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Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block
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FUSION-8330; No. of Pages 5
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Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block Weishan Kang a,∗ , Jiming Chen a , Jihong Wu a , Erwu Niu b a b
Southwestern Institute of Physics, P.O. Box 432, Chengdu 610064, PR China China International Nuclear Fusion Energy Program Execution Center, 15B Fuxing Rd., Beijing 100862, PR China
h i g h l i g h t s • The importance of depth, location and number of slit were studied individually. • The effects of the cooling channels were also examined. • Brick-like meshing was applied on the SB with complex interface to get a regular hexahedral mesh.
a r t i c l e
i n f o
Article history: Received 21 August 2015 Accepted 9 November 2015 Available online xxx Keywords: ITER Blanket Shield block Electromagnetic
a b s t r a c t Electromagnetic (EM) load is one of the most concerned design issues for the in-vessel components in the Tokamak device. For shield block (SB), quite a few of slits cut on the SB are designed to mitigate the EM load. In this study, a solid model of blanket system with other main surrounding components, such as vacuum vessel, was developed, and FE analyses were performed to address the eddy current and Lorentz force during major disruption (MD) with ANSYS EMAG code package. In order to get a regular hexahedral mesh of the SB with complex interface, a brick-like meshing is used to get a more reliable result. Key factors which potentially have great impacts on the eddy current were studied individually by SB04 of the standard blanket module, such as the depth, location and number of the slits. To better understand the effects of cooling channels on the EM load, SB04 without cooling channel are calculated to make comparisons. Two important conclusions can be made from this study. The first one is that cooling channels have a little impact on the EM load. This is because the cooling channels cut into the eddy current locally, and the global current loop is not affected. The second is that slit configuration is important to control the EM load, and their depths, locations and numbers are also important. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Electromagnetic (EM) load is one of the most concerned design issues for the in-vessel components in the tokamak device. Plasmas transient, such as major disruption (MD) and vertical displacement event (VDE), can produce eddy currents and corresponding Lorentz forces on the conducting components surrounding the plasmas. For ITER blanket shield block (SB), quite a few of slits cut on the SB are designed to mitigate the EM load. The slits will cut into the eddy current loop and mitigate the magnitude of the current. On the other side, too many slits will weaken the manufacturability of the SB, and make the SB cooling design more difficult. For the reason, reasonable number of slits is necessary to be studied for the SB
∗ Corresponding author. Tel.: +86 28 8285 0419. E-mail address: [email protected] (W. Kang).
design, and other key factor impacting the EM load, such as depth and location of slits should be examined and optimized. The main function of the SB is to provide thermal and nuclear shielding to the components in the device, and SB and first wall panel are comprised of blanket module. In order to remove the nuclear heat deposited in the SB, a matrix of cooling channels and headers/covers are designed [1]. The SB has a very complicated interface to be compatible with various kinds of surrounding components [1]. For this reason, the slits on the SB cannot be cut at random. This study will focus on a very regular and standard blanket module No. 4, which is located right above the equatorial plane of the device, to study the effect of slits on the eddy current of the SB, and optimize the slit configuration for other SBs by deducing the common rules. The plasmas event, MD upward with exponential current quenching (ECQ), was chose to exemplify the calculation of the EM load on the SB04, and the results from other kinds of plasmas events should be similar.
