With ANSYS towards Fusion Power Generation Cornelis Jong

Design Integration Division, ITER Garching Joint Work Site

Abstract The ITER project is an unprecedented international collaboration in which scientists and engineers from Europe, Japan, Russia, USA, China, South Korea and in the near future India, are working together on the next step for the development of fusion. ITER’s mission is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes and it will be the first fusion device to produce thermal energy at the level of an electricity-producing power plant. This fusion device will be built in Cadarache, France.

The International Thermonuclear Experimental Reactor (ITER) is an experimental fusion reactor based on the tokamak concept in which superconducting coils, operating at 4K, are positioned around a toroidal vessel providing a magnetic configuration in which to create and maintain the conditions for controlled fusion reactions. The machine consists of complex and high-quality technological components such as the in-vessel components, like the divertor and blanket, and out-vessel components like the magnet system.

The finite element program ANSYS is used by all participating parties in order to support the engineering design activities. The type of finite element analysis is diverse and ranges over; dynamic analyses, non-linear thermal analysis, electro-magnetic analyses, and non-linear structural analyses.

Extensive non-linear structural analyses have been performed to investigate several design options of the magnet system consisting of the toroidal field (TF), poloidal field (PF) and central solenoid (CS) magnet systems. For the analyses of the ITER Magnet systems, large complex 3-dimensional non-linear finite element models have been developed, as well as 2-dimensional local finite element models. Evaluation of the results has been mainly focused on acceptable static and cyclic stresses (for fatigue) in the magnet system during normal operating conditions and fault conditions [1]. This paper gives an overview of some of the studies performed and results obtained with several ANSYS FE-models [2], which support the design of the ITER magnet system as illustrated in Figure 1 – Present ITER Design.

Figure 1. Present ITER Design

Introduction

The ITER Magnet System The magnet system of ITER, required to provide the magnetic configuration in which the controlled fusion reactions takes place, consists of 18 toroidal field (TF) coils, a freestanding central solenoid (CS), six poloidal field (PF) coils, and a set of corrections coils (CCs). Figure 2 shows the ITER magnet system. The TF coils are designed to provide the magnetic field necessary to maintain a 15 MA plasma. The TF coils have a D-shape geometry, are 9 m wide and 13.5 m high, use an Nb3Sn-type superconductor, are cooled with supercritical helium in the range of 4.4 - 4.7K and operate at a maximum field of 11.8 T. The operating current in the TF-Coil conductor is 68 kA providing a total current in each coil of 9.13 MA, which results in a total magnetic energy in the toroidal field of 40 GJ. The ITER Central Solenoid (CS) contains 6 identical but electrically independent modules. The operating range for each module allows, in principle, currents in the range ±25MA and a maximum magnetic field of 13T.

Figure 2. ITER Magnet System

The Toroidal Field Coil System The TF coil cases, which enclose the TF winding packs, are the main structural components of the magnet system. These cases have to withstand a combination of static in-plane loads due to the self-field of the TF coils, and cyclic out-of-plane loads due to the interaction of the TF coil current with the poloidal magnetic field.

Toroidal Field In-plane Magnetic Forces After energisation, each TF coil experiences a bursting force as well as a resultant centring force towards the centre of the machine. The resultant centring forces are reacted by the cylindrical vault formed by the inboard straight legs of the TF coils (wedged concept). The bursting force on each coil is reacted by a combination of the coil case and the winding pack. The magnetic forces occur on the winding pack and there is some localised slip between the winding pack and the surrounding case. The winding pack tends to

be pushed outwards against the outer case, slipping at the sides and leaving a small gap around the inner (plasma side) surface.

The coils are pressed together in firm contact along the inboard leg region, but once the coil begins to curve outwards, the resultant centring forces reduce to zero rapidly and the coils tend to separate. On the outboard equator of each coil, the bursting forces tend to produce a local radial outward movement of the coil, despite the inward movement in the central vault. Both of these movements are detrimental to the out-of-plane support design as they make linking the coils more difficult. Using pre-compression rings located above and below the central vault reduces the radial outward movement. These rings provide a constant radial force of 70 MN/coil (35 MN at the top and 35 MN at the bottom) under cryogenic conditions, i.e. after cool-down of the machine. The pre-compression rings pull the TF coils into contact in the inner curved region, particularly where the poloidal shear keys are located and reduce the gap between the poloidal shear keys and their keyways during operation. These rings will also reduce the tension in the toroidal direction in the four OIS 'bands', simplifying the design of the joints needed for assembly and for insulation.

Toroidal Field Out-of-Plane Magnetic Forces The CS, PF coils and the plasma create time varying out-of-plane (i.e. toroidal) forces on each of the TF coils. These forces vary around the perimeter of the coil. The resultant force on each TF coil is zero but there is a resultant moment about the machine radial axis (the so-called overturning moment). The overturning moments on the TF coils are supported by links between the coils, as the overall overturning moment on all 18 coils is zero. These links are formed from three elements:

Friction between the coil legs in the central vault

The Inner Intercoil Structures (IIS)

The Outer Intercoil Structures (OIS).

