HexagonalGridDivision

Divide the mesh along a hexagonal grid. Numbering of pin divisions increases first counterclockwise, then expanding outwards from the inner ring, then axially. Inner-numbering is within a radial ring, outer-numbering is axial divisions

Points that lie outside the hexagonal grid may be assigned to the grid outer bins using the "assign_domain_outside_grid_to_border" parameter. This is the current treatment for background/duct regions around hexagonal pins in an assembly.

Using a Positions object as the "center_positions" parameter, multiple hexagonal grids can be created around each position computed by that object. The division index of a point is then:

var element = document.getElementById("moose-equation-bc6fae4e-66f7-47f6-bc59-65010978182f");katex.render("\\text{division index} = (i - 1) N_{\\text{single division}} + \\text{division index in hexagonal grid centered around position i}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

with $var element = document.getElementById("moose-equation-a61802f3-9ea5-473e-8bc1-79ff419caa85");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the index in the Positions object of the position nearest from the point and $var element = document.getElementById("moose-equation-ae183aea-270f-4973-a09a-940bd2842508");katex.render("N_{\\text{single division}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the number of divisions for a single hexagonal grid, based on the number of rings and axial discretization specified.

note

For points lying within the standard tolerance of an internal boundary of the hexagonal grid, this object will output a warning. If you do not mind the indetermination on which bins they belong to but do mind that a warning is output, please reach out to a MOOSE (or any MOOSE app) developer.

Input Parameters

lattice_flat_to_flatDistance between two (inner) opposite sides of a lattice. Also known as bundle pitch or inner flat-to-flat distance
C++ Type:double
Controllable:No
Description:Distance between two (inner) opposite sides of a lattice. Also known as bundle pitch or inner flat-to-flat distance
nrNumber of hexagonal rings
C++ Type:unsigned int
Controllable:No
Description:Number of hexagonal rings
nzNumber of divisions in Z
C++ Type:unsigned int
Controllable:No
Description:Number of divisions in Z
pin_pitchDistance between pins
C++ Type:double
Controllable:No
Description:Distance between pins
z_maxMaximum axial extent of the lattice
C++ Type:double
Controllable:No
Description:Maximum axial extent of the lattice
z_minMinimal axial extent of the lattice
C++ Type:double
Controllable:No
Description:Minimal axial extent of the lattice

Required Parameters

assign_domain_outside_grid_to_borderFalseWhether to map the domain outside the grid back to the border of the grid
Default:False
C++ Type:bool
Controllable:No
Description:Whether to map the domain outside the grid back to the border of the grid
centerCenter of the hexagonal grid
C++ Type:libMesh::Point
Controllable:No
Description:Center of the hexagonal grid
center_positionsCenters of the hexagonal grids
C++ Type:PositionsName
Controllable:No
Description:Centers of the hexagonal grids

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/reactor/test/tests/meshdivisions/hexagonal_division.i)
(modules/reactor/test/tests/meshdivisions/hexagonal_division_positions.i)

(modules/reactor/test/tests/meshdivisions/hexagonal_division.i)

# Increase resolution to check results visually
resolution = 3
z_resolution = 3

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 3
    dx = '1.5 2.4 0.1'
    dy = '1.3 0.9'
    dz = '0.4 0.5 0.6 0.7'
    ix = '${fparse 2 * resolution} ${fparse resolution} ${fparse z_resolution}'
    iy = '${fparse 2 * resolution} ${fparse 3 * z_resolution}'
    iz = '${fparse resolution} ${fparse resolution} ${fparse resolution} ${fparse z_resolution}'
  []
  # To keep VPP output consistently ordered
  allow_renumbering = false
[]

[MeshDivisions]
  [hexagonal_div]
    type = HexagonalGridDivision
    nr = 4
    nz = 2
    lattice_flat_to_flat = 4
    pin_pitch = 0.6
    z_min = 0
    z_max = 3
    center = '1 1 0'
  []
[]

[AuxVariables]
  [div]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [mesh_div]
    type = MeshDivisionAux
    variable = div
    mesh_division = 'hexagonal_div'
  []
[]

[VectorPostprocessors]
  [div_out]
    type = ElementValueSampler
    variable = 'div'
    sort_by = 'id'
    outputs = csv
  []
[]

[Postprocessors]
  [npos]
    type = NumMeshDivisions
    mesh_division = 'hexagonal_div'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

(modules/reactor/test/tests/meshdivisions/hexagonal_division_positions.i)

pin_hex_size = 5
n_rings = 2
hex_size = '${fparse (2*n_rings - 1) * pin_hex_size}'

[Mesh]
  [hex_pin]
    type = PolygonConcentricCircleMeshGenerator
    num_sides = 6
    num_sectors_per_side = '2 2 2 2 2 2'
    # Two position rings
    ring_radii = '${fparse pin_hex_size / 2}'
    ring_intervals = 1
    polygon_size = ${pin_hex_size}
    preserve_volumes = on
  []
  [pattern_assembly]
    type = PatternedHexMeshGenerator
    inputs = 'hex_pin'
    pattern = '0 0;
              0 0 0;
               0 0'
    hexagon_size = ${hex_size}
    background_intervals = 1
    # If we deform the pin mesh to ease the transition with the background,
    # we can get the wrong index for the hexagonal division
    deform_non_circular_region = false
  []
  [pattern_core]
    type = PatternedHexMeshGenerator
    inputs = 'pattern_assembly'
    pattern = '0 0;
              0 0 0;
               0 0'
    generate_core_metadata = true
    pattern_boundary = none
    # If we deform the pin mesh to ease the transition with the background,
    # we can get the wrong index for the hexagonal division
    deform_non_circular_region = false
  []

  # To keep VPP output consistently ordered
  allow_renumbering = false
[]

[Positions]
  [assembly_centers]
    type = InputPositions
    # Assembly centers
    positions = '0 0 0
                 ${fparse -tan(pi/3) * hex_size} ${fparse -hex_size} 0
                 ${fparse -tan(pi/3) * hex_size} ${fparse hex_size} 0
                 0 ${fparse -2 * hex_size} 0
                 0 ${fparse 2 * hex_size} 0
                 ${fparse tan(pi/3) * hex_size} ${fparse -hex_size} 0
                 ${fparse tan(pi/3) * hex_size} ${fparse hex_size} 0'
  []
[]

[MeshDivisions]
  [hexagonal_div]
    type = HexagonalGridDivision
    nr = ${n_rings}
    nz = 1
    lattice_flat_to_flat = '${fparse 2 * hex_size}'
    pin_pitch = '${fparse 2 * pin_hex_size}'
    z_min = 0
    z_max = 0
    center_positions = assembly_centers
  []
[]

[AuxVariables]
  [div]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [mesh_div]
    type = MeshDivisionAux
    variable = div
    mesh_division = 'hexagonal_div'
  []
[]

[VectorPostprocessors]
  [div_out]
    type = ElementValueSampler
    variable = 'div'
    sort_by = 'id'
    outputs = csv
  []
[]

[Postprocessors]
  [npos]
    type = NumMeshDivisions
    mesh_division = 'hexagonal_div'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

Input Parameters
Input Files