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
www.ecotransflux.com
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
Standard Transverse Flux Induction Heating (TFIH) Device
Electromagnetic Properties of a Magnetic Sheet Temperature dependence of carbon steel magnetic nonlinearity Temperature dependence of carbon steel resistivity
Thermal Properties of the Magnetic Sheet Temperature dependence of carbon steel heat capacity Temperature dependence of carbon steel thermal conductivity
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
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!!!!
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!!!!
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!!!!
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!!!!
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!!!!
Magnetic Flux Density and Induced Current Density (Z025, Jmax time)
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
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
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!!!!
Comparison between results of Time Domain (TD) and Frequency Domain (FD) Analyses TD FD B(H) FD Be(H) FD B(He) PJ [kw] 117.29 125.95 124.66 125.59 J [A/mm2] 240.39 247.88 246.99 247.53 Bx2a [mt] 1839 1848 2308 1937 Bz2a [mt] 59.35 36.24 37.77 36.81 Bz20 [mt] 101.5 113.3 115.4 108.5
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
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
The Non-Magnetic Sheet Model for Different Values of the Sheet Thickness Sheet Model 2a [mm] Magnetic Nonlinear 0.5 1.0 2.0 Non-magnetic 4.0 0.5 1.0 2.0 4.0 J0 [A/mm2] 246.9 Ja [A/mm2] 247.1 137.0 67.4 11. 5 251.1 141.7 74. 1 37.7 138.6 81. 6 78. 9 251.1 141.7 74. 1 37.7
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
Induced Current Density (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s
Magnetic Flux Density (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s
Sheet Temperature (first and last time steps) Thickness 2a = 0.5 mm, speed v = 0.8 m/s
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
Relative Magnetic Permeability last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s
Sheet Resistivity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s
Sheet Thermal Conductivity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s
Sheet Heat Capacity last time step Thickness 2a = 0.5 mm, speed v = 0.8 m/s
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
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
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
Electromagnetic and Magnetic Screening of the Sheet Lateral Sides in TFIH
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
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
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
Magnetic Screening magnetic screens NO magnetic screens YES Thick sheet 2a = 4.0 mm, speed v = 0.35 m/s
GOT-It optimizer
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
Electromagnetic Screens : GOT-It optimization
SSO optimization Sequential Surrogate Optimizer : number of iterations Tol. Comp. time [hours] g [mm] d [mm] Gap_P [%] 3 1e-6 2:36 80.1 140.8 17.9971 5 1e-6 3:57 77.5 141.4 17.8583 10 1e-6 7:06 75.7 141.4 17.8123 20 1e-6 7:06 75.7 141.4 17.8123 Max. Iter.
SSO optimization Sequential Surrogate Optimizer : tolerance Tol. Max. Iter. Comp. time [hours] g [mm] d [mm] Gap_P [%] 1e-2 10 2:40 80.1 140.8 17.9969 1e-4 10 3:29 80.1 140.8 17.9971 1e-6 10 7:36 75.7 141.4 17.8123
HLHRBF optimization HLHRBF approximation optimizer : number of iterations Tol. Comp. time [hours] g [mm] d [mm] Gap_P [%] 3 1e-6 3:20 108.9 160.0 30.0141 5 1e-6 12:15 79.1 139.4 18.1259 10 1e-6 24:58 77.0 141.0 17.8944 Max. Iter.
NICHING optimization Max. Gen. Comp. Pop. g time Size [mm] [hours] d [mm] Gap_P [%] 5 20 20.45 79.0 140.6 17.9879 10 20 40.43 75.6 141.4 17.811 20 20 49.36 75.6 141.4 17.811
GENETIC ALGORITHM optimization Max. Gen. Pop. Size Comp. time [hours] g [mm] d [mm] Gap_P [%] 5 20 6:03 80.1 140.2 18.0605 10 20 8:52 80.0 141.0 17.9715 20 20 15:30 75.9 140.8 17.8883 30 20 24.22 76.2 141.4 17.8239 40 20 33.43 75.6 141.4 17.811
Transversal profile of volume density of induced power integrated along the sheet NO SHEET SCREENING
Optimum position of COPPER SCREENS g =75.6 mm and d = 141.4 mm
Comparison with and without copper screens
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
THANKS FLUX Conference 2013, October 16-18, Aix-les-Bains, France