Limit analysis of complex welds between plasma vessel and ports in W7-X cryostat system

Highlights

• Modeling of the sophisticated nonstandard geometry components.

• 3D FE analysis using shell-to-solid element connection.

• Structural integrity analysis of the welded connections of W7-X fusion reactor.

• Limit analysis by finite element method.

Abstract

Wendelstein 7-X (W7-X) is an experimental modular stellarator of the HELIAS type, currently in the second phase of operation in Greifswald, Germany. The stellarator is a complex 3D structure with high level safety requirements. As a result, sophisticated methods are necessary for the analysis of critical components and it is very important to evaluate structural strength of the welded connections between the plasma vessel and the ports.

The structural integrity analysis of the welded connection between plasma vessel and ports has been performed for several critical and/or representative port welds. The modelling of the welded connection was performed in two steps. First the geometrical 3D models of these port welds were prepared using the SolidWorks software. The model of a welded connection of the complex shape was modelled by creating a big number of sketches around the perimeter of the port-to-PV connection. Later, the sketches were connected using a loft feature and was transferred to the ABAQUS/Standard FE software. The limit analysis by means of finite element method (ABAQUS code) was used to confirm static strength reliability of port welds. According to the results of the analysis it is possible to conclude that the proposed welding between the plasma vessel and the analysed ports fully meets the structural requirements.

Introduction

Wendelstein 7-X (W7-X) is an optimized modular stellarator of the HELIAS type [1], [2] which shall demonstrate the possibility to use such a system for a nuclear fusion power plant in the future. The W7-X is in the second phase of operation in Greifswald, Germany by the Max-Planck-Institut für Plasmaphysik (IPP) [3]. A fragment of the W7-X machine is given in Fig. 1.

The W7-X cryostat mainly consists of the Outer Vessel (OV), the Plasma Vessel (PV), and 254 ports with bellows that connect the vessels [2], [4]. The PV is the innermost cryostat wall, with its shape generally following the complex shape of the plasma. The PV with in-vessel components provides a physical separation between the plasma and the rest of the stellarator. The PV main body is made from 17 mm thick stainless steel shell covered by thermal insulation on the outer side facing magnet system. The ports have different dimensions, thicknesses (3–15 mm) and inclination angles to the main vessel.

The OV is the vessel that covers the superconducting magnet system. The supply and diagnostic PV ports penetrate the OV/PV interspace between the coils of the magnet system and are attached to the PV at one end and to the OV at the other using bellows to compensate mutual movements of two vessels [4]. The ports provide the only way to access the plasma and in-vessel components from the outside. Each port is basically a tube with a round, oval, rectangular or with an irregular cross section. In a place where the port is attached to the PV, the PV shell has an opening corresponding to the shape of the port. The port is inserted into the opening in the PV shell until it reaches the inner surface of the shell, and is welded to the PV shell from the inside with a partially penetration weld. During assembly, the other side of the PV shell/port interface is not accessible, because the layout inside the cryostat is designed to minimize the distance between the coils and the thermal insulation of the ports and the vessels. Moreover, minimization of weld throat is necessary to significantly reduce the assembly time and efforts. Due to these facts, the reliable evaluation of the structural integrity of welds is very important for safe operation of the cryostat system.

During operation, the cryostat system of the W7-X stellarator is subjected to many different types of loads applied simultaneously to the same or different parts of the system [2], [5], [6]. The thermal movement of the plasma vessel requires that all ports should be equipped with bellows which vary between 100 mm circular and 1170 mm × 570 mm rectangular sizes. The axial and lateral stiffness of all bellows creates a resulting spring-force which acts directly on the vessel supports [7]. The magnitude of this force varies between different load cases.

On the other hand, the W7-X stellarator has a clear advantage of being a low cycle experimental machine, which is reflected in the choice of codes and standards for the W7-X stellarator, following the same multicode approach as accepted by ITER [8]. Therefore, structural criteria developed for tokamaks such as ITER were correspondingly expanded or relaxed on the basis of tests and experience to achieve a reasonable cost reduction. This approach also includes finite element (FE) limit analyses, which is a powerful method accepted by the project.

Usually limit state criteria are used to design and assess the safety of many engineering components and structures, from simple metal forming problems to large-scale engineering structures and nuclear power plants. Plastic collapse is the limit state of the structure, and the corresponding load is called the limit load. Limit analysis is used to determine the limit load [9], [10], [11], [12].

Both analytical and sophisticated numerical methods can be used for calculation of the limit load. One of the most popular analytical methods is the yield-line theory method [13], [14]. The yield-line theory method is employed to achieve fast calculation of the ultimate load. The concept is based on the upper bound of the ultimate load. The yield-line theory method does not require an input of boundary stiffness or an array of structure parameters for modelling non-linearity of the material. The FE method (FEM) is usually used for the limit load analysis of different structures [15], [16], [17], [18]. Numerical methods based on non-linear finite element analyses are increasingly popular, due to complexities of modern devices associated with their geometry and loading conditions. The FE limit analysis is presently performed for estimation of safety criteria (factors) for critical components, welds, handmade insulation, and unique elements [19], [20], [21]. Such an analysis can also take into account specific material serration effects observed at low cryogenic temperatures [21].

A reliable prediction of the W7-X structural behaviour is only possible by employing complex FE simulations with a hierarchical set of FE models [22]. The strategy of the W7-X structural analysis [19], [22] is similar to the approaches used for many other unique and large facilities. Two types of models are intensively used: global models for the choice of main system parameters, and local models for detailed analyses of the critical components.

In particular, local models are used for analysis of individual ports. This paper describes a structural integrity analysis of the welded connection in a form of a limit analysis that has been performed for several critical and/or representative port welds. The following welded connections were analysed:

• Welded connection between the port designed for installation of video diagnostic (AEQ20) and the PV shell with a gap between port and shell of 1 mm after port installation (open surface ∼ 0.0108 m²);

• Welded connection between the port designed for installation of bolometry and/or tomography and in use for PV horizontal centering system (AEU30) and the PV shell with gaps of 1 mm and 6 mm (open surface ∼ 0.0679 m²);

• Welded connection between the port designed for the installation of a complex neutral beam injector (NBI) (AEK20) and the PV shell with a gap of 1 mm (open surface ∼ 0.3681 m²).

In this paper, the description of the modelling, methodology of analysis and the analysis results are presented for the big and complex port AEK20 (see Fig. 4-b and Fig. 5). At end of the paper, in section 4, the summarised results of analysis for the other mentioned ports are also included.

The schematic cross section of the PV and the 12 mm thick AEK20 port weld in the area where the mutual local inclination between shells (α) is 90° is presented in Fig. 2 for the case with 1 mm gap. The designed curved surface of the weld (the dashed line in Fig. 2) was simplified and modelled as such a surface that would project a straight line on the cross section. The FE model of the port has been developed based on the detailed three-dimensional CAD model of the port. The FE limit analyses using elastic-plastic material behaviour has followed the complex geometry modelling. The local FE model of the port was loaded with forces, moments, and pressure provided by IPP on the basis of the results of the calculations on the global model of the cryostat system.

The limit analysis of the AEK20 port welds was performed using the ABAQUS code. The non-linearity of the systems, simplification of the model, other uncertainties and possible variations of nominal parameters were evaluated as presented in the following chapter of the paper.