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import openmc
import numpy as np
import argparse as ap
import csv
#> Apollonian 52-element CANDU fuel bundle in OpenMC for AnnCon2026.
#> Connor Moore, March 2026. <connor.moore@ontariotechu.net>
### Argparser for parametric analysis ###
parser = ap.ArgumentParser(prog="52-Element Apollonian Bundle Analysis",
description="Variable pin radius for calculating ratios and criticality.")
parser.add_argument("-fmr","--fuel-moderator-ratio",help="Ratio of the radius of fuel to whole circle. Default is 0.75",default="0.75")
parser.add_argument("-bt","--bundle-type",help="Apollonian bundle type [normal/alt], default=normal",default="normal")
args = parser.parse_args()
### Material Definitions ###
#> Materials marked PNNL-15870 are from the 2021 revision of "Compendium of Material
#> Composition Data for Radiation Transport Modeling" published by the U.S. Department
#> of Homeland Security and Pacific Northwest National Laboratory.
#> <https://www.pnnl.gov/main/publications/external/technical_reports/PNNL-15870Rev2.pdf>
#> The natural UO2 fuel
mat_fuel = openmc.Material(name="Natural Uranium Fuel (UO2)")
mat_fuel.add_element("U", 1.0, enrichment=0.71)
mat_fuel.add_element("O", 2.0)
mat_fuel.set_density("g/cc", 10.6)
#> Density of 10.6 g/cc is from The Essential CANDU, Ch. 17 (Fuel), sec. 2.2, pp. 11
#> Pressure tube and calandria tube use Zircaloy-2
mat_zircaloy_2 = openmc.Material(name="Zircaloy-2 (PNNL-15870)")
mat_zircaloy_2.add_nuclide("O16", 0.001194,"wo")
mat_zircaloy_2.add_nuclide("O17", 0.000000,"wo")
mat_zircaloy_2.add_nuclide("O18", 0.000003,"wo")
mat_zircaloy_2.add_element("Cr", 0.000997,"wo")
mat_zircaloy_2.add_element("Fe", 0.000997,"wo")
mat_zircaloy_2.add_element("Ni", 0.000499,"wo")
mat_zircaloy_2.add_nuclide("Zr90", 0.498109,"wo")
mat_zircaloy_2.add_nuclide("Zr91", 0.109835,"wo")
mat_zircaloy_2.add_nuclide("Zr92", 0.169730,"wo")
mat_zircaloy_2.add_nuclide("Zr94", 0.175752,"wo")
mat_zircaloy_2.add_nuclide("Zr96", 0.028918,"wo")
mat_zircaloy_2.add_element("Sn", 0.013962,"wo")
mat_zircaloy_2.set_density("g/cc",6.56)
#> The fuel cladding uses Zircaloy-4
mat_zircaloy_4 = openmc.Material(name="Zircaloy-4 (PNNL-15870")
mat_zircaloy_4.add_nuclide("O16", 0.001193,"wo")
mat_zircaloy_4.add_nuclide("O17", 0.000000,"wo")
mat_zircaloy_4.add_nuclide("O18", 0.000003,"wo")
mat_zircaloy_4.add_element("Cr", 0.000997,"wo")
mat_zircaloy_4.add_element("Fe", 0.001993,"wo")
mat_zircaloy_4.add_nuclide("Zr90", 0.497860,"wo")
mat_zircaloy_4.add_nuclide("Zr91", 0.109780,"wo")
mat_zircaloy_4.add_nuclide("Zr92", 0.169646,"wo")
mat_zircaloy_4.add_nuclide("Zr94", 0.175665,"wo")
mat_zircaloy_4.add_nuclide("Zr96", 0.028904,"wo")
mat_zircaloy_4.add_element("Sn", 0.013955,"wo")
mat_zircaloy_4.set_density("g/cc",6.56)
#> Heavy water is used for moderation and cooling
mat_d2o = openmc.Material(name="Heavy Water (PNNL-15870)")
mat_d2o.add_nuclide("H2", 0.201133,"wo")
mat_d2o.add_nuclide("O16", 0.796703,"wo")
mat_d2o.add_nuclide("O17", 0.000323,"wo")
mat_d2o.add_nuclide("O18", 0.001842,"wo")
mat_d2o.add_s_alpha_beta("c_D_in_D2O")
mat_d2o.set_density("g/cc",1.1044)
materials = openmc.Materials([mat_fuel, mat_zircaloy_2, mat_zircaloy_4, mat_d2o])
materials.export_to_xml()
### Geometry Definition ###
fuel_region_list = []
clad_region_list = []
fuel_rad_list = []
fuel_area_list = []
clad_area_list = []
clad_circumference_list = []
#> Define a function to create a fuel "pin" using a radius.
