Virgiliu FIRETEANU, Alex-Ionel CONSTANTIN Patrick LOMBARD, Diana MAVRUDIEVA. FLUX Conference 2013, October 16-18, Aix-les-Bains, France

Transcription

1 Transverse Flux Induction Heating of the Magnetic Nonlinear Sheets. The Non-magnetic Sheet Model. Transversal Non-uniformity of Heating. Sheet Screening Optimization Virgiliu FIRETEANU, Alex-Ionel CONSTANTIN Patrick LOMBARD, Diana MAVRUDIEVA FLUX Conference 2013, October 16-18, Aix-les-Bains, France

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3 Summary Description of a Transverse Flux Induction Heating (TFIH) Device Time Domain Analysis of the Electromagnetic Field in the Study of Magnetic Nonlinear Sheets TFIH Frequency Domain Analysis of the Electromagnetic Field in the Study of Magnetic Nonlinear Sheets TFIH Non-Magnetic Sheet Model Magnetic Sheets Magneto-thermal with Motion Coupling in TFIH Transversal Non-uniformity of Sheet Heating and Sheet Lateral Sides Screening GOT-It Optimisation of Electromagnetic Screens Conclusions

4 Standard Transverse Flux Induction Heating (TFIH) Device

5 Electromagnetic Properties of a Magnetic Sheet Temperature dependence of carbon steel magnetic nonlinearity Temperature dependence of carbon steel resistivity

6 Thermal Properties of the Magnetic Sheet Temperature dependence of carbon steel heat capacity Temperature dependence of carbon steel thermal conductivity

7 Time Domain Analysis of the Electromagnetic Field Computation Data: - total current in each inductor coil : harmonic, 14 ka rms value, frequency 1000 Hz - sheet thickness : 2a = 0.5 mm Voltage of the current source harmonic time variation!!!! Time variation of the instantaneous Joule power in the sheet

8 Magnetic Flux Density B( /2,0,0,t) in the point [ /2,0,0] of sheet symmetry plane z = 0 (Z0) Non - Harmonic Time Variation of B!!!!

9 Magnetic Field Strength H( /2,0,0,t) in the point [ /2,0,0] of the sheet symmetry plane z = 0 (Z0) Non - Harmonic Time Variation of H!!!!

10 Magnetic Flux Density B( /2,0,a,t) in the point [ /2,0,a] of the sheet surface z = a (Z025) Non - Harmonic Time Variation of B!!!!

11 Magnetic Field Strength H( /2,0,a,t) in the point [ /2,0,a] of the sheet surface z = a (Z025) Non - Harmonic Time Variation of H!!!!

12 Time variation of the induced current density J(t) in the point [0,0,0] (Z0); practically same result in (Z025) Harmonic Time Variation of J!!!!

13 Magnetic Flux Density and Induced Current Density (Z025, Jmax time)

14 Frequency Domain Analysis : Equivalent Harmonic Electromagnetic Fields B(t) harmonic: B(H) curve B(He) B1 HdB 0 = (B1H1e)/2 H(t) harmonic: B(H) curve Be(H) B1 HdB 0 = (B1eH1)/2

15 The scalar model T - - r of the harmonic electromagnetic field (1) solid conductor regions, electric vector T (J2 = curlt) and magnetic scalar potentials: curl[ curlt] + j (H)(T - grad ) = 0, divt = 0, div[ (H)(T - grad )] = 0 (2) nonconductive and no-source regions with high magnetic permeability, potential div[ (H)grad )] = 0 (3) non-conductive and non-magnetic regions, source with current density J1 included, reduced magnetic scalar r potential: H = H0 grad r, where H0 the source field is H0 div( 0grad r) = div( 0H0) J1 x r 1 3 dv 4π V r

16 Comparison of three formulations (MH models) of the harmonic electromagnetic field in a TFIH problem with the same geometry and mesh T - - r is a very efficient one!!!!

17 Comparison between results of Time Domain (TD) and Frequency Domain (FD) Analyses TD FD B(H) FD Be(H) FD B(He) PJ [kw] J [A/mm2] Bx2a [mt] Bz2a [mt] Bz20 [mt]

18 Non-Magnetic Sheet Model in the Study of Magnetic Sheets TFIH Induced current density on the sheet surface, z = a = 0.25 mm Magnetic Nonlinear Sheet Non-magnetic Sheet Model

19 Non-Magnetic Sheet Model in the Study of Magnetic Sheets TFIH Magnetic flux density on the sheet surface, z = a = 0.25 mm Magnetic Nonlinear Sheet Non-magnetic Sheet Model

20 The Non-Magnetic Sheet Model for Different Values of the Sheet Thickness Sheet Model 2a [mm] Magnetic Nonlinear Non-magnetic J0 [A/mm2] Ja [A/mm2]

21 Magneto-thermal with Translating Motion TFIH Model. Electromagnetics FD + Thermal TD cd /dt = J22 + div[ grad ] Time variation of the active power in the sheet region Thickness 2a = 4.0 mm, speed v = 0.1 m/s Thickness 2a = 0.5 mm, speed v = 0.8 m/s