The IIS consists of two sets of four poloidal shear keys located in the upper and lower inboard curved regions. The OIS in the outboard region consists of 4 segments. The upper- and lower-OIS segments have a box-type geometry and pre-loaded superbolts are used for the connection between segments. The two intermediate OIS segments are so-called friction joints. To obtain the required toroidal stiffness, several plates with a thickness of 20 mm (called fingers) are slid into each other (like a praying hand) and are compressed together with bolts/pins. In this way a relatively flexible structure results for perpendicular loads and a stiff structure is provided for parallel shear loads.

Due to the relatively low stiffness of the coil case in bending and torsion, the inboard out-of-plane supports (friction in the central leg and the four poloidal keys) are largely decoupled from the outboard supports. The poloidal keys not only act to transmit shear between coils but also block local torsion of the coil case in a region where the mutual support from other coils in the central vault is rather weak. The distribution of the out-of-plane forces is such that the central vault region, up to the poloidal keys, is subject to torsion about a vertical axis. The outboard legs of the coils, together with the intermediate OIS rings, form a second outboard torsion cylinder, which is twisted the opposite way to the central vault. Between the inboard and outboard torsion cylinders, the relatively flexible TF coils are bent into an 'S' shape to adapt to the shape imposed by the torsion cylinders. The most critical regions of the TF-coil case are in the sidewalls at the bottom of the straight leg, in the lower curved regions just before the poloidal keys, where a combination of bending and torsion creates high cyclic shear stress, and in the outboard leg in the intermediate OIS segments and at the point where the lower OIS structure joins the case. The poloidal keys of the IIS, and the associated keyways, also have high stresses.

CS Magnet System The magnetic field and current combinations needed to drive the ITER plasma scenarios yield a wide range of radial (or hoop) loads and a wide range of vertical loads on the CS modules [3,4,5]. The hoop loads and compressive vertical loads are supported by the conductor jacket but vertical tensile loads must be reacted by a pre-compression structure. Each module consists of a steel jacketed conductor bonded by glass fibre-

kapton insulation with epoxy resin filler. The insulation can carry shear and compression but has limited tensile strength normal to the glass fabric. Although secondary tensile stresses between conductors are unavoidable (and released by local debonding) the ITER design criteria require near zero primary tensile stress in the insulation because of the risk of damage to the kapton electrical insulation. Pre-compression at room temperature and differential contraction during cool-down are used to eliminate primary vertical tensile stresses from the modules. Pre-compression is typically limited by the room-temperature, allowable stress in the pre-compression structure tie-plates.

The CS pre-compression system contains upper and lower flanges, buffer plates, a set of 9 inner and 9 outer tie-plates together with wedges and connecting bolts. Pre-compression is obtained by heating the tie-plates to T∆ degrees above room temperature, drawing in the pre-compression wedges and then cooling the assembly to its working temperature ( T∆ is thus a convenient way to identify the extent of pre-compression). The conductor jacket is made of modified steel (type JK2LB) with lower thermal contraction than the tie plates, which helps to reduce the required preload T∆ . The pre-compressed CS is hung from the top of the TF coils by support plates that resist net vertical loads but are flexible in the radial direction. A locating mechanism at the bottom of the CS supports the assembly against dynamic horizontal loads.

Plasma Scenario and Lorentz Forces Time points of interest during the plasma scenario include: initial magnetization (IM); X-point formation (XPF); Start of Flattop (SOF); Start of Burn (SOB); End of Burn (EOB) and End of plasma Cooling (EOC). A plasma disruption occurring at the end of burn (EOB+PD) is also considered.

Resultant Lorentz forces for each CS module are listed in Table I for several time points during the plasma scenario. The Lorentz forces vary widely throughout the plasma scenario, especially for the top and bottom modules (CS3U and CS3L) in the CS stack.

Table 1 – Radial and Vertical Loads [MN] on CS Modules at several time points at plasma scenario IM XPF SOF SOB EOB EOC EOB+PD

CS Fx Fy Fx Fy Fx Fy Fx Fy Fx Fy Fx Fy Fx Fy 3U 1268 -348 294 -16 5 -11 7 -14 27 -28 -43 74 14 -13 2U 1393 -34 123 48 172 -147 190 -145 733 -351 965 -507 746 -321 1U 1414 -4 -9 -3 778 -218 681 -165 1217 -122 1201 -43 1259 -110 1L 1413 5 -9 4 777 238 679 185 1208 162 1171 126 1227 153 2L 1386 39 152 -77 127 201 143 185 594 384 679 407 608 356 3L 1238 364 546 13 69 75 33 -47 -2 -11 -6 -22 -6 -23

Analysis

FE-Models For the analysis of the mechanical behaviour of the CS and TF-coil magnet system during normal operating conditions, 2D and 3-Dimensional non-linear local and global finite element models have been developed, representing particular regions or symmetry sections of the ITER magnet system. Due to the complex geometry and the special features required in the FE-model the ‘connection kit’ between the CAD- and FE-program is not used and the FE-model has been developed ‘from scratch’ by using bottom up solid modelling within the ANSYS pre-processing module PREP7 [1].