http://dx.doi.org/10.1016/j.fusengdes.2015.11.014 0920-3796/© 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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2. Methodology and FE models FE code package, such as ANSYS EMAG, can be employed to address the EM problems. The most important load input in the analysis is the plasmas excitation current. In ITER the MHD code, DINA, is used to simulate plasma disruptions, and the plasma is usually reproduced by means of a cloud of current filament in the DINA. The magnitudes, numbers and positions of these current filaments will change with time, and the fact makes a very fine mesh of the plasmas region required [2]. The method where current filaments are directly loaded in the FE analysis with detailed meshing is called primary excitation. However, under some condition, a so call secondary excitations method can be used to avoid a very detailed meshing of the plasmas region [3,4]. The 3D model of the EM analysis is a large scale one. Besides the blanket system, air, plasmas region and large conducting component, such as vacuum vessel, should be included. According to ANSYS EMAG [5], air element is required to fill with all of the free space, including tiny air gap between the slits and in the cooling channels. The central solenoid (CS) and poloidal field (PF) coils should be modeled, but toroidal filed (TF) coils are excluded, which can be added in the post-procession by using the following correlation: BTF = 32.86/x
(1)
where, BTF is the magnetic field by TF coils, and x is the radial coordinate in global cylindrical coordinate system with the origin located at the machine center. Because TF coil was excluded in the model, it is a cyclic symmetry analysis, a 20◦ sector can be cut from the full model, and cyclic boundary condition can be applied on the both side to simplify the problem. In order to study the slit impact on the SB in detail, all of the SB’s main features should be reflected in the FE model. On the other side, a regular hexahedral mesh is crucial to get reliable results in the EM analyses. Obviously, hexahedral mesh is impossible to implement on the SB due to its complex interface. However, a bricklike meshing can solve this problem. At first a box-like SB model was built, and a very regular mapped meshing was applied to it, where the size of the mesh should be fine enough. Then the SB could be modeled by removing the mesh element at the location corresponding to “void”, for instance, the cooling channels, slits and other interface. The “void” mesh element was removed by changing its resistivity to infinitely great, which is equal to that of air. The smaller the mesh size is, the more accurate the model will be. The CAD and FE model of the current design of SB04 can be seen in Fig. 1. It can be seen that the cut-out due to the interface of SB04 is well reflected in the FE model in Fig. 1b. The cooling channels inside the SB were also detailedly modeled, see Fig. 1c.
3. Element types, boundary conditions and material properties ANSYS EMAG is a commercial program based on Maxwell’s equations to solve EM problems, and primary degrees of freedoms (DOFs) that the solution calculates are magnetic and electric potentials. In the EM analysis, the element type of Solid 97 with DOF of magnetic potential was applied to the non-conducting structure, such as air, plasmas region and CS and PF coils, and Solid 97 with DOF of magnetic and electric potential was applied to all of the conducting components including the SBs and vacuum vessel. Cyclic boundary condition was applied on the both side of the 20◦ sector. To implement the cyclic boundary condition, coupled DOF was applied to the pair of nodes on the both sides of the sector. For DOF coupling, an APDL code was programmed to pick up the
Fig. 1. (a) CAD model of the current design of SB04; (b) brick-like meshing of FEmodel of SB and (c) brick-like meshing of cooling channels with header. Table 1 Summary of material properties. Material
Resistivity [ m]
Relative permeability
SS316L (N) Air
0.800E-6 –
1 1
Fig. 2. Illustration of eddy current loop in SB04 (B: change of magnetic field; J: eddy current; t: toroidal; p: poloidal and r: radial).
nodes on the both sides, and the node on one side was geometrically identical to the node on the other side. SS316L (N) has been selected as the material for SBs and VV in ITER, and the material properties used in the analyses are summarized in Table 1. 4. Eddy current loops and slits During plasmas disruption, for the current induced in the SB, the current flows in such a direction that its own magnetic field opposes the change that produced the current according to Lenz’s law. For SB04, because the magnetic field produced by plasmas current decays in the poloidal and radial direction, the currents on the horizontal and vertical planes are induced accordingly. Fig. 2 shows the typical eddy current loop in SB04.
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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Fig. 4. Correlation between Lorentz force and depth of six pairs of slits. Table 2 Comparisons of peak Lorentz force on SB04 by slits’ toroidal location. Fig. 3. Poloidal slits (top) and radial slits (bottom) with number.
Obviously, slit can mitigate the EM load on the SB by cutting into these eddy current loops and decreasing the loop length, and they should cut into the current loop directly to reduce the EM load effectively. In the design, there are two types of slits, poloidal and radial slits, and they are named after the direction of the end holes which are drilled at the end of each slit to reduce the stress concentration, see Fig. 3. The poloidal slits are cut all through the SB in the poloidal direction, and they cut into the eddy current loop induced by poloidal magnetic field changes, see the current loop circulating on the horizontal plane in Fig. 2. The radial slits are cut all through the SB in radial direction, and they can cut into the eddy current loop caused by radial magnetic field changes, see the current loop circulating on the vertical plane in Fig. 2. It is noticed that both poloidal and radial slits appears in pairs due to the symmetric structure of SB.
Radial slits no.
Peak radial force (kN)
Peak poloidal force (kN)
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
None 1, 6 2, 7 3, 8 4, 9 5, 10
42.0 41.1 40.3 38.5 37.4 38.4
40.3 39.5 38.4 35.3 33.8 35.6
Table 3 Comparisons of peak Lorentz force on SB04 by deep slits’ number. Case
Radial slits no.
