problem simulating electrical field in non-linear insulation material

[heilke]

Hello Elmer users,

I am trying to simulate the electric field distribution in a HVDC cable. The field in the insulation depends on the conductivity κ of
the insulation material which is affected by the temperature T and the electric field strength |E|.

The model is given by the weakly coupled set of equations (stationary case):
∇( κ grad(ϕ) ) = 0
-∇λ grad(T) = Q

The functions for the material properties (electric conductivity κ and thermal conductivity λ) are described in the literature. The temperature difference ΔT between the inside conductor and the outside field shielding has a significant influence on the electric field distribution in the insulation material.

For a simulation in Comsol see Ye et al.

2011 Ye et al - Coupled Electro-thermal Field Simulation in HVDC Cables.pdf

(497.56 KiB) Downloaded 42 times

My model is clearly wrong because the electric field doesn't change if I change ΔT. I used the Static Current Conduction and the Heat Equation model to calculate the electric field and temperature distributions. I think the problem lies in the way I tried to implement the dependence of κ on T and |E|, but I don't find the error.

See the calculated field distributions for ΔT = 0, 2 and 12 K (no significant change):

dTall_Em_line.png (23.25 KiB) Viewed 387 times

See also my .sif file.

case.sif

(3.03 KiB) Downloaded 35 times

Thanks for your help.

Heilke

[kevinarden]

Made a mesh from the pdf paper.
You are running steady state and each solver runs one after another
Your heat conductivity depends on temperature and your conductivity depends on temperature and electrical field
The electrical field solver goes first, but the temperature field has not been calculated
The heat solver goes second and calculates the temperature field
However you have
Steady State Max Iterations = 1
so the solution stops, I changed it to 10, so know the field calculator and the temperature calculator
are passing the results back and forth, instead of 1 time.
I don't know if 10 iterations is enough, maybe it has not converged, but at least results vary with Delta T

results.PNG

(64.4 KiB) Not downloaded yet

[raback]

Hi

I think the Joule heating term Q is missing. Look at test case "current_heat_control". The "joule heat = true" activates it (this has some control too, but don't use it). As Kevin rightly pointed out you need some steady state iterations. Also set nonlinear system iterations to 1 and relaxation factor to, say 0.5. This is usually enough for fixed point iteration of this kind of problems if there are convergence issues.

-Peter

[heilke]

Hi Kevin, Peter,

Thanks for your quick and clear responses. I understand better the iteration scheme.

I implemented your suggestions (increase steady state iterations, include Joule heating term, set solver parameters) in the model, but now the solver doesn't seem to converge. After 3 iterations I get the message
"At line 5525 of file D:/ElmerBuilder/elmerfem/fem/src/Lists.F90
Fortran runtime error: Bad real number in item 1 of list input"

The resulting temperature and electric field profiles look strange:

dT12_T_line.png (21.59 KiB) Viewed 369 times

dT12_Em_line.png (26.12 KiB) Viewed 369 times

(ΔT = 12)

Here's my .sif file:

case.sif

(2.91 KiB) Downloaded 36 times

Would appreciate it very much if you could have a look at it again.

Thanks,
Heilke

[kevinarden]

setting nonlinear system iterations to 1 and relaxation factor to, 0.5
in both solvers resulted in convergence