Electric potential and charge density around a high voltage wire

Update: June 1, 2017
OpenFOAM 4.x

Case directory

$FOAM_TUTORIALS/electromagnetics/electrostaticFoam/chargedWire

Summary

We will calculate the electric potential Φ and the charge density ρ from the following equations.

\Delta \phi + \frac{\rho}{\varepsilon_0} = 0 (Poisson equation)

\frac{\partial\rho}{\partial t}+\nabla\cdot\boldsymbol{j}=0 (principle of conservation of charge)

where ε0 is the permittivity of free space, j is the current density(current density definition), and k is the ion mobility.

The model geometry is as follows. The region up has a potential of 0 V and a charge gradient of 0. The region hole has a potential of 45000 V and a charge density of 3.57e-05 C/m2. The left, right, and down regions are symmetric boundaries, and the calculation is performed as a two-dimensional problem with a single mesh in the Z direction.

Model geometry Model geometry

The meshes are as follows.

Mesh Meshes
Mesh Meshes (XY plane)

To visualize the calculated potential and charge density, check "phi" and "rho" in the "Properties" tab on ParaView.

Check phi and rho Check "phi" and "rho"

We can see how the electric potential and charge density decrease around the region "hole".

Electric potential (phi) Electric potential (phi)
Charge density (rho) Charge density (rho)

Also, we can see how the temperature is spread by advection and diffusion.

Commands

cp -r $FOAM_TUTORIALS/electromagnetics/electrostaticFoam/chargedWire chargedWire
cd chargedWire

blockMesh
electrostaticFoam

paraFoam

Calculation time

--- *Single, Core(TM) i7-2600 CPU @ 3.40GHz 3.40GHz

Reference