Peak radial force (kN)
Peak poloidal force (kN)
Case 7 Case 8 Case 9 Case 10 Case 11
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 7, 8, 9, 10 3, 4, 5, 8, 9, 10 4, 5, 9, 10 5, 10
29.4 30.8 32.4 35.4 38.4
27.1 28.2 29.2 31.9 35.6
5.1. Slits’ depth
5. Impacts of slits configuration on EM load Theoretically, more slits are designed on the SB, more effectively the EM load will be mitigated. However, the number of slits has to be balanced between efficiency and manufacturability of the SB. In the following sub-sections, the depth, location and number of radial slit are examined individually, and Lorentz forces of on SB04 are calculated to compare with each other to find out the best solution. The situation of poloidal slits is similar with the radial slits. In ANSYS EMAG, eddy current and Lorentz force can be calculated at the element level. The Lorentz force on a certain element can be given by: → − → − → − FL = J × B
Case
(2)
− → where, J is eddy current in an element and can be calculated − → directly from ANSYS EMAG. B is magnetic field intensity, and it also can be obtained by numerical results. It is noticed that the − → toroidal component of B should be calculated from Eq. (1). So the Lorentz force on each element can be calculated, and each component of Lorentz force on the SB can be obtained by adding the corresponding component value of all of the elements together. For better comparison of EM load, the peak value of each component during MD was calculated, and it is worthy of note that there is no toroidal component of Lorentz force on SB04.
Because the depth of slits has significant effect on the EM load on the SB, the relationship of slits’ depth with EM load was the first to examine. Six pairs of radial slits with same depth, Slit 1, Slit 2, Slit 3, Slit 6, Slit 7 and Slit 8 in Fig. 3, were selected, and other radial and poloidal slits were all removed. Several cases with different depth’s value of these same slits were calculated, and the results are shown in Fig. 4. Two conclusions can be made from Fig. 4. The first is that when the depth of slits is larger than about 50 mm, the Lorentz force on the SB can reduce quickly with the increase of slits’ depth. The second is that the correlation between both radial and poloidal component of Lorentz force and slits’ depth is approximately linear when the depth is larger than 50 mm. In order to make sure slits can work well, the depth of slits should be larger than 50 mm in SB design. 5.2. Slits’ location In this part of study, only two pairs of radial slits with same toroidal position were kept to examine the effect of their toroidal locations on the Lorentz force, and the other slits were all removed. The depths of the radial slits are all 270 mm. The results are given in Table 2.
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Fig. 5. Time history of radial and poloidal components of Lorentz force on the SB with and without cooling channel during the MD: (a) radial component and (b) poloidal component.
It can be found out that radial slits near the central region have much less effect on the Lorentz force than those near two sides’ ends, which means that deep slits should be tried to cut near two sides’ ends. For the slits near the sides’ ends, the Lorentz force in the Case 5 is relatively smaller than the other two cases (Case 4 and Case 6). By this point of view, deep radial slits should be designed near the middle of the half SB and the region of SB with largest radial thickness.
5.3. Deep slits’ number According to the previous study, deep slits are very important to control the EM load on the SB. In order to study the relationship of deep slits’ number with EM load, the radial slits in the current design of SB (see Fig. 3) without poloidal slit were removed pair by pair to perform analyses and make comparisons. The depths of all of the radial slits’ were also 270 mm. The analyses results are listed in Table 3. With the increase of the radial deep slit’s number, the radial and poloidal Lorentz force decrease. However, once the number of slits reaches 12, i.e., six pairs, the Lorentz force does not reduce obviously. It is probably because slits near the central region (Slit 1, Slit 2, Slit 6 and Slit 7) have much less effect on the EM load than the other radial slits. For the reason and considering the space limitation of SB04, six pairs of deep slits are enough for SB04. For other larger SBs, the number of deep slits should be more than that.
6. Impacts of cooling channels The case of SB without cooling channel was also studied to examine the effects of cooling channels on the EM load. Two individual FE analyses were done to make a comparison. The first one is the current design of SB04 with cooling channel, and another one is the current design of SB04 without cooling channel. The time history of radial and poloidal component of Lorentz force on the SB with and without cooling channel during the MD is shown in Fig. 5. It can be seen that the difference of peak Lorentz force between these two cases is limited. The cooling channels reduce by 1.0% and 14.0% of peak Lorentz force in the radial and poloidal direction, respectively. Examples of eddy current loop cut by cooling channels and slits are shown in Fig. 6. Obviously, on the cross section of SB cut vertically, eddy current loop is slightly affected by cooling channels, and the cooling channels’ effects are only local. However, in Fig. 6b, slits can split large eddy current loop into several smaller one. These smaller eddy current loops circulate in a smaller space, its loop’s length is shortened and its magnitude is mitigated. Compared with cooling channel, slits have significant effect on the EM load.
