COMSOL Simulation for Design of Induction Heating System ...

Research ArticleCOMSOL Simulation for Design of Induction Heating System inVULCAN Facility

Jinkun Min 12 Guangyu Zhu 234 Yidan Yuan2 and Jingquan Liu 1

1Tsinghua University Beijing 100084 China2China Nuclear Power Engineering Co Ltd Beijing 100840 China3Nuclear and Radiation Safety Center MEE Beijing 100082 China4State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and ValidationBeijing 102488 China

Correspondence should be addressed to Jingquan Liu jingquantsinghuaeducn

Received 4 March 2021 Accepted 11 August 2021 Published 20 August 2021

Academic Editor Leon Cizelj

Copyright copy 2021 Jinkun Min et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

(e experimental facility VULCAN was setup to study the fuel-coolant interaction (FCI) phenomena in a postulated severeaccident of light water reactors(e heating system is important for the facility to preparemoltenmaterial in a crucible(is articleis concerned with the design of the heating system which applies electromagnetic induction heating method (e COMSOL codewas employed to simulate the induction heating characteristics of a graphite crucible under different current and frequency of thework coil (inductor) Given a frequency the relationship between the cruciblersquos average temperature and the inductorrsquos current isobtained which is instrumental to select the power supply of the induction heating systemMeanwhile the skin effect of inductionheating is analyzed to guide the choice of frequency and inductor of the heating system According to the simulation results theinduction heating system of frequency 47 kHz is suitable for the experiment with a good agreement in temperature between themeasured and the predicted

1 Introduction

During a hypothetical severe accident in light water re-actors (LWR) molten fuel (corium) may get contact withcoolant (water) resulting in fuel-coolant interactions(FCI) Under certain conditions the heat transfer areabetween the melt and coolant will increase rapidly and thetime scale of heat transfer becomes much smaller than thetime scale of decompression which may lead to the gen-eration of shock wave (is violent phase-change phe-nomenon is called steam explosion [1] During a severeaccident of a nuclear power plant the steam explosion maycause a strong shock wave that affects the availability ofequipment in the containment and even destroy the in-tegrity of the pressure vessel and containment [2] (esteam explosions were extensively investigated by manyresearch projects including the OECDNEA projectsSERENA Phase I and Phase II launched in 2002 and 2008respectively [3 4] and both experiment and simulation

were directed to reduce the uncertainty caused by materialproperties and experimental conditions for steam explo-sions Yet steam explosion is still an unresolved issue forsevere accident research as indicated by the high-levelranking of research priorities in severe accident concludedfrom the EU project SARNET (Severe Accident ResearchNETwork of Excellence) in 2014 [5]

Experiments related to FCI can be divided into twocategories decoupled and coupled experiments in terms ofphysical phenomena (e decoupled experiments areseparate-effect tests performed to address the physicalphenomena involved in FCI such as the breakup of a meltjet and collapse of the vapor film Vapor film collapseexperiments usually use solid balls or heating tubes insteadof melt to study the criteria of vapor film collapse [6 7] (evapor film behavior under different experimental condi-tions was also widely studied including the difference ofthe vapor film behavior between a moving ball and astationary ball [8 9] the influence of shock wave on vapor

HindawiScience and Technology of Nuclear InstallationsVolume 2021 Article ID 9922503 12 pageshttpsdoiorg10115520219922503

film [10] and the influence of different solutions on vaporfilm [11ndash14] (e experiments of jet breakup are usuallyperformed in an isothermal system to study the influence ofhydrodynamics on the behavior of jet in FCI [15ndash17] Moreattention was paid to the influence of experimental con-ditions such as jet material and coolant material on jetbreakup [18 19] Coupled experiments were the integraltests performed to investigate the multiple physicalmechanisms of FCI in large scale of 10sim1000 kg [20ndash25]and mediumsmall scale of 1 gsim10 kg [26ndash30] of melt massLarge-scale experiments are intended to obtain the generalpicture of FCI process while small- and medium-scaleexperiments are focused on the understanding of physicalmechanisms in FCI

(e present study is concerned with the development ofa small-scale test facility named the VULCAN (Violentinteraction of molten fUeL with CoolANt) facility which isconceived to perform fundamental experiment of high-temperature single droplet falling into a water pool underwell-controlled conditions with the objective to investigatethe physical mechanisms of fuel-coolant interactions Inparticular the focus is the design of the heating systememployed in the VULCAN facility

(e preparation and release of the molten droplet areimportant to the success of such a very high-temperatureexperiment (e heating methods are different in the pre-vious studies according to the characteristics of the meltmaterials employed in experiment (e electrode heatingmethod of the FARO experiment [20ndash23] is characterized bylong service life and simple operation It requires electricalconduction of melt material to create an arc between theelectrodes (e KROTOS experiment [24] heats the ex-perimental material by radiation of tungsten element thatheated by resistive heating (is method has no additionalrequirement for material but the radiation heat transfermakes the heating rate slow (e TRIO experiment [25]adopted a cold crucible with direct induction heating of meltmaterial in a solidified shell of the melt itself (e methodgreatly reduces the requirements of crucible material and itis applicable to prototypical material of corium Howeverthe cold crucible has complexity in operation and difficultyin energy balance between induction power and heat dis-sipation which may cause instability of the cold cruciblewall (e DEFOR [28 29] and MISTEE [30] experimentsadopt the induction heating of a crucible which heats themelt material ie so-called ldquohot-cruciblerdquo method which issimple to operate and easy to implement

