Hi,
Can you show the simulation result of volume current density (Fig. 3 ) as shown in the following conference paper?
https://ieeexplore.ieee.org/document/8480595

Is the distribution of volume current density in the cylindrical volume uniform?

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
asandip
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Re: Magnetic field induced by current in a cylindrical wire

Post by asandip »

I don't have access to the the full pdf. Could you share Figure 3?
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