High-burnup Structure Formation

This model describes the formation of the high-burnup structure (HBS) through a restructuring (phase transformation) law expressed in terms of effective burnup. The model updates the Restructured volume fraction and is enabled through the input option iHighBurnupStructureFormation.

The implementation follows Simulation::HighBurnupStructureFormation().

Activation

The model is executed only if:

  • iHighBurnupStructureFormation > 0

Option summary

  • 0: not considered (no restructuring).

  • 1: HBS formation model from Barani et al. (2020).

Inputs

The model uses:

  • iHighBurnupStructureFormation (input option)

  • Effective burnup (sciantix variable): used as the independent variable for restructuring

  • Effective burnup increment: used as the integration increment

Main output:

  • Restructured volume fraction (sciantix variable)

Model formulation (case 1)

For option 1, the model defines two constants:

  • Avrami constant: \(A = 3.54\)

  • Transformation rate: \(k = 2.77 \times 10^{-7}\)

Two additional parameters are defined in the code:

  • resolution_layer_thickness = \(1.0\times 10^{-9}\) m

  • resolution_critical_distance = \(1.0\times 10^{-9}\) m

Note

In the current implementation of Simulation::HighBurnupStructureFormation(), the two “resolution” parameters are stored in the model parameter vector but are not used in the restructuring update.

Restructuring rate

A burnup-dependent coefficient is computed as:

\[c = A\,k\,B_{\mathrm{eff}}^{2.54}\]

where \(B_{\mathrm{eff}}\) is the effective burnup (Effective burnup).

Update equation

The restructured volume fraction \(\alpha_r\) is updated using solver.Decay(...) with effective burnup increment \(\Delta B_{\mathrm{eff}}\):

\[\alpha_r^{n+1} = \mathrm{Decay}\left(\alpha_r^{n},\; c,\; c,\; \Delta B_{\mathrm{eff}}\right)\]

In other words, the evolution is written in a “decay + source” form with equal coefficients for the decay and source terms, as implemented in the solver.

Reference