Simulation of Induction Heating

of Slabs Using ELTA 6.0

Valentin Nemkov

Fluxtrol, Inc.

V. Bukanin, A. Zenkov, A. Ivanov

St. Petersburg Electrotechnical University

Modelling for Electromagnetic Processes, September 16-19, 2014

Overview: New Aspects of Old Problem

• End and Edge Effects in slab heating in longitudinal field • Analytical Studies • Elta 6.0 program • Numerical Simulation of Edge effects in the process of

heating of magnetic slabs: - Characteristic temperature distributions - Temperature distribution color maps - Power density distribution color maps - Dynamics of surface power density • Case of multi-stage slab heating • End and 3D Corner effects • Conclusions

Analytical Study

d

b

Study of Dr. V. Peysakhovich, 1961:

- Case of non-magnetic slab in uniform

longitudinal magnetic field

- Formulas for E, H, Pv, R and X

- Pattern of power density

R + jX = 2ρ(b+d)(G+jQ)/a𝜹

Edge and End Effects in Slab

Heating

𝜋

End and Edge effects at low (color)

and high frequencies (black)

Normalized surface power density dis-

tribution near the edge of a wide slab

x’ = b/2 - x

Surface power p’=2 𝑝𝑣 𝑑𝑥𝑑/2

0; p’c – its value in the central zone of slab (x=0, y=0)

The most uniform (“uniform in large”) power distribution along x occurs at d/δ = 𝜋

Source: V. Nemkov, V. Demidovich, Theory an Calculation of Induction Heating Devices , Energoatomizdat, 1988

Elta 6.0 program

• Multipurpose engineering programs Elta are based on 1D FDM simulation of cylindrical and flat bodies with semi-analytical account for a finite length of the system

• Elta 6.0 has a block of 2D FDM simulation of EM+Thermal fields in slab or plate cross-sections

• It is a very good tool for study of Edge effects in non-linear systems and design of the heating process with different thermal conditions and power source characteristics

• Main system configurations in Elta 6.0: Basic, Scanning, Slab Heating

Multi-Stage Slab Heating

Specifications:

• Slab dimensions: d x b x a = 200 x 1200 x 2000 mm

• Material: low carbon steel

• Weight: 3.75 t

• Production rate: 33 t/hr

• Temperatures: initial 20 C, final before transportation 1200 + 50 0C

Frequency selection:

• Optimal frequency for final heating stage must correspond to a ratio

d/δ = 3.14 for uniform heating and high efficiency

• Frequency 50 Hz gives a ratio d/δ = 2.86, i.e. a little bit low

• Higher frequency (150 Hz) may be used for temperature equalization

at the end of heating

• For 60 Hz line the second frequency may not be necessary

• Elta 6.0 allows us to find the optimal process (heating time, powers and

frequencies) and design coils for effective heating.

Power Diagram

Stage 2

50 Hz

Inductor 2

400 sec

Stage 1

50 Hz

Inductor 1

400 sec

Stage 4

Holding

Inductor 3

200 sec

Stage 3

150 Hz

Inductor 3

400 sec

Temperature distribution along A-D

Temperature Distribution along ¼ of

Perimeter

Normalized Surface Power

Color Map of Heat Sources: Stage 1 Heat Source Density at t = 100 s

Heat Source Density at t = 200 s

Heat Source Density at t = 400 s

Color Map of Temperature: Stage 1

Temperature at t = 400 s

T= 750 0C Temperature at t = 100 s

Temperature at t = 200 s

Color Map of Heat Sources and

Temperature: Stage 2

Temperature at t = 800 s

Heat Source Density at t = 800 s

Color Map of Heat Sources and

Temperature: Stage 3 and 4

Temperature at t = 1200 s

Temperature at t = 1400 s

Heat Source Density at t = 1200 s

Animation of Heat Sources and

Temperature

End Effects for d/𝛿 = 2

Magnetic field lines and power density color maps

Surface power density p’ in the end zone

Flux2D program

Interference of slab and coil end effects Uniform external magnetic field

Power Density Map Demonstrating Interference of End and Edge Effects

Frequency 9.5 kHz; d/𝛿 = 2

Slab heating study in CIT laboratory:

V. Nemkov, R. Ruffini, R. Goldstein

2001

Flux3D program

2001

C C

Conclusions

• Study demonstrated effectiveness of using 2D simulation block in Elta 6.0

for analysis of coupled EM and Thermal phenomena in the process of

heating of slabs and strips in longitudinal magnetic field

• Analysis of Edge Effects showed dramatic variation of power distribution in

the slab width during a long period of time

• A width of the edge effect zone is always less than slab’s thickness

• With proper processing, the edge zones of slab don’t augment minimal

heating time compared to the central zone where the process is governed

by Fourier number Fo=at/d2

• Heating process optimization may be made in operator guided mode by

proper selection of power and frequency variation in time

• Elta 6.0 allows us to design heating coils with good practical accuracy

• Additional studies of End and 3D effects using Flux 2D/3D showed that

their influence may be compensated by the coil design; Flux 2D/3D

program was used for this study.

www.fluxtrol.com, ph. +1 248 393 2000 www.nsgsoft.com

Thank you!