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The ITER EC H&CD upper launcher: EM disruption analyses
Fusion Engineering and Design 88 (2013) 1042–1045
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
The ITER EC H&CD upper launcher: EM disruption analyses A. Vaccaro a,∗ , G. Aiello a , G. Grossetti a , A. Meier a , T.A. Scherer a , S. Schreck a , P. Späh a , D. Strauß a , G. Saibene b , M. Cavinato b a b
Karlsruhe Institute of Technology, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe, Germany, Institut für Angewandte Materialien - Angewandte Werkstoffphysik Fusion for Energy, C/Josep Pla 2, Torres Diagonal Litoral-B3, E-08019 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 13 September 2012 Received in revised form 14 January 2013 Accepted 15 January 2013 Available online 20 February 2013 Keywords: ITER Upper launcher Electromagnetic analysis Plasma disruption
a b s t r a c t In the frame of the new grant started in November 2011 between Fusion for Energy (F4E) and the ECHULCA consortium, the development process of the Electron Cyclotron Heating and Current Drive (EC H&CD) upper launcher (UL) in ITER has moved a step toward the final design phase. Based on the 2009 preliminary design review version, the new configuration of the UL now features a thicker single-wall mainframe (up to 90 mm), a recessed first wall panel (100 mm, to reduce the impact of halo currents) and a new arrangement of the internal shield blocks. The main design drivers for the structural components are still the electromagnetic (EM) loads, which need to be reassessed for the new configuration of the UL. In this paper the results of a new EM 20◦ sector model of ITER, specialized for the UL, are shown. Six different disruption scenarios are considered in this work: upward linear (36 ms) and exponential (36 ms) vertical displacement events (VDE), upward linear (36 ms) and exponential (16 ms) major disruptions (MD), category II upward slow and slow–fast VDEs. Comparing the analyses’ results allowed to define a set of structural loads to be used as a reference for the forthcoming structural calculations. © 2013 Karlsruhe Institute of Technology (KIT). Published by Elsevier B.V. All rights reserved.
1. Introduction The ITER ECH system contains 24 gyrotrons providing a maximum ECH injected power of 20 MW. Two different types of EC launcher are foreseen: one equatorial launcher (EL) for plasma heating and four upper launchers (UL) for plasma mode stabilization. In November 2011 the grant GRT-161 between F4E and the ECHUL-CA consortium (KIT Karlsruhe, CRPP Lausanne, ITER-NL, CNR Milano and IPP Garching) has been signed, moving the design of the EC H&CD UL toward the final design phase [1]. The structural system of the UL consists mainly of two components: The BSM (Blanket Shield Module) and the Launcher Mainframe, which are connected by a bolted joint, capable to be loosened by RH (Remote Handling) procedures [2]. New assessments of the EM loads acting on the UL are necessary [3,4], considering not only the latest changes in the design of the UL [5,6], but also the new plasma scenarios calculated by use of the DINA code (latest scenarios available are from 2010, the last scenario used for the UL was from 2004 [7]). Six different plasma disruption scenarios have been selected and analyzed, in order to provide a complete insight of the
∗ Corresponding author at: Karlsruhe Institute of Technology, Association KITEURATOM, P.O. Box 3640, D-76021 Karlsruhe, Germany. E-mail address: [email protected] (A. Vaccaro).
