Bucked and wedged TF design

In GitLab by @skahn on Mar 24, 2020, 10:58

Design description

The bucked and wedged TF design uses the CS as support structure for the TF coil. Peter Titus, PPPL ingeneer current team lead, has recently presented simplified model results and finite analysis comparison including the bucked and wedged solution, in the following presentation

FESS_Meeting_March_20_2020__Titus.pptx

and the spreadsheet calculation

TITUS_TF_stress_2018_FNSF_Baseline_plus_ARIES_RS_ITER_KDEMOComparison.xlsx

Model description

This very simple model proposed by Peter Titus, adds additionnal layer to the stress modelling, representing the CS.

The stress is calculated for the worst case, i.e. at the flux swing where the CS is generating no favorable outward pressure. The CS-TF shear stress calculations are not considered at the moment, even though they may play a significant role in the design.

This might be the next step of a bucked and wedge model

Case of a superconducting CS

In the case of a CS, we need to take the WP turn structure. Here is a proposal for a the effective young modulus.

Hypothesis : The dominant direction int the material of the material is the toroidal.
This hypothese is motivated by the result of J. Last last report attached here, where an
orthotropic anysotropy stress analysis has been performed. The effect if the variation of
the young modulus on the final stress on section 4.3.
tf_coil_forces___stress_progress_4.pdf

With this hypothesis, the effective young modulus $\overline{E}$ of the isotropic plane stress model is calculated using parallel smearing

$\overline{E} = f_\mathrm{steel}E_\mathrm{steel} + (1-f_\mathrm{steel})E_\mathrm{cable}$

with $f_\mathrm{steel}$ the volumic steel fraction in the CS.

Rem: I am not sure the volumic steel fraction is the right fraction to be used in this case. Maybe the steel surface fraction in the $(r,z)$ plane.

Once the calcultions done two unsmearing are necessay :

• To get the steel toroidal stress (parrallel) : $\sigma_\theta = \frac{\overline{\sigma_\theta}}{f_\mathrm{steel}}$
• To get the steel radial stress (series) : $\sigma_r = \frac{t_\mathrm{turn}}{2t_\mathrm{steel}}\overline{\sigma_r}$. This calculation is performed neglecting the presence of an insulator layer for simplicity.

with $t_\mathrm{turn} = \sqrt{A_\mathrm{turn}}$, and $A_\mathrm{turn}$ being already calculated in the pfcoil.f90 code section. $t_\mathrm{turn}$ is calculated assuming a
square turn geometry and an insulation thickness of the TF turn insulation (as both TF and CS turns are design to be able to carry currents around the maximum current density limit).

Assuming square turn geometry, we get

$t_\mathrm{steel} = \frac{t_\mathrm{turn} - 2t_\mathrm{ins} - \sqrt{(2t_\mathrm{ins} - t_\mathrm{turn})^2 - f_\mathrm{steel}t_\mathrm{turn}^2 } }{2}$

The unsmeared values has to be used to calculate the steel stress limits on the CS.

The maximium CS stress also takes the maximum value of the stress calculated at flux swing. So CS stress on the constraints equations is

$\sigma_\mathrm{CS} = \max{(\sigma_\mathrm{hoop},\sigma_\mathrm{bucked and weged}})$

with $\sigma_\mathrm{hoop}$ the stress calculated in the pfcoil.f90 module at maximum current in CS, and $\sigma_\mathrm{bucked and weged}$ the stress in the CS due to the TF compressing force at CS flux swing (no current in the CS).

Model new inputs

The only new inputs are the properties CS-TF layer properties. The layer is supposed to be made of Kapton for now :

$E_\mathrm{Kapton} = 2.5 GPa$
$\alpha_\mathrm{Kapton} = 0.34$
$\mathrm{Yield\ point} = 69 MPa$

$E_\mathrm{Kapton}$ and $\alpha_\mathrm{Kapton}$ are currently had-coded

Ref : https://www.dupont.com/content/dam/dupont/products-and-services/membranes-and-films/polyimde-films/documents/DEC-Kapton-summary-of-properties.pdf

First results

This simplified model has been implemented in the PROCESS branch https://git.ccfe.ac.uk/process/process/tree/issue-1031-bucked-and-wedged. Here are the results on the DEMO 2018 baseline.

The modifications are the following :

• Bucked and wedged option
• CS precompressor removed
• TF-CS gap decreased to 10 cm (as suggested by Peter's plot)

Here is the radial profile of the stress obtained on the DEMO 2018 optimisation case:

Bucked and wedged DEMO optimisation

The casing and the winding pack has significantly been reduced, allowing the baseline to
be reduced from $R_\mathrm{maj} = 9.17$ to $R_\mathrm{maj} = 8.57$. We can observe
that the aspect ratio has to be modified for that

Initial DEMO design (for comparison)

Case of the resisitive models

The resitive models currently uses the generalized plane strain formulation. This formulation has been initially setup for bonded layers, shearing the vertical strain. This is impossible for the CS - TF layer, as the CS vertically compresses and the TF vertically expands. A layer allowing sliding is necessary. For the stress calcualtions, it means that the TF vertical forces does not transvers to the CS ones. For this the stress calculations must be modified.
This has been done by setting the "generalized plane strain coeficients" in the boundary conditions matrix to 0 for the CS layer and not including the CS layers in the "generalized plane strain coeficients" containing a sum in all layers.

Best regards
Sebastien Kahn

Ref: @mkovari, @stuartmuldrew, @jmorris-uk

Start by reviewing the design description, the issue-1031-bucked-and-wedged branch, and the pfcoil.f90 references. Compare the superconducting and resistive model requirements with the attached calculations and first results. Done means the bucked-and-wedged stress model, inputs, and boundary-condition changes are implemented and reproduce the described results.