Multigroup Cross Section Generation Part II: Advanced Features¶
This IPython Notebook illustrates the use of the openmc.mgxs module to calculate multi-group cross sections for a heterogeneous fuel pin cell geometry. In particular, this Notebook illustrates the following features:
- Creation of multi-group cross sections on a heterogeneous geometry
- Calculation of cross sections on a nuclide-by-nuclide basis
- The use of tally precision triggers with multi-group cross sections
- Built-in features for energy condensation in downstream data processing
- The use of the
openmc.datamodule to plot continuous-energy vs. multi-group cross sections - Validation of multi-group cross sections with OpenMOC
Note: This Notebook was created using OpenMOC to verify the multi-group cross-sections generated by OpenMC. You must install OpenMOC on your system in order to run this Notebook in its entirety. In addition, this Notebook illustrates the use of Pandas DataFrames to containerize multi-group cross section data.
Generate Input Files¶
In [1]:
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('dark_background')
import openmoc
import openmc
import openmc.mgxs as mgxs
import openmc.data
from openmc.openmoc_compatible import get_openmoc_geometry
%matplotlib inline
In [2]:
# create a model object to tie together geometry, materials, settings, and tallies
model = openmc.Model()
First we need to define materials that will be used in the problem. We'll create three distinct materials for water, clad and fuel.
In [3]:
# 1.6% enriched fuel
fuel = openmc.Material(name='1.6% Fuel')
fuel.set_density('g/cm3', 10.31341)
fuel.add_nuclide('U235', 3.7503e-4)
fuel.add_nuclide('U238', 2.2625e-2)
fuel.add_nuclide('O16', 4.6007e-2)
# borated water
water = openmc.Material(name='Borated Water')
water.set_density('g/cm3', 0.740582)
water.add_nuclide('H1', 4.9457e-2)
water.add_nuclide('O16', 2.4732e-2)
# zircaloy
zircaloy = openmc.Material(name='Zircaloy')
zircaloy.set_density('g/cm3', 6.55)
zircaloy.add_nuclide('Zr90', 7.2758e-3)
With our materials, we can now create a Materials object that can be exported to an actual XML file.
In [4]:
# Instantiate a Materials collection
model.materials = openmc.Materials([fuel, water, zircaloy])
Now let's move on to the geometry. Our problem will have three regions for the fuel, the clad, and the surrounding coolant. The first step is to create the bounding surfaces -- in this case two cylinders and six reflective planes.
In [5]:
# Create cylinders for the fuel and clad
fuel_outer_radius = openmc.ZCylinder(x0=0.0, y0=0.0, r=0.39218)
clad_outer_radius = openmc.ZCylinder(x0=0.0, y0=0.0, r=0.45720)
# Create box to surround the geometry
box = openmc.model.RectangularPrism(1.26, 1.26, boundary_type='reflective')
With the surfaces defined, we can now create cells that are defined by intersections of half-spaces created by the surfaces.
In [6]:
# Create a Universe to encapsulate a fuel pin
pin_cell_universe = openmc.Universe(name='1.6% Fuel Pin')
# Create fuel Cell
fuel_cell = openmc.Cell(name='1.6% Fuel')
fuel_cell.fill = fuel
fuel_cell.region = -fuel_outer_radius
pin_cell_universe.add_cell(fuel_cell)
# Create a clad Cell
clad_cell = openmc.Cell(name='1.6% Clad')
clad_cell.fill = zircaloy
clad_cell.region = +fuel_outer_radius & -clad_outer_radius
pin_cell_universe.add_cell(clad_cell)
# Create a moderator Cell
moderator_cell = openmc.Cell(name='1.6% Moderator')
moderator_cell.fill = water
moderator_cell.region = +clad_outer_radius & -box
pin_cell_universe.add_cell(moderator_cell)
We now must create a geometry with the pin cell universe and export it to XML.
In [7]:
# Create Geometry and set root Universe
model.geometry = openmc.Geometry(pin_cell_universe)
Next, we must define simulation parameters. In this case, we will use 10 inactive batches and 40 active batches each with 10,000 particles.
In [8]:
# OpenMC simulation parameters
batches = 50
inactive = 10
particles = 10000
# Instantiate a Settings object
settings = openmc.Settings()
settings.batches = batches
settings.inactive = inactive
settings.particles = particles
settings.output = {'tallies': True}
# Create an initial uniform spatial source distribution over fissionable zones
bounds = [-0.63, -0.63, -0.63, 0.63, 0.63, 0.63]
uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)
settings.source = openmc.IndependentSource(space=uniform_dist)
# Activate tally precision triggers
settings.trigger_active = True
settings.trigger_max_batches = settings.batches * 4
model.settings = settings
Now we are finally ready to make use of the openmc.mgxs module to generate multi-group cross sections! First, let's define "coarse" 2-group and "fine" 8-group structures using the built-in EnergyGroups class.
