KENO V.a Requires Cuboidal Outermost Region to Enable the Use of Albedo Boundary Conditions
In all versions of SCALE, the Monte Carlo code KENO V.a only implements the use of non-vacuum albedo boundary conditions (e.g., mirror, periodic, white) when the outermost geometry region of the model is a cuboidal region. This limitation is noted in the user documentation in the section on Albedo data, where it is stated that “Albedo boundary conditions are applied only to the outermost region of a problem. In KENO V.a this geometry region must be a rectangular parallelepiped.”
It was recently discovered that—beginning with the release of SCALE 6.1 in 2011—KENO V.a will accept non-compliant input that specifies albedo boundary conditions for non-cuboidal outer shapes and will then attempt to complete the calculation. For example, a user can specify a cylinder as the outermost region and add a mirror boundary condition on the top or bottom to effectively double the volume of the system considered. A user could also add a mirror boundary condition to both the top and the bottom of the cylinder to simulate a bounding case of an infinite system. While these scenarios are accepted and perform as expected in KENO-VI, KENO V.a requires the addition of a cuboidal region (typically an empty void region) to enable the use of these albedo boundary conditions.
For calculations using KENO V.a in SCALE 6.1–6.2.2 with non-compliant input in which albedo boundary conditions are applied but without the required cuboidal outermost region, the calculation will proceed without warning, and an underestimation of k-eff often results. The magnitude of underestimation in k-eff can vary widely, depending on the system modeled and the desired boundary conditions, but it can exceed several percent in k-eff.
It is strongly recommended that users who rely on albedo boundary conditions in KENO V.a review their input models to ensure that the outermost region is a cube or cuboid, per the documentation requirement. Note that input models that were generated and applied with SCALE 6 and earlier versions that included the check for the cuboidal outer boundary will continue to produce the expected results with SCALE 6.1–6.2.2.
In testing the extent of this issue by placing mirror boundary conditions on non-cuboidal outer shapes, it was found that cylinders oriented along the x-, y-, or z-axis most often produce non-conservative results without warning. The calculation will terminate prior to completion for cases in which a sphere is the outermost shape. The calculation will terminate with an error message for cases in which a hemicylinder or hemisphere is the outermost shape. The calculation performs as expected for cases in which a cube or cuboid is the outermost shape.
This issue applies to all SCALE 6.1–6.2.2 sequences that implement KENO V.a, including CSAS5, TSUNAMI-3D-K5, T5-DEPL, and STARBUCS. No other SCALE sequences are impacted by this issue. The error condition for the attempted use of albedo boundary conditions on non-cuboidal outer shapes in KENO V.a will be restored in the pending release of SCALE 6.2.3, thus preventing users from inadvertently entering non-compliant input.