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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2. FEM analysis and results

The DTT is an extremely complex machine where different physical mechanisms interact and influence each other. A comprehensive analysis of the facility should embrace different engineering fields, from heat transfer to manufacture and maintenance issues. As regards the work presented in this paper, electromagnetism and structural mechanics are the main disciplines involved, requiring a reliable data transfer between dedicated software. Numerical code TOSCA® supplied the components of the magnetic field (initial time instant t = 0 s of the Single Null scenario, when only the 18 TF coils are fed) acting at the nodes of a regular grid occupying the same volume of the WP. An operative current of 44 kA passes through each conductor cable. The density of force per volume ⃗⃗⃗⃗ ⃗ ( ) is computed at the nodes of the regular mesh, where the pointwise current density ( ) and magnetic field ⃗ ( ) are given. According to the notorious Loren tz’s cross product, we have: ⃗ ⃗⃗⃗ ⃗ ( ) = ( ) × ⃗ ( ) (1) The mapping procedure embedded in ANSYS® Workbench™ works according to a proximity criterion: for each target node, the surrounding source points are considered and a value is assigned on a distance basis. This automatic workflow allowed shifting the computed forces per volume to the nodes of the structural mesh for the stress assessment. Fig. 2 shows the process employed in Workbench to load the model geometry and the force densities as external data. The information flow is represented with the threads connecting the different modules. The comparison between the force resultants calculated over the source grid and over the FEM mesh demonstrated the reliability of the mapping procedure. In the case of study, the total force loading the structure presented a component along y exceeding in several orders of magnitude the x and z components, Table 1 shows that data transfer satisfied force balance with an error on the force resultant lower than 1%.

Fig. 2. Workflow used to load the force densities as an external data file.

Table 1. Force components calculated over the source grid and over the FEM mesh. Force resultant component Source value Target value F X [N] 10.7 -8153.6 F Y [N] - 5.44∙10 7 - 5.40∙10 7 F Z [N] 308.4 -6933.7

The mechanical analysis consisted of two steps: i) temperature drop from 293 K to 4.2 K with no external loads active (cool down), ii) at the temperature of 4.2 K, introduction of the electromagnetic loads. At the considered instant of the Single Null scenario, the resultant force acting on the WP is purely centripetal, while the distribution of force is symmetric with respect to the mid-plane containing the coil loop. Only one coil constitutes the FEM model adopted for the study here proposed: a constraint of cyclic symmetry between the outer surfaces of the represented structure simulates the interaction with the adjacent bodies belonging to the repetitive pattern. A single support preventing the vertical and toroidal displacements of the pedestal basis rounds off the constraint set.