Customizing the depletion mesh
Instead of fixing the location and distribution of exposure meshes during assembly construction, depletion meshes are used to customize how materials are activated for a given application. A depletion mesh is automatically added when a burn bundle is specified, and is usually defined by the assembly type. One can also add certain custom bundles to any assembly. See Specifying burn bundles.
All depletion meshes are defined by first grouping the discrete fueled primitives into bundles, then subdividing them into smaller radial and axial segments.
Note
When using an homogenized model, the exposure mesh is defined during model construction, and modifying the depletion mesh has no effect.
Attention
When using Monte Carlo codes, the depletion mesh does not affect the flux calculation. The average reaction rates calculated for the burnable material will be correct. The only approximation occurs in how the different elements of the assembly undergo transmutation.
What are fueled primitives?
These are usually defined by the assembly type and/or burn bundle. For example:
Plate fuel assembly have individual plates as fueled primitives,
Pin assemblies have pins as primitives,
The overlay mesh bundle has individual cells as primitives
Since assemblies can have more than one burn bundle, it can also have more than one type of primitive. For example, in the Plate assembly with burnable absorbers, the fuel_bundle has plates as primitives, while the ba_bundle has wires as primitives.
Note
The term fueled primitive is a bit misleading, as it actually refers to any structure with transmutable material, and not only fissionable parts of an assembly.
Grouping primitives into bundles
The first step in defining the depletion mesh, is to set how individual primitives should be grouped into separate bundles. All primitives in a bundle will be activated with a single set of average reaction rates, and they share a single burnable material.
-
bundles
: list
Primitives are grouped by assigning an integer in \([0, B-1]\) to each primitive. Here \(B\) is the total number of bundles. How these integers are assigned, depends on the bundle type. See for instance Depletion meshes for plate type assemblies, Depletion meshes for pin type assemblies.
The core.depletion_mesh contains some tags for specifying simple bundle grouping. For example,
asm.burn_bundle[bundle_tags.fuel].depletion_mesh.bundles = grouping_tags.all_separate
will place each primitive in its own bundle, and
asm.burn_bundle[bundle_tags.fuel].depletion_mesh.bundles = grouping_tags.all_together
will place all primitives in a single bundle.
How primitives are indexed depends on the burn bundle. Plates are always indexed using arrays, pins using two dimensional grids, etc. More information on how to specify bundles for a particular assembly type can be found in the assemblies documentation.
Attention
Since further subdivision is performed per bundle, it is important that each bundle contains primitives of the same type and size.
Radial meshing
Each bundle can be further subdivided into radial segments.
-
segments
: list
Defines how each bundle should be segmented radially. This is specified with a list of fractions for each bundle. For example, if there are three bundles,
asm.burn_bundle[bundle_tags.fuel].depletion_mesh.segments = [[0.25, 0.5, 0.25]] * 3
will divide each primitive in each bundle into three radial segments, of size 25%, 50% and 25% of the total radial area. The shape of the radial segments depend on the primitive:
Plates are segmented into pieces along the length of the plate.
Pins, wires, and annular regions are segmented into radial rings.
If left at its default value, no radial subdivision will be performed.
Attention
The number of entries must be equal to the number of bundles.
Axial meshing
Subdivide each bundle into axial segments.
- axial_layers
Defines the axial depletion mesh. If a single integer \(n\), each bundle will be subdivided into \(n\) equal pieces. Otherwise, a list of fraction per bundle must be specified, similar to the notation used in
segments:asm.burn_bundle[bundle_tags.fuel].depletion_mesh.axial_layers = [[0.25, 0.25, 0.25, 0.25]] * 3
The resulting material mesh
The final number of burnable materials generated is:
where \(S_b\) and \(A_b\) are the number of radial and axial segments for bundle \(b\).
Attention
The amount of storage used by assembly inventories scales linearly with the number of depletion meshes, and it will also take significantly more time to write input files, and read data from output files. Many target codes will also have a limit on the number of burnable materials it or your computing hardware can support. When using Monte Carlo codes, there is also the possibility that estimated reaction rates will not be well converged on very detailed depletion meshes.
With the currently available tools, it is recommended to only use detailed (per primitive) depletion meshes for assembly level applications such as exposure and lattice calculations. When moving to core calculations, a courser mesh (usually only axial segmentation and a limited number of radial subdivisions) should be used.