SEFOR Mesh Model for Core I-E

The MOOSE Reactor Module was used to set up geometry for Griffin calculations. To accurately model the heterogeneous SEFOR core, several specialized mesh generators within the Reactor Module were utilized (Shemon et al., 2023). As depicted in Listing 1, the cylindrical reactor components, specifically fuel pins, insulators, support-rods, and absorber pins, were generated using the AdvancedConcentricCircleGenerator mesh generator.

Listing 1: MOOSE Reactor Module input for modeling a single fuel pin.

[Mesh]
  [std_fuel_pin]
    type = AdvancedConcentricCircleGenerator
    num_sectors = ${accg_num_sectors}
    #                       fuel     gap     ss316
    ring_radii = '1.11426  1.13331 1.23518'
    ring_intervals = '2        1       1'
    ring_block_ids = '110 111  112     113'
    preserve_volumes = on
  []
[]
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)

Listing 2 shows that the HexagonConcentricCircleAdaptiveBoundaryMeshGenerator was used for the central tightener pin and its surrounding duct, which provides adaptive boundary meshing optimized for hexagonal structures.

Listing 2: MOOSE Reactor Module input for forming the central rod and its tightener.

[Mesh]
  [std_central_pin_w_duct]
    type = HexagonConcentricCircleAdaptiveBoundaryMeshGenerator
    num_sectors_per_side = ${hmg_num_sector_per_side}
    hexagon_size = 1.31158
    #                       beo     gap     ss316
    ring_radii = '0.98942 1.01239 1.11426'
    ring_intervals = '2       1       1'
    ring_block_ids = '114 115 116     117'
    background_intervals = 1
    background_block_ids = '118'
    duct_sizes = '1.22244'
    duct_sizes_style = apothem
    duct_block_ids = '119'
    duct_intervals = '1'
    flat_side_up = true
    preserve_volumes = on
  []
[]
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)

Following this, the fuel assemblies, including their ducts and assembly gaps, were defined using the FlexiblePatternGenerator mesh generator as illustrated in Listing 3, which supports different assembly types. The generated mesh of the different types of fuel assemblies is shown in Figure 1 .

Listing 3: MOOSE Reactor Module input for forming a standard fuel assembly.

  [std_assm]
    type   = FlexiblePatternGenerator
    inputs = 'std_fuel_pin std_wire std_central_pin_w_duct'
    use_auto_area_func = true
    boundary_type    = hexagon
    boundary_sectors = ${num_boundary_sectors}
    boundary_size    = 7.71667
    circular_patterns  = '0 0 0 0 0 0;
                          1 1 1 1 1 1'
    circular_radii     = '2.78130 3.47540'
    circular_rotations = '90 0'
#                                Na
    background_subdomain_id   = '121'
    extra_positions            = '0.0 0.0 0.0'
    extra_positions_mg_indices = '2'
  []
  [std_assm_w_duct]
    type   = FlexiblePatternGenerator
    inputs = 'std_assm'
    use_auto_area_func = true
    boundary_type    = hexagon
    boundary_sectors = ${num_boundary_sectors}
    boundary_size    = 8.02228
#                                Duct
    background_subdomain_id   = '122'
    extra_positions            = '0.0 0.0 0.0'
    extra_positions_mg_indices = '0'
  []
  [std_assm_w_duct_gap]
    type = FlexiblePatternGenerator
    inputs = 'std_assm_w_duct'
    use_auto_area_func = true
    boundary_type    = hexagon
    boundary_sectors = ${num_boundary_sectors}
    boundary_size    = 8.04775
#                                Na
    background_subdomain_id   = '123'
    extra_positions            = '0.0 0.0 0.0'
    extra_positions_mg_indices = '0'
  []

###############################################################################
#   Fuel Assembly with 2 Guinea Pigs
###############################################################################
##  Fuel pin
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)
Mesh model of SEFOR Core I-E fuel assemblies: (a) Standard Assembly (SA), (b) SA with a GP rod and a B<sub>4<sub>C rod, (c) SA with 2 GP rods, and (d) AFA

Figure 1: Mesh model of SEFOR Core I-E fuel assemblies: (a) Standard Assembly (SA), (b) SA with a GP rod and a B<sub>4<sub>C rod, (c) SA with 2 GP rods, and (d) AFA

These assemblies were arranged into the complete reactor core layout using the PatternedHexMeshGenerator mesh generator as illustrated in Listing 4.

