# Capacitor in 3D

All the files needed for this tutorial can be downloaded here.

## Problem Definition

A rotational symmetric capacitor is modelled in 3D as a quarter model. The rotationaly symmetry is not used to illustrate 3D modelling in Trelis.

The capacitor plates have a radius $r$ and are seperated by $d$. We use a potential difference of $V$ between the electrodes.

The capacitance can be computed from the total energy $U=\frac{CV^2}{2}$.


Sketch of the domain

<-V->
<-d->

;;iiiiiiiiiiiiiiiiiiiii;;;;;;;iiiiiiiiiiiiiiiiiiiiiii;;    ^
;;tCCCCCCCCCCCCCCCCCCCG1;;;;;i                      t;;    |
i;1GCCCCCCCCCCCCCCCCCCG1;;;;;i                      1;i    |  r
;1GCCCCCCCCCCCCCCCCCCG1;;;;;i                      1;     v
LCCCCCCCCCCCCCCCCG1iiiiiiii1111111111111111111111
L////////////////////////////////////////////L1
L//////////////////////////////////////////L
L////////////  air domain  ////////////L
L//////////////////////////////////L
L/////////////////////////L
LLLLLLLLLLLLLLLL



## Meshing

1. Type 'trelis' on the terminal.
2. On the Trelis GUI open up the journal file capacitor.jou and run it.
3. A geometry of a rotational symmetric capacitor modelled in 3D as a quarter model is created.
4. Export the geometry as an ANSYS-cdb mesh file capacitor.cdb.
5. You can also save the created geometry as capacitor.trelis to open it directly on Trelis (optional).
6. Look into the journal file capacitor.jou to see the Trelis commands to create the mesh.
7. These commands could also have been run interactively in Trelis.

The file capacitor.cdb was created this way.

## Simulation with CFS

Use an XML-editor (e.g. oXygen or eclipse) to define the simulation input for CFS.

The input file capacitor.xml is the simulation input. In the file mat.xml the material porperties are defined. Both files are complete, and can be used for the example problem.

To start the computation run the following command in the terminal

cfs -p capacitor.xml job


where job can be any name you choose for the simulation.

CFS will write some output on the terminal, and produce the two files * job.info.xml, which contains some details about the run, and * job.cfs in the results_hdf5 directory, which you can view with ParaView.

## Postprocessing

1. use ParaView to visualize the field results in results_hdf5/capacitor.cfs. You can use the state file post.pvsm
2. study the integrated results in history/*, e.g. the electric energy in the region between the capcitor plates saved in capacitor-elecEnergy-region-V_elec.hist
3. campare with the analytic estimates

## Further Suggestions

You can modify the example to answer the following questions:

• How large is the influence of the stray field on the total capacitance?
• How large must the air domain around the capacitor be modelled?
• What changes if one uses polyimide between the electrodes?