Fig. 6. Eddy current distribution on two cross sections of SB04 cut vertically to compare the impacts of cooling channels and slits on the EM load. (a) Eddy current loop cut by cooling channels and (b) eddy current loop cut by slits.
7. Discussions All of these FE analyses in the study were focused on the radial slits, and it can be expected that the situation of poloidal slits is similar. Generally speaking, slit is very effective to control EM load on the SB. The larger depth of slits are, the more EM load will be reduced. Considering the space limitation of SB, the slit’s depth from 200 mm to 300 mm will be preferable. Deep slits should be designed near the middle of the half SB and the region of SB with largest radial thickness, which makes slit work more effectively. For the SB’s size like SB04, six pairs of deep radial slits are enough to control EM load, and for larger SBs, the number of deep slits should be more than that. The effects of cooling channels were also examined. The results indicate that cooling channels’ effects are limited. From the engineering of view, the cooling channels can be possibly ignored in some preliminary FE analyses.
Acknowledgments This work was partially supported by the National Magnetic Confinement Fusion Science Program (Contract 2014GB126000). It only reflects the view of the authors, and the views and opinions expressed herein do not necessarily reflect those of the ITER Organization
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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References [1] ITER, Blanket design description document (2013 FDR). ITER IDM Document, 2013. [2] D.-H. Kim, D.-K. Oh, S. Pak, Eddy current induced electromagnetic loads on shield blankets during plasma disruptions in ITER: a benchmark exercise, Fusion Eng. Des. 85 (2010) 1747–1758. [3] M. Roccella, A. Marin, F. Lucca, M. Merola, Detailed electromagnetic numerical evaluation of eddy currents induced by toroidal and poloidal
magnetic field variation and halo currents, Fusion Eng. Des. 83 (2008) 1625–1630. [4] R. Roccella, L.V. Bocaccini, M. Meyder, S. Raff, M. Roccella, Assessment of EM load on the EU HCPB TBM during plasma disruption and normal operating scenario including ferromagnetic effect, Fusion Eng. Des. 83 (2008) 1212–1216. [5] ANSYS, ANSYS User’s Manual, 2010 (Release 13.0).
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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FUSION-8330; No. of Pages 5
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block Weishan Kang a,∗ , Jiming Chen a , Jihong Wu a , Erwu Niu b a b
Southwestern Institute of Physics, P.O. Box 432, Chengdu 610064, PR China China International Nuclear Fusion Energy Program Execution Center, 15B Fuxing Rd., Beijing 100862, PR China
h i g h l i g h t s • The importance of depth, location and number of slit were studied individually. • The effects of the cooling channels were also examined. • Brick-like meshing was applied on the SB with complex interface to get a regular hexahedral mesh.
a r t i c l e
i n f o
Article history: Received 21 August 2015 Accepted 9 November 2015 Available online xxx Keywords: ITER Blanket Shield block Electromagnetic
a b s t r a c t Electromagnetic (EM) load is one of the most concerned design issues for the in-vessel components in the Tokamak device. For shield block (SB), quite a few of slits cut on the SB are designed to mitigate the EM load. In this study, a solid model of blanket system with other main surrounding components, such as vacuum vessel, was developed, and FE analyses were performed to address the eddy current and Lorentz force during major disruption (MD) with ANSYS EMAG code package. In order to get a regular hexahedral mesh of the SB with complex interface, a brick-like meshing is used to get a more reliable result. Key factors which potentially have great impacts on the eddy current were studied individually by SB04 of the standard blanket module, such as the depth, location and number of the slits. To better understand the effects of cooling channels on the EM load, SB04 without cooling channel are calculated to make comparisons. Two important conclusions can be made from this study. The first one is that cooling channels have a little impact on the EM load. This is because the cooling channels cut into the eddy current locally, and the global current loop is not affected. The second is that slit configuration is important to control the EM load, and their depths, locations and numbers are also important. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Electromagnetic (EM) load is one of the most concerned design issues for the in-vessel components in the tokamak device. Plasmas transient, such as major disruption (MD) and vertical displacement event (VDE), can produce eddy currents and corresponding Lorentz forces on the conducting components surrounding the plasmas. For ITER blanket shield block (SB), quite a few of slits cut on the SB are designed to mitigate the EM load. The slits will cut into the eddy current loop and mitigate the magnitude of the current. On the other side, too many slits will weaken the manufacturability of the SB, and make the SB cooling design more difficult. For the reason, reasonable number of slits is necessary to be studied for the SB
∗ Corresponding author. Tel.: +86 28 8285 0419. E-mail address: [email protected] (W. Kang).
