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Induction heating of the material with temperature dependent properties

QuickField simulation example

A steel billet is heated in the inductor. Electromagnetic and thermal properties of the billet are highly dependent on the temperature. QuickField simulation of the electromagnetic and thermal processes is performed using the specially developed script which automates the multiphysics coupling with temperature-adjusted material properties.
The general idea, geometry model dimensions and material properties are taken from this paper [1].

Engineering question
How to find induction heating of billets with temperature-dependent material properties?

Engineering answer
Set up an axisymmetric QuickField AC Magnetics problem for a billet with temperature-dependent material properties and evaluate induction heating from computed field results.

Typical applications
induction heating billets, longitudinal flux heaters, Curie temperature heating systems

Problem Type
Axisymmetric multiphysics problem of AC magnetics coupled to transient Heat transfer.

Geometry
Induction heating permeability A steel billet is heated in the inductor. During the heating process the electrical, magnetic and thermal properties of the billet are changing. Fire resistant material Coil Billet Insulating material Air Ø 140 mm Ø 110 mm Ø 100 mm Ø 84 mm Ø 55 mm

Given
The initial temperature is 25°C.
Coil linear current density is 700 A (r.m.s) per 1 cm of the coil length. Frequency is 8 kHz.
Billet density 7860 kg/m³.

At the temperature above 760°C magnetic permeability is 1.1.

Task
Calculate the temperature distribution in the billet during the induction heating process.

Solution
We follow the simulation approach laid out in [1], and utilize a specially developed Microsoft Excel VBA script to automate it workflow of the simulation process:

  1. Geometry model is prepared with the billet divided into several zones, to use the B-H curve tables specific to the average temperature of each zone.
    Billet induction heating Billet 0.2 mm 0.5 mm 1 mm 2 mm 5 mm 10 mm Axis of rotation
  2. AC Magnetic and Transient Heat Transfer problem are created for this geometry model. Simulated time period is very short, to consider material properties not varying significantly during this time interval (later called 'stage').
  3. AC magnetic problem and then Transient Heat Transfer problems are solved, eddy losses distribution is imported to the Transient Heat Transfer problem. Temperature rise over a first time stage is calculated.

    Following actions are performed automatically, using Microsoft Excel VBA script:

  4. Temperature distribution at the end of the finished stage is imported into the AC magnetic problem. Internal algorithms of QuickField use electrical conductivities related to the current temperature for any point of the model. The B-H curve data for each zone of the heated billet are generated by the script, basing on the average temperature of the zone.
    Billet induction heating Loss power Initial T = +25°C Time AC magn AC magn #1 AC magn #2 Trans. thermal Trans. thermal #1 Trans. thermal #2 Attenuate material properties to the new temperature distribution Pass so far calculated temperature distribution as an initial state to the next thermal problem
  5. Using controls of the script, these actions are repeated for the specified number of time stages, or till the specified temperature is reached. All the corresponding AC Magnetic and Transient Heat Transfer problems, which form a chain of time stages, are saved in the separate directory.

Results

Temperature variation in time
Temperature variation in time

Reference:
1. H. Kagimoto, D. Miyagi, N. Takahashi, N. Uchida and K. Kawanaka, "Effect of Temperature Dependence of Magnetic Properties on Heating Characteristics of Induction Heater", in IEEE Transactions on Magnetics, vol. 46, no. 8, pp. 3018-3021, Aug. 2010.