Structural analysis of the W7-X cryogenic pipe system

Wendelstein 7-X (W7-X), a modular advanced stellarator, is presently under construction at the Max-Planck-Institut für Plasmaphysik in Greifswald. Its magnet system (MS) consists of 50 non-planar and 20 planar superconducting coils which are arranged in five identical modules. The cryogenic cooling pipe system (CPS) for the MS is one of the remaining major components under manufacture. Since it is the easiest to adapt, its design and structural analysis had to be postponed until the design of the main MS components like coils, structure, and bus-bar system, influencing the layout and mechanical behaviour of the piping, had been finalized. The complex three-dimensional routing of the cooling pipes is governed by avoiding clashes with the structure during cool-down and operation. Most of the pipe supports allow sliding and limited rotation in order to reduce stress levels, forces and moments in the pipes and supports. This given fact, in combination with high deformations of the supporting magnet system, makes the CPS behaviour highly non-linear. Furthermore, several connected components such as valves and coil terminals cannot take any significant loads. As a consequence, the transmission of forces and movements through these interfaces has to be limited by kinematic separation, using flexible hoses and compensators. The non-linear finite element (FE) model created for the first MS module to be assembled includes 159 pipe sections with a total length of 470 m. The system encompasses approximately 80 flexible hoses and compensators, as well as 136 supports with clamps interconnecting up to 6 neighbouring lines. This paper presents the strategy of the CPS analysis, the FE model, as well as the various boundary conditions and limitations due to design requirements. The results of this most challenging parametric study are discussed, including variations of hose and compensator flexibilities as well as of the support gap sizes.