design, and other key factor impacting the EM load, such as depth and location of slits should be examined and optimized. The main function of the SB is to provide thermal and nuclear shielding to the components in the device, and SB and first wall panel are comprised of blanket module. In order to remove the nuclear heat deposited in the SB, a matrix of cooling channels and headers/covers are designed [1]. The SB has a very complicated interface to be compatible with various kinds of surrounding components [1]. For this reason, the slits on the SB cannot be cut at random. This study will focus on a very regular and standard blanket module No. 4, which is located right above the equatorial plane of the device, to study the effect of slits on the eddy current of the SB, and optimize the slit configuration for other SBs by deducing the common rules. The plasmas event, MD upward with exponential current quenching (ECQ), was chose to exemplify the calculation of the EM load on the SB04, and the results from other kinds of plasmas events should be similar.
http://dx.doi.org/10.1016/j.fusengdes.2015.11.014 0920-3796/© 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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2. Methodology and FE models FE code package, such as ANSYS EMAG, can be employed to address the EM problems. The most important load input in the analysis is the plasmas excitation current. In ITER the MHD code, DINA, is used to simulate plasma disruptions, and the plasma is usually reproduced by means of a cloud of current filament in the DINA. The magnitudes, numbers and positions of these current filaments will change with time, and the fact makes a very fine mesh of the plasmas region required [2]. The method where current filaments are directly loaded in the FE analysis with detailed meshing is called primary excitation. However, under some condition, a so call secondary excitations method can be used to avoid a very detailed meshing of the plasmas region [3,4]. The 3D model of the EM analysis is a large scale one. Besides the blanket system, air, plasmas region and large conducting component, such as vacuum vessel, should be included. According to ANSYS EMAG [5], air element is required to fill with all of the free space, including tiny air gap between the slits and in the cooling channels. The central solenoid (CS) and poloidal field (PF) coils should be modeled, but toroidal filed (TF) coils are excluded, which can be added in the post-procession by using the following correlation: BTF = 32.86/x
(1)
where, BTF is the magnetic field by TF coils, and x is the radial coordinate in global cylindrical coordinate system with the origin located at the machine center. Because TF coil was excluded in the model, it is a cyclic symmetry analysis, a 20◦ sector can be cut from the full model, and cyclic boundary condition can be applied on the both side to simplify the problem. In order to study the slit impact on the SB in detail, all of the SB’s main features should be reflected in the FE model. On the other side, a regular hexahedral mesh is crucial to get reliable results in the EM analyses. Obviously, hexahedral mesh is impossible to implement on the SB due to its complex interface. However, a bricklike meshing can solve this problem. At first a box-like SB model was built, and a very regular mapped meshing was applied to it, where the size of the mesh should be fine enough. Then the SB could be modeled by removing the mesh element at the location corresponding to “void”, for instance, the cooling channels, slits and other interface. The “void” mesh element was removed by changing its resistivity to infinitely great, which is equal to that of air. The smaller the mesh size is, the more accurate the model will be. The CAD and FE model of the current design of SB04 can be seen in Fig. 1. It can be seen that the cut-out due to the interface of SB04 is well reflected in the FE model in Fig. 1b. The cooling channels inside the SB were also detailedly modeled, see Fig. 1c.
