# HW4: Transient Coil

### Description

Consider an axi-symmetric model of a coil and a plate as depicted in the figure. The inner and outer radii of the coil, r_1 and r_2 , are 5 mm and 10 mm, respectively. The length of the coil, l_1 , is 8 mm. The plate thickness, l_2 , is 3 mm. The point C is located in the center of the coil, the point P in the middle of the plate at r = (r_1 + r_2)/2.

The plate is either made from iron or aluminum, with electric conductivity and linear magnetic permeability given in the table below. The coil has 40 turns and is fed by a controlled current.

iron | alu | |
---|---|---|

conductivity in S/m | 5.000e+06 | 3.500e+07 |

permeability H/m | 2.704e-03 | 1.257e-06 |

### Tasks

- Create a regular hexaedral mesh using Trelis.
**(1 Points)** - Create input-xml files for the required CFS++ simulations.
**(1 Points)** - Document your results by answering the questions below.
**(13 Points)**

### Hints

- Use the provided template
`coil.xml`

. - Adapt the Trelis input
`geometry-ue.jou`

. - Use the static simulation to check the prescribed current and boundary conditions.
- Use a time resolution of 20 steps per period.
- You can use an element result or
`sensorArray`

to obtain results at the points C and P.

### Submission

Submit all your input files (`*.jou`

, `*.xml`

) as well as a concise PDF report of your results. Name the archive according to the format `HWn_eNNNNNNN_Lastname.zip`

.

### Mesh Size

Estimate the skin depth for both materials. What element size do you suggest? Motivate your suggestion! **(2 Points)**

### Static Analysis

Compute the static magnetic field for a coil current of 10 A. Plot the vector field of the magnetic flux density and the prescribed current density in the coil (in one figure). Compare the cases for iron and copper plate. What is the difference? **(3 Points)**

### Transient Analysis

Set up a transient analysis with a sinusoidal coil current with an amplitude of 10 A and a frequency of 50 Hz. Compute the solution for 4 periods of the coil current. Plot the time signal of the radial flux component B_{\rm r} at the point P and the axial flux component B_{\rm z} at the point C. Describe the time signals: Are there transient effects? Do the amplitudes correspond with the static ones? **(4 Points)**

### Skin Depth

Show the total current density as well as the vector field of the magnetic flux density for the time t = 2.5/ f (in one plot for each plate material). How do the eddy currents decay over the thickness of the plate? What is the difference between the plate materials? **(4 Points)**

You can download the templates linked on this page individually by *right click --> save target as*.
Alternativey, head over to the git repository and use the *download button* on the top right:
Here is a direct link to the **zip archive**.