def make_apollonian_pin(rg: float, rfm: float, x0: float, y0: float) -> None:
fuel_surf = openmc.ZCylinder(r=rg*rfm, x0=x0, y0=y0)
#> Hard-coded cladding thickness of 0.4 mm
clad_surf = openmc.ZCylinder(r=fuel_surf.r+0.04, x0=x0, y0=y0)
fuel_region = -fuel_surf
clad_region = +fuel_surf & -clad_surf
fuel_region_list.append(fuel_region)
clad_region_list.append(clad_region)
fuel_area_list.append(np.pi*fuel_surf.r**2)
clad_area_list.append(np.pi*(clad_surf.r**2 - fuel_surf.r**2))
clad_circumference_list.append(2*np.pi*clad_surf.r)
return
#> Import gasket points from file
filename = "gasket-geometry/apollonian-gasket-52-normal.csv" if args.bundle_type=="normal" else "gasket-geometry/apollonian-gasket-52-alt.csv"
rfm = eval(args.fuel_moderator_ratio)
with open(filename, "r", newline="", encoding="utf-8") as file:
reader = csv.reader(file)
try:
header = next(reader)
except StopIteration:
header = []
for row in reader:
make_apollonian_pin(float(row[2]),rfm,float(row[0]),float(row[1]))
#> Combine the regions to make a fuel cell and a cladding cell
fuel_cell = openmc.Cell(name="UO2 Fuel Regions", region=openmc.Union(fuel_region_list), fill=mat_fuel)
clad_cell = openmc.Cell(name="Zircaloy-4 Cladding Regions", region=openmc.Union(clad_region_list), fill=mat_zircaloy_4)
#> Add the pressure tube
pt_inner = openmc.ZCylinder(r=5.16890, x0=0.0, y0=0.0)
pt_outer = openmc.ZCylinder(r=5.60320, x0=0.0, y0=0.0)
pt_region = +pt_inner & -pt_outer
pt_cell = openmc.Cell(name="Pressure Tube", region=pt_region, fill=mat_zircaloy_2)
#> Pack the fuel with D2O
pt_d2o_region = ~(fuel_cell.region | clad_cell.region) & -pt_inner
pt_d2o_cell = openmc.Cell(name="D2O Coolant", region=pt_d2o_region, fill=mat_d2o)
#> Add the calandria tube
ct_inner = openmc.ZCylinder(r=6.44780, x0=0.0, y0=0.0)
ct_outer = openmc.ZCylinder(r=6.58750, x0=0.0, y0=0.0)
ct_region = +ct_inner & -ct_outer
ct_cell = openmc.Cell(name="Calandria Tube", region=ct_region, fill=mat_zircaloy_2)
#> The space between the calandria tube and pressure tube is considered void
pt_ct_region = +pt_outer & -ct_inner
pt_ct_cell = openmc.Cell(name="Annulus Gap", region=pt_ct_region, fill=None)
#> The lattice pitch for the assembly is 28.575, so apply a reflecting boundary
outer_boundary = openmc.model.RectangularPrism(width=28.575, height=28.575, origin=(0.0, 0.0), boundary_type="reflective")
ct_d2o_region = +ct_outer & -outer_boundary
ct_d2o_cell = openmc.Cell(name="D2O Moderator", region=ct_d2o_region, fill=mat_d2o)
universe = openmc.Universe(cells=[fuel_cell, clad_cell, pt_cell, pt_d2o_cell, ct_cell, pt_ct_cell, ct_d2o_cell])
geometry = openmc.Geometry(universe)
geometry.export_to_xml()
### Settings definition ###
settings = openmc.Settings()
settings.particles = 10000
settings.batches = 400
settings.inactive = 80
#> Set up the source to sample inside the pressure tube region uniformly
settings.source = openmc.IndependentSource()
settings.source.space = openmc.stats.CylindricalIndependent(
r = openmc.stats.PowerLaw(a=0, b=pt_inner.r, n=1),
phi = openmc.stats.Uniform(0, 2*np.pi),
z = openmc.stats.Discrete([0.0], [1.0])
)
settings.source.energy = openmc.stats.Watt()
settings.export_to_xml()
### Area and DTU Calculations ###
V_fuel = sum(fuel_area_list)
V_clad = sum(clad_area_list)
C_clad = sum(clad_circumference_list)
V_mod = np.pi*pt_inner.r**2 - (V_fuel + V_clad) + (28.575**2 - np.pi*ct_outer.r**2)
d_fuel = mat_fuel.get_nuclide_atom_densities()
N_fuel = sum(density for nuclide,density in d_fuel.items() if "U" in nuclide)
N_mod = mat_d2o.get_nuclide_atom_densities()["H2"]
DTU_ratio = (V_mod * N_mod) / (V_fuel * N_fuel)
##> Print these for the final table
print(f"Flow area, cm² = {V_mod}")
print(f"Cladding circumference, cm = {C_clad}")
print(f"Fuel mass per length, g/cm = {V_fuel*mat_fuel.density}")
print(f"Cladding mass per length, g/cm = {V_clad*mat_zircaloy_4.density}")
print(f"DTU ratio = {DTU_ratio}")
#> Run the model!
openmc.run()
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