TF-Magnet System Due to the wedged design, the CS is a freestanding component and is therefore not required for the mechanical analysis of the TF coil. Also the PF coils are not modelled. Each of the PF coils is self-supporting regarding the radial magnetic loads as well as the hoop tension loads. The vertical loads on each PF coil, plus bending moments (due to the coil loads caused by the residual toroidal field ripple) are

transmitted through the PF supports to the TF-coil cases. These loads are relatively small and their influence on the mechanical behaviour of the TF-magnet system is therefore also small.

Almost all components of the single 3D Global FE-model of the TF-coil have been modelled with 8-node brick elements (SOLID185) with 3 degrees of freedom. Mapped meshing is applied as much as possible. Due to the complex geometry of the two middle OIS segments, the use of 8-node brick elements and mapped meshing for these geometries was impossible. In these sections 10 node tetrahedron elements and 20-node brick elements with three degrees of freedom have been used instead, i.e. SOLID187 and SOLID186 elements with mid-side nodes removed at some interfaces. The connectivity of the finite element mesh of the four OIS segments and sections in the TF coil gravity support do not correspond with the finite element mesh of the adjacent components. These components are ‘merged’ or ‘tied’ together by using constraint equations (CEINTF command) defined by using the element shape functions.

The non-linear interfaces between the TF-coil inner legs and the poloidal shear keys in the lower and upper curved region are modelled with 2-node gap elements (CONTA52 elements) with friction capabilities. It is assumed that possible contact between the coils can occur at the inboard straight leg and the upper and the lower curved regions of the casing only (wing section) and that surface matching in these regions is considered to be perfect at the interface (no tolerance effects included – means zero initial gap size). Contact between the flanges at the top and bottom housing the pre-compression rings cannot occur. The toroidal pressure on the poloidal keys at assembly and during operation will benefit from this. The behaviour of the poloidal shear keys is modelled with 3 gap elements, i.e. one gap element in the toroidal direction and two gap elements in the poloidal direction with a certain angle with respect to the casing. This is done to take into account the separating force caused by these shear keys. The angle chosen is based on the solid circular shear key and is equal to 32 degrees.

In such a large 3D global model it is impossible to model the TF coil winding pack in detail. Therefore a homogeneous winding pack, consisting of brick elements, has been used. These winding pack elements have been given equivalent orthotropic smeared mechanical properties. The winding pack – casing interface is modelled as an asymmetric flexible-to-flexible contact interface with CONTA173 and TARGA170 elements.

The TF coil support is located at the outboard leg region and consists of a pedestal with a stack of 21 plates, which are flexible in the radial direction. Their shape is trapezoidal with a width of 1035 mm at the top and a width of 1500 mm at the bottom. The length of the plates is 2250 mm. Also the support section is modelled with 8 node bricks.

Figure 3 shows the complete finite element model consisting of 81.000 elements and 125.000 nodes resulting in more than 300.000 degrees of freedom. With this ANSYS FE-model a large amount of electro-magnetic analyses and mechanical analyses have been performed. This model has been used for extensive studies in which the symmetry conditions are applicable. Several design options for the outer intercoil structures have been analysed as well as different positions and key length for the poloidal shear keys. Also the effect of different material properties for the casing has been investigated.

Figure 3. FE-Model of Single TF-Coil

The 3D global model described so far has also some restrictions. During the development of this FE-model simplifications are applied to avoid a too complex model. As a result, some information obtained is not accurate enough. For example: the model will not provide accurate information about the stresses and strains in the shear key region, the TF coil cross section, and shear panels in the two intermediate OIS segments. The model is also not suitable for non-symmetry loading conditions.

The Inner Intercoil Structure (IIS) consists of 4 poloidal shear keys with variable length. The first key has a length of 500 mm; the second key a length of 750 mm and the remaining two keys a length of 1 m. The keys are made of Inconel 718 and have a diameter of 150 mm. To obtain detailed information about the stresses in the keyways and key insulation, a modified 3D model was developed. In that particular 3D global model the lower curved region was modelled in detail as shown in Figure 4. That detailed section was ’glued’ into the global model by using the CEINTF command.

Figure 4. FE-Model of Lower Curved Region

The reference configuration for the TF winding pack is according to the radial plate design consisting of circular Nb3Sn cables-in-conduit, jacketed in circular stainless steel tubes, which are embedded in strengthened austenitic steel plates. To obtain information about the stresses in these radial plates, a detailed local finite element model of the TF-coil inboard leg cross section has been developed and analysed. The analyses have been performed by using the ‘generalized’ plain strain approach. Figure 5 shows the finite element mesh of the TF-coil cross section. This detailed FE-model consists of 28,800 elements with 55,500 nodes and is build with 8-node SOLID185 elements with three degrees of freedom. The non-linear interface between winding pack and casing is modelled with the CONTA173/TARGE170 elements with a friction coefficient of 0.2. As a result of symmetry only half of the cross section area has been modelled. With this model the in-plane Lorentz forces on the conductors have been calculated with ANSYS by making a thermal analysis with SOLID70 elements. For the Lorentz force calculation, the model is extended in radial direction by modelling ‚air’. The material property ’thermal conductivity’ is equal to the free space permeability, which is 4π *1.0e-7 H/m and the thermal load ’heat generation’ is equal to the current density. The calculated thermal gradient multiplied with the current and volume gives information about the Lorentz forces. This is applicable for the in-plane loads. The loads in the winding direction, i.e. perpendicular to the 2D FE-model, have been taken from the 3D global model.

