Multiscale Nuclear Fuel Analysis via Asymptotic Ex

Multiscale analysis aims to improve predictions at the macro-scale by utilizing high-fidelity models running at a lower length-scale. The lower length-scale models provide a detailed view of the material behavior that is used to determine the average material response to be used at the macro-scale. This approach is especially useful in the nuclear field, since irradiation experiments are difficult and expensive to conduct. The lower length-scale models complement the experiments, reducing the total number of experiments that are needed. Multiscale modeling is a critical part of the BISON-MARMOT fuel performance codes being developed at Idaho National Laboratory (Williamson et al. (2012), Tonks et al. (2010)).

One critical aspect of multiscale modeling is the ability to extract the relevant information from the lower length-scale simulations. One approach, the asymptotic expansion homogenization (AEH) technique (Guedes et al. (1990), Ghosh et al. (1995), Hassani and Hinton (1998), Laschet and Apel (2010), and Oliviera et al. (2011)), has proven to be an effective method for determining homogenized material parameters. The AEH technique prescribes a system of equations to solve at the micro-scale that are used to compute homogenized material constants for use at the macro-scale.

In this work, we employ AEH to explore the effect of evolving microstructural thermal conductivity on nuclear fuel performance. This builds on the work of Tonks et al. (2010) and Williamson et al. (2012), where a direct calculation was used to obtain average thermal conductivity. We show that the AEH approach fits cleanly into the BISON and MARMOT codes and provides a natural, multidimensional homogenization capability.