phenomena that most affect the UL: upward linear (36 ms) and exponential (36 ms) major disruptions (MD), upward linear (36 ms) and exponential (16 ms) vertical displacement events (VDE), category II upward slow and slow–fast VDEs. Two additional analyses have been run with respect to the worst case scenario (the one delivering the highest loads) to check the quality of the model: the first has a refined mesh at the region of the upper launcher, the second is used to verify the assumptions made on the material properties (see Sections 2.2 and 2.3). 2. The FEM model 2.1. Geometry The geometry is entirely generated by ANSYS Parametric Design Language (APDL) commands, in order to avoid errors due to tolerances (disconnected lines/surface, holes, etc.) that are usual when CAD geometries are directly imported in ANSYS. A cross section of the model is shown in Fig. 1. It consists of a 20◦ sector of ITER including the vacuum vessel, blanket modules, equatorial and upper ports and plugs. The model is specialized for the upper level of ITER, thus the divertor is not included. The geometry of many portions of the model is a simplified representation of the real structures. This is the case, for example, of the cooled walls of the upper launcher, and the blanket modules, which would otherwise require a very fine mesh. As described in Section 2.3,
0920-3796/$ – see front matter © 2013 Karlsruhe Institute of Technology (KIT). Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.01.058
A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
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Fig. 2. Cross-section of the mesh of the UL, showing the internal shields. Different colors indicate different material properties. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. Cross section of the 20◦ sector model used for the EM analyses. Different colors indicate different material properties. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
equivalent material properties must be defined for such portions of the model. The central solenoid (CS), poloidal field (PF) and toroidal field (TF) coils are also included. Therefore, the total magnetic field is calculated and no components need to be added analytically in a second stage. The geometry of the CS and PF coils is defined in the disruption scenario (DINA results file). The TF coils are defined as a constant-cross-section conductor. As two adjacent TF coils converge to the center creating a very small gap, their thickness has been slightly reduced (from 828.6 mm to 700 mm) in order to improve the mesh quality at the central axis of the model. Such modified configuration still delivers an error below 1%, calculated as the relative difference between the toroidal field returned by the FEM model and the one provided by the analytical law (Btot × r = 5.3 × 6.15, being r the radius in meters and Btot the toroidal field in tesla), at every point within the plasma region, i.e. 3.5 ≤ r ≤ 8.3. The blanket modules feature different layered materials for the first wall (i.e. one Be layer facing the plasma, one actively cooled Cu layer, one actively cooled SS), plus the main block (actively cooled, too). A similar structure (plasma facing SS layer, actively cooled Cu, actively cooled SS) is defined for the first wall panel of the Blanket Shield Module (BSM), located at the tip of the UL. A spherical sector with a diameter of 20 m models the vacuum space all around the model. The origin of the global coordinate system is located at the center of the machine, the z-axis is oriented in vertical direction and the x–z plane is coincident to the vertical mid-plane of the FEM model.
(namely the equatorial port and the divertor). The cross section of the UL is shown in Fig. 2. This first setup of the EM model enables the calculation and comparison of the loads induced in the six disruption scenarios currently selected. The scenario that delivers the highest loads (up-ward linear VDE, as discussed in Section 3) is run again on a different model with a refined mesh and shorter time steps. The refined portions of the model are the UL and the PF coils (to get a better description of the poloidal magnetic field). The number of nodes/elements in the refined model is 429k/239k (52k/57k for the upper launcher, about the double as in the coarser model). The element SOLID97 is used to model the conducting structures, the vacuum regions, the plasma and the CS/PF/TF coils. ANSYS provides more advanced elements that deliver very good calculation performance (SOLID117 and the more recent SOLID236). Unfortunately, the formulation of the magnetic potential requires the use of gauging for these elements, thus submodeling is in general not possible. The only limitation of SOLID97 (besides the longer calculation time) is its inability to deal with interfaces of materials with different magnetic permeability. This is not a problem for the current model, as it does not contain any ferromagnetic material. The element INFIN111, which models an open boundary of a 3D unbounded field problem, is used to define the boundary of the domain. 2.3. Material properties In order to properly model the simplified portions of the model, equivalent material properties must be defined. One criterion is to introduce geometrical factors that take into account for equivalent cross-sections of the conducting structures. For example, the equivalent resistivity of a generic cooled wall like the one shown in Fig. 3 (left) would be given by the resistivity of the pure material (Cu, in this example) scaled by the factor 16a2 /(16a2 − a2 ), that is the ratio between the area of the full wall (without cooling channels) divided by the area of the real structure. Unfortunately,
2.2. Mesh and element types The mesh of the main model consists of 280k/176k nodes/elements, of which 21.6k/25.6k belong to the conductive structure of the launcher. Such relatively low number of nodes/elements has been achieved by refining the mesh only where necessary (front portion of the launcher and blanket modules that are closer to the launcher) and by removing/simplifying features that are not considered to crucially affect the results
Fig. 3. Sub-division of a generic cooled wall made of Cu (left) in three layers (right), two of which consist of pure material.
