Model Investigation: CS Tresca Stress Tresca yield criterion

[grmtrkngtn]

Context

As part of a review into PROCESS, we evaluated the Large Tokamak input file to find active constraints. This was done to aid prioritization of model development.

This reveled that the CS Tresca yield criterion was a limiting factor (constraint equation 072).

Task

We want to investigate this model to understand it better:

- Does the model make sense in isolation? Is it continuous are or there discontinuties?
- Run the model in isolation for realistic values and plot the results
- Has the model been bench marked against anything (experiments, literature, other codes) ?
- Does the documentation reflect what it is doing?

Outcome

Document model behaviour and determine whether improvements are required and the scale of them.

[mkovari]

There are numerous files called large tokamak. Please attach the input and output files. @ym1906

[mkovari]

As the CS is pulsed, I would expect it would fail in fatigue, not yield. Therefore, if the CS fatigue constraint is turned on, and working correctly, I would expect that constraint would be active, not the Tresca yield criterion.

Note that I doubt the CS fatigue model in the code is consistent with the documentation, so don't rely on that.

[mkovari]

I would certainly be happy if this was removed:

[mkovari]

I have a suspicion the pre-compression is not taken into account.

[grmtrkngtn]

I would certainly be happy if this was removed:

It seems odd to have a line in our docs that says something has no physical justification.

[grmtrkngtn]

I looked at the models involved in constraint 72:

• Hoop stress is computed from Wilson (1983), axial stress from Iwasa (1994).
• Radial stress neglected.
• Combined via Tresca maximum shear criterion:

$$ \sigma_{\text{Tresca}} = \max \left( \left| \sigma_{\text{hoop}} - \sigma_{z} \right|,, \left| \sigma_{z} \right|,, \left| \sigma_{\text{hoop}} \right| \right) $$

Results from isolated runs and plots

• Hoop stress (Wilson): decreases smoothly across thickness.

• • **Axial stress (Iwasa): compressive, decreases in magnitude with coil half-height

And the tresca equivalent calculation is trivial to verify.

4. Has the model been benchmarked?

The formulations are directly taken from Wilson and Iwasa, both widely cited magnet design references.

Overall

[grmtrkngtn]

@mkovari do you have any other comments on this issue or want to take any actions?

I think the model itself is fine

[mkovari]

These results don't look right.

Is the CS 1.4 m thick? That's a lot.
The axial stress plot I don't even understand.
Could you share the full set of files used for these plots?

[grmtrkngtn]

These plots were produced using standalone versions of the stress equations with simplified toy inputs, just to verify behaviour (monotonicity, sign conventions, continuity). The point is to evaluate the models in isolation, we're not looking at specific outcome for a specific machine

[mkovari]

OK, that's a relief. I am still not sure I understand the plots.

[mkovari]

As I mentioned, I would expect the CS to fail in fatigue, not yield. Therefore, if the CS fatigue constraint is turned on, and working correctly, I would expect that constraint would be active, not the Tresca yield criterion.

[grmtrkngtn]

I think that’s a separate issue, beyond the scope of this papercut - this review is focused on the model formulation itself, rather than on why the constraint becomes active in a given example.

[mkovari]

I would certainly be happy if the axial stress was always taken into account.
However, we then need to understand why our resulting max shear stress is so much bigger than other people's.