In [9]:
# Instantiate a "coarse" 2-group EnergyGroups object
coarse_groups = mgxs.EnergyGroups([0., 0.625, 20.0e6])
# Instantiate a "fine" 8-group EnergyGroups object
fine_groups = mgxs.EnergyGroups([0., 0.058, 0.14, 0.28,
0.625, 4.0, 5.53e3, 821.0e3, 20.0e6])
Now we will instantiate a variety of MGXS objects needed to run an OpenMOC simulation to verify the accuracy of our cross sections. In particular, we define transport, fission, nu-fission, nu-scatter and chi cross sections for each of the three cells in the fuel pin with the 8-group structure as our energy groups.
In [10]:
# Extract all Cells filled by Materials
openmc_cells = model.geometry.get_all_material_cells().values()
# Create dictionary to store multi-group cross sections for all cells
xs_library = {}
# Instantiate 8-group cross sections for each cell
for cell in openmc_cells:
xs_library[cell.id] = {}
xs_library[cell.id]['transport'] = mgxs.TransportXS(energy_groups=fine_groups)
xs_library[cell.id]['fission'] = mgxs.FissionXS(energy_groups=fine_groups)
xs_library[cell.id]['nu-fission'] = mgxs.FissionXS(energy_groups=fine_groups, nu=True)
xs_library[cell.id]['nu-scatter'] = mgxs.ScatterMatrixXS(energy_groups=fine_groups, nu=True)
xs_library[cell.id]['chi'] = mgxs.Chi(energy_groups=fine_groups)
Next, we showcase the use of OpenMC's tally precision trigger feature in conjunction with the openmc.mgxs module. In particular, we will assign a tally trigger of 1E-2 on the standard deviation for each of the tallies used to compute multi-group cross sections.
In [11]:
# Create a tally trigger for +/- 0.01 on each tally used to compute the multi-group cross sections
tally_trigger = openmc.Trigger('std_dev', 1e-2)
# Add the tally trigger to each of the multi-group cross section tallies
for cell in openmc_cells:
for mgxs_type in xs_library[cell.id]:
xs_library[cell.id][mgxs_type].tally_trigger = tally_trigger
Now, we must loop over all cells to set the cross section domains to the various cells - fuel, clad and moderator - included in the geometry. In addition, we will set each cross section to tally cross sections on a per-nuclide basis through the use of the MGXS class' boolean by_nuclide instance attribute.
In [12]:
# Instantiate an empty Tallies object
tallies = openmc.Tallies()
# Iterate over all cells and cross section types
for cell in openmc_cells:
for rxn_type in xs_library[cell.id]:
# Set the cross sections domain to the cell
xs_library[cell.id][rxn_type].domain = cell
# Tally cross sections by nuclide
xs_library[cell.id][rxn_type].by_nuclide = True
# Add OpenMC tallies to the tallies file for XML generation
for tally in xs_library[cell.id][rxn_type].tallies.values():
tallies.append(tally, merge=True)
model.tallies = tallies
Now we a have a complete set of inputs, so we can go ahead and run our simulation.
In [13]:
# Run OpenMC
sp_file = model.run()
/home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=53. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=21. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=2. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=3. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=4. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=41. warn(msg, IDWarning) /home/pshriwise/.pyenv/versions/3.9.1/lib/python3.9/site-packages/openmc/mixin.py:70: IDWarning: Another Filter instance already exists with id=15. warn(msg, IDWarning)
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| The OpenMC Monte Carlo Code
Copyright | 2011-2022 MIT, UChicago Argonne LLC, and contributors
License | https://docs.openmc.org/en/latest/license.html
Version | 0.13.1
Git SHA1 | 33bc948f4b855c037975f16d16091fe4ecd12de3
Date/Time | 2022-10-05 23:55:59
MPI Processes | 1
OpenMP Threads | 2
Reading settings XML file...
Reading cross sections XML file...
Reading materials XML file...
Reading geometry XML file...