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A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
Table 1 Skin depth of different materials compared to the thickness of some cooled structures of the UL. Part
Thickness (mm)
Material
Skin depth (mm)
BSM-DW BSM-FWP Cu BSM-FWP SS
50 22 68
SS Cu SS
86 17 86
this methodology is difficult to apply, as it is often valid in one direction only (the direction of the cooling channels, in this case) and many structures can have non-constant thicknesses (for example the cooling channels could be not parallel, as it happens for the BSM). Finally, skin depth is to be considered to check which portion of the volumes is actually affected by the induction. In this work, the equivalent resistivity is assumed as weighted average according to the fractions in volume of the different materials in the mixture. As a consequence, the structure in Fig. 3 is modeled by single homogeneous layer with constant resistivity. A calculation of the skin depth associated to the first harmonic of a sawtooth function with a period of 36 ms (roughly approximating a linear current quench) suggests that the majority of the thickness of the cooled walls is interested by the EM induction. Table 1 shows a comparison between the skin depth and the thickness of the double wall (DW) shell of the Blanket Shield Module (BSM) and the Cu and stainless steel layers of the first wall panel (FWP). This approach has been validated by introducing a further subdivision of the (actively cooled) copper layer of the first wall in three layers, as shown in Fig. 3 (right). In this model, the volume for which pure material can be assumed is increased, therefore the impact of the approximations made decreases. The same modification is made on the SS layer, too.
Table 2a Forces induced on the UL by each different disruption. Values are given in MN.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
3. Results The peak loads acting on the entire UL have been assessed for the six scenarios and are shown in Tables 2a and 2b. The moments are referred to the geometrical center of the UL, the x, y, and z directions are aligned to the global coordinate system (as defined at the end of Section 2.1). The loads have comparable order of magnitude for all cases but the VDE-UP slow. As expected, the highest loads are induced during the fast VDEs: when the disruption starts, the plasma has moved in upward direction, therefore it is closer to the UL. The results also show that higher loads are induced during linear VDEs rather than during the exponential ones. This result is not
Fy
Fz
0.085 0.125 0.192 0.262 0.018 0.164
−0.070 −0.088 −0.120 −0.132 0.013 −0.059
−0.055 0.026 −0.080 0.079 −0.060 −0.086
Table 2b Moments induced on the UL by each different disruption. Values are given in MN m.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Mx
My
Mz
0.344 0.488 0.734 1.023 −0.159 0.920
0.570 0.619 0.913 1.103 0.262 1.097
0.718 0.923 1.352 1.568 0.138 1.074
Table 3a Forces induced on the BSM by each different disruption. Values are given in MN.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Fx
Fy
Fz
−0.330 −0.518 −0.754 −0.958 0.098 −0.689
−0.042 −0.055 −0.085 −0.095 0.008 −0.056
0.088 0.141 0.166 0.237 0.012 0.190
Table 3b Moments induced on the BSM by each different disruption. Values are given in MN m.
2.4. Boundary conditions and loads Cyclic periodicity is applied to the cut planes at the two sides of the 20◦ model, while the external surface of the spherical volume is flagged as infinite, as prescribed by the ANSYS documentation. The CS and PF coils currents are defined in the DINA results file at each time step and are applied as homogeneous current density to the coils. The TF coil’s total current is constant during the disruption and equal to 68 kA times 134 turns. The plasma is converted to a tabular definition (called table arrays in ANSYS APDL) of current density, function of the x and z coordinates, at each time step. Such definition is then directly interpolated by ANSYS on the mesh. A typical DINA results file can contain six hundred or even more than one thousand time steps. Simulating all this steps would require a non-acceptable calculation time and extremely large results files. As a compromise, every 25th time step is used for the disruption analysis. This frequency was reduced to every 15th time step in the refined model.