Figure 5. FE-Model of TF-Coil Cross Section

To obtain detailed information about the stresses and deformations of the shear panels in the two intermediate friction joints, a 3-dimensional local model has been developed as shown in Figure 6. This model consists of 182,000 elements with 152,000 nodes. The SOLID185 (8-node brick) elements have been used for the pins, the panels and the sheets of insulation between the fingers. Asymmetric contact is considered by using the TARGE170/CONTA173 elements between the fingers. The pins are pre-loaded at room temperature. This is achieved with the PRETS179 elements. The washers are modelled with SOLID187 elements (mid-side nodes removed). As loading conditions, prescribed displacements at the two ends, obtained from the global model have been used. In the 3D global model a path operation is performed to obtain the three displacements. These displacements are transferred into a third order polynomial as function of the path length and are applied on the two edges. With this approach many different load cases can be analysed very quickly without updating the local FE-model. This is only applicable when the stiffness of the panels in the global model corresponds with the stiffness of the local model. For the solution the PCG solver was used. With the SPARSE solver it was impossible to obtain a converged solution with acceptable run-time.

Figure 6. FE-Model of Shear Panel in Friction Joint OIS

In the case of an electrical fault, such as a short circuit or a quench in a TF coil without discharge of the others, the current distribution becomes non-uniform. The time-scale of these events are controlled by the electro-magnetic time constants and is in the range of seconds. This time scale is much more than the lower eigenvalues of the structure and therefore it will not lead to or excite the structural natural frequencies. At a short circuit or a quench , the electromagnetic force distribution is not symmetric and the mechanical response to the out-of-plane loads is altered. The concern is that during these situations, the wedging and friction force might be overcome, resulting in excessive loads on the magnet system. As a result, large displacements might occur and the clearance with other components reduces to zero, which can cause severe damage to other components. The analyses of such fault events require large and extremely detailed finite element models. Details such as the CS and the preload structure and contact surfaces have to be properly modelled. Non-linear effects such as contact and friction forces have to be included, etc. The approach chosen is based on a kind of sub-modelling, starting with a large global model to determine the loads and displacements which can be used on smaller detailed models. Figure 7 shows the 3D global FE-model used for the analysis of fault conditions. This FE-model describes a 180-degree section of the magnet system and includes all the important non-linearity’s and components. This FE-model consists of 83,000 elements and 85,000 nodes. The element types used are SOLID45, SHELL63, CONTA52, and CONTA173/TARGE170 elements. Also in this case all required electro-magnetic and non-linear mechanical analyses have been performed with ANSYS.

Figure 7. FE-Model TF-Coils for Fault Condition Analyses

CS Magnet System For the analysis of the mechanical behaviour of the CS and to determine the required pre-compression at room temperature, a 3D global model has been developed, representing a 40 degree symmetry section. Figure 8 shows the model used for the global analyses in which the /EXPAND command has been used to enlarge the graphic display. The 3D global model consists of (only) 35.500 elements and 43.300 nodes. Homogeneous modules have been assumed which has been given orthotropic material properties. The main element type used is SOLID185. The interface between the CS modules has been modelled with CONTA173/TARGE170 elements. The model also contains 40-degree sections of the PF coils and Plasma (not shown in the figure) which are required for the electro-magnetic analyses. For the analysis of the Lorentz forces the 3D global model is ‘converted’ into an electro-magnetic model by using a special developed input script. The calculated Lorentz forces in the nodes are ‘moved’ into ANSYS input statements to be applied as loads in the stress analyses. The 3D global model does not provide accurate information about the deformations and stresses in the steel jacket and insulation. For that purpose an axi-symmetric detailed local model (see Figure 8) has been developed representing three layers. Two different configurations are considered, i.e. the aligned and mis-aligned layout. On these local models, the vertical loads obtained with the global model have been applied. However, the radial Lorentz forces in the conductors have been analysed separately by making ‘new’ electro-magnetic analyses.

Figure 8. 3D Global FE-Model of Central Solenoid Modules and detailed

axi-symmetric Models of CS Pancakes

For the development of almost all FE-models as described in the previous section, the ANSYS ADPL capability has been used as much as possible. Also specially input files have been developed to obtain a certain amount of flexibility and to reduce the effort when design changes are applied. Many sections of the FE-models have been developed ‘independently’ and simple linear analyses have been made to check the performance, accuracy, and ‘robustness’ of the model. During the solution, several parameters that control the accuracy and performance of the analyses, such as SOLCONTROL, CNVTOL, PRED, LINESEARCH have been used. These parameters are combined with ‘acceptable’ real constants values such as the normal and tangential stiffness of the contact elements. For example, the 3D FE-model used for the fault conditions analyses has been ‘benchmarked’ against the results obtained with the single coil 3D FE-model by making normal conditions analysis. Despite all the difficulties which had to be solved, it can be concluded that, due to flexibility of the ANSYS program, fast and robust analyses have been performed with acceptable results. A good understanding of the mechanical behaviour of the TF magnet system has been obtained.

