STRUCTURAL ANALYSES OF THE DIVERTOR OF “DEMO” NUCLEAR FUSION REACTOR

Nuclear fusion is the reaction in which two or more atomic nuclei fuse to form a heavier nucleus. Nuclei of hydrogen atoms, collide and fuse to form nuclei of helium atoms, releasing large amounts of energy during the reaction. Nuclear fusion occurs in the Sun, where the core reaches an extreme temperature of 15 million degrees Celsius, allowing hydrogen to turn into plasma.

To sustain fusion on Earth, a magnetic confinement method is used to confine the plasma to a temperature of 150 million degrees Celsius. The device designed for this purpose is the Tokamak, a toroidal chamber equipped with magnetic coils that generate a powerful containment field. The largest Tokamak currently in operation is the Joint European Torus (JET), while ITER, another Tokamak, is currently under construction.

The DEMOnstration Fusion Power Plant (DEMO) will be ITER’s successor, serving as an experimental fusion reactor aimed at demonstrating the net production of electricity from nuclear fusion. DEMO’s design has been initiated by the EUROfusion Consortium as part of the EU fusion roadmap under the Horizon 2020 program (https://euro-fusion.org/programme/demo/).

DEMO reactor power plant

The divertor is one of the main DEMO in-vessel components among all plasma facing components and can be perhaps considered as the most critical one [1]. The DEMO divertor will extract the alpha particle power, helium and impurities, but also the heat load that comes from the plasma “scrape-off” layer during normal operations and during the foreseen off-normal events [2]. The divertor consists of several parts, the main ones being: the cassette, the shielding liner, the vertical targets, the reflector plates and the cooling pipes.

Being a heavily loaded component, the structural response of the divertor must be assessed with the highest accuracy so as to guarantee the safe operation of the machine.

It should be noted that the design and study of the DEMO divertor are ongoing, and consequently the final configuration may be subject to modification.

The divertor is subjected to Vertical Displacement Events that induce ElectroMagnetic (EM) loads on it due to anomalies potentially occurring during the operations. VDEs induce transient EM loads with specific spatial distributions that can be analyzed by means of FEM dynamic analyses, thus requiring significant computational efforts [3-4]. Moreover, the device, during normal operating conditions, is subjected to gravitational loads, pressure for internal cooling, thermal loads, ferromagnetic loads and a preload.

The research intended to implement a theoretically-based methodology to calculate a so-called Dynamic Amplification Factor (DAF). In particular, such a methodology leads to the estimation of the maximum dynamic response by using less demanding numerical analyses, i.e. “equivalent” static analyses, this latter considering strain and stress values comparable to the maximum dynamic ones [5-9]. This allows for faster designing, optimizations and life prediction calculations [10-12]. Calculations are carried out with Ansys Workbench and Ansys Mechanical [13].

 

NUMERICAL MODEL AND LOAD CONDITIONS

The 3D model of the divertor undergoes continuous updates during the design phase in order to progressively improve its features. Although the ongoing analysis and researches refer to the current and latest CAD model (2022 version [14]).

The divertor’s cassette is made of EUROFER [15] and internally filled with a coolant, i.e. water at pressure of 35 bar. The cassette is supported at the two ends, with two spherical joints at the nose side and with a wishbone at the other side (in particular, a revolute joint between the wishbone and the ground).

During its lifetime, the divertor can be subjected to different loads due to different conditions. In Normal Operating Conditions, the divertor is subjected to:

– Ferromagnetic load: mechanical loads produced by the ferromagnetic effects on magnetic materials;

– Earth gravity;

– Pressure for internal cooling: pressure due to the presence of pressurized internal cooling water – DEMO Divertor cooling system;

– Thermal load;

– Wishbone Pre-load: pre-load along the radial direction (Nose-Wishbone) to keep the structure in position during operations. 

The divertor may be subject to electromagnetic (EM) loads in addition to the normal loads. The EM loads involve mechanical forces caused by interactions between induced currents and magnetic fields. In particular, the divertor can undergo an impulsive electromagnetic load during event of a malfunction, i.e. due to the potential instability of the plasma. This load presents significant spatial and temporal variability and has been calculated through dedicated EM FEM simulations [3].

To enhance the visualization of electromagnetic (EM) loads, a dedicated MATLAB tool has been developed. This tool enables users to view the spatial distribution of EM loads on the divertor, as well as to track the temporal evolution of the resultant load, including its corresponding point of application.

 

ANALYSIS AND RESULTS

The research has been divided into several phases involving the analysis of increasingly complex models subjected to different load conditions, considering both static and dynamic analysis.

Modal analyses were carried out in order to calculate the modal shapes and natural frequencies of the system. Moreover, the modal analysis is useful to investigate the potential couplings between EM harmonic loads and the system modal behaviour. The  results showed that 90% of the cumulative participation mass is reached around the 12th mode.

Using the Transient Structural tool in Ansys, three Dynamic analyses (2%, 4% and 6% damping ratio) and a Quasi-Static analysis were carried out.