Fx
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Mx
My
Mz
−0.147 0.179 0.245 0.409 −0.063 0.320
0.105 0.142 0.244 0.272 −0.020 0.155
0.246 0.334 0.504 0.574 −0.046 0.331
obvious, since the loads depend on the electric impedance of the system, which is not known a priori. In general, the loads depend on both the speed and the total duration of the quench: the current quench is faster in the exponential cases (higher dIp /dt, being Ip the plasma current), but the inductive inertia of the conductive structure prevents the loads from yielding significantly. The analysis of the refined model described in Section 2.2 has been run for the upward VDE linear 36 ms scenario (that is, the scenario delivering the highest loads). The model, which has both finer mesh and finer time resolution, has confirmed the results of the coarse model, the peak loads differing by less than 3% with respect to the coarse model. The EM loads have also been calculated for several subcomponents of the UL. The loads acting on the BSM, for example, are very important for the design of the bolted connection [7]. Such loads are reported in Tables 3a and 3b. Again, the x, y, and z directions refer to the global coordinate system. A comparison with the loads from the previous analyses (reported in [4]) shows that the current radial force (x-direction) acting on the BSM during a linear upward VDE is circa 10 times higher than in the past. Since most of the induction is localized at the FWP and is due to the lower resistivity of the copper layer, a justification for the higher loads must be researched in the different definition of the material properties. In fact, in the model from 2004 the entire FWP is modeled by a single layer
A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
of elements, taking into account for the Be, Cu and SS layers at the same time. In the present model, instead, the three layers (the Be being substituted by SS, according to the present design) are modeled individually, each with the appropriate material properties. Discriminating the Cu layer has introduced an effect (higher loads) that was not visible in the past model. Finally, a second refined model with a further subdivision of the actively cooled CU and SS layers of the BSM, as discussed in Section 2.3, has again confirmed the results of both the coarse and the first refined models by delivering the same results (relative difference, again, below 2%), thus suggesting that the further refinement of the actively cooled walls was not necessary.
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the overall stability of the structure, it might make the design of the bolted connection of the BSM more challenging [8]. Acknowledgments This work was supported by Fusion for Energy under the Grant Contract No. F4E-2010-GRT-161. The views and opinions expressed herein reflect only the author’s views. Fusion for Energy is not liable for any use that may be made of the information contained therein. The Grant F4E-2010-GRT-161 is supported by the IO Task Agreement C52TD39FE. References
4. Conclusions New plasma disruption analyses for assessment of the loads acting on the upper launcher in ITER were required, as both the plasma scenarios and the geometric configuration of the launcher have changed during the past years. Six different disruption scenarios have been analyzed and the loads induced during each current quench have been compared. The study has confirmed the upward VDE as the worst-case scenario and the magnitude of the loads acting on the whole UL in comparison to the past calculations. Nevertheless, down to the components level, a higher radial force have been found at the BSM as a result of a better description of the layered structure of the FWP. Although such loads act in radial direction, thus not compromising
