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Electromagnetic analysis on Korean Helium Cooled Ceramic Reflector (HCCR) TBM during plasma major disruption
Fusion Engineering and Design 98–99 (2015) 1825–1828
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Electromagnetic analysis on Korean Helium Cooled Ceramic Reflector (HCCR) TBM during plasma major disruption Youngmin Lee a,∗ , Duck Young Ku a , Mu-Young Ahn a , Seungyon Cho a , Yi-Hyun Park a , Dong Won Lee b a b
National Fusion Research Institute, Daejeon, Republic of Korea Korea Atomic Energy Research Institute, Daejeon, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 1 June 2015 Accepted 29 June 2015 Available online 21 July 2015 Keywords: ITER Korean Helium Cooled Ceramic Reflector (HCCR) TBM Electromagnetic analysis Plasma major disruption Lorentz force
a b s t r a c t Korean Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) will be installed at the #18 equatorial port of the Vaccum Vessel in order to test the feasibility of the breeding blanket performance for forthcoming fusion power plant in the ITER TBM Program. Since ITER tokamak contains Vaccum Vessel and set of electromagnetic coils, the TBM as well as other components is greatly influenced by magnetic field generated by these coils. By the electromagnetic (EM) fast transient events such as major disruption (MD), vertical displacement event (VDE) or magnet fast discharge (MFD) occurred in tokamak system, the eddy current can be induced eventually in the conducting components. As a result, the magnetic field and induced eddy current produce extremely huge EM load (force and moment) on the TBM. Therefore, EM load calculation is one of the most important analyses for optimized design of TBM. In this study, a 20-degree sector model for tokamak system including central solenoid (CS) coil, poloidal field (PF) coil, toroidal field (TF) coil, vaccum vessel, shield blankets and TBM set (TBM, TBM key, TBM shield, TBM frame) is prepared for analysis by ANSYS-EMAG tool. Concerning the installation location of the TBM, a major disruption scenario is particularly applied for fast transient analysis. The final goal of this study is to evaluate the EM load on HCCR TBM during plasma major disruption. © 2015 Elsevier B.V. All rights reserved.
1. Introduction International Thermonuclear Experimental Reactor (ITER) is very meaningful international project to verify the nuclear fusion science and technology for forthcoming fusion power plant. Especially, Korea has developed a Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) in order to validate the feasibility of the breeding blanket performance for Demonstration Power Plant (DEMO) under the ITER TBM program [1,2]. Since the superconducting coils in the ITER tokamak machine produce the strong magnetic field, the various components including TBM is extremely affected by this field. The magnetic field and the eddy current induced by the electromagnetic (EM) transient events such as fast variation of plasma current generate strongly huge EM loads (force and moment) in the structure and the components. Therefore, EM load estimation [3–7] is one of the most important analyses for optimized design of TBM. The
∗ Corresponding author.. E-mail address: [email protected] (Y. Lee). http://dx.doi.org/10.1016/j.fusengdes.2015.06.128 0920-3796/© 2015 Elsevier B.V. All rights reserved.
National Fusion Research Institute (NFRI) has conducted the intensive research for the assessment of the EM load on the TBM. This paper focuses on the evaluation of the EM load by ANSYS-EMAG tool on the HCCR TBM during plasma major disruption.
2. Modeling of TBM-set and assumption for calculation HCCR TBM-set will be installed with Japanese Water Cooled Ceramic Breeder (WCCB) TBM-set at the #18 equatorial port of the Vaccum Vessel. However, in this study HCCR TBM-set is only considered because of the lack of the information about WCCB TBMset. Therefore, this single equatorial port includes the identical two HCCR TBM-sets. Since the single equatorial port is located inside the 20◦ sector of Vaccum Vessel periodically, the computation of the EM analysis has performed in the 20◦ sector model for the reduction of computational cost. This 20◦ sector model includes the central solenoid (CS) coil, poloidal field (PF) coil, toroidal field (TF) coil, vaccum vessel, TBM-set, TBM Frame and the neighboring shield blankets surrounding the equatorial port. Fig. 1 shows the configuration of the HCCR TBM-set. The TBMset consists of the TBM, TBM key and TBM shield, and two identical
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1.0x10
Radial Toroidal Vertical
4
8.0x10
Force (N)