Given the small scale of the VULCAN facility and themedium range of operational temperature the similar ldquohot-cruciblerdquo method with induction heating is chosen in thedesign due to its advantages mentioned above During thepreparation period of a melt droplet the droplet is preventedby an Aerodynamic Levitation System (ALS) from falling outof the crucible To design the heating system the COMSOLcode is applied to simulate the induction heating charac-teristics of a graphite crucible under different current andfrequency of the work coil (inductor) Based on the simu-lation results the induction heating system has been setup Atest of the heating system is also performed and the

measured temperature has a good agreement with thepredicted under the same frequency and current of theinductor indicating a reasonable design of the heatingsystem in the VULCAN facility

2 Experimental Setup

Figure 1 shows a schematic of the experimental apparatuswhich includes induction heating system interaction zoneexternal trigger system data acquisition system inert gaslevitation and protection system and high-speed photog-raphy system

Induction heating system is mainly composed of afurnace an induction heater (host and controller) and anindustrial chiller

Figure 2 shows the structure of furnace which includes afurnace shell an insulated pipe and a crucible (e furnaceshell is stainless steel cylinder and its outer diameter innerdiameter and height are 180mm 170mm and 135mmrespectively (e crucible is supported by a tube which canadjust the crucible to the specified position and an obser-vation window is placed at the top of the furnace forwatching and photographing the heating state in the cru-cible Argon is filled from the bottom of furnace at a flow raterange of 1sim10times10minus5 kgm3 to provide the levitation forceand protective atmosphere

(e heating element is an induction coil which is buriedin MgO thermal insulation powders between furnace shelland insulated pipe As shown in Figure 3 the spiral coil ismade of 5 turns spiral copper pipe (e inside diameteroutside diameter and height for the spiral coil are 66mm82mm and 60mm respectively (e inner diameter andouter diameter of copper pipe are 6mm and 8mm

(e crucible has a double-layer structure that has twoadvantages

(i) (e inner and outer crucible can be made of differentmaterials Materials with good induction heatingeffect can be adopted for the outer crucible whereasmaterials that do not react with experimental ma-terials can be selected for the inner crucible to ensurethe intact droplet In this work both the innercrucible and the outer crucible are made of graphite

(ii) (e inner crucible can be taken out freely for re-placement whereas the thermocouple can be fixed inthe positioning hole of the outer crucible to measurethe temperature of the crucible

Figures 4 and 5 show the dimensions of the innercrucible and the outer crucible in the single-drop furnace

(e coil is power supplied by a medium-frequencypower (GYM25AB) (e nominal output electrical powerand frequency are 25 kW and 47 kHz respectively deter-mined by simulation and experiment (e current in the coilis adjustable for different heating temperature requirements

A 5 HP industrial chiller is equipped to cool the in-duction heaters and the coils (e cooling capacity of thechiller is 13350W and the target outlet temperature can beset to specified value

2 Science and Technology of Nuclear Installations

3 COMSOL Model of Simulation

31 COMSOL Multiphysics (e preparation of the melt isan important process of FCI experiment In order to guidethe design of crucible and coil COMSOL Multiphysicsreg(referred as COMSOL) was used to simulate electromagnetic

induction and solid heat transfer phenomenon to obtain themelt condition under different operating parameters andprovide a reference for experimental operation COMSOL isan advanced numerical simulation software designed withfinite element analysis method It has the advantages of wideapplication range easy operation and multiphysical fieldcoupling analysis [31]

InfraredThermometer

ThermocoupleSignals

Laser Signals

Pressure Sensorand ThermocoupleSignals

TriggerSignals

Capacitor

HighndashSpeedCamera

LaserReceiver

LaserProducer

PneumaticActuator

ThreendashwaySpherical Value

BackgroundLamp Board

GasBottle Ar

Electromagnetic Coil

Pressure Gage

Reducing Valve

Flow-meter

Stop Valve

Figure 1 Schematic of test facility

Inner crucible

Outer crucible

Insulated pipe

Furnace shellGas vent

Observation window

Gas inlet

Figure 2 Schematic of the furnace for single droplet

82 mm

66 mm

6 mm8 mm

Figure 3 Schematic of the inductor (work coil)

Science and Technology of Nuclear Installations 3

32 Geometric Model (e geometric models and dimen-sions of inner and outer crucible are shown in Figures 4 and5(e positioning hole of thermocouple in the outer cruciblewas ignored in this simulation

For COMSOL two methods can be used to build the coilarea geometric model One is to build the spiral coilstructure directly as shown in Figure 6(a) (e other is tosimplify the coil into a cylindrical structure with the settingof the coil parameters which is only applicable for regularcoils as shown in Figure 6(b) (e first method can be usedto obtain the real current distribution in the coil wire and thereal magnetic field distribution(e secondmethod can onlyobtain the real magnetic field distribution while the sim-ulation speed is significant improved In this article we didnot focus on the current distribution in the wire of the coiland thus the second method is selected for modeling

