High frequency strip heating

The Surface Impedance approach enables simulation of high frequency induction heating in few minutes, without building a huge mesh. Induced heat in a steel strip is accurately calculated in 10 minutes for 300 kHz, while traditional FEM simulation takes about 10 hours.

Induced heat in the steel strip at 300 kHz and 750 A

About the surface impedance approach

For induction heating with high frequencies, when EM field has very shallow penetrates into a workpiece, the skin depth may be measured in microns. Traditional FEM calculations, which require resolution of the skin layer by a mesh, takes hours and even days.

However, for such small penetration, induced current can be precisely calculated including a surface impedance to the equations and neglecting magnetic field inside the workpiece. In this case, we can avoid building a super fine mesh for the workpiece but use rough 2D surface mesh only.

The computational gain depends on frequency. While computational time of traditional FEM dramatically increases with frequency, exceeding a week for MHz cases, the Surface Impedance approach always delivers results in several minutes.

Read more about the Surface Impedance approach in the paper by Nerg & Partanen (2001)

Calculation accuracy

The Surface Impedance approach is mostly used to estimate induced current and Joule heat distribution, since it is predicted within 97% of accuracy already at relatively low frequencies. The skin-depth to workpiece-thickness (d/D) is suggested as a non-dimensional criteria here.

While the Surface Impedance approach predicts apparent power in a coil and Joule heat in a workpiece already at d/D < 10%, accurate temperature prediction is possible only at d/D < 0.5%. Heat is defined as a surface source, alike a cooling condition (convection or/and radiation). Therefore, temperature is underestimated with up to 30% inaccuracy for lower frequencies.

So, the Surface Impedance approach, implemented in CENOS Induction Heating simulation software, is a powerful design tool for high frequency installations.