4
6.0x10
4
4.0x10
4
2.0x10
0.0 Fig. 1. The configuration of the HCCR TBM-set.
16ms
22ms
sf
36ms
up
vde
Scenarios
TBM-sets are inserted in the TBM frame. There are a lot of pipes and cooling channels in the TBM-set and these pipes connect to the auxiliary system. However, in this study the modeling of these pipes and channels are excluded in the electromagnetic analysis for the simplification of the finite element modeling. The conservative results are expected because the structure material is filled in the region for cooling channels. The structure material for TBM is facing the high heat load and the high neutron irradiation simultaneously during operation phase. The Reduced Activation Ferritic Martensitic (RAFM) steel is first candidate complying with the requirement for structure material [8]. The HCCR TBM use the RAFM steel, called Advanced Reduced Activation Alloy (ARAA) developed by Korea recently [9], as a structural material. However, in this study the Eurofer database [10] has been used for the physical properties in EM analysis because of insufficient data about ARAA material when this analysis was carried out. 3. Finite element models and load conditions For EM analysis, the solid 236 element which uses edge-flux formulation for the magnetic degree of freedom on the ANSYS-EMAG tool has been used because the nonlinearity of physical property for the RAFM steel should be considered. This element is very suitable for general application of magnetic property for RAFM steel without particular methodology. The structures such as vacuum vessel, TBM-set, TBM frame and shield blanket is modeled as a solid conductor. And the plasma, various superconducting coils and the vacuum area is modeled as non-conducting region. This region only use one magnetic vector potential (AZ) for the degree of freedom (DOF). Whereas the conductive components use two DOFs described by magnetic vector potential (AZ) and electric potential (VOLT). Fig. 2 shows the finite element configurations of TBM-sets (left) and TBM frame (right). The TBM-sets and TBM frame are
Fig. 3. Forces on the two TBM-sets.
meshed as hexahedral element for convergence and accuracy of solutions. For the EM analysis, relative permeability has been set as one in all domains except for the region designed by RAFM steel. This setting value means these regions have the same magnetic property with vacuum area. The B–H curve of EUROFER is used for the permeability value in the RAFM steel region. For 20◦ sector model, the cyclic symmetry boundary conditions have been applied at the boundary of toroidal direction of the model. Symmetry conditions are applied by coupling method on the DOFs described as the magnetic vector potential (AZ) and the electric potential (VOLT). For numerical convergence the one point in conducting region is grounded by setting electric potential as zero at one node of the conductor. For the EM analyses the following DINA plasma disruption scenarios are applied: Case I: MD downward (DW) exponential 16 ms (Cat. II) Case II: MD DW exponential 22 ms (Cat. I) Case III: MD DW slow-fast (Cat. IV) Case IV: MD DW linear 36 ms (Cat. II) Case V: MD upward (UP) exponential 16 ms (Cat. II) Case VI: VDE DW exponential 16 ms (Cat. II) In general, the eddy current is induced in the conducting region due to plasma current variation. This induced eddy current and the magnetic field due to the superconducting coils produce extremely huge EM loads (force and moment) in the conductive component including TBM-set. The currents in the plasma, CS and PF coils can be obtained from DINA data. The TF coil current is constant value (9.112 MA) for all cases. In this study the halo current simulation is not performed considering the location of the installed TBM-set. Present research is focused on the analyses of Lorentz Force Density (F = J × B) on the HCCR TBM-set. Therefore, the loads due to magnetization in the RAFM steel regions are not carried out in this study. These loads also will be computed in the near future. 4. Analysis results
Fig. 2. The finite element configurations of the HCCR TBM-sets and TBM frame.
The EM loads versus time have been computed on the considered all components. The total forces and moments (absolute values) on the two TBM-sets and TBM frame are summarized from Figs. 3–6. The reference point for moment calculation uses the center of gravity of TBM structure. The main component of force and moment is in radial direction for all load cases. In the result of TBMsets forces have quite comparable values (9.0*104 N) except for VDE DW exponential 16 ms case. In the result of moment calculation
Y. Lee et al. / Fusion Engineering and Design 98–99 (2015) 1825–1828
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380
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Fig. 7. Forces versus time on the two TBM-sets.
Fig. 4. Moments on the two TBM-sets.