Reading U235 from /home/pshriwise/data/xs/openmc/nndc_hdf5/U235.h5
Reading U238 from /home/pshriwise/data/xs/openmc/nndc_hdf5/U238.h5
Reading O16 from /home/pshriwise/data/xs/openmc/nndc_hdf5/O16.h5
Reading H1 from /home/pshriwise/data/xs/openmc/nndc_hdf5/H1.h5
Reading Zr90 from /home/pshriwise/data/xs/openmc/nndc_hdf5/Zr90.h5
Minimum neutron data temperature: 294 K
Maximum neutron data temperature: 294 K
Reading tallies XML file...
Preparing distributed cell instances...
Reading plot XML file...
Writing summary.h5 file...
Maximum neutron transport energy: 20000000 eV for U235
Initializing source particles...
====================> K EIGENVALUE SIMULATION <====================
Bat./Gen. k Average k
========= ======== ====================
1/1 1.23300
2/1 1.22712
3/1 1.23403
4/1 1.23023
5/1 1.20250
6/1 1.20565
7/1 1.23034
8/1 1.21931
9/1 1.23826
10/1 1.25090
11/1 1.21111
12/1 1.20786 1.20948 +/- 0.00162
13/1 1.23784 1.21894 +/- 0.00950
14/1 1.22692 1.22093 +/- 0.00701
15/1 1.20622 1.21799 +/- 0.00617
16/1 1.20024 1.21503 +/- 0.00584
17/1 1.20624 1.21378 +/- 0.00510
18/1 1.20491 1.21267 +/- 0.00455
19/1 1.20434 1.21174 +/- 0.00412
20/1 1.22590 1.21316 +/- 0.00395
21/1 1.20102 1.21206 +/- 0.00374
22/1 1.23117 1.21365 +/- 0.00376
23/1 1.22446 1.21448 +/- 0.00356
24/1 1.22469 1.21521 +/- 0.00338
25/1 1.23859 1.21677 +/- 0.00351
26/1 1.25129 1.21893 +/- 0.00393
27/1 1.22524 1.21930 +/- 0.00371
28/1 1.22082 1.21938 +/- 0.00350
29/1 1.21838 1.21933 +/- 0.00331
30/1 1.24252 1.22049 +/- 0.00335
31/1 1.23912 1.22138 +/- 0.00330
32/1 1.22704 1.22163 +/- 0.00316
33/1 1.22330 1.22171 +/- 0.00302
34/1 1.20966 1.22120 +/- 0.00294
35/1 1.20998 1.22076 +/- 0.00285
36/1 1.21069 1.22037 +/- 0.00277
37/1 1.20250 1.21971 +/- 0.00274
38/1 1.20573 1.21921 +/- 0.00269
39/1 1.23647 1.21980 +/- 0.00266
40/1 1.22719 1.22005 +/- 0.00258
41/1 1.23410 1.22050 +/- 0.00254
42/1 1.23220 1.22087 +/- 0.00249
43/1 1.23399 1.22127 +/- 0.00244
44/1 1.23143 1.22156 +/- 0.00239
45/1 1.23144 1.22185 +/- 0.00234
46/1 1.22653 1.22198 +/- 0.00227
47/1 1.21239 1.22172 +/- 0.00223
48/1 1.22858 1.22190 +/- 0.00218
49/1 1.20952 1.22158 +/- 0.00214
50/1 1.20497 1.22117 +/- 0.00213
Triggers unsatisfied, max unc./thresh. is 1.2584438813928658 for flux in tally
53
The estimated number of batches is 74
Creating state point statepoint.050.h5...