Listing 4: MOOSE Reactor Module input for forming the fuel core lattice from the assembly meshes.

[Mesh]
  [pattern_core]
    type = PatternedHexMeshGenerator
    inputs = 'fred_w_duct_gap   std_assm_w_duct_gap assm12_w_duct_gap
              assm13_w_duct_gap assm21_w_duct_gap   assm23_w_duct_gap
              assm24_w_duct_gap assm25_w_duct_gap   assm41_w_duct_gap
              assm42_w_duct_gap assm43_w_duct_gap   dummy'
    pattern_boundary = none
    generate_core_metadata = true

    pattern = '              11  11  11  11  11  11  11  11  11;
                           11  11  11  11  11  11  11  11  11  11;
                         11  11  11  11  1   1   1   11  11  11  11;
                       11  11  11  1   1   1   7   1   1   11  11  11;
                     11  11  1   1   4   1   3   1   1   1   1   11  11;
                   11  11  1   1   1   1   1   1   1   1   5   1   11  11;
                 11  11  1   1   1   1   1   5   1    9  1   1   1   11  11;
               11  11  11  1   1   8   1   1   1   1   1   6   1   11  11  11;
             11  11  11  1   4   1   1   1   0   1   1   1   1   1   11  11  11;
               11  11  11  1   1   1   1   1   1   4   1   1   1   11  11  11;
                 11  11  1   1   2   1   5   1   1   1   1   7   1   11  11;
                   11  11  1   1   1   1   1   10  1   1   1   1   11  11;
                     11  11  1   1   1   1   1   1   5   1   1   11  11;
                       11  11  11  1   1   4   1   1   1   11  11  11;
                         11  11  11  11  1   1   1   11  11  11  11;
                           11  11  11  11  11  11  11  11  11  11;
                             11  11  11  11  11  11  11  11  11'
  []
[]
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)

Additionally, peripheral reactor regions such as the downcomer, outer vessel, radial reflector, and radial shield were integrated with the core using the PeripheralRingMeshGenerator mesh generator shown in Listing 5. At this stage, the reactor mesh represented a 2-D configuration as illustrated in Figure 2 (a).

Listing 5: MOOSE Reactor Module input for forming radial layers outside the fuel lattice.

  [del_dummy]
    type = BlockDeletionGenerator
    input = 'pattern_core'
    block = '999'
    new_boundary = 10000
  []

  [downcomer_iv]
    type = PeripheralRingMeshGenerator
    input = 'del_dummy'

    peripheral_layer_num   = 2
    peripheral_ring_radius = 53.486
    peripheral_ring_block_id =  '601'
    input_mesh_external_boundary = 10000
  []

  [downcomer_ov]
    type = PeripheralRingMeshGenerator
    input = 'downcomer_iv'

    peripheral_layer_num   = 1
    peripheral_ring_radius = 58.4860
    peripheral_ring_block_id =  '602'
    input_mesh_external_boundary = 10000
  []

  [radial_reflector]
    type = PeripheralRingMeshGenerator
    input = 'downcomer_ov'

    peripheral_layer_num   = 2
    peripheral_ring_radius = 73.5530
    peripheral_ring_block_id =  '603'
    input_mesh_external_boundary = 10000
  []

  [radial_shield]
    type = PeripheralRingMeshGenerator
    input = 'radial_reflector'

    peripheral_layer_num   = 1
    peripheral_ring_radius = 87.0340
    peripheral_ring_block_id =  '604'
    input_mesh_external_boundary = 10000
  []
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)
Mesh model of SEFOR Core I-E with (a) X-Y view (b) X-Z view