Analysis Results & Discussion For almost all required analyses the in-plane and out-of-plane Lorentz forces have been calculated with ANSYS and are applied as nodal forces in the structural analyses. The number of load cases and the sequence of the analyses have been decided within the team of engineers involved in the design. With the use of special developed ADPL input files the structural FE-model(s), as shown in the previous section, have been ‘transferred’ into electro-magnetic models with appropriate degrees of freedom. The electro-magnetic FE-models consist, beside the TF winding pack, of the CS, PF, and plasma with corresponding current scenarios. As a result of this approach, a direct coupling between the electro-magnetic and

mechanical analyses has been achieved which has many advantages. For the loads of the single TF-coil model the symmetry option has been used. However, for the analyses of the loads during fault conditions a full 360-degree model of the TF magnet winding pack, CS, PF and plasma, has been used, due to the asymmetric situation. The results from the electro-magnetic analyses used for the structural analyses are the Lorentz forces. The loads are ‘converted’ to input statements by special scripts (FORTRAN, C++, SED, and AWK filters). Due to the usage of so-called non-conservative elements, all loads in the mechanical analyses are applied very gradually as nodal forces, along the full load history path, and in the proper sequence. The main load cases include pre-load of the pre-compression rings at assembly (PCRload), cool-down from room temperature to 4K, energisation of the TF coil (TFonly), Plasma Initiation (IM), X-Point Formation (XPF), Start of Flattop (SOF), Start of Burn (SOB), End of Burn (EOB), End of Cooling (EOC) and End of Burn + Plasma Disruption (EOB+PD). In almost all situations the ANSYS restart capability has been used.

Deformations TF Coils In Table 2 the radial and vertical displacements of the equatorial plane (inner and outer legs) are tabulated for several load cases. The 35 MN radial force at the top and bottom of the coil, applied by the pre-compression rings, results in a moment which bends the inner leg region resulting in a radial outward movement of 2.4 mm. This movement results in a toroidal gap between the TF coils of 0.84 mm. When energized, the coil wants to expand and moves in a radial inward direction as a result of the centring magnetic force of 402 MN. The absolute radial displacements of the TF coil, inner and outer legs, amounts to 11.9 and 34.9 mm, respectively, and stay constant during the plasma pulse.

Table 2: In-plane Displacements TF-Coil during Normal Operation Equatorial plane inner leg Equatorial plane outer leg Urad [mm] Uvert [mm] Urad [mm] Uvert [mm]

PCRload 2.4 0.2 -2.3 0.2 Cool down -4.2 -15.3 -35.0 -14.7

TFonly -11.9 -13.9 -34.9 -13.1 End of Burn -11.9 -14.2 -34.7 -13.1

End of Burn + Disruption -11.9 -14.3 -34.7 -13.1

The 35 MN radial force at the top and bottom of the coil, applied by the pre-compression rings, results in a moment which bends the inner leg region resulting in a radial outward movement of 2.4 mm. This movement results in a toroidal gap between the TF coils of 0.84 mm. When energized, the coil wants to expand and moves in a radial inward direction as a result of the centring magnetic force of 402 MN. The absolute radial displacements of the TF coil, inner and outer legs, amounts to 11.9 and 34.9 mm, respectively, and stay constant during the plasma pulse.

Figure 9 shows the out-of-plane displacements along the perimeter of the coil. For this figure the nodes at the nose of the TF-coil casing are taken starting at one side of the termination zone at the bottom of the coil in the clockwise direction. It should be noted that the starting and end point are not the same. The calculated displacements are stored in an ANSYS array parameter combined with the *VGET command and transferred to a Microsoft Office application. The maximum out-of-plane displacement amounts to 22 mm (@ disruption) and occurs in the outer leg region. This figure shows the ‘swing’ of the coil during operation determined by the difference in out-of-plane displacement between the load case IM and EOB. This ‘swing’ results in cyclic stresses which are evaluated for the fatigue assessment.

Figure 9. Out-of-Plane Displacements along Perimeter of TF-Coil

Stresses in TF coil Winding Pack The radial Lorentz force in the inner straight leg region is about 52.6 MN/m poloidal length, which would give an average nose pressure of 78 MPa when there is no wedging between winding pack and casing. However, the FE-analyses have shown that the nose pressure in the TF coil winding pack is 62 MPa, which means that 16 MPa of the radial pressure is passed by side friction from the winding pack to the case. The maximum poloidal hoop tension stress in the winding for load case TFonly is 335 MPa and occurs on the plasma side in both curved regions. This poloidal hoop stress is made up of a membrane stress equal to 195 MPa and bending stress of 140 MPa. When the out-of-plane loads become active the poloidal hoop stress will increase. The highest poloidal hoop stress occurs at load case EOB. In the lower curved region the poloidal hoop tension stress becomes 371 MPa. The highest increase in poloidal hoop stress occurs in the outer leg region where this stress increases locally by 157 MPa, i.e. from 307 MPa to 464 MPa.