51/1 1.22506 1.22126 +/- 0.00208
Triggers unsatisfied, max unc./thresh. is 1.2360657756693463 for flux in tally
53
The estimated number of batches is 73
52/1 1.22892 1.22144 +/- 0.00204
Triggers unsatisfied, max unc./thresh. is 1.206696013966578 for flux in tally
53
The estimated number of batches is 72
53/1 1.20425 1.22104 +/- 0.00203
Triggers unsatisfied, max unc./thresh. is 1.1794033562761703 for flux in tally
53
The estimated number of batches is 70
54/1 1.18761 1.22028 +/- 0.00212
Triggers unsatisfied, max unc./thresh. is 1.1745090363258377 for flux in tally
53
The estimated number of batches is 71
55/1 1.21624 1.22019 +/- 0.00208
Triggers unsatisfied, max unc./thresh. is 1.1488291964971802 for flux in tally
53
The estimated number of batches is 70
56/1 1.22056 1.22020 +/- 0.00203
Triggers unsatisfied, max unc./thresh. is 1.1253755542228503 for flux in tally
53
The estimated number of batches is 69
57/1 1.22213 1.22024 +/- 0.00199
Triggers unsatisfied, max unc./thresh. is 1.1013090664425782 for flux in tally
53
The estimated number of batches is 68
58/1 1.23192 1.22049 +/- 0.00196
Triggers unsatisfied, max unc./thresh. is 1.0814142069475086 for flux in tally
53
The estimated number of batches is 67
59/1 1.23142 1.22071 +/- 0.00193
Triggers unsatisfied, max unc./thresh. is 1.0688144272705478 for flux in tally
53
The estimated number of batches is 66
60/1 1.23744 1.22104 +/- 0.00192
Triggers unsatisfied, max unc./thresh. is 1.0845694915740336 for flux in tally
53
The estimated number of batches is 69
61/1 1.24681 1.22155 +/- 0.00195
Triggers unsatisfied, max unc./thresh. is 1.0650160561418593 for flux in tally
53
The estimated number of batches is 68
62/1 1.23159 1.22174 +/- 0.00192
Triggers unsatisfied, max unc./thresh. is 1.0628835462503399 for flux in tally
53
The estimated number of batches is 69
63/1 1.21588 1.22163 +/- 0.00189
Triggers unsatisfied, max unc./thresh. is 1.0440750211689802 for flux in tally
53
The estimated number of batches is 68
64/1 1.21867 1.22158 +/- 0.00186
Triggers unsatisfied, max unc./thresh. is 1.0258844139280563 for flux in tally
53
The estimated number of batches is 67
65/1 1.22410 1.22162 +/- 0.00182
Triggers unsatisfied, max unc./thresh. is 1.038412688234605 for flux in tally
53
The estimated number of batches is 70
66/1 1.20786 1.22138 +/- 0.00181
Triggers unsatisfied, max unc./thresh. is 1.0213633609643367 for flux in tally
53
The estimated number of batches is 69
67/1 1.21064 1.22119 +/- 0.00178
Triggers unsatisfied, max unc./thresh. is 1.019182247265982 for flux in tally
53
The estimated number of batches is 70
68/1 1.23857 1.22149 +/- 0.00178
Triggers unsatisfied, max unc./thresh. is 1.0128609683027328 for flux in tally
53
The estimated number of batches is 70
69/1 1.21603 1.22139 +/- 0.00175
Triggers unsatisfied, max unc./thresh. is 1.0113107304662599 for flux in tally
53
The estimated number of batches is 71
70/1 1.19730 1.22099 +/- 0.00177
Triggers unsatisfied, max unc./thresh. is 1.025023774532644 for flux in tally
53
The estimated number of batches is 74
71/1 1.22459 1.22105 +/- 0.00174
Triggers unsatisfied, max unc./thresh. is 1.0084011441757024 for flux in tally
53
The estimated number of batches is 73
72/1 1.24564 1.22145 +/- 0.00176
Triggers unsatisfied, max unc./thresh. is 1.0083223109528934 for flux in tally
53
The estimated number of batches is 74
73/1 1.21948 1.22142 +/- 0.00173
Triggers unsatisfied, max unc./thresh. is 1.0051824390021815 for flux in tally
53
The estimated number of batches is 74
74/1 1.20923 1.22123 +/- 0.00171
Triggers satisfied for batch 74
Creating state point statepoint.074.h5...
=======================> TIMING STATISTICS <=======================
Total time for initialization = 1.0770e-01 seconds
Reading cross sections = 1.0300e-01 seconds
Total time in simulation = 2.9592e+01 seconds
Time in transport only = 2.9528e+01 seconds
Time in inactive batches = 1.8603e+00 seconds
Time in active batches = 2.7732e+01 seconds
Time synchronizing fission bank = 4.2199e-02 seconds
Sampling source sites = 2.5148e-02 seconds
SEND/RECV source sites = 1.6948e-02 seconds
Time accumulating tallies = 1.1797e-03 seconds
Time writing statepoints = 8.0299e-03 seconds
Total time for finalization = 1.1328e-03 seconds
Total time elapsed = 2.9709e+01 seconds
Calculation Rate (inactive) = 53753.6 particles/second
Calculation Rate (active) = 23078.2 particles/second
============================> RESULTS <============================
k-effective (Collision) = 1.22070 +/- 0.00153
k-effective (Track-length) = 1.22123 +/- 0.00171
k-effective (Absorption) = 1.22336 +/- 0.00157
Combined k-effective = 1.22204 +/- 0.00135
Leakage Fraction = 0.00000 +/- 0.00000
Tally Data Processing¶
Our simulation ran successfully and created statepoint and summary output files. We begin our analysis by instantiating a StatePoint object.