Figure 2: Mesh model of SEFOR Core I-E with (a) X-Y view (b) X-Z view

To expand this into a complete 3-D reactor geometry, the AdvancedExtruderGenerator mesh generator was employed as shown in Listing 6, which allowed flexible axial extrusion of the existing 2-D mesh into the full axial height. This mesh generator also offers functionality to interchange or redefine axial regions, to enable accurate representation of complex axial geometry variations in the SEFOR reactor core . The 3-D axial core mesh depicted Core I-E in Figure 2 (b).

Listing 6: MOOSE Reactor Module input for extruding the 2D radial core into a 3D, assigning axial segments as needed.

[Mesh]
  [core_3d]
    type = AdvancedExtruderGenerator
    input = 'radial_shield'

    heights = '30.745  10.7870 0.9525 52.4291 0.9525 3.2820 0.9525 33.5227 0.7775 0.0962 0.0788 10.7082 0.0788 20.2390'
    num_layers = '6       2       1      10      1      1      1      7       1      1      1      2       1      4'
    direction = '0 0 1'
    #                       First axial to last axial, separated by ;
    subdomain_swaps = ' 110 1001  111 1002  112 1002  113 1002  114 1001  115 1002  116 1002  117 1002  118 1002  119 1002  120 1001  121 1001  122 1001  123 1001
                        210 1001  211 1002  212 1001  213 1002  214 1002  215 1002  216 1001  217 1002  218 1002  219 1002  220 1002  221 1002  222 1001  223 1001  224 1001  225 1001
                        310 1001  311 1002  312 1002  313 1002  314 1001  315 1002  316 1002  317 1002  318 1001  319 1002  320 1002  321 1002  322 1002  323 1002  324 1001  325 1001  326 1001  327 1001
                        410 1001  411 1002  412 1001  413 1002  414 1002  415 1002  416 1001  417 1002  418 1002  419 1002  420 1001  421 1002  422 1002  423 1002  424 1002  425 1002  426 1001  427 1001  428 1001  429 1001
                        510 1001  511 1002  512 1002  513 1001  514 1001  515 1001
                        603 605;

                        110 170   111 171   112 172   113 173   114 174   115 175   116 176   117 177   118 178   119 179   120 180   121 181   122 182   123 183
                        210 170   211 171   212 170   213 171   214 172   215 173   216 174   217 175   218 176   219 177   220 178   221 179   222 180   223 181   224 182   225 183
                        310 370   311 371   312 372   313 373   314 374   315 375   316 376   317 377   318 378   319 379   320 380   321 381   322 382   323 383   324 384   325 385   326 386   327 387
                        410 370   411 371   412 370   413 371   414 372   415 373   416 374   417 375   418 376   419 377   420 378   421 379   422 380   423 381   424 382   425 383   426 384   427 385   428 386   429 387;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 336   317 337   318 338   319 339   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 336   419 337   420 338   421 339   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        ;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 336   317 337   318 338   319 339   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 336   419 337   420 338   421 339   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        110 150   111 151   112 152   113 153   114 154   115 155   116 156   117 157   118 158   119 159   120 160   121 161   122 162   123 163
                        210 150   211 151   212 150   213 151   214 152   215 153   216 154   217 155   218 156   219 157   220 158   221 159   222 160   223 161   224 162   225 163
                        310 350   311 351   312 352   313 353   314 354   315 355   316 356   317 357   318 358   319 359   320 360   321 361   322 362   323 363   324 364   325 365   326 366   327 367
                        410 350   411 351   412 350   413 351   414 352   415 353   416 354   417 355   418 356   419 357   420 358   421 359   422 360   423 361   424 362   425 363   426 364   427 365   428 366   429 367;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 336   317 337   318 338   319 339   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 336   419 337   420 338   421 339   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        ;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 336   317 337   318 338   319 339   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 336   419 337   420 338   421 339   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 395   317 337   318 338   319 339   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 395   419 337   420 338   421 339   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        110 130   111 131   112 132   113 133   114 134   115 135   116 136   117 137   118 138   119 139   120 140   121 141   122 142   123 143
                        210 130   211 131   212 130   213 131   214 132   215 133   216 134   217 135   218 136   219 137   220 138   221 139   222 140   223 141   224 142   225 143
                        310 330   311 331   312 332   313 333   314 334   315 335   316 395   317 337   318 378   319 379   320 340   321 341   322 342   323 343   324 344   325 345   326 346   327 347
                        410 330   411 331   412 330   413 331   414 332   415 333   416 334   417 335   418 395   419 337   420 378   421 379   422 340   423 341   424 342   425 343   426 344   427 345   428 346   429 347;

