What Causes the Non-Circular Distribution of Magnetic Fields in Steel Ducts?

[Willy]

Hi all, first time on this forum.

I know this may sound like a stupid question, but how does the magnetic field distribute?

I am working on FEMM and i am analysing magnetic losses on steel ducts. I was checking the flux density and the magnetic field distributions and i was surprised when i did not see a circular distribution of the magnetic field (magnetic field generated from 3ph HV line).

Now, i have studied that an infinite wire can generate a circular magnetic field according to the equation: I/(2*pi*r). As there are no material parameters i have concluded that the magnetic field distribution would be circular INDIPENDTLY FROM THE ENVIRONMENT conditions.

i was not expecting a circular distribution obviously, but for sure the field intensity would decrease linearly with the distance. This did not happen: the magnetic field dramatically decreases in the duct and then increases again.

Why does it decrease in the steel duct? i have changed the conductivity to 0 but nothing changed. Though it changes when i modify the permeability.

I know flux density depends on the permeability of the material, but the magnetic field should not be influenced by it.

What am i missing?

 

[Baluncore]

Welcome to PF.

It would really help if we knew the geometry of the system you are analysing.
Please post a sketch or plot of the geometry.

What FEMM software are you using?
What are the ducts, how big are they?
What passes through the ducts?
How does the 3PH HV generate the field?
I would expect the current in the 3PH conductors would sum to zero.

 

[Willy]

Hi

I am using FEMM 4.2.

The duct thickness is 3mm. Its permeability is 37. Inside the duct there is only air (and of course the cables), the duct is surrounded of soil(peat,loam). In this model the conductivity of the duct is not 0, i checked if changing the value to 0 would have an effect: nothing changed.

3ph HV cables (copper) are installed in the duct . In each cable flows a peak current equal to sqrt(2)*800 A 120° phased from each other. So yes: the sum of the three currents is equal to zero.

The image above shows the magnetic field intensity of the model.
Probably would not be easy to see, but in the duct the magnetic field is really low. So it abruptly decreases in the duct and then it increases again. The next image will show the magnetic field intensity near the duct (the left part is the magnetic field inside the duct):

I have basically two questions: Does the magnetic field H depend on the environment? If so, what affects it?

Thanks in advance.

 

[Baluncore]

The currents induced on the inside of the duct will circulate with the phases. The inside of the duct is a mirror of the phase currents.

Work out the skin depth in the duct material and compare that with the duct wall thickness.

Some of the currents induced on the inside of the duct will generate magnetic field that escapes to the outside of the duct. That may explain the (yellow) small circulating field outside the duct.

 

[Willy]

Changed the conductivity of the duct to 10^-9, so i guess the eddy currents are not affecting the magnetic field that much. Though, if i change the permeability...

Permeability of the duct=1, conductivity=10^-9. For what i know, this does not make sense.

I would really appreciate if anyone could tell me what is going on.

 

[Baluncore]

I would really appreciate if anyone could tell me what is going on.

The feeling is mutual. You know what assumptions you have made, and what is undocumented.
We can only guess.
What are the duct dimensions ?
What do the line graphs show ?
Is "distance, mm" = radius from centre of conductors or an arbitrary section across what ?
At what mm length in the line graphs is the inside and outside of the conduit ?

I believe I can see the rotating field in the colour plot, can you ?

 

[Willy]

The two graphs show the magnetic field from the inside of the duct through the duct going outside the duct.
The problem unit measurement is mm, working at 50 Hz.
Duct is 490x490x3.

The rotating field is not the problem, it makes sense that is circular as the currents are balanced, the fact is: if you take the magnetic field formula generated by currents, the relative permeability does not appear.

Though, the magnetic field in the duct changes if i change the permeability of the duct (from 4 to 7mm in the graphs). Conductivity has a really low impact on the magnetic field, but i could expect that as the eddy currents would generate an opposite magnetic field.

 

[Baluncore]

Does the magnetic field H depend on the environment?

the fact is: if you take the magnetic field formula generated by currents, the relative permeability does not appear.

The magnetic field due to an electric current is B.
https://en.wikipedia.org/wiki/Magnetic_field#The_B-field

H is dependent on μ = permeability; H = B / μ
https://en.wikipedia.org/wiki/Magnetic_field#The_H-field
https://en.wikipedia.org/wiki/Magnetic_field#H-field_and_magnetic_materials

 

[Baluncore]

Probably would not be easy to see, but in the duct the magnetic field is really low. So it abruptly decreases in the duct and then it increases again. The next image will show the magnetic field intensity near the duct (the left part is the magnetic field inside the duct):

How is the top of the duct attached? The internal circulating current wave appears to escape through the gap, to then flow over the outside of the duct. I guess that is generating the field outside the duct. Maybe you could test that by welding the cap numerically onto the conduit, so it would not leak from the internal surface conductance discontinuity.

Conductivity has a really low impact on the magnetic field, but i could expect that as the eddy currents would generate an opposite magnetic field.

The more conductive the sheet, the shallower are the eddy currents, and the more efficient is the surface as a mirror. But the energy reflected can never exceed the incident energy. So the sum of incident and reflected can approach zero, but it can never go negative, even though it is a counter current.