Automated depletion zone division

Serpent 2 has the capability to perform automated depletion zone division for materials in burnup calculation. There are two options:

• The number of radial regions in 2D pin-type objects can be entered directly in the material card ("Serpent 1" type division).
• The div card can be used to perform 3D depletion zone division.

Both approaches are discussed below. With automated depletion zone division it important to always check the volumes using the Monte Carlo based volume checker routine, and if necessary, define the volumes manually.

Division with divisor card

The div card can be used to separate each cell into its own depletion zone, and further sub-divide pin-type objects into axial-, radial and angular sub-zones. The division takes into account the universe-based geometry structure, so the same cell in two different univeses is treated as two separate cells. For fuel assembly geometries, for example, each pin can be treated as a separate material. If the assembly is put in a core lattice, the same pin in two different assembly positions can be treated separately and so on.

The basic methodology is best illustrated by an example involving a BWR fuel assembly geometry consisting of a 10 x 10 lattice of fuel pins with 13 different fuel types (fuel1, fuel2, ... fuel13):

Simple cell-based division

Defining a div-card for each fuel composition:

div fuel1 sep 1
div fuel2 sep 1
...
div fuel13 sep 1

divides identical compositions into different depletion zones:

Some of the colors in the plot may appear similar, but each regions now contains a different material. The value after the sep-entry defines the geometry level at which the division is performed. Value 1 refers to the last level, which essentially means that all cells in the geometry are handled separately. The use of the sep entry is revisited at the end of this example.

Radial, axial and angular sub-division

Accounting for the depletion of burnable absorber requires radial sub-division, which for pin-type material regions can be done automatically. If it is assumed that the absorber is mixed in fuel types 9-13, sub-division into 10 rings can be done using the subr-entry:

div fuel9  sep 1 subr 10 0.0 4.38E-01
div fuel10 sep 1 subr 10 0.0 4.38E-01
div fuel11 sep 1 subr 10 0.0 4.38E-01
div fuel12 sep 1 subr 10 0.0 4.38E-01
div fuel13 sep 1 subr 10 0.0 4.38E-01

The division is made between 0 and 0.438 cm into 10 rings with equal cross-sectional area:

If necessary, the fuel pins can be further sub-divided into angular sectors using the subs-entry, for example:

div fuel1 sep 1 subs 4 45.0
div fuel2 sep 1 subs 4 45.0
...
div fuel13 sep 1 subr 10 0.0 4.38E-01 subs 4 45.0

The pins are divided into 4 sectors and tilted by 45 degrees:

The axial division works in a similar manner using the subz-enetry, taking the number of axial zones and minimum and maximum coordinate as the input values.

When the divisor card is used, Serpent tries to calculate the sub-zone volumes automatically. Since this may fail, it is always a good idea to check the volumes using the Monte Carlo based volume checker routine, and if necessary, define the them manually.

Division and geometry levels

The division can be used with any configuration, but if the volumes cannot be calculated for the original cells, they cannot be calculated for divisions either.