22 Induced Current Density (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s

23 Magnetic Flux Density (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s

24 Sheet Temperature (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s

25 Transversal Profile of Sheet Temperature last time step Gap_teta = (teta_max teta_min)/teta_y0 = 28.5 % Transversal path after the sheet exit from inductor Thickness 2a = 0.5 mm, speed v = 0.8 m/s

26 Relative Magnetic Permeability last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s

27 Sheet Resistivity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s

28 Sheet Thermal Conductivity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s

29 Sheet Heat Capacity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s

30 Non-Magnetic Sheet Model in the Study of Magnetic Sheets TFIH Current Density Magnetic non-linear sheet Non-magnetic sheet model Thin sheet 2a = 0.5 mm, speed v = 0.8 m/s

31 Non-Magnetic Sheet Model in the Study of Magnetic Sheets TFIH Thin Sheet Temperature Magnetic non-linear sheet - max = 1134 degrees Non-magnetic sheet model - max = 1136 degrees Thin sheet 2a = 0.5 mm, speed v = 0.8 m/s

32 Thick Sheet Temperature Magnetic non-linear sheet - max = 1220 degrees Non-magnetic sheet model - max = 1066 degrees Thick sheet 2a = 4.0 mm, speed v = 0.1 m/s

33 Electromagnetic and Magnetic Screening of the Sheet Lateral Sides in TFIH

34 Magnetic Nonlinear or Non-magnetic Sheet Model????? Transversal profile of sheet temperature Magnetic non-linear model: (Gap_ )mgnlin = 40.4 % Computation time 165 hours Non-magnetic model: (Gap_ )non-mg = 61.0 % Computation time 6.33 hours Thick sheet 2a = 4.0 mm, speed v = 0.35 m/s

35 Electromagnetic Screening : copper plates gap Gap_ = 27.9 % Copper plates gap, g = 40 mm Gap_ = 22.7% Copper plates gap, g = 80 mm Gap_ = 35.0 % Copper plates gap, g = 120 mm Sheet 2a = 4.0 mm, speed v = 0.35 m/s; copper plates sheet superposition 140 mm

36 Electromagnetic Screening : copper plates sheet superposition Gap_ = 36.3 % Copper plates sheet superposition, d = 110 mm Gap_ = 22.7 % Copper plates sheet superposition, d = 140 mm Gap_ = 30.8 % Copper plates sheet superposition, d = 170 mm Sheet 2a = 4.0 mm, speed v = 0.35 m/s; copper plates gap = 80 mm

37 Magnetic Screening magnetic screens NO magnetic screens YES Thick sheet 2a = 4.0 mm, speed v = 0.35 m/s

38 GOT-It optimizer

39 Electromagnetic Screens : GOT-It optimization Notice: The objective function Gap_P is the difference between the maximum and minimum values in the transversal profile of the volume density of induced power integrated along the sheet. A TFIH magnetoharmonic model, sheet 4.0 mm is considered

40 Electromagnetic Screens : GOT-It optimization

41 SSO optimization Sequential Surrogate Optimizer : number of iterations Tol. Comp. time [hours] g [mm] d [mm] Gap_P [%] 3 1e-6 2: e-6 3: e-6 7: e-6 7: Max. Iter.

42 SSO optimization Sequential Surrogate Optimizer : tolerance Tol. Max. Iter. Comp. time [hours] g [mm] d [mm] Gap_P [%] 1e : e : e :

43 HLHRBF optimization HLHRBF approximation optimizer : number of iterations Tol. Comp. time [hours] g [mm] d [mm] Gap_P [%] 3 1e-6 3: e-6 12: e-6 24: Max. Iter.

44 NICHING optimization Max. Gen. Comp. Pop. g time Size [mm] [hours] d [mm] Gap_P [%]

45 GENETIC ALGORITHM optimization Max. Gen. Pop. Size Comp. time [hours] g [mm] d [mm] Gap_P [%] : : :

46 Transversal profile of volume density of induced power integrated along the sheet NO SHEET SCREENING

47 Optimum position of COPPER SCREENS g =75.6 mm and d = mm

48 Comparison with and without copper screens

49 Conclusions The finite element analysis of the electromagnetic field in time domain requires important computation times in case of magnetic non-linear sheets. An important decrease is ensured through the frequency domain analysis of an equivalent harmonic field. If the magnetic non-linear sheets are electromagnetically thin, the computation of transverse flux heating through a non-magnetic sheet model is very efficient and offers satisfactory results. In case of electromagnetically thick sheets the results with the non-magnetic sheet model become more and more approximates when the ratio between the sheet thickness and the penetration depth of the electromagnetic field increases. Both variant, electromagnetic and magnetic screening of the sheet lateral sides can reduce the transversal non-uniformity of the sheet heating. The GOT-It optimization of the electromagnetic screens position with respect the sheet was a very attractive and useful experience

50 THANKS FLUX Conference 2013, October 16-18, Aix-les-Bains, France