A suitable reactor model had to be selected for testing the Serpent-Ants-Serpent calculation sequence. So far, Ants has been mainly verified and validated in PWR geometries. Again, to eliminate additional uncertainties, the PWR reactor type was chosen for micro depletion testing. This way the work could focus on studying the micro depletion itself knowing that the two-step neutronics solution should give decent results in the selected geometry. Besides, the work could build on existing workflows and input files.
The PWR core design used in this thesis is based on a simplified version of an SMR core used in [33]. The model is based on NuScale licensing documents [37]
with fuel specifications from the BEAVRS benchmark [34]. Fuel assembly spacers, instrumentation equipment, and control rods were removed to reduce the required number of calculations for homogenization. The first two simplifications have only slight effects locally and they do not have any major impact on fuel depletion itself.
Control rods have a more crucial role in reactor physics. However, PWR cores can be operated with control rods fully withdrawn and the excess reactivity is compensated with boron shim. Thus the full-power fuel cycle could be simulated without control rods.
Fuel depletion was additionally calculated in a simple two-dimensional infinite fuel assembly lattice. Nevertheless, this section focuses on the SMR core description starting from the pin level and ending up with the full-core model. Two-dimensional single-assembly models relied on identical pin and assembly geometries. The main difference to the full-core model is the limited geometry and reflective boundary conditions. Thus, describing the geometry of the full core will include all essential features of the two-dimensional assembly models.
3.2.1 Pins
The reactor core is composed of fuel assemblies and they are further composed of pin- level structures. The modeled geometry has three main types of pins: uranium oxide fuel pins, control rod (CR) guide tubes, and borosilicate glass rods. Specifications of these three different pin types are presented in figure3.2. All pins are surrounded by borated water.
Only fuel and borosilicate glass materials are set as burnable in depletion cal- culations. Each fuel pin and burnable poison rod is depleted individually and they are further divided into sub-regions. Each fuel pin has a 0.3 mm thick rim region defined as a separate burnup zone, thus resulting in two burnup regions radially.
Borosilicate glass rods are divided radially into 5 burnup zones with equal volume.
In 3D geometries, both fuel and burnable absorber rods are further divided axially into 20 cm long regions.
These three pins are enough for describing the fundamental pieces of the reactor core. As mentioned earlier, control rods are not required in the studied fuel cycle simulation thus they are not modeled. Some pin-level descriptions are required for modeling the non-active regions above and below fuel rods in the 3D core and they
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are described in the BEAVRS benchmark [34]. In addition, fuel rods have a varying enrichment of the fissile isotope 235U depending on the fuel assembly type.
Fuel rod
Material ∆R (mm)
Fuel 3.9218
Helium 0.0787
Zirconium alloy 0.5715 Total radius 4.5720
CR guide tube
Material ∆R (mm)
Water 5.6134
Zirconium alloy 0.4064 Total radius 6.0198
Borosilicate glass rod
Material ∆R (mm)
Air 2.1400
Steel 0.1651
Helium 0.1079
Borosilicate glass 1.8542
Helium 0.1016
Steel 0.4699
Total radius 4.8387
Figure 3.2: The three main pin structures are constructed from nested cylindrical surfaces.
Each material is represented by a different color and they are listed in adjacent tables starting from the center of the pin. The thickness of the material layer is given in the second column. The borosilicate glass rod is inserted into a control rod guide tube. The subdivision of fuel and borosilicate glass into burnable regions is also drawn with black circles. Material compositions are given in appendixA.
3.2.2 Assemblies
The next level in the geometry is composed of fuel assemblies. A total of seven different types of fuel assemblies were modeled with varying number of burnable absorber rods and different enrichments. All fuel assembly variations are shown in figure 3.3. Assemblies are composed of 17x17 rectangular lattice structures with 264 fuel rods and 25 control rod guide tubes. The CR guide tube in the center of the assembly is used for instrumentation, but none of the modelled assemblies had any instrumentation equipment. The lattice pitch is 1.25984 cm thus the total width of an assembly is 21.41728 cm.
Figure 3.3: All modelled fuel assemblies with varying level of enrichment and number of burnable absorber rods. Each color indicates different level of enrichment and they are in ascending order: red 1.6 wt%, yellow 2.4 wt%, blue 3.1 wt%, green 3.2 wt%, and orange 3.4 wt%. Assemblies at the bottom row have burnable absorber rods inserted into control rod guide tubes.
3.2.3 Full core model
The final level of the geometry is the reactor composed of a radial reflector and fuel assemblies. The core contains 37 fuel assemblies in a rectangular lattice as shown in figure 3.4a. The lattice pitch is 21.50364 cm which is only slightly larger than the width of a fuel assembly. The reactor core is surrounded by a cylindrical radial reflector with a diameter of 188.00 cm. The reflector material is composed of a mixture of water and stainless steel with 7.85 % and 92.15 % volume fractions respectively.
The model extends radially by an additional 43.16 cm before the boundary and the gap is filled with water.
The axial structure of the reactor is shown in figure 3.4b. From the bottom to the top the reactor core structure is the following: core bottom support plate, fuel
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(a) Horizontal cross section of the SMR core (b) Vertical cross section of the SMR core
16 20 20
20 20
16 16
16
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(c)Horizontal cross section of the homogeneous SMR core.
(d) Vertical cross section of the homogeneous SMR core
Figure 3.4: Full core geometry cross-section images in both heterogeneous and homoge- neous geometries. The light blue color represents water and the cyan color represents the radial reflector in the heterogeneous model. Fuel assembly colors are consistent with their descriptions in figure3.3. Node materials in the homogeneous geometry correspond to their counterparts illustrated with gray lines in the heterogeneous reactor. Numbers in figure 3.4cindicate the number of burnable absorber rods in the assembly. Vertical cross-section images are not in scale and the division of fuel into ten axial nodes is not shown.
rod bottom plugs, active fuel, fuel rod plenum, fuel top plugs, and reactor top nozzle.
The height of the active fuel is 200.00 cm and the total height of the core is 246.116 cm. The geometry is extended from the bottom by 20.0 cm and the top by 28.124 cm similar to the radial geometry.
The heterogeneous model of the reactor is depleted with Serpent calculations.
However, Ants relies on a homogenized model shown in figure3.4c and 3.4d. The main difference is that the sub-assembly level spatial detail is lost and material regions are represented by homogenized nodes. Radially the homogeneous model is composed of a square lattice with 9x9 nodes with a 21.50364 cm width. Axially the active fuel is composed of ten 20.0 cm high blocks. Radial reflectors extend from the bottom to the top of the geometry. Regions below the core are represented by two axial reflectors and above the core by three axial reflectors. These reflectors are not divided radially into different regions.
Despite the reactor model is simple, it provides essential features for studying fuel depletion in a small pressurized water reactor. The small size of the core makes the depletion with Monte Carlo approachable by reducing the required number of simulated histories to get decent statistics for a reference solution. A small core poses an additional challenge for the diffusion method itself as the modeling of reflectors and neutron leakage is emphasized compared to a large core. The homogenization process itself is similar regardless of the size of the core. The spatial homogenization of the reactor is described in the following section.