Structural analysis of W7-X: From design to assembly and operation
Introduction
Wendelstein 7-X (W7-X) will be the largest stellarator in the world with an average major radius of 5.5 m, an average minor plasma radius of 0.53 m, and a total weight of 725 t. It shall operate at reactor relevant plasma parameters [1]. The first three modules of the magnet system (out of 5) have been successfully completed within schedule and are already installed in the torus hall [2], [3].
The main structural components of W7-X are the magnet system, and the cryostat system (Fig. 1).
The W7-X magnet system consists of 50 super-conducting non-planar coils (NPC), 20 superconducting planar coils (PLC), and the mechanical structure encompassing the central support structure (CSS) and the inter-coil support structure. The CSS stands on the machine base (MB) by 10 cryolegs (see Fig. 2). The NPCs have complex 3D geometry to ensure the required magnet field configuration (Fig. 3). The coils are arranged toroidally in five equal modules, with each one consisting of two flip-symmetric half modules. One half module includes five differently shaped NPCs and two PLCs. Each NPC and PLC is fastened to the CSS by two central support elements (CSE). The CSE is a bolted connection with possible opening of the flange. The narrow support elements (NSE, 29 per half module) and the lateral support elements (LSE) connect adjacent NPC casings on the high field and on the low field sides of the machine, respectively (Fig. 3). The NSEs are sliding contacts, while LSEs are welded connections with the exception of the inter-module ones which are bolted. The planar support elements (PSE) connect the two types of PLC (A, B) to the NPC. One PSE per coil (PSE-A1, PSE-B1) is a fixed bolted connection, while other PSEs follow the NSE design [4].
The cryostat system consists of the plasma vessel (PV), outer vessel (OV), the ports and the machine base. The PV corresponds to the twisted shape of the plasma and is manufactured from 17 mm thick stainless steel (SS) segments. 254 ports with different shapes (round, oval, and rectangular) connect the PV to the 25 mm thick SS OV. The magnet system is located between the PV and the OV, and kept at cryogenic temperature (4 K) in high vacuum (∼10−4 Pa) [5].
A reliable prediction of the W7-X structural behaviour is only possible with extensive finite element (FE) analyses [6], [7], [8], [9].
The magnet system analysis is a most challenging task due to the complexity of the coil geometries and the non-linear behaviour of the coil support system. The whole structure is highly sensitive to initial contact gap openings, contact friction factor, coil stiffness, bolt pretension, etc.
The strategy of W7-X structural analysis [9] is similar to the approach for many other unique and large facilities. Two types of models are intensively used: global models (GMs) for the choice of main system parameters, and local models for detail analysis of the critical components.
The magnet system global FE model includes the coils and their support structure, the cryostat system global FE model encompasses the OV, the PV, the ports with bellows, and the MB. Both global models are analysed separately with some specific assumptions [6].
Two additional GMs have been created and analysed for auxiliary systems of the magnet system: (1) the cryopipe system GM [10] and (2) the bus-bar GM [11]. Both GMs represent complex mechanical structures that include relatively long and flexible lines together with numerous supports which are mounted on the coils, the CSS, and other components. The supports for both systems are non-linear due to intentionally introduced gaps, and the cryopipe system includes numerous flexible hoses and bellows in addition.
The results of the GM FE analyses are transferred to the local models in terms of forces and moments, in terms of displacements in case sub-modelling procedures are used, or the local component model is embedded in the GM [5], [6], [7], [8], [9], [26].
Besides for evaluation of structural integrity, the global and local model results were also used for the definition of positions for the mechanical instrumentation of the structure [33].
Section snippets
Strong and experienced team
Unique devices like W7-X, ITER and other large fusion experiments require strong and experienced teams for structural analysis from the beginning of the project. The team should further grow gradually in size and experience towards construction of the device. An example shall demonstrate what might happen if the man-power is not sufficient: The W7-X planar coil case is a bolted and pinned structure. Due to lack of resources, modeling and analysis of the case was originally performed only as for
Current and future activities
Structural analysis of the magnet system concentrates now on the verification of elements to be installed in the module separation interface (see e.g. [26]), the support of assembly processes, reliable prediction of the stellarator structural behaviour at the maximum design value of 3T, establishing limits for machine operation, and study of new plasma scenarios and operational regimes. A further task is structural simulation of fault scenarios with deduction of corresponding operation
Conclusions
Resolving the main critical issues in the design of a complex fusion device is only possible with an accurate prediction of the system behaviour. A strategy for extensive FE structural analyses has to be developed and implemented in order to validate the adopted design solutions, and to perform a proper choice of parameters. The FE model tree should also provide the possibility to analyze non-conformities reported by manufacturers, and to accept or reject inconsistencies with the reference
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