33Mesh (e numerical simulations were carried out on ablock-structured mesh which is obtained by rotation of thecross section In addition a mesh-sensitivity analysis wasconducted by considering the meshes numbers that rangedfrom 8104 to 785993 under the coil current of 100A andthe frequency of 47 kHz (e average temperature andmaximum temperature in the crucible were taken as ver-ification criteria Figure 7 shows the variation of thenumber of criteria with the number of grids When thenumber of grids reaches 41508 the differences of simu-lation results is small enough (erefore the grid with totalnumber of 75152 shown in Figure 8 were used for sub-sequent calculations and the mesh quality is shown inFigure 9

34 Physical Model Magnetic insulation boundary wherethe magnetic field disappears is necessary to be defined inelectromagnetic simulation calculation In this work themaximum boundary diameter of the coil is 82mm(erefore the sphere boundary with a diameter of 200mm isenough to define as magnetic insulation boundary Solidcoupling model was selected to describe the close contact ofdouble-layered crucibles Forced convection heat model wasselected as the thermal boundary condition of the innercrucible cooling by argon

According to the results from He and Xiao [32] theconvective heat transfer coefficient was about 100W(m2middotK) (e outer boundary of the outer crucible appliesnatural convection and the heat transfer coefficient is35W(m2middotK) [32] (e water loop inside copper tube thecoil was set as isothermal boundary condition with atemperature of 30degC

(e physical properties of materials used in the modelare shown in Table 1 (e range of coil current is 20ndash500Aand the range of frequency is 10ndash200 kHz in simulation

3240

118deg

55

ϕ25ϕ19

ϕ19

ϕ9

Figure 4 Dimensions ((a) unit mm) and schematic (b) of the inner crucible

ϕ45ϕ25

ϕ19

ϕ9ϕ35

354010

55

Figure 5 Dimensions ((a) unit mm) and schematic (b) of theouter crucible


4020

0-20

-400

20

40

4020

0-20

-40

mm

mm

mm

(a)

0

0

20

20

40

mm

mm

-20

-20

020mm

(b)

Figure 6 Two modeling methods in COMSOL

510

508

506

504

502

500

498

Tem

pera

ture

[K]

104 105 106

Total number of meshes

Average TemperatureMaximum Temperature

Figure 7 (e average and the maximum temperature variations with total number of mesh

40

20

0

mm

mm mmndash20 ndash10 0 10 20 0xy

z

(a)

mm

mmmmndash20 ndash10 0 10 20 20

20

10

0

ndash10

ndash20

xz

y

(b)

Figure 8 (e view of mesh (a) (e cross section view of crucible (b) (e top view of crucible


4 Results and Discussion

41 Skin Effect (e skin effect of high-frequency electro-magnetic induction has an important effect on the distri-bution of magnetic field In order to study the skin effectinduction-heating simulation with different coil currentfrequencies was carried out

(e magnetic flux density distribution under the coilcurrent of 100 A and frequency of frequency 10 kHz(a)47 kHz(b) or 200 kHz(c) are shown in Figure 10 All ofresults show that the magnetic flux density is obviouslyconcentrated on the outer surface of the crucible and forthe higher current frequency the skin effect is more sig-nificant (e effects of frequencies on the magnetic fluxdensity of cross section at the height of 25mm are shown inFigure 11 and the skin depth (1e) standard line is shownby the dashed line in this figure It can be learnt that whenthe frequencies is 10 kHz or 20 kHz the magnetic fluxdensity distribution in the crucible is smoother whichmeans the thickness of the crucible wall does not reach theskin depth

Focus on the distribution of flux density varies withdepth at a certain frequency taking the flux density dis-tribution under the frequency of 200 kHz and the current of100A as an example (e exponential function is used forfitting and the results are as follows

lnB

Bmax1113888 1113889 minus02519x minus 00184 (1)

where B is the magnetic flux density Bmax is the maximum ofthe magnetic flux density x is the depth from the surface ofthe crucible and correlation coefficient is 09943

(e curve of skin depth with frequency is shown inFigure 12 which was obtained from Figure 10 (e theo-retical curve is calculated from the skin depth formula [37]

δ

2

μwσ

1113971

(2)

where μ is the magnetic permeability in [Hm] w is theangular frequency in [rads] σ is the conductivity in [Sm]and δ is the skin depth in [mm]

Under the frequency of 47 kHz the theoretical value ofskin depth is 734mm the simulated value is 815mm andthe difference is 11 Under the frequency of 100 kHz thetheoretical value of skin depth is 356mm the simulatedvalue is 360mm and the difference is 1 It can be seenfrom Figure 12 that the simulated calculation results areroughly consistent with the theoretical values and thesimulation deviation may be caused by the uneven distri-bution of the magnetic flux density on the Z coordinate sincethe length of the coil is finite and the shape of crucible isirregular

Figure 13 shows the distribution of the current density atdifferent frequency and same current of 100A Comparedwith Figures 10 and 13 it can be seen that the distribution ofcurrent density in the crucible is gentler than the distributionof magnetic flux density which follows the skin depth ofequation (1) (erefore the skin depth of the current isdeeper and the penetration ability is stronger as shown inFigures 14 and 15