[1] Y. Kitazawa, K. Sugiyama, Journal of Plasma Fusion Research 16 (2001) 40. [2] P. Späh, et al., The ITER EC H&CD upper launcher: structural system, in: Proc. 27th SOFT, Liege, 2012. [3] D. Strauss, et al., FEM analyses and prototype tests of the UPP structure for the ECRH in ITER, Fusion Engineering and Design 84 (2009) 1799–1802. [4] A. Vaccaro, D. Strauss, et al., Mechanical analysis of the EC upper launcher with respect to electromagnetic loads, Fusion Engineering and Design 84 (2009) 1896–1900. [5] A. Vaccaro, et al., The ITER EC H&CD upper launcher: transient mechanical analysis, Fusion Engineering and Design 86 (2011) 851–854. [6] C.S. Pitcher, Upper Port Plug Exposure to Disruptions in ITER, ITER D 23HSK3, ITER Org. Int. Document. [7] M. Roccella, Summary of EM Analyses on the Plug Limiter of the Upper Port (draft of results), ITER D 22LZ98, ITER Org. Int. Document. [8] R. Gessner, et al., The ITER EC H&CD upper launcher: design, analysis and testing of a bolted joint for the Blanket Shield Module, in: Proc. 27th SOFT, Liege, 2012.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
The ITER EC H&CD upper launcher: EM disruption analyses A. Vaccaro a,∗ , G. Aiello a , G. Grossetti a , A. Meier a , T.A. Scherer a , S. Schreck a , P. Späh a , D. Strauß a , G. Saibene b , M. Cavinato b a b
Karlsruhe Institute of Technology, Association KIT-EURATOM, P.O. Box 3640, D-76021 Karlsruhe, Germany, Institut für Angewandte Materialien - Angewandte Werkstoffphysik Fusion for Energy, C/Josep Pla 2, Torres Diagonal Litoral-B3, E-08019 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 13 September 2012 Received in revised form 14 January 2013 Accepted 15 January 2013 Available online 20 February 2013 Keywords: ITER Upper launcher Electromagnetic analysis Plasma disruption
a b s t r a c t In the frame of the new grant started in November 2011 between Fusion for Energy (F4E) and the ECHULCA consortium, the development process of the Electron Cyclotron Heating and Current Drive (EC H&CD) upper launcher (UL) in ITER has moved a step toward the final design phase. Based on the 2009 preliminary design review version, the new configuration of the UL now features a thicker single-wall mainframe (up to 90 mm), a recessed first wall panel (100 mm, to reduce the impact of halo currents) and a new arrangement of the internal shield blocks. The main design drivers for the structural components are still the electromagnetic (EM) loads, which need to be reassessed for the new configuration of the UL. In this paper the results of a new EM 20◦ sector model of ITER, specialized for the UL, are shown. Six different disruption scenarios are considered in this work: upward linear (36 ms) and exponential (36 ms) vertical displacement events (VDE), upward linear (36 ms) and exponential (16 ms) major disruptions (MD), category II upward slow and slow–fast VDEs. Comparing the analyses’ results allowed to define a set of structural loads to be used as a reference for the forthcoming structural calculations. © 2013 Karlsruhe Institute of Technology (KIT). Published by Elsevier B.V. All rights reserved.
1. Introduction The ITER ECH system contains 24 gyrotrons providing a maximum ECH injected power of 20 MW. Two different types of EC launcher are foreseen: one equatorial launcher (EL) for plasma heating and four upper launchers (UL) for plasma mode stabilization. In November 2011 the grant GRT-161 between F4E and the ECHUL-CA consortium (KIT Karlsruhe, CRPP Lausanne, ITER-NL, CNR Milano and IPP Garching) has been signed, moving the design of the EC H&CD UL toward the final design phase [1]. The structural system of the UL consists mainly of two components: The BSM (Blanket Shield Module) and the Launcher Mainframe, which are connected by a bolted joint, capable to be loosened by RH (Remote Handling) procedures [2]. New assessments of the EM loads acting on the UL are necessary [3,4], considering not only the latest changes in the design of the UL [5,6], but also the new plasma scenarios calculated by use of the DINA code (latest scenarios available are from 2010, the last scenario used for the UL was from 2004 [7]). Six different plasma disruption scenarios have been selected and analyzed, in order to provide a complete insight of the
∗ Corresponding author at: Karlsruhe Institute of Technology, Association KITEURATOM, P.O. Box 3640, D-76021 Karlsruhe, Germany. E-mail address: [email protected] (A. Vaccaro).
