Electric Shielding Comparison

The electric shielding boundary condition is meant to approximate a thin layer of highly conductive material that provides an additional current path tangential to a boundary. This example compares the electric shielding boundary condition to a full-fidelity model and discusses the range of applicability of this boundary condition.

Figure 1: A square 2D domain of conductive material, with a circular inclusion. The wall of the inclusion are made of a material with higher conductivity.

Model Definition

The situation being modeled is shown in Figure 1. A 1 m square two-dimensional domain of conductive material has a DC voltage difference applied to it. Within the square domain, there is a circular inclusion of radius 0.25 m. The 0.01 m thick walls of this inclusion are modeled two ways, first using a full fidelity model that includes the thickness of the walls, and also using the electric shielding boundary condition. The inside of the inclusion has the same properties as the bulk.

The location of the electric shielding condition is at the centerline, midway between the inner and outer radii of the full fidelity model. Note that, when using the electric shielding condition, the total volume of the surrounding material is slightly larger, since the thickness of the wall is not being explicitly modeled. The conductivity of the wall of the inclusion is varied.

Results and Discussion

The voltage distribution and the electric field strength is plotted in Figure 2 for the case where the electric conductivity is one thousand times greater in the wall of the inclusion than in the bulk. This represents a thin walled object that allows significant current flow along its surface, that is, it shields whatever is inside the inclusion from the electric fields and current flow. The current can be observed to flow toward the inclusion, and then along the surface. The solutions for the full fidelity and electric shielding model agree well for the cases where the conductivity is greater than the surrounding medium.

Figure 2: A surface plot of the electric field norm, together with isolines of the electric potential and an arrow plot indicating the electric field direction, for the case of a thin layer of material that has a high conductivity. The full fidelity (left) and electric shielding (right) solutions are almost identical.

Figure 3 shows the case where the electric conductivity in the wall of the inclusion is only ten times greater than the surroundings. The electric shielding condition still agrees well with the full fidelity model.

Figure 3: A surface plot of the electric field norm, together with isolines of the electric potential and an arrow plot indicating the electric field direction, for the case of a thin layer of material that has conductivity ten times greater than the surrounding material.

Figure 4 shows the case where the electric conductivity in the wall of the inclusion is ten times less than the surroundings. The electric shielding condition no longer agrees with the full fidelity model. Although an additional conduction path has been added tangential to the boundary, the magnitude of this conduction path is less than in the surrounding material, thus it does not noticeably alter the current flow. The electric shielding boundary condition also does not impede the current flow normal to the boundary, which is the case, as can be seen in the full fidelity model. The Contact Impedance boundary condition would be more appropriate for this case.

The electric shielding boundary condition can be used in cases where the thickness of the boundary being approximated is much smaller than the characteristic size of the model domain, and when the conductivity of the layer is greater than the surrounding medium. When this boundary condition can be used, the resulting mesh size is much smaller, saving solution time and memory.

Figure 4: For the case of a thin layer of material that has conductivity ten times less than the surrounding material. The solutions do not agree for this case.

ACDC_Module/Resistive_Devices/electric_shielding_comparison

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
sigma_1	1[S/m]	1 S/m	Conductivity, material 1
sigma_2	1[S/m]	1 S/m	Conductivity, material 2

Geometry 1

Square 1 (sq1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.05.

Square 2 (sq2)

In the toolbar, click

In the window for , locate the section.

In the text field, type -1.05.

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.245.

Locate the section. In the text field, type 0.55.

In the text field, type 0.5.

Circle 2 (c2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.25.

Locate the section. In the text field, type -0.55.

In the text field, type 0.5.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.01

Form Union (fin)

In the toolbar, click

Click the

button in the toolbar.

The geometry on the left side describes the full fidelity model. The geometry on the right side replaces the thin layer with a boundary in order to use the feature.

Create a set of selections for use before setting up the physics. First, create a selection for the wall of the inclusion.

Definitions

Full Fidelity

In the toolbar, click

Select Domains 2–5 only.

In the window for , type Full Fidelity in the text field.

Next, add a selection for the electric shielding boundaries.

Electric Shielding

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Boundaries 21–24 only.

In the text field, type Electric Shielding.

Bulk

In the toolbar, click

In the window for , locate the section.

Under , click

In the dialog box, select in the list.

Click .

In the window for , type Bulk in the text field.

Electric Currents (ec)

Ground 1

In the window, under right-click and choose .

Select Boundary 10 only.

Ground 2

In the toolbar, click

and choose .

Select Boundary 2 only.

Terminal 1

In the toolbar, click

and choose .

Select Boundary 11 only.

In the window for , locate the section.

From the list, choose .

Terminal 2

In the toolbar, click

and choose .

Select Boundary 3 only.

In the window for , locate the section.

From the list, choose .

Electric Shielding 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_1	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Material 2 (mat2)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_2	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Material 3 (mat3)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_2	S/m	Basic