(e temperature distribution of the crucible cross section atthe height of 25mm under the coil current of 100A and thefrequency of 47 kHz is shown in the Figure 16 A high-tem-perature zone forms in the middle outboard part of the cru-cible Conversely a cold zone forms in the inner bottom part ofthe crucible(is temperature differencemay be due to the skineffect of induced current which caused the outboard Joule heathigher than inboard part and the argon forced convectioncooling inside the crucible (e maximum temperature dif-ference between two zones mentioned above is about 1

(e crucible is heated by the Joule heat of the eddycurrent while the distribution of temperature in the crucibleis flatter than the distribution of current Because thethermal conductivity of graphite crucible is good thetemperature difference in the crucible is small although thedistribution of internal heat source caused by the skin effectof current is obviously uneven (erefore it is reasonable tomeasure the temperature at mounting position shown inFigure 5 as the crucible temperature

42 Effect of Inductorrsquos Current and Frequency (e mag-nitude and the frequency of the coil current are importantfactors of induction heating As shown in Figures 17 and 18

035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

Figure 9 (e quality of mesh (worse in left and better in right)

Table 1 (e physical properties of materials

Material Argon Graphite Copper WaterRelative permittivity 1 10a 1 DefaultElectrical conductivity (Sm) 001 1e5b 588e7d 55eminus6c

Relative permeability 1 1 1 DefaultSpecific heat capacity [J(kgmiddotK)] Default 7077c 3850d Default

Density [kgm3] Default Default Default Default(ermal conductivity [W(mmiddotK)] Default 240c 3850d Default

aData from reference [33] bdata from reference [34] cdata from reference[35] and ddata from reference [36]


when the coil current is maintained at 100A the averagemagnetic flux density and the average induced currentdensity in the crucible increased with the increase in fre-quency besides the average magnetic flux density and theaverage induced current density increased more rapidly atlow frequency When the current frequency is 47 kHz theaverage magnetic flux density has reached 98 of it at thefrequency of 200 kHz and the average current density hasreached 80 of it at the frequency of 200 kHz

Figures 19 and 20 show the mean temperature and thedistribution of temperature under different frequency re-spectively With the consideration of the skin depth inmagnetic field cost performance and uniformity of tem-perature distribution the calculated frequency of 50 kHz wasselected for experiment bench design and the actualmanufactured frequency was 47 kHz Figure 21 shows theaverage temperature of crucible under different coil currentsand frequency With the increase of coil current the average

temperature of the crucible increases exponentially (iscorrespondence could be expressed as follows

ln Tmean( 1113857 564 + 000702lowast I(f 47 kHz) (3)

where the correlation coefficient is 09928


where the correlation coefficient is 09974 Tmean is theaverage temperature of the crucible I is the magnitude ofcoil current and f is the frequency of coil current It shouldbe noted that the melting model was not considered in thesimulation calculation model and the calculated tempera-ture may reach more than the melting point of graphite

As shown in Figure 22 the temperature inhomogeneityof the crucible increases as the coil current increases (etemperature inhomogeneity is about 4 and 10 under thecoil current of 300A and 500A respectively When thecurrent below 100A the temperature inhomogeneity can bealmost ignored

Magnetic Flux Density under Frequencyof 10 kHz and Current of 100A [T] 828times10-3

times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T

209times10-4209times10-4

9

8

7

6

5

3 3

2

4

112

(c)

Figure 10 Distribution of magnetic flux density at different frequency and same current of 100A

1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y

0 5 10 15Depth From Crucible of Surface [mm]

10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e

Figure 11 Magnetic flux density of cross section at the height of25mm under different frequencies

0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]

Result of SimulationTheoretical Value

Figure 12 Skin depth variation with frequency


Current Density under Frequencyof 10 kHz and Current of 100A [Am^2] 456times105

times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)

Current Density under Frequencyof 200 kHz and Current of 100A [Am^2]

354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)

Figure 13 Distribution of current density at different frequency and the same current of 100A

1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e

Figure 14 Current density of cross section at the height of 25mm under different frequencies

0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]




Temperature [K] 536K

536

535

534

533

532

531531

Figure 16 Cloud image of temperature distribution in the cruciblersquos cross section

95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A

Figure 17 Mean of magnetic flux density varies with frequency

times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A

Figure 18 Mean current density variation with frequency


(e crucible can be heated to more than the heatingrequirement of 2500K by the adjusted coil output currentwithin 300A under the frequency of 47 kHz and the tem-perature difference in the crucible is less than 4 under thiscondition

5 Testing of the Heating System

A test is conducted with the induction heating system whosecurrent ranges from 40A to 250A under the frequency of47 kHz given the furnace and crucible as described in thepreceding section A C-type thermocouple and an infraredthermometer are used to measure the cruciblersquos temperaturebelow 1500K and above 1500K respectively

0 5 10 15Depth From Crucible Surface [mm]

1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz

Figure 20 Distribution of temperature under different frequency

0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]

Simulation Result5768lowastIn(f+8182)-2232

Figure 19 Mean temperature variation with frequency

10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz

T=2809e702e-03lowastI


Figure 21 Average temperature of the crucible vs inductorrsquoscurrent


105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A

Figure 22 Normalized temperature profile along the cross sectionof the crucible at the height of 25mm under different inductorrsquoscurrent and the same frequency

