Elmer Discussion Forum

Hello,

I have been working through the tutorial - Magnetic field induced by current in a cylindrical wire (Tutorial 7) and tested the steady state case available in elmerfem-devel/fem/tests/mgdyn_steady_wire2. I had a couple of questions regarding this:

1. How can I change the radius of the wire? What value in wire.grd file would need to be changed?

2. In tutorial 7, I solved for max. magnetic flux density (analytical) and it comes out to be 0.374 T (Mfd_analytical_1.jpeg) and not 0.0374 T as listed in the turorial. Am I missing something?

3. In mgdyn_steady_wire2, for an electric field strength of 5.340 x 10^-4 V/m, I get max. magnetic flux density (analytical) to be 2 x 10^-4 T (Mfd_analytical_2.jpeg). In the case.sif file, the number for the electric field strength is one order lower - - 5.340 x 10^-5 V/m -- that results in the same max. magnetic flux density (2 x 10^-4 T). What am I missing here?

4. In mgdyn_steady_wire2, I worked through the units and I end up with Weber/m and not Tesla (Mfd_analytical_3.jpeg). Why is this?

Thank you for any information you can provide.

Ilaj

Calculations

1. http://www.nic.funet.fi/pub/sci/physics ... Manual.pdf

The mesh is defined as rectangles and then revolved into a cylinder, the rectangles are the subcell divisions

Hello,

Thank you for sharing the manual. I went through it (chapter 3 in particular),and I do have a better understanding of the .grd file. But I am still not sure how to modify the wire.grd file to change the radius (or the diameter) of the wire.

***** ElmerGrid input file for structured grid generation *****
Version = 210903
Coordinate System = Cartesian 2D
Subcell Divisions in 2D = 3 1 ##3 sub cells in X and 1 in Y
Subcell Limits 1 = 0 0.5 1.0 5.0 ##x coordinate
Subcell Limits 2 = 0 10.0 ##y coordinate
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

I am assuming the sub cell limits 1 and 2 the X and Y coordinates of the points on the rectangle. The radius of the wire, 0.01 m, should be the difference in X coordinates, but the difference in the X coordinates for any of the combinations is not 0.01. Also, what are the coordinates of the rectangle?

Thanks again.

Ilaj

In the sif the coordinates are scaled

Coordinate Scaling = 1.0e-3

Therefore in the grd file 10 is .01 in the simulation, but the wire radius in grid file appears to be 1 so the wire radius is .001 in simulation, possibly explains your question 2, 3, and 4.

Elmergrid file is this
ends up like this in GUI, Revolve Blocks = 4 means 360 degrees ( 0 , 90 , 180, 360)
Wire diameter in simulation is 0.001

Thanks! I was able to modify the radius of the wire using the .grd file.

One follow up question. I am attempting to determine the magnetic field density for a specific electric current density.

In the tutorial (mgdyn_steady_wire), for an electric field strength of 5.340 x 10^-4 V m-1, the magnetic field density is 1.99 x 10-4 Tesla . The analytical solution was 2 x 10^-4 Tesla. Please find the case.sif file attached.

Using the electric conductivity and electric field strength listed above, I determined the electric current density.
Electric current density = Electric conductivity x Electric field strength
Electric current density = 59.56 A m-2 V x 5.340 x 10^-4 V m-1
= 31821.06 A m3
(electric conductivity of copper is 59.56 A m-2 V)

I then used that as the input in the Elmer file instead of the electric field strength. Please find the modified_case.sif file attached.

The magnetic field density does not match with the case above as it should considering the same numbers were used, except that the input was electric current density and not electric field strength. I referred to model 16 -- computation of magnetic fields in 3D -- in Elmer Modes Manual but I couldn't find a solution to the problem that I am having. How should I proceed?

Hi

Quickly looking I think you should define the potential AV on the ground.

At least one node of the potential needs to be fixed since otherwise the system does not have a unique solution. Even then if you just give Neumann conditions they should allow for a divergence free solution. Now you have an outlet current but no inlet current.

-Peter

Hi Peter,

Thanks for letting me know. I had a follow up question -

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.

Ilaj

P.S. My attempt:
Elmer value for max. joule heating = 2.048488472220E+003
Analytical value max. joule heating = 0.5341 x 10^-4 W

Hi

Is the the integral or local value of the Joule heating that you report for Elmer? What if multiplied by volume?

-Peter