The TF-coil winding pack in the 3D global models is modelled with only a few 8-node brick elements and ‘smeared’ orthotropic material properties are used. Therefore, the detailed 2D FE-model of the cross section (Figure 5) has been used to obtain more accurate information about the stresses in the conductors, winding pack insulation system, and radial plates. The maximum stress intensity in the radial plates amounts to 650 MPa and occurs only in a few locations (teeth) of radial plates. The linearized membrane (Pm) and membrane+bending stress (Pm+Pb) in the teeth of the radial plates amounts to 560 MPa and 580 MPa showing that the 650 MPa is a localized peak stress. Also the stresses in the TF conductor jacket are acceptable.

The stresses in the conductor and radial plate insulation have also been evaluated. The shear stress is the most important component. For the insulation system it is known that the allowable shear stress is dependent on the compressive stress. For the assessment of the insulation system a special ANSYS macro has been written, to take into account the advantage of the compressive stress. This assessment resulted in the conclusion that the static and cyclic stresses in the insulation system are below the allowable values.

The evaluation of the results obtained with the 3D global FE-models and local TF-Coil cross section FE-model has shown that all static and cyclic stresses in the TF winding pack which occur during normal operating conditions are within the allowable values and no critical regions occurs. Even under fault conditions the stresses in the TF winding pack are within the static allowable values. Under fault conditions a fatigue assessment is not required.

Stresses in TF coil Casing The maximum toroidal stress due to the wedging pressure is 536 MPa and occurs at the nose of the TF coil casing. This wedging pressure decreases in the radial direction to 30 MPa in the sidewalls and then increases to 385 MPa at the back plate (plasma side). The maximum stress intensity is 685 MPa and occurs also in the inner leg of the TF coil. The stresses in the TF coil inner leg are static stresses and the linearized Pm and Pm+Pb amount to 547 MPa and 695 MPa respectively. These values are below the allowable of 667 MPa (Pm) and 867 MPa (Pm+Pb). The maximum poloidal hoop tension under load case TFonly is 315 MPa and occurs at the bottom of the coil. Due to the out-of-plane loads, the coil bends and twists and the hoop stress in this region increases to 455 MPa at load case Eoburn and 484 MPa under load case Eoburn+PD. The most critical area was found to be the casing lower inboard curved region where the combination of in-plane loads and cyclic out-of-plane loads is particularly severe. The maximum principal stresses in this region, used for the fatigue assessment, are 310 MPa in the closure weld ( S∆ = 260 MPa) and 234 MPa in the back plate ( S∆ = 295 MPa). In these regions, the supporting structures (IIS) consist mainly of two sets of four shear keys with the key axis in a direction normal to the coil contour. These keys are able to carry the shear loads, due to the out-of-plane forces, varying from 15-25 MN/m in the lower curved region, but tend to become loose due to a radial outward displacement of the coils when they are energised. This effect has been reduced by means of the pre-compression rings. The analyses performed with the FE-model as shown in Figure 4, resulted in a maximum principal stress of 433 MPa ( S∆ = 200 MPa) in the second key slot. These analyses also showed that small gaps occur between the coils during operation.

The fatigue assessment performed is based on the crack growth (da/dN) analysis, assuming an initial defect size and taking into account certain safety factors. Two important input parameters are the maximum principal stress and the cyclic principal stress. These components are shown in Figure 10 and Figure 11 respectively.

Figure 10. Maximum Cyclic Principal Stress

Figure 11. Maximum Principal Stress

The fatigue assessment carried out is such that the either the maximum allowable defect size is calculated to sustain 60,000 cycles (safety factor of 2 on cycles) or the amount of allowable cycles for given defect. This calculation of the maximum allowable defect size or cycles is done outside ANSYS. The six stress components are exported and the calculation of the principal stress and cyclic principal stress is done with a C-program. In the fatigue analysis many assumptions are made, such as different residual stresses in base metal and welds, different plate thicknesses, safety factors, rotating principal stresses, etc. The casing will be manufactured from different classes of strengthened austenitic steel as shown in Figure 12. The different types of steel have their own static and fatigue characteristic.

Figure 12. Classes of Material in TF Coil Casing

Because ANSYS allows modification/alternation of calculated nodal point quantities (DNSOL/DESOL-command), the ANSYS plotting capability is used to visualize the fatigue parameter. An example of this is shown in Figures 13 and 14, which show the maximum subsurface defect size in the lower curved region of the TF coil casing and OIS outboard region. The maximum allowable defect in the lower curved region amounts to 135 mm2 in the back plate. In the closure weld (residual stress is 200 MPa) the maximum allowable defect amounts to 142 mm2. The fatigue assessment performed for the shear key region show that for a 10 mm2 initial sub-surface defect the amount of allowable cycles is 150,000, which is more than the required 30,000 cycles.