Table 2 Comparison of measured and simulated temperatures

Current ofinductor(A)

Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation

403 3439 3386 minus53 minus15598 4021 3955 minus66 minus16811 4974 4751 minus223 minus45997 6127 5774 minus353 minus582000 15098 14314 minus784 minus522513a 23641a mdasha(e experiment of 300A was not carried out because the predictedtemperature under this condition is close to the melting point of graphite


(e cruciblersquos temperatures measured in the test andpredicted in the simulation are shown in Table 2 (emaximum difference between the measured and predictedtemperatures is 58 which indicates the reasonable designof the induction heating system

6 Conclusions

Motivated by the development of the test facility VULCANto investigate melt-coolant interaction the inductionheating of a graphite crucible was simulated by the COM-SOL code and studied with the objective to design theheating system for the facility Based on the simulationresults and a verified test on the facility the followingconclusions can be drawn

(i) (e skin effect of induction heating is reproduced bythe COMSOL simulation with the magnetic fluxdensity concentrated on the outer surface of thecrucible and decreasing exponentially with thedepth from the outer surface

(ii) (e heating power increases with the increase of theinductorrsquos frequency and current (e averagetemperature of the crucible increases exponentiallywith the increase of the inductorrsquos current (etemperature difference in the crucible is negligibleie insensitive to the skin effect Hence it is rea-sonable to measure the temperature of the outercrucible as the average temperature of the crucible

(iii) In the verified test performed on the facility themaximum difference between the measured andpredicted temperatures of the crucible is 58 in-dicating the capability of COMSOL for such sim-ulation and the reasonable design of the heatingsystem

Data Availability

(e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

(e authors declare that they have no conflicts of interest

Acknowledgments

(e authors are grateful for the financial support of theFundamental Research Funds for the National Key RampDProgram of China (Grant no 2018YFB1900100)

References

[1] L Cizelj B Koncar and M Leskovar ldquoVulnerability of apartially flooded PWR reactor cavity to a steam explosionrdquoNuclear Engineering and Design vol 236 no 14 pp 1617ndash1627 2006

[2] G Berthoud ldquoVapor explosionsrdquo Annual Review of FluidMechanics vol 32 no 1 2000

[3] D T P S T H Lma ldquoOecd programme serena (steam ex-plosion resolution for nuclear applications) work programmeand first resultsrdquo Work vol 21 pp 1ndash13 2003

[4] OECDNEA ldquoAgreement on the OECDNEA SERENAProject ndash to address remaining issues on fuel-coolant inter-action mechanisms and their effect on ex-vessel steam ex-plosion energeticsrdquo 2008

[5] W Klein-Heling M Sonnenkalb D Jacquemain B Clementand I Lindholm ldquoConclusions on severe accident researchprioritiesrdquo Annals of Nuclear Energy vol 74 pp 4ndash11 2014

[6] S J Board and RW Hall ldquoRecent advances in understandinglarge scale vapor explosionsrdquo in Proceedings of the Commu-nication Safety and Nuclear Installation Meeting pp 249ndash293Sodium-Fuel Interact Fast Reactor Tokyo Japan September1976

[7] R Freud R Harari and E Sher ldquoCollapsing criteria for vaporfilm around solid spheres as a fundamental stage leading tovapor explosionrdquo Nuclear Engineering and Design vol 239no 4 pp 722ndash727 2009

[8] J W Stevens and L C Witte ldquoDestabilization of vapor filmboiling around spheresrdquo International Journal of Heat andMass Transfer vol 16 no 3 pp 669-670 1973

[9] L Manickam S (akre and W Ma ldquoAn experimental studyon void generation around hot metal particle quenched intowater poolrdquo International Topical Meeting on Nuclear Reactorermal Hydraulics vol 32 2015

[10] A Inoue and S G Bankoff ldquoDestabilization of film boilingdue to arrival of a pressure shockmdashpart i experimentalrdquoJournal of Heat Transfer vol 103 no 3 1981

[11] A Sakurai M Shiotsu and K Hata ldquoEffects of systempressure on minimum film boiling temperature for variousliquidsrdquo Experimentalermal and Fluid Science vol 3 no 4pp 450ndash457 1990

[12] H Kim J Buongiorno L W Hu T J Mckrell andG L Dewitt ldquoExperimental study on quenching of a smallmetal sphere in Nano-fluidsrdquo ASME International Mechan-ical Engineering Congress amp Exposition vol 11 2008

[13] T Arai and M Furuya ldquoEffect of hydrated salt additives onfilm boiling behavior at vapor film collapserdquo Journal of En-gineering for Gas Turbines amp Power vol 10 2009

[14] P K Kanin V A Ryazantsev M A Lexin A R Zabirov andV V Yagov ldquoHeat transfer enhancement at increasing waterconcentration in alcohol in the process of non-stationary filmboilingrdquo Journal of Physics Conference Series vol 980 no 1Article ID 12029 2018