3. Element types, boundary conditions and material properties ANSYS EMAG is a commercial program based on Maxwell’s equations to solve EM problems, and primary degrees of freedoms (DOFs) that the solution calculates are magnetic and electric potentials. In the EM analysis, the element type of Solid 97 with DOF of magnetic potential was applied to the non-conducting structure, such as air, plasmas region and CS and PF coils, and Solid 97 with DOF of magnetic and electric potential was applied to all of the conducting components including the SBs and vacuum vessel. Cyclic boundary condition was applied on the both side of the 20◦ sector. To implement the cyclic boundary condition, coupled DOF was applied to the pair of nodes on the both sides of the sector. For DOF coupling, an APDL code was programmed to pick up the
Fig. 1. (a) CAD model of the current design of SB04; (b) brick-like meshing of FEmodel of SB and (c) brick-like meshing of cooling channels with header. Table 1 Summary of material properties. Material
Resistivity [ m]
Relative permeability
SS316L (N) Air
0.800E-6 –
1 1
Fig. 2. Illustration of eddy current loop in SB04 (B: change of magnetic field; J: eddy current; t: toroidal; p: poloidal and r: radial).
nodes on the both sides, and the node on one side was geometrically identical to the node on the other side. SS316L (N) has been selected as the material for SBs and VV in ITER, and the material properties used in the analyses are summarized in Table 1. 4. Eddy current loops and slits During plasmas disruption, for the current induced in the SB, the current flows in such a direction that its own magnetic field opposes the change that produced the current according to Lenz’s law. For SB04, because the magnetic field produced by plasmas current decays in the poloidal and radial direction, the currents on the horizontal and vertical planes are induced accordingly. Fig. 2 shows the typical eddy current loop in SB04.
Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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3
Fig. 4. Correlation between Lorentz force and depth of six pairs of slits. Table 2 Comparisons of peak Lorentz force on SB04 by slits’ toroidal location. Fig. 3. Poloidal slits (top) and radial slits (bottom) with number.
Obviously, slit can mitigate the EM load on the SB by cutting into these eddy current loops and decreasing the loop length, and they should cut into the current loop directly to reduce the EM load effectively. In the design, there are two types of slits, poloidal and radial slits, and they are named after the direction of the end holes which are drilled at the end of each slit to reduce the stress concentration, see Fig. 3. The poloidal slits are cut all through the SB in the poloidal direction, and they cut into the eddy current loop induced by poloidal magnetic field changes, see the current loop circulating on the horizontal plane in Fig. 2. The radial slits are cut all through the SB in radial direction, and they can cut into the eddy current loop caused by radial magnetic field changes, see the current loop circulating on the vertical plane in Fig. 2. It is noticed that both poloidal and radial slits appears in pairs due to the symmetric structure of SB.
Radial slits no.
Peak radial force (kN)
Peak poloidal force (kN)
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
None 1, 6 2, 7 3, 8 4, 9 5, 10
42.0 41.1 40.3 38.5 37.4 38.4
40.3 39.5 38.4 35.3 33.8 35.6
Table 3 Comparisons of peak Lorentz force on SB04 by deep slits’ number. Case
Radial slits no.
Peak radial force (kN)
Peak poloidal force (kN)
Case 7 Case 8 Case 9 Case 10 Case 11
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 7, 8, 9, 10 3, 4, 5, 8, 9, 10 4, 5, 9, 10 5, 10
29.4 30.8 32.4 35.4 38.4
27.1 28.2 29.2 31.9 35.6
5.1. Slits’ depth
5. Impacts of slits configuration on EM load Theoretically, more slits are designed on the SB, more effectively the EM load will be mitigated. However, the number of slits has to be balanced between efficiency and manufacturability of the SB. In the following sub-sections, the depth, location and number of radial slit are examined individually, and Lorentz forces of on SB04 are calculated to compare with each other to find out the best solution. The situation of poloidal slits is similar with the radial slits. In ANSYS EMAG, eddy current and Lorentz force can be calculated at the element level. The Lorentz force on a certain element can be given by: → − → − → − FL = J × B
Case
(2)
− → where, J is eddy current in an element and can be calculated − → directly from ANSYS EMAG. B is magnetic field intensity, and it also can be obtained by numerical results. It is noticed that the − → toroidal component of B should be calculated from Eq. (1). So the Lorentz force on each element can be calculated, and each component of Lorentz force on the SB can be obtained by adding the corresponding component value of all of the elements together. For better comparison of EM load, the peak value of each component during MD was calculated, and it is worthy of note that there is no toroidal component of Lorentz force on SB04.
