Coupled FEM-DBEM method to assess crack growth in magnet system of Wendelstein 7-X

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany. The superconducting coils of the magnet system are bolted onto a central support ring and interconnected with five so-called lateral support elements (LSEs) per half module. After welding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that could potentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to the appearance of first cracks during assembly, the Stress Intensity Factors (SIFs) were calculated and corresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially critical position and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests at cryogenic temperature. In this paper the Dual Boundary Element Method (DBEM) is applied in a coupled FEM-DBEM approach to analyze the propagation of multiple cracks with different shapes. For this purpose, the crack path is assessed with the Minimum Strain Energy density criterion and SIFs are calculated by the Jintegral approach. The Finite Element Method (FEM) is adopted to model, using the commercial codes Ansys or Abaqus;, the overall component whereas the submodel analysis, in the volume surrounding the cracked area, is performed by FEM (“FEM-FEM approach”) or alternatively by DBEM (“FEM-DBEM approach”). The “FEM-FEM approach” considers a FEM submodel, that is extracted from the FEM global model; the latter provide the boundary conditions for the submodel. Such approach is affected by some restrictions in the crack propagation phase, whereas, with the “FEM-DBEM approach”, the crack propagation simulation is straightforward. In this case the submodel is created in a DBEM environment with boundary conditions provided by the global FEM analysis; then the crack is introduced and a crack propagation analysis has been performed to evaluate the effects of the crack shape and of the presence of nearby cracks on the allowed number of EM load cycles

Buckling curves of hot rolled H steel sections submitted to fire

Report of the research work at the base of the design equation introduced in Eurocode 3 (EN 1993-1-2) for the stability of steel columns under axial loading or combined axial and bending loading

Real-time detection of overloads on the plasma-facing components of Wendelstein 7-X

Wendelstein 7-X (W7-X) is the leading experiment on the path of demonstrating that stellarators are a feasible concept for a future power plant. One of its major goals is to prove quasi-steady-state operation in a reactor-relevant parameter regime. The surveillance and protection of the water-cooled plasma-facing components (PFCs) against overheating is fundamental to guarantee a safe steady-state high-heat-flux operation. The system has to detect thermal events in real-time and timely interrupt operation if it detects a critical event. The fast reaction times required to prevent damage to the device make it imperative to automate fully the image analysis algorithms. During the past operational phases, W7-X was equipped with inertially cooled test divertor units and the system still required manual supervision. With the experience gained, we have designed a new real-time PFC protection system based on image processing techniques. It uses a precise registration of the entire field of view against the CAD model to determine the temperature limits and thermal properties of the different PFCs. Instead of reacting when the temperature limits are breached in certain regions of interest, the system predicts when an overload will occur based on a heat flux estimation, triggering the interlock system in advance to compensate for the system delay. To conclude, we present our research roadmap towards a feedback control system of thermal loads to prevent unnecessary plasma interruptions in long high-performance plasmas.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053.Peer ReviewedArticle signat per 22 autors/es: Aleix Puig Sitjes* 1, Marcin Jakubowski 1, Dirk Naujoks 1, Yu Gao 1, Peter Drewelow 1, Holger Niemann 1, Joris Fellinger 1, Victor Moncada 2, Fabio Pisano 3, Chakib Belafdil 2, Raphael Mitteau 2, Marie-Hélène Aumeunier 2, Barbara Cannas 3, Josep Ramon Casas 4, Philippe Salembier 4, Rocco Clemente 4, Simon Fischer 1, Axel Winter 1, Heike Laqua 1, Torsten Bluhm 1, Karsten Brandt 1, and The W7-X Team † 1. Max-Planck-Institut für Plasmaphysik, Wendelsteinstr. 1, 17491 Greifswald, Germany / 2. Commissariat à l’Énergie Atomique et aux Énergies Alternatives (CEA), Institut de Recherche sur la Fusion par Confinement Magnétique (IRFM), F-13108 Saint Paul-lez-Durance, France / 3. Department of Electrical and Electronic Engineering, University of Cagliari (UniCa), Piazza d’Armi, 09126 Cagliari, Italy / 4. Department of Signal Theory and Communications, Universitat Politècnica de Catalunya (UPC), Jordi Girona 1-3, 08034 Barcelona, Spain / * Author to whom correspondence should be addressed. / † Membership of the Team Name is provided in Acknowledgments.Postprint (published version

Analysis of the neutral fluxes in the divertor region of Wendelstein 7-X under attached and detached conditions using EMC3-EIRENE

This paper analyzes the neutral fluxes in the divertor region of the W7-X standard configuration for different input powers, both under attached and detached conditions. The performed analysis is conducted through EMC3-EIRENE simulations. They show the importance of the horizontal divertor to generate neutrals, and resolve the neutral plugging in the divertor region. Simulations of detached cases show a decrease in the number of generated neutrals compared to the attached simulations, in addition to a higher fraction of the ion flux arriving on the baffles during detachment. As the ionization takes place further inside the plasma during detachment, a larger percentage of the generated neutral particles leave the divertor as neutrals. The leakage in the poloidal and toroidal direction increases, just as the fraction of collected particles at the pumping gap. The fraction of pumped particles increases with a factor two, but stays below one percent. This demonstrates that detachment with the current target geometry, although it improves the power exhaust, is not yet leading to an increased particle exhaust