[15] M Pilch and C A Erdman ldquoUse of breakup time data andvelocity history data to predict the maximum size of stablefragments for acceleration-induced breakup of a liquid droprdquoInternational Journal of Multiphase Flow vol 13 no 6pp 741ndash757 1987

[16] T N Dinh V A Bui and R R Nourgaliev ldquoExperimentaland analytical studies of melt jet-coolant interactions asynthesisrdquo Nuclear Engineering and Design vol 189 no 1pp 299ndash327 1999

[17] K H Bang J M Kim and D H Kim ldquoExperimental study ofmelt jet breakup in waterrdquo Journal of Nuclear Science andTechnology vol 40 no 10 pp 807ndash813 2003

[18] B W Marshall D F Beck and M Berman ldquoMixing ofisothermal and boiling molten-core jets with water the initialconditions for energetic FCIs (fuel-coolant interactions)rdquo inConference International European Nuclear SocietyAmericanNuclear Society Meeting on ermal Reactor Safety AvignonFrance October 1988


[19] BW Spencer J D Gabor and J C Cassulo ldquoEffect of boilingregime on met stream breakup in waterrdquo in ParticulatePhenomena and Multiphase Transport T N Veziroglu EdHemisphere Publishing London UK 1988

[20] D Magallon and H Hohmann ldquoHigh pressure corium meltquenching tests in FAROrdquo Nuclear Engineering and Designvol 155 no 1-2 pp 253ndash270 1995

[21] D Magallon I Huhtiniemi and H Hohmann ldquoLessonslearnt from FAROTERMOS corium melt quenching ex-perimentsrdquo Nuclear Engineering and Design vol 189 no 1-3pp 223ndash238 1999

[22] DMagallon and I Huhtiniemi ldquoCoriummelt quenching testsat low pressure and subcooled water in FAROrdquo NuclearEngineering and Design vol 204 no 1-3 pp 369ndash376 2001

[23] A Annunziato A Yerkess and C Addabbo ldquoFARO andKROTOS code simulation and analysis at JRC Isprardquo NuclearEngineering and Design vol 189 no 1 pp 359ndash378 1999

[24] I Huhtiniemi DMagallon andHHohmann ldquoResults of recentKROTOS FCI tests alumina versus corium meltsrdquo NuclearEngineering and Design vol 189 no 3 pp 379ndash389 1999

[25] J H Song I K Park Y J Chang Y S Shin J H Kim andB T Min ldquoExperiments on the interactions of molten ZrO2with water using TRIO facilityrdquo Nuclear Engineering andDesign vol 213 no 2 pp 97ndash110 2002

[26] T A Dullforce D J Buchanan and R S Peckover ldquoSelf-triggering of small-scale fuel-coolant interactionsI Experimentsrdquo Journal of Physics D Applied Physics vol 9no 9 pp 1295ndash1303 2001

[27] L S Nelson and L Buxton Steam Explosion TriggeringPhenomena Stainless Steel and Corium-E Simulants Studieswith a Floodable Arc Melting Apparatus NUREGCR-0112Sandia National Lab Albuquerque NM USA 1978

[28] A Karbojian W M Ma P Kudinov and T N Dinh ldquoAscoping study of debris bed formation in the DEFOR testfacilityrdquo Nuclear Engineering and Design vol 239 no 9pp 1653ndash1659 2009

[29] P Kudinov A Karbojian C-T Tran and W VillanuevaldquoAgglomeration and size distribution of debris in DEFOR-Aexperiments with Bi2O3-WO3 corium simulant meltrdquo Nu-clear Engineering and Design vol 263 pp 284ndash295 2013

[30] H S Park R C Hansson and B R Sehgal ldquoFine fragmentationof molten droplet in highly subcooled water due to vaporexplosion observed by x-ray radiographyrdquo Experimentalermal and Fluid Science vol 29 no 3 pp 351ndash361 2005

[31] ldquoCOMSOLrdquo 2021 httpcncomsolcom[32] C He and F Xiao Principles of Chemical Industry (e

Science Publishing Company Singapore 2007[33] M Hotta M Hayashi M T Lanagan D K Agrawal and

K Nagata ldquoComplex permittivity of graphite carbon blackand coal powders in the ranges of X-band frequencies (82 to124 GHz) and between 1 and 10 GHzrdquo ISIJ Internationalvol 51 no 11 pp 1766ndash1772 2011

[34] P N Nirmalraj T Lutz S Kumar G S Duesberg andJ J Boland ldquoNanoscale mapping of electrical resistivity andconnectivity in graphene strips and networksrdquo Nano Lettersvol 11 no 1 pp 16ndash22 2011

[35] A W Blackwood ldquoProperties of pure metals properties andselection nonferrous alloys and special-purpose materialsrdquo inASM Handbook pp 1099ndash1201 ASM International NoveltyOH USA 1990

[36] R L David CRC Handbook of Chemistry and Physics CRCPress Boca Raton FL USA 80th edition 1999