Figure 13. Max. Allowable Subsurface Defect in Inboard Region of TF Coil

Figure 14. Maximum Allowable Subsurface Defect in Outboard Region TF-Coil

The stress level and cyclic principal stress in the shear panel of the two intermediate OIS segments results in much smaller allowable defect (below 10mm2) The high stresses are very localized and a steep stress gradient is present. A fatigue crack growth rate analysis is considered to be too conservative. Therefore, in addition to this crack growth analysis, a fatigue assessment based on S-N curves has also been performed. The stress amplitude is calculated, including a means stress correction, and compared with design fatigue curves which included the safety factors. For all considered locations the allowable stress amplitude is higher than the stress amplitude, which occurs during operation.

Outer Intercoil Structures and Poloidal Shear Keys Table 3 shows the toroidal hoop tension acting on the four OIS. The pre-compression rings pull the OIS into compression (negative values), but when the TF coil is energized the OIS are loaded with a toroidal tension force (positive values). These toroidal tension forces stay constant during a plasma pulse. The same table shows the shear forces on the OIS for load case “Eoburn” and for the situation during a plasma disruption. The table shows that the OIS segments must transmit large shear loads between adjacent coils, varying from ~2.7 MN at the upper most OIS segment to 25 MN at Eoburn, or even 30 MN at a plasma disruption, at the lower intermediate OIS segment. A structural assessment of the shear panels in the friction joints in terms of static and fatigue analyses has been performed (see previous section) and has shown that all stresses are below the allowable values. The present design is the result of an extensive study to optimise the shape and dimensions as much as possible to reduce the cost.

Table 3 - Toroidal and Shear loads acting on 4 OIS segments at normal Operating Conditions PCRload TFonly EOB EOB+PD

Ftor [MN]

Ftor [MN]

Ftor [MN]

Frad [MN]

Fver [MN]

Ftor [MN]

Frad [MN]

Fver [MN]

Upper BOX OIS -6.9 8.4 7.5 1.0 2.5 7.4 2.8 3.8 Upper Friction Joint -9.8 3.7 4.0 0.3 20.0 4.0 0.4 26.9 Lower Friction Joint -11.3 1.9 2.8 0.0 24.3 2.8 0.1 30.3

Lower Box OIS -6.7 9.6 5.5 0.3 4.9 5.2 0.6 5.8

Initially, the intension is to load the pins in the friction joint up to the allowable stress of 750 MPa. This corresponds with a pre-load of 5.9 MN. After cool down from room temperature to 4K this preload is reduced with 12% due to the difference in thermal contraction coefficient between the materials used.

The maximum stress intensity in the shear panels amounts to 520 MPa and occurs at EOB. Figure 15 shows the distribution of the most important stress component in the friction joint OIS structure, i.e. the out-of-plane shear stress. This stress is a cyclic component and has a major effect on the allowable defect size in this structure. The maximum shear stress occurs at EOB and amounts to 180 MPa. The fatigue assessment performed showed that an initial sub-surface defect of 30 mm2 (defect at time=zero) is acceptable and will sustain the required amount of cycles.

Figure 15. Out-of-plane Shear Stress in Friction Joint Outer Intercoil Structure

The maximum (cyclic) shear stress in the insulation material between the fingers amounts to 20 MPa and is below the allowable. The analyses have shown that large assembly tolerances should be avoided. Small assembly gaps will result in some plastic deformation at room temperature at the root of the fingers during assembly. However, this will not have a significant detrimental effect on the performance of the structure.

Table 4 shows the average shear load on the four lower poloidal shear keys as well as the maximum gap size between coils. The first key is the closest to the straight leg region. The shear loads on the keys in the upper region are a factor 3 lower and the gap size between coils at the upper keys is 2 times smaller.

Table 4 - Average Shear Load [MN/m] and Toroidal Gap Size [mm] on

Upper and Lower Poloidal Shear Keys Upper Poloidal Shear Keys Lower Poloidal Shear Keys EOB EOB + PD EOB EOB + PD

Shear Load

Gap size

Shear Load

Gap size

Shear Load

Gap size

Shear Load

Gap size

First Key 5.4 0.18 7.6 0.21 20.6 0.34 25.0 0.42 Second Key 4.9 0.20 6.5 0.23 17.6 0.46 20.7 0.55 Third Key 4.6 0.21 5.8 0.24 16.2 0.53 18.6 0.60 Fourth Key 4.4 0.22 5.3 0.24 16.4 0.50 18.5 0.55