22ms
340
Time [ms]
Scenarios
16ms
320
up
vde
Scenarios Fig. 5. Forces on the TBM frame.
the MD DW exponential 16 ms scenario has the maximum radial moment (9.2*105 N m). In all cases on the TBM frame the radial forces gives almost similar values around 2.5*105 N. In particular, the MD DW exponential 16 ms scenario has a slightly higher value (2.6*105 N) than those in other scenarios. The maximum moment
value (5.4*106 N m) on the TBM frame is also obtained in the MD DW exponential 16 ms scenario. However, there is little difference between this value and the value of UP exponential 16 ms load case. As a result, the worst load case is the MD DW exponential 16 ms. However, some load cases cannot be ignored because the difference between the values of the forces and moments are not large. Figs. 7–10 show time behavior of the forces and moments on the two TBM-sets and TBM frame in the MD DW exponential 16 ms scenario. In all cases there are maximum values in the early phase of the disruption. As the plasma vary suddenly in initial stage, the huge amount current is induced in the TBM part such as Fig. 11. As time goes on, the plasma current decreases and the induced current is also reduced and flows to TBM shield part along the TBM key. Therefore, while the TBM is dominant component in the initial stage, the TBM Shield becomes dominant component on forces computed in the final stage. Generally, the moments and forces in the TBM Frame are bigger than those in the TBM-sets because of the difference of the volume in the structure materials. In order to evaluate the effect of magnetic property of RAFM steel, the electromagnetic analysis using constant value (setting as one) as relative permeability for structure material has been computed in the same geometry and finite element model. The solid line and dashed line describe the results without/with B–H curve respectively in Fig. 12. In the MD DW exponential 16 ms load case, the maximum radial force in the TBM-set using B-H curve is about
6
6x10
Radial Toroidal Vertical
6
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6
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radial toroidal vertical
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8.0x10 6
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Torque (N*m)
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3x10
6
2x10
6.0x10
5
4.0x10
5
2.0x10 6
1x10
0.0
0 16ms
22ms
sf
36ms
Scenarios Fig. 6. Moments on the two TBM frame.
up
vde
260
280
300
320
340
360
Time [ms] Fig. 8. Moments versus time on the two TBM-sets.
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400
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Y. Lee et al. / Fusion Engineering and Design 98–99 (2015) 1825–1828 5
radial toroidal vertical
2x10
5
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0
5
-1x10
5
-2x10
5
-3x10
2 260
280
300
320
340
36 60
380
400
Time [ms] Fig. 12. Comparison of results according to the presence or absence of B-H curve.
Fig. 9. Forces versus time on the TBM frame.
current and the generated magnetic flux are very significant factor to determine the direction of Lorentz Force. The toroidal component of magnetic flux and vertical component of induced current are so dominant in this case respectively that the Lorentz Force in the radial component changes greatly.
6
6x10
radial toroidal vertical
6
5x10
6
Torque [N*m]
4x10
5. Conclusions 6
3x10
Lorentz forces and moments due to major disruptions and vertical displacement event are calculated on the HCCR TBM-set. Time behavior of forces and moments are also computed and maximum peak values are summarized in the various load cases. In this study the MD DW exponential 16 ms scenario is the most severe load case. The obtained results are used for the stress analysis and the optimization of TBM-set design.
6
2x10
6
1x10
0 2 260
280
300
320
340
36 60
380
400
Time [ms] Fig. 10. Moments versus time on the TBM frame.
Acknowledgments This work was supported by R&D Program through National Fusion Research Institute (NFRI) funded by the Ministry of Education, Science and Technology of the Republic of Korea (NFRIIN1403-3). References
Fig. 11. Current density on the TBM-set.