[37] H A Wheeler ldquoFormulas for the skin effectrdquo Proceedings ofthe IRE vol 30 no 9 pp 412ndash424 1942


film [10] and the influence of different solutions on vaporfilm [11ndash14] (e experiments of jet breakup are usuallyperformed in an isothermal system to study the influence ofhydrodynamics on the behavior of jet in FCI [15ndash17] Moreattention was paid to the influence of experimental con-ditions such as jet material and coolant material on jetbreakup [18 19] Coupled experiments were the integraltests performed to investigate the multiple physicalmechanisms of FCI in large scale of 10sim1000 kg [20ndash25]and mediumsmall scale of 1 gsim10 kg [26ndash30] of melt massLarge-scale experiments are intended to obtain the generalpicture of FCI process while small- and medium-scaleexperiments are focused on the understanding of physicalmechanisms in FCI

(e present study is concerned with the development ofa small-scale test facility named the VULCAN (Violentinteraction of molten fUeL with CoolANt) facility which isconceived to perform fundamental experiment of high-temperature single droplet falling into a water pool underwell-controlled conditions with the objective to investigatethe physical mechanisms of fuel-coolant interactions Inparticular the focus is the design of the heating systememployed in the VULCAN facility

(e preparation and release of the molten droplet areimportant to the success of such a very high-temperatureexperiment (e heating methods are different in the pre-vious studies according to the characteristics of the meltmaterials employed in experiment (e electrode heatingmethod of the FARO experiment [20ndash23] is characterized bylong service life and simple operation It requires electricalconduction of melt material to create an arc between theelectrodes (e KROTOS experiment [24] heats the ex-perimental material by radiation of tungsten element thatheated by resistive heating (is method has no additionalrequirement for material but the radiation heat transfermakes the heating rate slow (e TRIO experiment [25]adopted a cold crucible with direct induction heating of meltmaterial in a solidified shell of the melt itself (e methodgreatly reduces the requirements of crucible material and itis applicable to prototypical material of corium Howeverthe cold crucible has complexity in operation and difficultyin energy balance between induction power and heat dis-sipation which may cause instability of the cold cruciblewall (e DEFOR [28 29] and MISTEE [30] experimentsadopt the induction heating of a crucible which heats themelt material ie so-called ldquohot-cruciblerdquo method which issimple to operate and easy to implement

Given the small scale of the VULCAN facility and themedium range of operational temperature the similar ldquohot-cruciblerdquo method with induction heating is chosen in thedesign due to its advantages mentioned above During thepreparation period of a melt droplet the droplet is preventedby an Aerodynamic Levitation System (ALS) from falling outof the crucible To design the heating system the COMSOLcode is applied to simulate the induction heating charac-teristics of a graphite crucible under different current andfrequency of the work coil (inductor) Based on the simu-lation results the induction heating system has been setup Atest of the heating system is also performed and the

measured temperature has a good agreement with thepredicted under the same frequency and current of theinductor indicating a reasonable design of the heatingsystem in the VULCAN facility

2 Experimental Setup

Figure 1 shows a schematic of the experimental apparatuswhich includes induction heating system interaction zoneexternal trigger system data acquisition system inert gaslevitation and protection system and high-speed photog-raphy system

Induction heating system is mainly composed of afurnace an induction heater (host and controller) and anindustrial chiller

Figure 2 shows the structure of furnace which includes afurnace shell an insulated pipe and a crucible (e furnaceshell is stainless steel cylinder and its outer diameter innerdiameter and height are 180mm 170mm and 135mmrespectively (e crucible is supported by a tube which canadjust the crucible to the specified position and an obser-vation window is placed at the top of the furnace forwatching and photographing the heating state in the cru-cible Argon is filled from the bottom of furnace at a flow raterange of 1sim10times10minus5 kgm3 to provide the levitation forceand protective atmosphere

(e heating element is an induction coil which is buriedin MgO thermal insulation powders between furnace shelland insulated pipe As shown in Figure 3 the spiral coil ismade of 5 turns spiral copper pipe (e inside diameteroutside diameter and height for the spiral coil are 66mm82mm and 60mm respectively (e inner diameter andouter diameter of copper pipe are 6mm and 8mm

(e crucible has a double-layer structure that has twoadvantages

(i) (e inner and outer crucible can be made of differentmaterials Materials with good induction heatingeffect can be adopted for the outer crucible whereasmaterials that do not react with experimental ma-terials can be selected for the inner crucible to ensurethe intact droplet In this work both the innercrucible and the outer crucible are made of graphite

(ii) (e inner crucible can be taken out freely for re-placement whereas the thermocouple can be fixed inthe positioning hole of the outer crucible to measurethe temperature of the crucible

Figures 4 and 5 show the dimensions of the innercrucible and the outer crucible in the single-drop furnace

(e coil is power supplied by a medium-frequencypower (GYM25AB) (e nominal output electrical powerand frequency are 25 kW and 47 kHz respectively deter-mined by simulation and experiment (e current in the coilis adjustable for different heating temperature requirements

A 5 HP industrial chiller is equipped to cool the in-duction heaters and the coils (e cooling capacity of thechiller is 13350W and the target outlet temperature can beset to specified value





InfraredThermometer

ThermocoupleSignals

Laser Signals


TriggerSignals

Capacitor


LaserReceiver

LaserProducer

PneumaticActuator



GasBottle Ar


Pressure Gage

Reducing Valve

Flow-meter

Stop Valve


Inner crucible

Outer crucible

Insulated pipe


Observation window

Gas inlet


82 mm

66 mm

6 mm8 mm









3240

118deg

55

ϕ25ϕ19

ϕ19

ϕ9


ϕ45ϕ25

ϕ19

ϕ9ϕ35

354010

55



4020

0-20

-400

20

40

4020

0-20

-40

mm

mm

mm

(a)

