HB 001 - Harmonic balance - Joule heating AC

Model definition

In this example, AC joule heating in a small section of aluminium wire is considered. Below is an image of the model in Quanscient Allsolve model view.

Beam model

Simulation setup guide

Step 1 - Create the geometry

In the Model section, create a box to form the beam geometry:

Name	Element type	Center point (m)	Size (m)	Rotation (deg)
box	Box	X: 0	X: 1e-3	X: 0
		Y: 0	Y: 1e-4	Y: 0
		Z: 0	Z: 1e-4	Z: 0

Click Confirm model changes.

Step 2 - Define shared expressions and materials

Proceed to the Properties section.

First, define a shared expression:

Name	Description	Expression
freq	AC frequenzy	5

Then, to define the material of the beam, pick Aluminium from the materials database and assign it to the beam volume.

Now, your shared expressions and model materials are defined.

Step 3 - Define the physics

Proceed to the Physics section to define the physics.

For joule heating, Current flow and Heat solid are needed.

Current flow

Let current flow target default to the whole geometry.
Add Constraint.
- Name it as Ground.
- As target, select an end surface of the beam with tag 2.
- Set constraint value to 0.
Add Lump I/V.
- As target, select an end surface of the beam with tag 1.
- As actuaction mode, select Current.
- Set the current expression to 1*sin(2*pi*freq*t).

Heat solid

Let Heat solid target default to the whole geometry.
Add Constraint.
- As target, select the end surfaces of the beam (tags 1 and 2).
- Set constraint value to 0.
Add Joule heating.
- As target, select the beam volume.

Now, your simulation physics are defined.

Step 4 - Set up the mesh

Proceed to the Simulations section to set up the mesh.

In this example, meshing is very simple, and can be done with the default settings. Run meshing and check the preview. The mesh should look roughly like in the image below:

Mesh

Step 5 - Simulate

In the Simulations section, create a new simulation:

Analysis type
- Multiharmonic
Fundamental frequency
- freq (5 Hz, this was set as a shared expression in Step 2)
Harmonics
- 1, 2, 3, 4, 5
Solver mode
- Direct solver
Node type
- Fast start (3 CPU, 10 GB)
Mesh
- Select the mesh you created in Step 4.
Input
- Add freq sweep with override expression linspace(1, 501, 41).
Output
- Add field outputs:
  - v harmonic 2
  - T harmonic 1
  - T harmonic 4
  - T harmonic 5
- Add custom outputs:
  - Max T1, output expression maxvalue(reg.aluminium, abs(harm(1, T)), 5)
  - Max T4, output expression maxvalue(reg.aluminium, abs(harm(4, T)), 5)
  - Max T5, output expression maxvalue(reg.aluminium, abs(harm(5, T)), 5)

Harmonics v1, v3, v4, v5 as well as T2 and T3 were omitted due to redundant results.

Run the simulation by clicking Not Run.

Step 6 - Plot results

In the Simulations section, add plots to see custom value outputs and visualizations to see field outputs.