FEM MODELLING OF AN INDUCTION HEATING SYSTEM

The principal geometry of the system is shown in Fig. 1. The inductor is two-layer, flat disc-type and multi-sectioned. The two layers are identical. The conductors are of rectangular crosssection.
The following notations are used for the Inductor:
The heated detail is a ferromagnetic disc of thickness h_det=0,003m. The temperature of ambient air is T₀=15^oC, the initial temperature of the heated detail is 27⁰C. The laboratory experimental setup is shown in Fig. 2.
Due to the axial symmetry of the geometry and to the cylindrical coordinates, the problem is considered as a two-dimensional one. So the numerical simulation of the heating process consists of analysis of two-dimensional electromagnetic problem coupled with transient thermal problem, taking into consideration the nonlinearities of the system (change of physical properties during the heating).     The electromagnetic problem is quasistationary and the field model with respect to the magnetic vector potential A is based on the equation:


where is angular frequency, is electric conductivity, is magnetic permeability and J is current density.
    The transient thermal field is modeled by:



where is thermal conductivity, T is temperature, is density, c is specific heat and q is power density. Equation is solved under convection and radiation boundary condition.     The coupled problem is solved using indirect coupling of the quasistationary electromagnetic and transient thermal problem. The electromagnetic problem is solved in a domain consisting of the whole system and a wide buffer zone around it. The thermal problem is solved only in the heated detail.
Two-dimensional numerical simulation of the coupled fields was carried out using FEM and ANSYS 9.0 software package.
The results are obtained for time period of 600 seconds. The following procedure was employed. The quasistationary electromagnetic problem was solved at every 10sec. taking into account the temperature dependence of the magnetic permeability and electric conductivity. As a result from the electromagnetic field analysis, the generated heat in the heated detail is obtained and used as heat source during the next 10 sec. The thermal problem was solved as nonlinear and temperature dependence of the thermal conductivity was taken into account. The finite element mesh for the electromagnetic field problem is shown in Fig.3. The results from electromagnetic field analysis are shown in Fig. 4.
For the investigated time period (600sec.) the point with maximal temperature was determined. It is the point of radius r= 0.15m and the temperature is 143⁰C. This time was considered because this was the time in which experiment was carried out. The transient heating process in this point is shown in Fig.5. The temperature distribution in the heated disc in radial direction in time t=600sec is shown in Fig. 6.

COMPARISON OF THE NUMERICAL AND EXPERIMENTAL RESULTS

The results obtained using the FEM model are compared to those obtained by experiment Temperature variations for the investigated period obtained numerically and by experiment are shown in Fig.7 for point with r= 0.06m and in Fig.8 for point with r= 0.15m. Relative error for point with r= 0.06m is shown in Fig. 9. The comparison between computation and experiment shows satisfactory agreement.

CONCLUSIONS

The results obtained using the FEM model are compared to experimental data for the transient temperature distribution. These results can be employed for further investigations concerning inverse and optimization problems when special requirements for temperature distribution in the heating detail are needed.



Fig. 7. Temperature variations for point with r= 0,06m.



Fig. 8. Temperature variations for point with r= 0,15m.



Fig. 9. Relative error for point with r= 0.06m

Fig. 1. Principal geometry of the induction system.

1 – heated flat disc
2 – upper layer of the inductor
3 – lower layer of the inductor

Fig.2. Experimental setup


Fig. 3. FE mesh for the electromagnetic field problem


Fig. 4. Magnetic flux lins


Fig. 5. Maximal temperature (point of radius r= 0.15m) – transient process


Fig. 6. Temperature distribution in radial direction at t= 600sec.