In [14]:
# Load the last statepoint file
sp = openmc.StatePoint(sp_file)
The statepoint is now ready to be analyzed by our multi-group cross sections. We simply have to load the tallies from the StatePoint into each object as follows and our MGXS objects will compute the cross sections for us under-the-hood.
In [15]:
# Iterate over all cells and cross section types
for cell in openmc_cells:
for rxn_type in xs_library[cell.id]:
xs_library[cell.id][rxn_type].load_from_statepoint(sp)
That's it! Our multi-group cross sections are now ready for the big spotlight. This time we have cross sections in three distinct spatial zones - fuel, clad and moderator - on a per-nuclide basis.
Extracting and Storing MGXS Data¶
Let's first inspect one of our cross sections by printing it to the screen as a microscopic cross section in units of barns.
In [16]:
nufission = xs_library[fuel_cell.id]['nu-fission']
nufission.print_xs(xs_type='micro', nuclides=['U235', 'U238'])
Multi-Group XS
Reaction Type = nu-fission
Domain Type = cell
Domain ID = 1
Nuclide = U235
Cross Sections [barns]:
Group 1 [821000.0 - 20000000.0eV]: 3.30e+00 +/- 2.34e-01%
Group 2 [5530.0 - 821000.0 eV]: 3.96e+00 +/- 1.53e-01%
Group 3 [4.0 - 5530.0 eV]: 5.52e+01 +/- 2.15e-01%
Group 4 [0.625 - 4.0 eV]: 8.83e+01 +/- 3.51e-01%
Group 5 [0.28 - 0.625 eV]: 2.90e+02 +/- 5.28e-01%
Group 6 [0.14 - 0.28 eV]: 4.49e+02 +/- 4.05e-01%
Group 7 [0.058 - 0.14 eV]: 6.87e+02 +/- 3.36e-01%
Group 8 [0.0 - 0.058 eV]: 1.44e+03 +/- 2.54e-01%
Nuclide = U238
Cross Sections [barns]:
Group 1 [821000.0 - 20000000.0eV]: 1.06e+00 +/- 2.64e-01%
Group 2 [5530.0 - 821000.0 eV]: 1.21e-03 +/- 2.83e-01%
Group 3 [4.0 - 5530.0 eV]: 5.51e-04 +/- 2.99e+00%
Group 4 [0.625 - 4.0 eV]: 6.54e-06 +/- 3.28e-01%
Group 5 [0.28 - 0.625 eV]: 1.07e-05 +/- 5.12e-01%
Group 6 [0.14 - 0.28 eV]: 1.55e-05 +/- 4.08e-01%
Group 7 [0.058 - 0.14 eV]: 2.30e-05 +/- 3.35e-01%
Group 8 [0.0 - 0.058 eV]: 4.24e-05 +/- 2.53e-01%
Our multi-group cross sections are capable of summing across all nuclides to provide us with macroscopic cross sections as well.
In [17]:
nufission = xs_library[fuel_cell.id]['nu-fission']
nufission.print_xs(xs_type='macro', nuclides='sum')
Multi-Group XS
Reaction Type = nu-fission
Domain Type = cell
Domain ID = 1
Cross Sections [cm^-1]:
Group 1 [821000.0 - 20000000.0eV]: 2.52e-02 +/- 2.51e-01%
Group 2 [5530.0 - 821000.0 eV]: 1.51e-03 +/- 1.50e-01%
Group 3 [4.0 - 5530.0 eV]: 2.07e-02 +/- 2.14e-01%
Group 4 [0.625 - 4.0 eV]: 3.31e-02 +/- 3.51e-01%
Group 5 [0.28 - 0.625 eV]: 1.09e-01 +/- 5.28e-01%
Group 6 [0.14 - 0.28 eV]: 1.69e-01 +/- 4.05e-01%
Group 7 [0.058 - 0.14 eV]: 2.58e-01 +/- 3.36e-01%
Group 8 [0.0 - 0.058 eV]: 5.40e-01 +/- 2.54e-01%
Although a printed report is nice, it is not scalable or flexible. Let's extract the microscopic cross section data for the moderator as a Pandas DataFrame .