Because the depth of slits has significant effect on the EM load on the SB, the relationship of slits’ depth with EM load was the first to examine. Six pairs of radial slits with same depth, Slit 1, Slit 2, Slit 3, Slit 6, Slit 7 and Slit 8 in Fig. 3, were selected, and other radial and poloidal slits were all removed. Several cases with different depth’s value of these same slits were calculated, and the results are shown in Fig. 4. Two conclusions can be made from Fig. 4. The first is that when the depth of slits is larger than about 50 mm, the Lorentz force on the SB can reduce quickly with the increase of slits’ depth. The second is that the correlation between both radial and poloidal component of Lorentz force and slits’ depth is approximately linear when the depth is larger than 50 mm. In order to make sure slits can work well, the depth of slits should be larger than 50 mm in SB design. 5.2. Slits’ location In this part of study, only two pairs of radial slits with same toroidal position were kept to examine the effect of their toroidal locations on the Lorentz force, and the other slits were all removed. The depths of the radial slits are all 270 mm. The results are given in Table 2.
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Fig. 5. Time history of radial and poloidal components of Lorentz force on the SB with and without cooling channel during the MD: (a) radial component and (b) poloidal component.
It can be found out that radial slits near the central region have much less effect on the Lorentz force than those near two sides’ ends, which means that deep slits should be tried to cut near two sides’ ends. For the slits near the sides’ ends, the Lorentz force in the Case 5 is relatively smaller than the other two cases (Case 4 and Case 6). By this point of view, deep radial slits should be designed near the middle of the half SB and the region of SB with largest radial thickness.
5.3. Deep slits’ number According to the previous study, deep slits are very important to control the EM load on the SB. In order to study the relationship of deep slits’ number with EM load, the radial slits in the current design of SB (see Fig. 3) without poloidal slit were removed pair by pair to perform analyses and make comparisons. The depths of all of the radial slits’ were also 270 mm. The analyses results are listed in Table 3. With the increase of the radial deep slit’s number, the radial and poloidal Lorentz force decrease. However, once the number of slits reaches 12, i.e., six pairs, the Lorentz force does not reduce obviously. It is probably because slits near the central region (Slit 1, Slit 2, Slit 6 and Slit 7) have much less effect on the EM load than the other radial slits. For the reason and considering the space limitation of SB04, six pairs of deep slits are enough for SB04. For other larger SBs, the number of deep slits should be more than that.
6. Impacts of cooling channels The case of SB without cooling channel was also studied to examine the effects of cooling channels on the EM load. Two individual FE analyses were done to make a comparison. The first one is the current design of SB04 with cooling channel, and another one is the current design of SB04 without cooling channel. The time history of radial and poloidal component of Lorentz force on the SB with and without cooling channel during the MD is shown in Fig. 5. It can be seen that the difference of peak Lorentz force between these two cases is limited. The cooling channels reduce by 1.0% and 14.0% of peak Lorentz force in the radial and poloidal direction, respectively. Examples of eddy current loop cut by cooling channels and slits are shown in Fig. 6. Obviously, on the cross section of SB cut vertically, eddy current loop is slightly affected by cooling channels, and the cooling channels’ effects are only local. However, in Fig. 6b, slits can split large eddy current loop into several smaller one. These smaller eddy current loops circulate in a smaller space, its loop’s length is shortened and its magnitude is mitigated. Compared with cooling channel, slits have significant effect on the EM load.
Fig. 6. Eddy current distribution on two cross sections of SB04 cut vertically to compare the impacts of cooling channels and slits on the EM load. (a) Eddy current loop cut by cooling channels and (b) eddy current loop cut by slits.
7. Discussions All of these FE analyses in the study were focused on the radial slits, and it can be expected that the situation of poloidal slits is similar. Generally speaking, slit is very effective to control EM load on the SB. The larger depth of slits are, the more EM load will be reduced. Considering the space limitation of SB, the slit’s depth from 200 mm to 300 mm will be preferable. Deep slits should be designed near the middle of the half SB and the region of SB with largest radial thickness, which makes slit work more effectively. For the SB’s size like SB04, six pairs of deep radial slits are enough to control EM load, and for larger SBs, the number of deep slits should be more than that. The effects of cooling channels were also examined. The results indicate that cooling channels’ effects are limited. From the engineering of view, the cooling channels can be possibly ignored in some preliminary FE analyses.
Acknowledgments This work was partially supported by the National Magnetic Confinement Fusion Science Program (Contract 2014GB126000). It only reflects the view of the authors, and the views and opinions expressed herein do not necessarily reflect those of the ITER Organization
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Please cite this article in press as: W. Kang, et al., Electromagnetic analyses and optimization for slit configuration of ITER blanket shield block, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.11.014
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