phenomena that most affect the UL: upward linear (36 ms) and exponential (36 ms) major disruptions (MD), upward linear (36 ms) and exponential (16 ms) vertical displacement events (VDE), category II upward slow and slow–fast VDEs. Two additional analyses have been run with respect to the worst case scenario (the one delivering the highest loads) to check the quality of the model: the first has a refined mesh at the region of the upper launcher, the second is used to verify the assumptions made on the material properties (see Sections 2.2 and 2.3). 2. The FEM model 2.1. Geometry The geometry is entirely generated by ANSYS Parametric Design Language (APDL) commands, in order to avoid errors due to tolerances (disconnected lines/surface, holes, etc.) that are usual when CAD geometries are directly imported in ANSYS. A cross section of the model is shown in Fig. 1. It consists of a 20◦ sector of ITER including the vacuum vessel, blanket modules, equatorial and upper ports and plugs. The model is specialized for the upper level of ITER, thus the divertor is not included. The geometry of many portions of the model is a simplified representation of the real structures. This is the case, for example, of the cooled walls of the upper launcher, and the blanket modules, which would otherwise require a very fine mesh. As described in Section 2.3,
0920-3796/$ – see front matter © 2013 Karlsruhe Institute of Technology (KIT). Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.01.058
A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
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Fig. 2. Cross-section of the mesh of the UL, showing the internal shields. Different colors indicate different material properties. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. Cross section of the 20◦ sector model used for the EM analyses. Different colors indicate different material properties. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
equivalent material properties must be defined for such portions of the model. The central solenoid (CS), poloidal field (PF) and toroidal field (TF) coils are also included. Therefore, the total magnetic field is calculated and no components need to be added analytically in a second stage. The geometry of the CS and PF coils is defined in the disruption scenario (DINA results file). The TF coils are defined as a constant-cross-section conductor. As two adjacent TF coils converge to the center creating a very small gap, their thickness has been slightly reduced (from 828.6 mm to 700 mm) in order to improve the mesh quality at the central axis of the model. Such modified configuration still delivers an error below 1%, calculated as the relative difference between the toroidal field returned by the FEM model and the one provided by the analytical law (Btot × r = 5.3 × 6.15, being r the radius in meters and Btot the toroidal field in tesla), at every point within the plasma region, i.e. 3.5 ≤ r ≤ 8.3. The blanket modules feature different layered materials for the first wall (i.e. one Be layer facing the plasma, one actively cooled Cu layer, one actively cooled SS), plus the main block (actively cooled, too). A similar structure (plasma facing SS layer, actively cooled Cu, actively cooled SS) is defined for the first wall panel of the Blanket Shield Module (BSM), located at the tip of the UL. A spherical sector with a diameter of 20 m models the vacuum space all around the model. The origin of the global coordinate system is located at the center of the machine, the z-axis is oriented in vertical direction and the x–z plane is coincident to the vertical mid-plane of the FEM model.
(namely the equatorial port and the divertor). The cross section of the UL is shown in Fig. 2. This first setup of the EM model enables the calculation and comparison of the loads induced in the six disruption scenarios currently selected. The scenario that delivers the highest loads (up-ward linear VDE, as discussed in Section 3) is run again on a different model with a refined mesh and shorter time steps. The refined portions of the model are the UL and the PF coils (to get a better description of the poloidal magnetic field). The number of nodes/elements in the refined model is 429k/239k (52k/57k for the upper launcher, about the double as in the coarser model). The element SOLID97 is used to model the conducting structures, the vacuum regions, the plasma and the CS/PF/TF coils. ANSYS provides more advanced elements that deliver very good calculation performance (SOLID117 and the more recent SOLID236). Unfortunately, the formulation of the magnetic potential requires the use of gauging for these elements, thus submodeling is in general not possible. The only limitation of SOLID97 (besides the longer calculation time) is its inability to deal with interfaces of materials with different magnetic permeability. This is not a problem for the current model, as it does not contain any ferromagnetic material. The element INFIN111, which models an open boundary of a 3D unbounded field problem, is used to define the boundary of the domain. 2.3. Material properties In order to properly model the simplified portions of the model, equivalent material properties must be defined. One criterion is to introduce geometrical factors that take into account for equivalent cross-sections of the conducting structures. For example, the equivalent resistivity of a generic cooled wall like the one shown in Fig. 3 (left) would be given by the resistivity of the pure material (Cu, in this example) scaled by the factor 16a2 /(16a2 − a2 ), that is the ratio between the area of the full wall (without cooling channels) divided by the area of the real structure. Unfortunately,
2.2. Mesh and element types The mesh of the main model consists of 280k/176k nodes/elements, of which 21.6k/25.6k belong to the conductive structure of the launcher. Such relatively low number of nodes/elements has been achieved by refining the mesh only where necessary (front portion of the launcher and blanket modules that are closer to the launcher) and by removing/simplifying features that are not considered to crucially affect the results
Fig. 3. Sub-division of a generic cooled wall made of Cu (left) in three layers (right), two of which consist of pure material.