In [18]:
nuscatter = xs_library[moderator_cell.id]['nu-scatter']
df = nuscatter.get_pandas_dataframe(xs_type='micro')
df.head(10)
Out[18]:
| cell | group in | group out | nuclide | mean | std. dev. | |
|---|---|---|---|---|---|---|
| 126 | 3 | 1 | 1 | H1 | 0.233979 | 0.003921 |
| 127 | 3 | 1 | 1 | O16 | 1.566955 | 0.006599 |
| 124 | 3 | 1 | 2 | H1 | 1.589223 | 0.003224 |
| 125 | 3 | 1 | 2 | O16 | 0.286382 | 0.001478 |
| 122 | 3 | 1 | 3 | H1 | 0.011405 | 0.000244 |
| 123 | 3 | 1 | 3 | O16 | 0.000000 | 0.000000 |
| 120 | 3 | 1 | 4 | H1 | 0.000015 | 0.000009 |
| 121 | 3 | 1 | 4 | O16 | 0.000000 | 0.000000 |
| 118 | 3 | 1 | 5 | H1 | 0.000005 | 0.000005 |
| 119 | 3 | 1 | 5 | O16 | 0.000000 | 0.000000 |
Next, we illustate how one can easily take multi-group cross sections and condense them down to a coarser energy group structure. The MGXS class includes a get_condensed_xs(...) method which takes an EnergyGroups parameter with a coarse(r) group structure and returns a new MGXS condensed to the coarse groups. We illustrate this process below using the 2-group structure created earlier.
In [19]:
# Extract the 8-group transport cross section for the fuel
fine_xs = xs_library[fuel_cell.id]['transport']
# Condense to the 2-group structure
condensed_xs = fine_xs.get_condensed_xs(coarse_groups)
Group condensation is as simple as that! We now have a new coarse 2-group TransportXS in addition to our original 8-group TransportXS. Let's inspect the 2-group TransportXS by printing it to the screen and extracting a Pandas DataFrame as we have already learned how to do.
In [20]:
condensed_xs.print_xs()
Multi-Group XS
Reaction Type = transport
Domain Type = cell
Domain ID = 1
Nuclide = U235
Cross Sections [cm^-1]:
Group 1 [0.625 - 20000000.0eV]: 7.77e-03 +/- 2.18e-01%
Group 2 [0.0 - 0.625 eV]: 1.82e-01 +/- 1.85e-01%
Nuclide = U238
Cross Sections [cm^-1]:
Group 1 [0.625 - 20000000.0eV]: 2.17e-01 +/- 1.32e-01%
Group 2 [0.0 - 0.625 eV]: 2.53e-01 +/- 1.91e-01%
Nuclide = O16
Cross Sections [cm^-1]:
Group 1 [0.625 - 20000000.0eV]: 1.45e-01 +/- 1.26e-01%
Group 2 [0.0 - 0.625 eV]: 1.74e-01 +/- 2.02e-01%
In [21]:
df = condensed_xs.get_pandas_dataframe(xs_type='micro')
df
Out[21]:
| cell | group in | nuclide | mean | std. dev. | |
|---|---|---|---|---|---|
| 3 | 1 | 1 | U235 | 20.715441 | 0.045146 |
| 4 | 1 | 1 | U238 | 9.579757 | 0.012606 |
| 5 | 1 | 1 | O16 | 3.155966 | 0.003977 |
| 0 | 1 | 2 | U235 | 485.656482 | 0.899766 |
| 1 | 1 | 2 | U238 | 11.191961 | 0.021372 |
| 2 | 1 | 2 | O16 | 3.790699 | 0.007656 |
Verification with OpenMOC¶
Now, let's verify our cross sections using OpenMOC. First, we construct an equivalent OpenMOC geometry.
In [22]:
# Create an OpenMOC Geometry from the OpenMC Geometry
openmoc_geometry = get_openmoc_geometry(sp.summary.geometry)
Next, we we can inject the multi-group cross sections into the equivalent fuel pin cell OpenMOC geometry.
In [23]:
# Get all OpenMOC cells in the gometry
openmoc_cells = openmoc_geometry.getRootUniverse().getAllCells()
# Inject multi-group cross sections into OpenMOC Materials
for cell_id, cell in openmoc_cells.items():
# Ignore the root cell
if cell.getName() == 'root cell':
continue
# Get a reference to the Material filling this Cell
openmoc_material = cell.getFillMaterial()
# Set the number of energy groups for the Material
openmoc_material.setNumEnergyGroups(fine_groups.num_groups)
# Extract the appropriate cross section objects for this cell
transport = xs_library[cell_id]['transport']
nufission = xs_library[cell_id]['nu-fission']
nuscatter = xs_library[cell_id]['nu-scatter']
chi = xs_library[cell_id]['chi']
# Inject NumPy arrays of cross section data into the Material
# NOTE: Sum across nuclides to get macro cross sections needed by OpenMOC
openmoc_material.setSigmaT(transport.get_xs(nuclides='sum').flatten())
openmoc_material.setNuSigmaF(nufission.get_xs(nuclides='sum').flatten())
openmoc_material.setSigmaS(nuscatter.get_xs(nuclides='sum').flatten())
openmoc_material.setChi(chi.get_xs(nuclides='sum').flatten())
We are now ready to run OpenMOC to verify our cross-sections from OpenMC.