                        110 170   111 171   112 172   113 173   114 174   115 175   116 176   117 177   118 178   119 179   120 180   121 181   122 182   123 183
                        210 170   211 171   212 170   213 171   214 172   215 173   216 174   217 175   218 176   219 177   220 178   221 179   222 180   223 181   224 182   225 183
                        310 370   311 371   312 372   313 373   314 374   315 375   316 376   317 377   318 378   319 379   320 380   321 381   322 382   323 383   324 384   325 385   326 386   327 387
                        410 370   411 371   412 370   413 371   414 372   415 373   416 374   417 375   418 376   419 377   420 378   421 379   422 380   423 381   424 382   425 383   426 384   427 385   428 386   429 387;

                        110 170   111 171   112 172   113 173   114 174   115 175   116 176   117 177   118 178   119 179   120 180   121 181   122 182   123 183
                        210 170   211 171   212 170   213 171   214 172   215 173   216 174   217 175   218 176   219 177   220 178   221 179   222 180   223 181   224 182   225 183
                        310 370   311 371   312 372   313 373   314 374   315 375   316 376   317 377   318 2001  319 2002  320 380   321 381   322 382   323 383   324 384   325 385   326 386   327 387
                        410 370   411 371   412 370   413 371   414 372   415 373   416 374   417 375   418 376   419 377   420 2001  421 2002  422 380   423 381   424 382   425 383   426 384   427 385   428 386   429 387;

                        110 2001  111 2002  112 2002  113 2002  114 2001  115 2002  116 2002  117 2002  118 2002  119 2002  120 2001  121 2001  122 2001  123 2001
                        210 2001  211 2002  212 2001  213 2002  214 2002  215 2002  216 2001  217 2002  218 2002  219 2002  220 2002  221 2002  222 2001  223 2001  224 2001  225 2001
                        310 2001  311 2002  312 2002  313 2002  314 2001  315 2002  316 2002  317 2002  318 2001  319 2002  320 2002  321 2002  322 2002  323 2002  324 2001  325 2001  326 2001  327 2001
                        410 2001  411 2002  412 2001  413 2002  414 2002  415 2002  416 2001  417 2002  418 2002  419 2002  420 2001  421 2002  422 2002  423 2002  424 2002  425 2002  426 2001  427 2001  428 2001  429 2001
                        603 605'
    top_boundary = 20000
    bottom_boundary = 30000
  []
[]
(sfr/sefor/Mesh/Mesh_Core-I-E_3D_450K.i)

References

  1. Emily Shemon, Yinbin Miao, Shikhar Kumar, Kun Mo, Yeon Sang Jung, Aaron Oaks, Scott Richards, Guillaume Giudicelli, Logan Harbour, and Roy Stogner. Moose reactor module: an open-source capability for meshing nuclear reactor geometries. Nuclear Science and Engineering, 197(8):1656–1680, 2023. URL: https://doi.org/10.1080/00295639.2022.2149231, doi:10.1080/00295639.2022.2149231.[BibTeX]