PSI - Issue 24

Andrea Chiappa et al. / Procedia Structural Integrity 24 (2019) 898–905 Andrea Chiappa et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

An energy supply able to satisfy industrial and domestic needs is paramount in modern society. An ever-growing energetic demand, expected more than doubled by 2050, and environmental concerns impose to find energetic sources virtually inexhaustible but still eco-friendly. Nuclear fusion is the process that powers the stars, based on the conversion of mass to energy, according to the relativity theory. Its application for civilian purposes combines the promise to sustain the energetic demand for thousands of years with a series of significant benefits compared to both conventional and renewable energy resources (https://www.iter.org/sci/Fusion). First, the amount of achievable energy is incomparable to that of current methods, such as combustion of coal, oil or gas. Fusion fuels (deuterium and tritium) are widely available; helium, which is inert and non-toxic, is the major by-product of the process. The reaction is intrinsically safe since no risk of chain reaction exists, furthermore the radioactivity of fusion waste lasts a way shorter with respect to the fission counterpart. The fusion reaction, which merges two light atoms to form heavier products whose total mass is less than that of the original reactants, takes place at millions of degree Celsius. At such temperatures, the ionized gas with positive and negative charges able to move freely is called plasma. Since no material could withstand a thermal load of this magnitude, the confinement of the superheated gas relies on a strong magnetic field, exploiting the electric nature of plasma. While this procedure is established at laboratory level, its feasibility at the scale of a power plant should been demonstrated. This is the purpose of ITER, the world’s largest experimental fusion facility, sited in the south of France. According to the European Roadmap (https://www.euro-fusion.org/eurofusion/roadmap/), it will be DEMO (DEMOnstration power plant) to show the world that nuclear fusion can produce net electricity, in a safe and reliable way. The knowledge accumulated with ITER will be extremely valuable for the DEMO design and putting into service. Anyway, a considerable difference in size exists between the two facilities and the risk that solutions valid for ITER may not extrapolate to DEMO is serious. To bridge this gap, the realization of intermediate structures, such as the Divertor Tokamak Test facility (DTT) are foreseen, whose operating conditions should be as close as possible to the ones of DEMO (Federici et al. (2016), Mazzitelli et al. (2017), Corato et al. (2016)). As detailed in the DTT Project Proposal (or “ blue book ” ), the DTT will allow to investigate alternative power exhaust solutions for DEMO, whose energy extraction device is called ‘divertor’. Further details on DEMO can be found in Zani et al. (2016) and Corato et al. (2018). The architecture of the DTT consists in a series of superconducting coils, wound by Cable-In-Conduit Conductors (CICCs), constituted of the low temperature superconducting (SC) materials Nb 3 Sn (for the 18 Toroidal Field coils and the 6 Central Solenoid modules) and NbTi (for the 6 Poloidal Field coils). The coils, with a high density of current flowing, generate the magnetic field capable to entrap the plasma within a circuit. Each set of coils (Toroidal, Poloidal and Central Solenoidal) has a different task, preventing the plasma from leaving its trajectory while keeping it in motion. Strong Lorentz forces derive from the interaction of the electricity flowing in the conductors and the magnetic field due to the coils and the moving plasma. A detailed structural analysis is mandatory to design the supports that will carry the afore-mentioned loads originating in the facility. This task relies on the usage of powerful finite element method (FEM) packages, given the extreme complexity of the system under study. Even though the deployment of state-of-the-art numerical tools, the mechanical analysis of a tokamak requires a great effort during both the modelling and analysis stages, often resorting to tailored strategies (Biancolini et al. (2015)). Biancolini et al. (2018) presented a mechanical analysis of a toroidal field coil (TFC) for the DEMO fusion reactor. The heterogeneous structure of Winding Pack (WP) was substituted by an equivalent, smeared material to work around the otherwise excessive computational burden required to analyze such huge mesh model. Local analysis of a restrained portion of the full-detailed geometry is left to the hierarchical approach of stress recovery. Multi-physics analyses, unless conducted within a monolithic solver, require a reliable strategy for data exchange between dedicated codes. In the two last mentioned works, this task is accomplished by radial basis functions (RBF) interpolation (Davis (1963)). Similar RBF applications recur in fluid structure interaction (FSI), for both accurate load (Biancolini et al. (2018)) and displacement (Biancolini et al. (2016)) transfer. Favorable mathematical properties of RBF, such as smoothness and scalability (Buhmann (2004)), make them a good candidate also for mesh morphing (Biancolini (2011)), when the numerical grid should adapt to geometrical modifications. This procedure is particularly advantageous whenever large meshes should be updated, as in the case of computational fluid dynamics (Biancolini et al. (2016)), or when the same grid is subject to repeated changes, e.g. during an optimization process (Groth et al. (2018)). A successful usage of RBF recur in many fields of science and engineering, from image