In [24]:
# Generate tracks for OpenMOC
track_generator = openmoc.TrackGenerator(openmoc_geometry, num_azim=128, azim_spacing=0.1)
track_generator.generateTracks()
# Run OpenMOC
solver = openmoc.CPUSolver(track_generator)
solver.computeEigenvalue()
[ NORMAL ] Initializing a default angular quadrature... [ NORMAL ] Initializing 2D tracks... [ NORMAL ] Initializing 2D tracks reflections... [ NORMAL ] Initializing 2D tracks array... [ NORMAL ] Ray tracing for 2D track segmentation... [ NORMAL ] Progress Segmenting 2D tracks: 0.09 % [ NORMAL ] Progress Segmenting 2D tracks: 10.02 % [ NORMAL ] Progress Segmenting 2D tracks: 19.94 % [ NORMAL ] Progress Segmenting 2D tracks: 29.87 % [ NORMAL ] Progress Segmenting 2D tracks: 39.80 % [ NORMAL ] Progress Segmenting 2D tracks: 49.72 % [ NORMAL ] Progress Segmenting 2D tracks: 59.65 % [ NORMAL ] Progress Segmenting 2D tracks: 69.58 % [ NORMAL ] Progress Segmenting 2D tracks: 79.50 % [ NORMAL ] Progress Segmenting 2D tracks: 89.43 % [ NORMAL ] Progress Segmenting 2D tracks: 100.00 % [ NORMAL ] Initializing FSR lookup vectors [ NORMAL ] Total number of FSRs 3 [ NORMAL ] Initializing MOC eigenvalue solver... [ NORMAL ] Initializing solver arrays... [ NORMAL ] Centering segments around FSR centroid... [ NORMAL ] Max boundary angular flux storage per domain = 0.42 MB [ NORMAL ] Max scalar flux storage per domain = 0.00 MB [ NORMAL ] Max source storage per domain = 0.00 MB [ NORMAL ] Number of azimuthal angles = 128 [ NORMAL ] Azimuthal ray spacing = 0.100000 [ NORMAL ] Number of polar angles = 6 [ NORMAL ] Source type = Flat [ NORMAL ] MOC transport undamped [ NORMAL ] CMFD acceleration: OFF [ NORMAL ] Using 1 threads [ NORMAL ] Computing the eigenvalue... [ NORMAL ] Iteration 0: k_eff = 0.423006 res = 1.792E-08 delta-k (pcm) = [ NORMAL ] ... -57699 D.R. = 0.0000 [ NORMAL ] Iteration 1: k_eff = 0.475905 res = 3.879E-08 delta-k (pcm) = [ NORMAL ] ... 5289 D.R. = 2.1646 [ NORMAL ] Iteration 2: k_eff = 0.491392 res = 3.463E-08 delta-k (pcm) = [ NORMAL ] ... 1548 D.R. = 0.8928 [ NORMAL ] Iteration 3: k_eff = 0.487335 res = 3.478E-09 delta-k (pcm) = [ NORMAL ] ... -405 D.R. = 0.1004 [ NORMAL ] Iteration 4: k_eff = 0.483788 res = 8.318E-09 delta-k (pcm) = [ NORMAL ] ... -354 D.R. = 2.3913 [ NORMAL ] Iteration 5: k_eff = 0.477110 res = 1.437E-08 delta-k (pcm) = [ NORMAL ] ... -667 D.R. = 1.7273 [ NORMAL ] Iteration 6: k_eff = 0.468745 res = 1.966E-09 delta-k (pcm) = [ NORMAL ] ... -836 D.R. = 0.1368 [ NORMAL ] Iteration 7: k_eff = 0.460108 res = 5.656E-08 delta-k (pcm) = [ NORMAL ] ... -863 D.R. = 28.7692 [ NORMAL ] Iteration 8: k_eff = 0.450367 res = 1.612E-07 delta-k (pcm) = [ NORMAL ] ... -974 D.R. = 2.8503 [ NORMAL ] Iteration 9: k_eff = 0.441143 res = 6.685E-08 delta-k (pcm) = [ NORMAL ] ... -922 D.R. = 0.4146 [ NORMAL ] Iteration 10: k_eff = 0.431749 res = 3.902E-08 delta-k (pcm) = [ NORMAL ] ... -939 D.R. = 0.5837 [ NORMAL ] Iteration 11: k_eff = 0.422685 