To evaluate the dynamic effect on the displacements, the reactions and the stress, a local Dynamic Amplification Factor can be evaluated for each node in the model. In the case of displacements and stress state, this has been done in Matlab by dividing the value obtained by the dynamic analyses, by the value at the same node of the Quasi-Static analysis. In this way, it is possible to plot a three-dimensional map of DAF and for each damping value.

In the case of displacements, the increase of damping results in a decrease of the DAF in both of setups. Furthermore, an increase in DAF values is observed for the same damping value when comparing setups 1 and 2. However, it is possible to identify the most dynamically amplified zone, which is the zone of the wishbone and the vertical part of the cassette attached to it.

In the case of stress state, the results illustrate several regions where a substantial amplification is observed. In particular, increasing the damping results in a reduction of extension and DAF intensity in these zones.

In the case of nose and wishbone reactions, the DAF was defined as the ratio between the maximum of the reaction resulting from the dynamic analysis and the maximum value of the same reaction in the Quasi-Static analysis.

 

CONCLUSIONS

The modal analysis has shown that a “more complete” configuration of the divertor puts it in a worse condition since the natural frequencies of its modes of vibration decrease.

The results from the dynamic analyses have shown how it is crucial to analyse the full model of the divertor with all the components since the variation of the results and the DAF values is relevant. Also, it has been possible to assess that on the divertor it is possible to define zones that are more dynamically amplified, and they became more evident with the increase of dynamic effects. The next step involves the conclusion of the analysis on the overall model and the development of new analyses on the updated model (version 2024).

For further information, please refer to [16-17].

 

REFERENCES

[1] Mazzone, G., et al.: Eurofusion-DEMO Divertor – Cassette Design and Integration, Fusion Engineering and Design, 157, 111656 (2020).

[2] You, J.-H., et al.: Divertor of the European DEMO: Engineering and technologies for power exhaust, Fusion Engineering and Design, 175, 113010 (2022).

[3] Maffucci, A.: Electromagnetic Analysis for Divertor Assembly 2022, DIV-DEMO.S.1-T014-D001, Deliverable: EFDA_D_2Q43ZK.

[4] Frosi, P., Mazzone, G., You, J.-H.: Structural design of DEMO Divertor Cassette Body: provisional FEM analysis and introductive application of RCC-MRx design rules, Fusion Engineering and Design, 109-111(A), 47-51 (2016).

[5] Zhang, K., Mantel, N., You, J.-H.: Dynamic structural response of DEMO divertor under electromagnetic loading, Fusion Engineering and Design, 187 113375 (2023).

[6] Kim, H.-G., Kim, E. and Cho, M.: Transformation of Dynamic Loads into Equivalent Static Load based on the Stress Constraint Conditions, Journal of the Computational Structural Engineering Institute of Korea. 26(2), 165-171 (2013).

[7] Chen, X., Kareem, A.: Equivalent Static Wind Loads on Buildings: New Model, Journal of Structural Engineering 130(10) (2004).

[8] Chopra, A.K.: Dynamics of structures – theory and applications to earthquake engineering. 4th edn. Pearson, Berkeley (2016).

[9] Clough, R.W., Penzien, J.: Dynamics of Structures, 2nd edn., McGraw-Hill, New York (1993).

[10] Giannella, V., Fellinger, J., Perrella, M., Citarella, R.: Fatigue life assessment in lateral support element of a magnet for nuclear fusion experiment “Wendelstein 7-X”, Eng Fract Mech, 178, 243-257 (2017).

[11] Fellinger, J., Citarella, R., Giannella, V., Lepore, M., Sepe, R., Czerwinski, M., Herold, F., Stadler, R., the W7-X Team: Fusion Eng. Des., 136, 292-297 (2018).

[12] Giannella, V., Citarella, R., Fellinger, J., Esposito, R.: LCF assessment on heat shield components of nuclear fusion experiment “Wendelstein 7-X” by critical plane criteria, Procedia Struct Integr, 8, 318-331 (2018).

[13] De Salvo, G.J., Swanson, J.A.: ANSYS Engineering Analysis System User’s Manual. Houston, Pa.: Swanson Analysis Systems (1985).

[14] Marzullo, D.: CAD Design – 2nd phase -2019, DIV-1-T006-D004, Deliverable: EFDA_D_2NL4LT.

[15] Mergia, K., Boukos, N.: Structural, thermal, electrical and magnetic properties of Eurofer 97 steel, Journal of Nuclear Materials, 373, 1-8 (2008).

[16] Petti, L., Cricrì, G., Zollo, A., Giannella, V., Mantel, N., You, J. H., & Citarella, R. (2023, September). Structural Response of DEMO Divertor Under Electromagnetic Loading. In International Conference of the Italian Association of Design Methods and Tools for Industrial Engineering (pp. 271-278). Cham: Springer Nature Switzerland.

[17] Petti, L., Lombardi, L., Cricrì, G., Mantel, N., You, J. H., & Citarella, R. (2025). Assessment of dynamic response of a DEMO divertor under electromagnetic impact loads. Part 1: A computational methodology for a cost-effective analysis. Fusion Engineering and Design, 211, 114809.