Central Solenoid The behaviour of the CS stack has been analysed under several loading and boundary conditions with the aim to optimize the (unwanted) vertical tensile stress in the CS modules. To avoid this stress a certain amount of pre-compression of the CS stack at room temperature is required. Factors which affect the pre-

compression are the preload temperature of the tie plates, the friction coefficient between the modules, the tie plate stiffness, and shape of the inter-module spacers. The initial pre-load at room temperature is based on a T∆ of the tie plates equal to 110°C and a friction coefficient between the modules of 0.3. This initial preload resulted in a tensile stress in the tie plates at of ~130 MPa. The compression between the two middle modules amounts to 16 MPa. Due to the difference in thermal contraction coefficient between the materials used, the pre-compression between the modules increases to 27 MPa and the tensile stress in the tie plates increases to 285 MPa. Vertical tensile stresses occur only at the load case EOB and are below 5 MPa. At all other load cases the vertical stress is compressive. The analyses have shown that, due to the wide variation of Lorentz forces, it is very difficult to suppress vertical tension in the CS modules throughout the ITER plasma scenario. Pre-compression at room temperature is necessary to minimize the vertical tensile stress, but simply increasing the preload temperature of the tie plates is inadequate. Based on the analyses performed the following requirements for ITER CS pre-compression system can be summarized as follows:

The preload temperature should be greater than 80°C. Extra compression is needed to compensate for bending of the CS stack, but simply increasing T∆ is not sufficient.

The friction coefficient should be as low as possible. Friction reduction is helpful to reduce tension for all plasma points but it is most effective when it promotes sliding during certain load cases.

Vertical stresses are sensitive to the ratio of the preload temperature or stiffness ratio of inner and outer tie plates. However, different ratios are also required to obtain minimize the vertical tensile stress.

The use of wedge shaped inter-module spacers to change the interaction between modules near the ends of the CS stack, and application of inward radial displacement near the supports to the TF coils are very effective for reducing tension.

Another important stress is the cyclic hoop stress. Because the currents are reversed during one plasma pulse, the central solenoid jacket is loaded twice. One maximum occurs at Initial Magnetisation and the other maximum occurs at EOB. Figure 16 shows the maximum hoop stress in the CS module at load case Initial Magnetisation. Due the fact that smeared equivalent properties are used for the CS winding pack (strains are correct but stresses not) the stress obtained with the 3D global model is not the real metal stress in the jacket. With the global model a hoop stress of 206 MPa is obtained, multiplied with the ratio of the Young’s modulus (almost 2) the real metal stress in the jacket amounts to 412 MPa. This corresponds with the results obtained with the 2D local model. The maximum hoop stress at load case EOB amounts to 370 MPa. The fatigue assessment performed for the CS jacket material has shown that these cyclic stresses are below to the allowable values, although the margin is very small.

Figure 16. Hoop stress in Central Solenoid Module at load case Initial Magnetisation

Conclusion The experience gained has shown that ANSYS gives engineers the opportunity to analyse all kinds of

magnetic, thermal, and mechanical problems in an efficient and flexible manner. Due to the open architecture of ANSYS, such as usage of ADPL and UPF, users can customize their working environment and analyse their particular sophisticated problem.

The analyses of the ITER magnet system performed so far with ANSYS have provided valuable information about the mechanical behaviour of the magnet system. Many design studies such as the effect of different friction coefficients between adjacent coils and between winding pack and casing, have been performed in a flexible and efficient manner, resulting in the present design of the magnet system.

All the analyses of the ITER-TF coils have highlighted that, despite the large operational loads during normal operation, only a few critical areas exist. The static and cyclic stresses in the TF coil casing are within the allowable limits. The Inner Intercoil Structure provides the required out-of-plane support, but to prevent too much separation of the key slots, pre-compression rings are required. The shear loads on the poloidal shear keys, and the gap between the coils is acceptable.

The analyses of the Central Solenoid have provided a large amount of information about the mechanical behaviour and have identified the critical regions. The amount of pre-compression, required to eliminate the vertical primary tensile stresses in the CS modules, has been optimized. Some design changes were suggested and a final design proposal has been made in which the analyses play an important role.

Acknowledgment This paper has been prepared as part of work undertaken within the framework of ITER transitional Arrangements (ITA). These are conducted by the Participants: the European Atomic Energy Community, Japan, The People’s Republic of China, The Republic of Korea, the Russian Federation, and the United States of America, under the auspices of the International Atomic Energy Agency. The views and opinions expressed herein do not necessarily reflect those of the Participants to the ITA, the IAEA or any agency

thereof. Dissemination of the information in this paper is governed by the applicable terms of the former ITER EDA Agreement.

References [1] ITER Structural Design Criteria for magnet Components (SDC-MC, DRG1 Annex, Naka Joint Work

Site, N11 FDR 50 01-07-05 R0.1

[2] ANSYS User’s Manuals and Procedures Guides Revision 9.0 and 10.1, Canonsburg, PA, Ansys Inc.

[3] Y. Fu, C. Jong, P. Michael, N. Mitchell, “Pre-compression Requirements for the ITER Central Solenoid”, MT19 Conference 2006.

[4] ITER FDR 2001, DDD11 Magnet, 2. Performance Analysis, 2.2 Structural Analysis.

[5] K. Yoshida, Y. Takahashi, N. Mitchell, D, Bessette, H. Kubo, M. Sugimoto, Y. Nunoya, K. Okuno, “Proposal for the Final design of the ITER Central Solenoid”, IEEE. Trans. Appl. Supercond., Vol 14, No 2, pp1405-1409,2004.