Real-Time Detection of Overloads on the Plasma-Facing Components of Wendelstein 7-X

Wendelstein 7-X (W7-X) is the leading experiment on the path of demonstrating that stellarators are a feasible concept for a future power plant. One of its major goals is to prove quasi-steady-state operation in a reactor-relevant parameter regime. The surveillance and protection of the water-cooled plasma-facing components (PFCs) against overheating is fundamental to guarantee a safe steady-state high-heat-flux operation. The system has to detect thermal events in real-time and timely interrupt operation if it detects a critical event. The fast reaction times required to prevent damage to the device make it imperative to automate fully the image analysis algorithms. During the past operational phases, W7-X was equipped with inertially cooled test divertor units and the system still required manual supervision. With the experience gained, we have designed a new real-time PFC protection system based on image processing techniques. It uses a precise registration of the entire field of view against the CAD model to determine the temperature limits and thermal properties of the different PFCs. Instead of reacting when the temperature limits are breached in certain regions of interest, the system predicts when an overload will occur based on a heat flux estimation, triggering the interlock system in advance to compensate for the system delay. To conclude, we present our research roadmap towards a feedback control system of thermal loads to prevent unnecessary plasma interruptions in long high-performance plasmas

Multiaxial LCF assessment on plasma facing components of nuclear fusion experiment “Wendelstein 7-x”

The Wendelstein 7-X modular advanced stellarator has started operations at the Max Planck Institute for Plasma Physics in Greifswald, Germany, in 2016. In the first phase, the machine operated restricting the plasma pulses to low power and short lengths. Plans to achieve actively cooled components are scheduled to start in 2020 when the machine will operate in steady-state at full power. FEM simulations for steady-state operations revealed high plastic strains at several locations, for most of all the rigidly supported Plasma Facing Components, therefore, there is the risk of a premature fatigue failure before the end of the scheduled operations of the machine. The aim of this study is to analyse by FEM the fatigue behavior of such critical components by means of an in house made routine estimating, eventually, their fatigue life

FEM-DBEM procedure for crack analysis in baffle module of Wendelstein 7-X

“Wendelstein 7-X” is the world’s largest nuclear fusion experiment of “stellarator type” in which a hydrogen plasma is confined in a magnet field, generated with external superconducting coils, allowing the plasma to be heated up to fusion temperature. The water-cooled Plasma Facing Components (PFC) protect the Plasma Vessel (PV) against radiative and convective heat from the plasma. After the manufacturing process of the heat shields and baffles, several cracks have been found in the braze and in the cooling pipes. Due to heat loads occurring during each Operational Phase (OP), thermal-stresses are generated in the heat sinks, brazes and cooling pipes, that encourage cyclic crack-growth and, eventually, the water leak through the pipes. The aim of this study is to predict the operational limits of the baffles and heat shields under cyclic heat loads, by using a numerical model based on a FEM-DBEM approach, in order to provide an assessment on the risks of premature failure for segments assembled in the PV

FEM-DBEM coupled procedure for assessment of cracks in lateral supports of the magnet system of Wendelstein 7-X

The superconducting coils of the magnet system of Wendelstein 7-X (W7-X) are bolted onto a central support ring and interconnected with five so-called lateral support elements (LSEs) per half module. After welding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that could potentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to the appearance of first cracks during assembly, the stress intensity factors (SIFs) were calculated and corresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially critical position and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests at cryogenic temperature. The Miner's rule was adopted to allow for different load combinations. The predefined semi-circular initial crack shape and crack growth limit, were set in such a way to avoid multiple crack coalescence even if such restrictions could have a significant effect on N. These results have been published in a first paper, whereas, in the current paper, this work has been extended with analyses of propagation of cracks with different shapes and affected by nearby cracks. For this purpose, the Dual Boundary Element Method (DBEM) was applied in a coupled FEM-DBEM approach: the crack path is assessed with the Minimum Strain Energy density criterion and the SIFs are calculated by the J-integral approach. The Finite element method (FEM) was adopted to model the overall component whereas the DBEM was adopted for the submodel analysis in the volume surrounding the cracked area. With this approach, the effects of the crack shape and the presence of nearby cracks on the allowed number of EM load cycles of the machine were demonstrated

FEM-DBEM Coupled Procedure To Analyse Crack Scenarios In A Baffle Cooling Pipe

Wendelstein 7-X is the world’s largest nuclear fusion experiment of stellarator type, in which a hydrogen plasma is confined by a magnet field generated with external superconducting coils, allowing the plasma to be heated up to fusion temperature. The water-cooled Plasma Facing Components (PFC) protect the Plasma Vessel (PV) against radiative and convective heat from the plasma. After the assembly process of heat shields and baffles, several cracks were found in the braze and cooling pipes. Due to heat loads occurring during each Operational Phase (OP), thermal-stresses are generated in the heat sinks, brazes and cooling pipes, capable to drive cyclic crack-growth and, eventually, a water leak through the pipe wall. The aim of this study is to predict the operational limits of the baffles and heat shields, by using numerical models based on FEM-DBEM approach in order to obtain a prediction of the number of tolerable load cycles