0

0

20

20

40

mm

mm

-20

-20

020mm

(b)


510

508

506

504

502

500

498

Tem

pera

ture

[K]

104 105 106




40

20

0

mm


z

(a)

mm


20

10

0

ndash10

ndash20

xz

y

(b)







lnB




δ

2

μwσ

1113971

(2)







035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

















times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References











































InfraredThermometer

ThermocoupleSignals

Laser Signals


TriggerSignals

Capacitor


LaserReceiver

LaserProducer

PneumaticActuator



GasBottle Ar


Pressure Gage

Reducing Valve

Flow-meter

Stop Valve


Inner crucible

Outer crucible

Insulated pipe


Observation window

Gas inlet


82 mm

66 mm

6 mm8 mm









3240

118deg

55

ϕ25ϕ19

ϕ19

ϕ9


ϕ45ϕ25

ϕ19

ϕ9ϕ35

354010

55



4020

0-20

-400

20

40

4020

0-20

-40

mm

mm

mm

(a)

0

0

20

20

40

mm

mm

-20

-20

020mm

(b)


510

508

506

504

502

500

498

Tem

pera

ture

[K]

104 105 106




40

20

0

mm


z

(a)

mm


20

10

0

ndash10

ndash20

xz

y

(b)







lnB




δ

2

μwσ

1113971

(2)







035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

















times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References














































3240

118deg

55

ϕ25ϕ19

ϕ19

ϕ9


ϕ45ϕ25

ϕ19

ϕ9ϕ35

354010

55



4020

0-20

-400

20

40

4020

0-20

-40

mm

mm

mm

(a)

0

0

20

20

40

mm

mm

-20

-20

020mm

(b)


510

508

506

504

502

500

498

Tem

pera

ture

[K]

104 105 106




40

20

0

mm


z

(a)

mm


20

10

0

ndash10

ndash20

xz

y

(b)







lnB




δ

2

μwσ

1113971

(2)







035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

















times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References








































4020

0-20

-400

20

40

4020

0-20

-40

mm

mm

mm

(a)

0

0

20

20

40

mm

mm

-20

-20

020mm

(b)


510

508

506

504

502

500

498

Tem

pera

ture

[K]

104 105 106




40

20

0

mm


z

(a)

mm


20

10

0

ndash10

ndash20

xz

y

(b)







lnB




δ

2

μwσ

1113971

(2)







035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

















times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References












































lnB




δ

2

μwσ

1113971

(2)







035

03

025

02

015

01

005

0

Ratio

of M

esh

Num

ber

0 02 04 06 08 1Quality

















times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References

















































times10-3

435times10-3

T

8

75

7

65

6

55

5

45

(a)


times10-3

T

209times10-3

9

8

7

6

5

4

3

(b)


times10-3

T


9

8

7

6

5

3 3

2

4

112

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Mag

netic

Flu

x D

ensit

y


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References









































times105

355times104

Am2

45

4

35

3

25

2

15

1

05

(a)


times106

Am2

77times104

12

1

08

06

04

02

(b)


354times106

times106

Am2

318times104

35

3

25

2

15

1

05

(c)


1

09

08

07

06

05

04

03

02

01

0

Nor

mal

ized

Cur

rent

Den

sity


10 kHz20 kHz47 kHz

100 kHz200 kHz

line1e


0 50 100 150 200Frequency [kHz]

16

14

12

10

8

6

4

2

Skin

Dep

th [m

m]





536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References









































536

535

534

533

532

531531


95

94

93

92

91

9

89

88

87

Mea

n of

Mag

nitu

de F

lux

Den

sity

[T]

times10-3

0 50 100 150 200Frequency [kHz]

100A


times105

0 50 100 150 200Frequency [kHz]

10

95

9

85

8

75

7

65

6

55

5

Mea

n of

Cur

rent

Den

sity

[Am

2 ]

100A







1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References












































1006

1004

1002

1

0998

0996

0994

0992

Nor

mal

ized

Tem

pera

ture

20 kHz40 kHz100 kHz

140 kHz200 kHz


0 50 100 150 200Frequency [kHz]

1100

1000

900

800

700

600

500

400

300

Mea

n Te

mpe

ratu

re [K

]



10000

9000

8000

7000

6000

5000

4000

3000

2000

0

1000

Mea

n Te

mpe

ratu

re o

f Cru

cibl

e [K]

0 100 200 300 400 500Coil Current [A]

47 kHz20 kHz





105

104

103

102

101

1

099

098

097

096

095

Nor

mal

ized

Tem

pera

ture

20A80A100A

300A500A




Measured(K)

Simulated(K)

Absolutedeviation

(K)

Relativedeviation




6 Conclusions





Data Availability




Acknowledgments


References









































6 Conclusions





Data Availability




Acknowledgments


References








































COMSOL Simulation for Design of Induction Heating System ...

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Transcript of COMSOL Simulation for Design of Induction Heating System ...