3.5 times higher than those in the same part using constant value because magnetic flux density in the RAFM steel region is generated more largely. However, forces in toroidal and vertical direction have almost same behavior. The vector direction of the induced eddy
[1] S. Cho, et al., Overview of Helium Cooled Ceramic Reflector Test Blanket Module development in Korea, Fusion Eng. Des. 88 (2013) 621–625. [2] S. Cho, et al., Design and R&D progress of Korean HCCR TBM, Fusion Eng. Des. 89 (2013) 1137–1143. [3] R. Roccella, et al., Assessment of EM loads on the EU HCPB TBM during plasma disruption and normal operating scenario including the ferromagnetic effect, Fusion Eng. Des. 83 (2008) 1212–1216. [4] S. Liua, P. Long, W. Wang, Q. Huang, Evaluation of electromagnetic forces on Chinese Dual Functional Lithium Lead Test Blanket Module in ITER, Fusion Eng. Des. 85 (2010) 2176–2180. [5] D.-H. Kim, et al., Eddy current induced electromagnetic loads on shield blankets during plasma disruptions in ITER: a benchmark exercise, Fusion Eng. Des. 85 (2010) 1747–1758. [6] S. Pak, et al., Electromagnetic load calculation of the ITER machine using a single finite element model including narrow slits of the in-vessel components, Fusion Eng. Des. 88 (2013) 3224–3237. [7] P. Testoni, F. Cau, A. Portone, R. Albanese, J. Juirao, F4E studies for the electromagnetic analysis of ITER components, Fusion Eng. Des. 89 (2014) 1854–1858. [8] J.-F. Salavy, et al., Must we use ferritic steel in TBM? Fusion Eng. Des. 85 (2010) 1896–1902. [9] Y.B. Chun, et al., Effects of alloying elements and heat treatments on mechanical properties of Korean reduced-activation ferritic–martensitic steel, J. Nucl. Mater. 455 (2014) 212–216. [10] K. Mergia, N. Boukos, Structural, thermal, electrical and magnetic properties of Eurofer 97 steel, J. Nucl. Mater. 373 (2008) 1–8.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Electromagnetic analysis on Korean Helium Cooled Ceramic Reflector (HCCR) TBM during plasma major disruption Youngmin Lee a,∗ , Duck Young Ku a , Mu-Young Ahn a , Seungyon Cho a , Yi-Hyun Park a , Dong Won Lee b a b
National Fusion Research Institute, Daejeon, Republic of Korea Korea Atomic Energy Research Institute, Daejeon, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 1 June 2015 Accepted 29 June 2015 Available online 21 July 2015 Keywords: ITER Korean Helium Cooled Ceramic Reflector (HCCR) TBM Electromagnetic analysis Plasma major disruption Lorentz force
a b s t r a c t Korean Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) will be installed at the #18 equatorial port of the Vaccum Vessel in order to test the feasibility of the breeding blanket performance for forthcoming fusion power plant in the ITER TBM Program. Since ITER tokamak contains Vaccum Vessel and set of electromagnetic coils, the TBM as well as other components is greatly influenced by magnetic field generated by these coils. By the electromagnetic (EM) fast transient events such as major disruption (MD), vertical displacement event (VDE) or magnet fast discharge (MFD) occurred in tokamak system, the eddy current can be induced eventually in the conducting components. As a result, the magnetic field and induced eddy current produce extremely huge EM load (force and moment) on the TBM. Therefore, EM load calculation is one of the most important analyses for optimized design of TBM. In this study, a 20-degree sector model for tokamak system including central solenoid (CS) coil, poloidal field (PF) coil, toroidal field (TF) coil, vaccum vessel, shield blankets and TBM set (TBM, TBM key, TBM shield, TBM frame) is prepared for analysis by ANSYS-EMAG tool. Concerning the installation location of the TBM, a major disruption scenario is particularly applied for fast transient analysis. The final goal of this study is to evaluate the EM load on HCCR TBM during plasma major disruption. © 2015 Elsevier B.V. All rights reserved.
1. Introduction International Thermonuclear Experimental Reactor (ITER) is very meaningful international project to verify the nuclear fusion science and technology for forthcoming fusion power plant. Especially, Korea has developed a Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) in order to validate the feasibility of the breeding blanket performance for Demonstration Power Plant (DEMO) under the ITER TBM program [1,2]. Since the superconducting coils in the ITER tokamak machine produce the strong magnetic field, the various components including TBM is extremely affected by this field. The magnetic field and the eddy current induced by the electromagnetic (EM) transient events such as fast variation of plasma current generate strongly huge EM loads (force and moment) in the structure and the components. Therefore, EM load estimation [3–7] is one of the most important analyses for optimized design of TBM. The
∗ Corresponding author.. E-mail address: [email protected] (Y. Lee). http://dx.doi.org/10.1016/j.fusengdes.2015.06.128 0920-3796/© 2015 Elsevier B.V. All rights reserved.
National Fusion Research Institute (NFRI) has conducted the intensive research for the assessment of the EM load on the TBM. This paper focuses on the evaluation of the EM load by ANSYS-EMAG tool on the HCCR TBM during plasma major disruption.