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A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
Table 1 Skin depth of different materials compared to the thickness of some cooled structures of the UL. Part
Thickness (mm)
Material
Skin depth (mm)
BSM-DW BSM-FWP Cu BSM-FWP SS
50 22 68
SS Cu SS
86 17 86
this methodology is difficult to apply, as it is often valid in one direction only (the direction of the cooling channels, in this case) and many structures can have non-constant thicknesses (for example the cooling channels could be not parallel, as it happens for the BSM). Finally, skin depth is to be considered to check which portion of the volumes is actually affected by the induction. In this work, the equivalent resistivity is assumed as weighted average according to the fractions in volume of the different materials in the mixture. As a consequence, the structure in Fig. 3 is modeled by single homogeneous layer with constant resistivity. A calculation of the skin depth associated to the first harmonic of a sawtooth function with a period of 36 ms (roughly approximating a linear current quench) suggests that the majority of the thickness of the cooled walls is interested by the EM induction. Table 1 shows a comparison between the skin depth and the thickness of the double wall (DW) shell of the Blanket Shield Module (BSM) and the Cu and stainless steel layers of the first wall panel (FWP). This approach has been validated by introducing a further subdivision of the (actively cooled) copper layer of the first wall in three layers, as shown in Fig. 3 (right). In this model, the volume for which pure material can be assumed is increased, therefore the impact of the approximations made decreases. The same modification is made on the SS layer, too.
Table 2a Forces induced on the UL by each different disruption. Values are given in MN.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
3. Results The peak loads acting on the entire UL have been assessed for the six scenarios and are shown in Tables 2a and 2b. The moments are referred to the geometrical center of the UL, the x, y, and z directions are aligned to the global coordinate system (as defined at the end of Section 2.1). The loads have comparable order of magnitude for all cases but the VDE-UP slow. As expected, the highest loads are induced during the fast VDEs: when the disruption starts, the plasma has moved in upward direction, therefore it is closer to the UL. The results also show that higher loads are induced during linear VDEs rather than during the exponential ones. This result is not
Fy
Fz
0.085 0.125 0.192 0.262 0.018 0.164
−0.070 −0.088 −0.120 −0.132 0.013 −0.059
−0.055 0.026 −0.080 0.079 −0.060 −0.086
Table 2b Moments induced on the UL by each different disruption. Values are given in MN m.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Mx
My
Mz
0.344 0.488 0.734 1.023 −0.159 0.920
0.570 0.619 0.913 1.103 0.262 1.097
0.718 0.923 1.352 1.568 0.138 1.074
Table 3a Forces induced on the BSM by each different disruption. Values are given in MN.
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Fx
Fy
Fz
−0.330 −0.518 −0.754 −0.958 0.098 −0.689
−0.042 −0.055 −0.085 −0.095 0.008 −0.056
0.088 0.141 0.166 0.237 0.012 0.190
Table 3b Moments induced on the BSM by each different disruption. Values are given in MN m.
2.4. Boundary conditions and loads Cyclic periodicity is applied to the cut planes at the two sides of the 20◦ model, while the external surface of the spherical volume is flagged as infinite, as prescribed by the ANSYS documentation. The CS and PF coils currents are defined in the DINA results file at each time step and are applied as homogeneous current density to the coils. The TF coil’s total current is constant during the disruption and equal to 68 kA times 134 turns. The plasma is converted to a tabular definition (called table arrays in ANSYS APDL) of current density, function of the x and z coordinates, at each time step. Such definition is then directly interpolated by ANSYS on the mesh. A typical DINA results file can contain six hundred or even more than one thousand time steps. Simulating all this steps would require a non-acceptable calculation time and extremely large results files. As a compromise, every 25th time step is used for the disruption analysis. This frequency was reduced to every 15th time step in the refined model.
