Effective Burnup

This model computes an effective burnup that accumulates only when the fuel temperature is below a threshold. The intent is to represent burnup-driven effects that are assumed to be active primarily at relatively low temperature.

Reference

  1. Khvostov et al., WRFPM-2005, Kyoto, Japan, 2005.

Inputs

The model uses:

  • Temperature (history variable)

  • Specific power (sciantix variable)

  • Time step (physics variable)

Model formulation

A temperature threshold is defined as:

\[T_{\mathrm{th}} = 1273.15~\mathrm{K}\]

The effective burnup rate is taken equal to the burnup rate when either:

  • the current temperature is below the threshold, or

  • the temperature crosses the threshold within the current step (from below to above).

Otherwise, the effective burnup rate is set to zero:

\[\begin{split}\dot{B}_{\mathrm{eff}} = \begin{cases} \dfrac{P_{\mathrm{spec}}}{86400} & \text{if } T \le T_{\mathrm{th}} \text{ or } (T > T_{\mathrm{th}} \ \wedge \ T^{n} < T_{\mathrm{th}}) \\ 0 & \text{otherwise} \end{cases}\end{split}\]

where \(P_{\mathrm{spec}}\) is the specific power.

Time integration

The effective burnup is updated by time integration:

\[B_{\mathrm{eff}}^{n+1} = B_{\mathrm{eff}}^{n} + \dot{B}_{\mathrm{eff}}\,\Delta t\]

In the implementation this is performed using solver.Integrator with the current Time step.