2. Modeling of TBM-set and assumption for calculation HCCR TBM-set will be installed with Japanese Water Cooled Ceramic Breeder (WCCB) TBM-set at the #18 equatorial port of the Vaccum Vessel. However, in this study HCCR TBM-set is only considered because of the lack of the information about WCCB TBMset. Therefore, this single equatorial port includes the identical two HCCR TBM-sets. Since the single equatorial port is located inside the 20◦ sector of Vaccum Vessel periodically, the computation of the EM analysis has performed in the 20◦ sector model for the reduction of computational cost. This 20◦ sector model includes the central solenoid (CS) coil, poloidal field (PF) coil, toroidal field (TF) coil, vaccum vessel, TBM-set, TBM Frame and the neighboring shield blankets surrounding the equatorial port. Fig. 1 shows the configuration of the HCCR TBM-set. The TBMset consists of the TBM, TBM key and TBM shield, and two identical
1826
Y. Lee et al. / Fusion Engineering and Design 98–99 (2015) 1825–1828 5
1.0x10
Radial Toroidal Vertical
4
8.0x10
Force (N)
4
6.0x10
4
4.0x10
4
2.0x10
0.0 Fig. 1. The configuration of the HCCR TBM-set.
16ms
22ms
sf
36ms
up
vde
Scenarios
TBM-sets are inserted in the TBM frame. There are a lot of pipes and cooling channels in the TBM-set and these pipes connect to the auxiliary system. However, in this study the modeling of these pipes and channels are excluded in the electromagnetic analysis for the simplification of the finite element modeling. The conservative results are expected because the structure material is filled in the region for cooling channels. The structure material for TBM is facing the high heat load and the high neutron irradiation simultaneously during operation phase. The Reduced Activation Ferritic Martensitic (RAFM) steel is first candidate complying with the requirement for structure material [8]. The HCCR TBM use the RAFM steel, called Advanced Reduced Activation Alloy (ARAA) developed by Korea recently [9], as a structural material. However, in this study the Eurofer database [10] has been used for the physical properties in EM analysis because of insufficient data about ARAA material when this analysis was carried out. 3. Finite element models and load conditions For EM analysis, the solid 236 element which uses edge-flux formulation for the magnetic degree of freedom on the ANSYS-EMAG tool has been used because the nonlinearity of physical property for the RAFM steel should be considered. This element is very suitable for general application of magnetic property for RAFM steel without particular methodology. The structures such as vacuum vessel, TBM-set, TBM frame and shield blanket is modeled as a solid conductor. And the plasma, various superconducting coils and the vacuum area is modeled as non-conducting region. This region only use one magnetic vector potential (AZ) for the degree of freedom (DOF). Whereas the conductive components use two DOFs described by magnetic vector potential (AZ) and electric potential (VOLT). Fig. 2 shows the finite element configurations of TBM-sets (left) and TBM frame (right). The TBM-sets and TBM frame are
Fig. 3. Forces on the two TBM-sets.
meshed as hexahedral element for convergence and accuracy of solutions. For the EM analysis, relative permeability has been set as one in all domains except for the region designed by RAFM steel. This setting value means these regions have the same magnetic property with vacuum area. The B–H curve of EUROFER is used for the permeability value in the RAFM steel region. For 20◦ sector model, the cyclic symmetry boundary conditions have been applied at the boundary of toroidal direction of the model. Symmetry conditions are applied by coupling method on the DOFs described as the magnetic vector potential (AZ) and the electric potential (VOLT). For numerical convergence the one point in conducting region is grounded by setting electric potential as zero at one node of the conductor. For the EM analyses the following DINA plasma disruption scenarios are applied: Case I: MD downward (DW) exponential 16 ms (Cat. II) Case II: MD DW exponential 22 ms (Cat. I) Case III: MD DW slow-fast (Cat. IV) Case IV: MD DW linear 36 ms (Cat. II) Case V: MD upward (UP) exponential 16 ms (Cat. II) Case VI: VDE DW exponential 16 ms (Cat. II) In general, the eddy current is induced in the conducting region due to plasma current variation. This induced eddy current and the magnetic field due to the superconducting coils produce extremely huge EM loads (force and moment) in the conductive component including TBM-set. The currents in the plasma, CS and PF coils can be obtained from DINA data. The TF coil current is constant value (9.112 MA) for all cases. In this study the halo current simulation is not performed considering the location of the installed TBM-set. Present research is focused on the analyses of Lorentz Force Density (F = J × B) on the HCCR TBM-set. Therefore, the loads due to magnetization in the RAFM steel regions are not carried out in this study. These loads also will be computed in the near future. 4. Analysis results
Fig. 2. The finite element configurations of the HCCR TBM-sets and TBM frame.