Fx
MD-UP exp 16 ms MD-UP lin 36 ms VDE-UP exp 36 ms VDE-UP lin 36 ms VDE-UP slow VDE-UP slow–fast
Mx
My
Mz
−0.147 0.179 0.245 0.409 −0.063 0.320
0.105 0.142 0.244 0.272 −0.020 0.155
0.246 0.334 0.504 0.574 −0.046 0.331
obvious, since the loads depend on the electric impedance of the system, which is not known a priori. In general, the loads depend on both the speed and the total duration of the quench: the current quench is faster in the exponential cases (higher dIp /dt, being Ip the plasma current), but the inductive inertia of the conductive structure prevents the loads from yielding significantly. The analysis of the refined model described in Section 2.2 has been run for the upward VDE linear 36 ms scenario (that is, the scenario delivering the highest loads). The model, which has both finer mesh and finer time resolution, has confirmed the results of the coarse model, the peak loads differing by less than 3% with respect to the coarse model. The EM loads have also been calculated for several subcomponents of the UL. The loads acting on the BSM, for example, are very important for the design of the bolted connection [7]. Such loads are reported in Tables 3a and 3b. Again, the x, y, and z directions refer to the global coordinate system. A comparison with the loads from the previous analyses (reported in [4]) shows that the current radial force (x-direction) acting on the BSM during a linear upward VDE is circa 10 times higher than in the past. Since most of the induction is localized at the FWP and is due to the lower resistivity of the copper layer, a justification for the higher loads must be researched in the different definition of the material properties. In fact, in the model from 2004 the entire FWP is modeled by a single layer
A. Vaccaro et al. / Fusion Engineering and Design 88 (2013) 1042–1045
of elements, taking into account for the Be, Cu and SS layers at the same time. In the present model, instead, the three layers (the Be being substituted by SS, according to the present design) are modeled individually, each with the appropriate material properties. Discriminating the Cu layer has introduced an effect (higher loads) that was not visible in the past model. Finally, a second refined model with a further subdivision of the actively cooled CU and SS layers of the BSM, as discussed in Section 2.3, has again confirmed the results of both the coarse and the first refined models by delivering the same results (relative difference, again, below 2%), thus suggesting that the further refinement of the actively cooled walls was not necessary.
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the overall stability of the structure, it might make the design of the bolted connection of the BSM more challenging [8]. Acknowledgments This work was supported by Fusion for Energy under the Grant Contract No. F4E-2010-GRT-161. The views and opinions expressed herein reflect only the author’s views. Fusion for Energy is not liable for any use that may be made of the information contained therein. The Grant F4E-2010-GRT-161 is supported by the IO Task Agreement C52TD39FE. References
4. Conclusions New plasma disruption analyses for assessment of the loads acting on the upper launcher in ITER were required, as both the plasma scenarios and the geometric configuration of the launcher have changed during the past years. Six different disruption scenarios have been analyzed and the loads induced during each current quench have been compared. The study has confirmed the upward VDE as the worst-case scenario and the magnitude of the loads acting on the whole UL in comparison to the past calculations. Nevertheless, down to the components level, a higher radial force have been found at the BSM as a result of a better description of the layered structure of the FWP. Although such loads act in radial direction, thus not compromising
[1] Y. Kitazawa, K. Sugiyama, Journal of Plasma Fusion Research 16 (2001) 40. [2] P. Späh, et al., The ITER EC H&CD upper launcher: structural system, in: Proc. 27th SOFT, Liege, 2012. [3] D. Strauss, et al., FEM analyses and prototype tests of the UPP structure for the ECRH in ITER, Fusion Engineering and Design 84 (2009) 1799–1802. [4] A. Vaccaro, D. Strauss, et al., Mechanical analysis of the EC upper launcher with respect to electromagnetic loads, Fusion Engineering and Design 84 (2009) 1896–1900. [5] A. Vaccaro, et al., The ITER EC H&CD upper launcher: transient mechanical analysis, Fusion Engineering and Design 86 (2011) 851–854. [6] C.S. Pitcher, Upper Port Plug Exposure to Disruptions in ITER, ITER D 23HSK3, ITER Org. Int. Document. [7] M. Roccella, Summary of EM Analyses on the Plug Limiter of the Upper Port (draft of results), ITER D 22LZ98, ITER Org. Int. Document. [8] R. Gessner, et al., The ITER EC H&CD upper launcher: design, analysis and testing of a bolted joint for the Blanket Shield Module, in: Proc. 27th SOFT, Liege, 2012.