OpenMC includes a few convenience functions for generationing TRISO particle locations and placing them in a lattice. To be clear, this capability is not a stochastic geometry capability like that included in MCNP. It's also important to note that OpenMC does not use delta tracking, which would normally speed up calculations in geometries with tons of surfaces and cells. However, the computational burden can be eased by placing TRISO particles in a lattice.
In [1]:
%matplotlib inline
from math import pi
import numpy as np
import matplotlib.pyplot as plt
import openmc
import openmc.model
Let's first start by creating materials that will be used in our TRISO particles and the background material.
In [2]:
fuel = openmc.Material(name='Fuel')
fuel.set_density('g/cm3', 10.5)
fuel.add_nuclide('U235', 4.6716e-02)
fuel.add_nuclide('U238', 2.8697e-01)
fuel.add_nuclide('O16', 5.0000e-01)
fuel.add_element('C', 1.6667e-01)
buff = openmc.Material(name='Buffer')
buff.set_density('g/cm3', 1.0)
buff.add_element('C', 1.0)
buff.add_s_alpha_beta('c_Graphite')
PyC1 = openmc.Material(name='PyC1')
PyC1.set_density('g/cm3', 1.9)
PyC1.add_element('C', 1.0)
PyC1.add_s_alpha_beta('c_Graphite')
PyC2 = openmc.Material(name='PyC2')
PyC2.set_density('g/cm3', 1.87)
PyC2.add_element('C', 1.0)
PyC2.add_s_alpha_beta('c_Graphite')
SiC = openmc.Material(name='SiC')
SiC.set_density('g/cm3', 3.2)
SiC.add_element('C', 0.5)
SiC.add_element('Si', 0.5)
graphite = openmc.Material()
graphite.set_density('g/cm3', 1.1995)
graphite.add_element('C', 1.0)
graphite.add_s_alpha_beta('c_Graphite')
To actually create individual TRISO particles, we first need to create a universe that will be used within each particle. The reason we use the same universe for each TRISO particle is to reduce the total number of cells/surfaces needed which can substantially improve performance over using unique cells/surfaces in each.
In [3]:
# Create TRISO universe
spheres = [openmc.Sphere(R=r*1e-4)
for r in [215., 315., 350., 385.]]
cells = [openmc.Cell(fill=fuel, region=-spheres[0]),
openmc.Cell(fill=buff, region=+spheres[0] & -spheres[1]),
openmc.Cell(fill=PyC1, region=+spheres[1] & -spheres[2]),
openmc.Cell(fill=SiC, region=+spheres[2] & -spheres[3]),
openmc.Cell(fill=PyC2, region=+spheres[3])]
triso_univ = openmc.Universe(cells=cells)
Next, we need a region to pack the TRISO particles in. We will use a 1 cm x 1 cm x 1 cm box centered at the origin.
In [4]:
min_x = openmc.XPlane(x0=-0.5, boundary_type='reflective')
max_x = openmc.XPlane(x0=0.5, boundary_type='reflective')
min_y = openmc.YPlane(y0=-0.5, boundary_type='reflective')
max_y = openmc.YPlane(y0=0.5, boundary_type='reflective')
min_z = openmc.ZPlane(z0=-0.5, boundary_type='reflective')
max_z = openmc.ZPlane(z0=0.5, boundary_type='reflective')
region = +min_x & -max_x & +min_y & -max_y & +min_z & -max_z
Now we need to randomly select locations for the TRISO particles. In this example, we will select locations at random within the box with a packing fraction of 30%. Note that pack_spheres can handle up to the theoretical maximum of 60% (it will just be slow).
In [5]:
outer_radius = 425.*1e-4
centers = openmc.model.pack_spheres(radius=outer_radius, region=region, pf=0.3)
Now that we have the locations of the TRISO particles determined and a universe that can be used for each particle, we can create the TRISO particles.
In [6]:
trisos = [openmc.model.TRISO(outer_radius, triso_univ, c) for c in centers]
Each TRISO object actually is a Cell, in fact; we can look at the properties of the TRISO just as we would a cell:
In [7]:
print(trisos[0])
Let's confirm that all our TRISO particles are within the box.
In [8]:
centers = np.vstack([t.center for t in trisos])
print(centers.min(axis=0))
print(centers.max(axis=0))
We can also look at what the actual packing fraction turned out to be:
In [9]:
len(trisos)*4/3*pi*outer_radius**3
Out[9]:
Now that we have our TRISO particles created, we need to place them in a lattice to provide optimal tracking performance in OpenMC. We can use the box we created above to place the lattice in. Actually creating a lattice containing TRISO particles can be done with the model.create_triso_lattice() function. This function requires that we give it a list of TRISO particles, the lower-left coordinates of the lattice, the pitch of each lattice cell, the overall shape of the lattice (number of cells in each direction), and a background material.
In [10]:
box = openmc.Cell(region=region)
lower_left, upper_right = box.region.bounding_box
shape = (3, 3, 3)
pitch = (upper_right - lower_left)/shape
lattice = openmc.model.create_triso_lattice(
trisos, lower_left, pitch, shape, graphite)
Now we can set the fill of our box cell to be the lattice:
In [11]:
box.fill = lattice
Finally, let's take a look at our geometry by putting the box in a universe and plotting it. We're going to use the Fortran-side plotter since it's much faster.
In [12]:
univ = openmc.Universe(cells=[box])
geom = openmc.Geometry(univ)
geom.export_to_xml()
mats = list(geom.get_all_materials().values())
openmc.Materials(mats).export_to_xml()
settings = openmc.Settings()
settings.run_mode = 'plot'
settings.export_to_xml()
p = openmc.Plot.from_geometry(geom)
openmc.plot_inline(p)
If we plot the universe by material rather than by cell, we can see that the entire background is just graphite.
In [13]:
p.color_by = 'material'
p.colors = {graphite: 'gray'}
openmc.plot_inline(p)