The EM loads versus time have been computed on the considered all components. The total forces and moments (absolute values) on the two TBM-sets and TBM frame are summarized from Figs. 3–6. The reference point for moment calculation uses the center of gravity of TBM structure. The main component of force and moment is in radial direction for all load cases. In the result of TBMsets forces have quite comparable values (9.0*104 N) except for VDE DW exponential 16 ms case. In the result of moment calculation
Y. Lee et al. / Fusion Engineering and Design 98–99 (2015) 1825–1828
1827
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6
1.0x10
6.0x10
Radial Toroidal Vertical
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360
380
400
Fig. 7. Forces versus time on the two TBM-sets.
Fig. 4. Moments on the two TBM-sets.
22ms
340
Time [ms]
Scenarios
16ms
320
up
vde
Scenarios Fig. 5. Forces on the TBM frame.
the MD DW exponential 16 ms scenario has the maximum radial moment (9.2*105 N m). In all cases on the TBM frame the radial forces gives almost similar values around 2.5*105 N. In particular, the MD DW exponential 16 ms scenario has a slightly higher value (2.6*105 N) than those in other scenarios. The maximum moment
value (5.4*106 N m) on the TBM frame is also obtained in the MD DW exponential 16 ms scenario. However, there is little difference between this value and the value of UP exponential 16 ms load case. As a result, the worst load case is the MD DW exponential 16 ms. However, some load cases cannot be ignored because the difference between the values of the forces and moments are not large. Figs. 7–10 show time behavior of the forces and moments on the two TBM-sets and TBM frame in the MD DW exponential 16 ms scenario. In all cases there are maximum values in the early phase of the disruption. As the plasma vary suddenly in initial stage, the huge amount current is induced in the TBM part such as Fig. 11. As time goes on, the plasma current decreases and the induced current is also reduced and flows to TBM shield part along the TBM key. Therefore, while the TBM is dominant component in the initial stage, the TBM Shield becomes dominant component on forces computed in the final stage. Generally, the moments and forces in the TBM Frame are bigger than those in the TBM-sets because of the difference of the volume in the structure materials. In order to evaluate the effect of magnetic property of RAFM steel, the electromagnetic analysis using constant value (setting as one) as relative permeability for structure material has been computed in the same geometry and finite element model. The solid line and dashed line describe the results without/with B–H curve respectively in Fig. 12. In the MD DW exponential 16 ms load case, the maximum radial force in the TBM-set using B-H curve is about
6
6x10
Radial Toroidal Vertical
6
5x10
6
1.0x10
radial toroidal vertical
5
8.0x10 6
5
Torque [N*m]
Torque (N*m)
4x10
6
3x10
6
2x10
6.0x10
5
4.0x10
5
2.0x10 6
1x10
0.0
0 16ms
22ms
sf
36ms
Scenarios Fig. 6. Moments on the two TBM frame.
up
vde
260
280
300
320
340
360
Time [ms] Fig. 8. Moments versus time on the two TBM-sets.
380
400
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radial toroidal vertical
2x10
5
Force [N]
1x10
0
5
-1x10
5
-2x10
5
-3x10
2 260
280
300
320
340
36 60
380
400
Time [ms] Fig. 12. Comparison of results according to the presence or absence of B-H curve.
Fig. 9. Forces versus time on the TBM frame.
current and the generated magnetic flux are very significant factor to determine the direction of Lorentz Force. The toroidal component of magnetic flux and vertical component of induced current are so dominant in this case respectively that the Lorentz Force in the radial component changes greatly.
6
6x10
radial toroidal vertical
6
5x10
6
Torque [N*m]
4x10
5. Conclusions 6
3x10
Lorentz forces and moments due to major disruptions and vertical displacement event are calculated on the HCCR TBM-set. Time behavior of forces and moments are also computed and maximum peak values are summarized in the various load cases. In this study the MD DW exponential 16 ms scenario is the most severe load case. The obtained results are used for the stress analysis and the optimization of TBM-set design.
6
2x10
6
1x10
0 2 260
280
300
320
340
36 60
380
400
Time [ms] Fig. 10. Moments versus time on the TBM frame.
Acknowledgments This work was supported by R&D Program through National Fusion Research Institute (NFRI) funded by the Ministry of Education, Science and Technology of the Republic of Korea (NFRIIN1403-3). References
Fig. 11. Current density on the TBM-set.
3.5 times higher than those in the same part using constant value because magnetic flux density in the RAFM steel region is generated more largely. However, forces in toroidal and vertical direction have almost same behavior. The vector direction of the induced eddy
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