Densification

This model accounts for fuel densification during irradiation, represented as a progressive reduction of the fabrication porosity towards a residual porosity. Densification is enabled through the input option iDensification and is driven by burnup.

Reference

Van Uffelen, P. (2002), PhD thesis, SCK•CEN Reports No. BLG-907. https://www.oecd-nea.org/science/wprs/fuel/Thesis_Van_Uffelen_BLG.pdf

Activation

If iDensification = 0, the model is not considered and no updates are performed. If iDensification = 1, densification is calculated according to a fit based on temperature.

Inputs

The model uses:

  • iDensification (input option)

  • Temperature (history variable)

  • Burnup increment (sciantix variable, used as the evolution variable)

  • Residual porosity (sciantix variable)

  • Fabrication porosity (sciantix variable)

Model formulation

A densification factor \(f_{\mathrm{dens}}\) is evolved with burnup using an exponential decay law (implemented through solver.Decay). For the default correlation (iDensification = 1), the parameters are:

  • \(a = 2.0\)

  • \(b = 0.006 \exp\!\left(0.002\,T\right)\)

where \(T\) is the fuel temperature.

The densification factor is bounded by:

\[f_{\mathrm{dens}} \le 1\]

Porosity update

The fabrication porosity is updated as a transition from its current value towards the residual porosity:

\[\varepsilon_{\mathrm{fab}} = \varepsilon_{\mathrm{res}} + \left(\varepsilon_{\mathrm{fab}} - \varepsilon_{\mathrm{res}}\right) \left(1 - f_{\mathrm{dens}}\right)\]

The total porosity is then incremented using the fabrication-porosity increment.

Outputs

The model updates:

  • Densification factor

  • Fabrication porosity

  • Porosity (incremented by the fabrication porosity increment)