res = 2.208E-08 delta-k (pcm) = [ NORMAL ] ... -906 D.R. = 0.5659 [ NORMAL ] Iteration 12: k_eff = 0.414237 res = 2.964E-08 delta-k (pcm) = [ NORMAL ] ... -844 D.R. = 1.3425 [ NORMAL ] Iteration 13: k_eff = 0.406456 res = 2.238E-08 delta-k (pcm) = [ NORMAL ] ... -778 D.R. = 0.7551 [ NORMAL ] Iteration 14: k_eff = 0.399125 res = 2.117E-08 delta-k (pcm) = [ NORMAL ] ... -733 D.R. = 0.9459 [ NORMAL ] Iteration 15: k_eff = 0.392814 res = 3.569E-08 delta-k (pcm) = [ NORMAL ] ... -631 D.R. = 1.6857 [ NORMAL ] Iteration 16: k_eff = 0.387174 res = 3.206E-08 delta-k (pcm) = [ NORMAL ] ... -564 D.R. = 0.8983 [ NORMAL ] Iteration 17: k_eff = 0.382416 res = 5.263E-08 delta-k (pcm) = [ NORMAL ] ... -475 D.R. = 1.6415 [ NORMAL ] Iteration 18: k_eff = 0.378489 res = 4.537E-08 delta-k (pcm) = [ NORMAL ] ... -392 D.R. = 0.8621 [ NORMAL ] Iteration 19: k_eff = 0.375392 res = 3.085E-08 delta-k (pcm) = [ NORMAL ] ... -309 D.R. = 0.6800 [ NORMAL ] Iteration 20: k_eff = 0.373239 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... -215 D.R. = 0.3137 [ NORMAL ] Iteration 21: k_eff = 0.372107 res = 1.210E-09 delta-k (pcm) = [ NORMAL ] ... -113 D.R. = 0.1250 [ NORMAL ] Iteration 22: k_eff = 0.371724 res = 4.235E-09 delta-k (pcm) = [ NORMAL ] ... -38 D.R. = 3.5000 [ NORMAL ] Iteration 23: k_eff = 0.372330 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 60 D.R. = 4.5714 [ NORMAL ] Iteration 24: k_eff = 0.373804 res = 5.686E-08 delta-k (pcm) = [ NORMAL ] ... 147 D.R. = 2.9375 [ NORMAL ] Iteration 25: k_eff = 0.376130 res = 4.840E-08 delta-k (pcm) = [ NORMAL ] ... 232 D.R. = 0.8511 [ NORMAL ] Iteration 26: k_eff = 0.379307 res = 3.509E-08 delta-k (pcm) = [ NORMAL ] ... 317 D.R. = 0.7250 [ NORMAL ] Iteration 27: k_eff = 0.383324 res = 3.993E-08 delta-k (pcm) = [ NORMAL ] ... 401 D.R. = 1.1379 [ NORMAL ] Iteration 28: k_eff = 0.388118 res = 8.469E-09 delta-k (pcm) = [ NORMAL ] ... 479 D.R. = 0.2121 [ NORMAL ] Iteration 29: k_eff = 0.393671 res = 1.452E-08 delta-k (pcm) = [ NORMAL ] ... 555 D.R. = 1.7143 [ NORMAL ] Iteration 30: k_eff = 0.399962 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 629 D.R. = 2.0000 [ NORMAL ] Iteration 31: k_eff = 0.406957 res = 3.146E-08 delta-k (pcm) = [ NORMAL ] ... 699 D.R. = 1.0833 [ NORMAL ] Iteration 32: k_eff = 0.414600 res = 6.896E-08 delta-k (pcm) = [ NORMAL ] ... 764 D.R. = 2.1923 [ NORMAL ] Iteration 33: k_eff = 0.422881 res = 1.815E-08 delta-k (pcm) = [ NORMAL ] ... 828 D.R. = 0.2632 [ NORMAL ] Iteration 34: k_eff = 0.431752 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... 887 D.R. = 0.5333 [ NORMAL ] Iteration 35: k_eff = 0.441164 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 941 D.R. = 3.0000 [ NORMAL ] Iteration 36: k_eff = 0.451113 res = 8.469E-09 delta-k (pcm) = [ NORMAL ] ... 994 D.R. = 0.2917 [ NORMAL ] Iteration 37: k_eff = 0.461526 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 1041 D.R. = 4.5714 [ NORMAL ] Iteration 38: k_eff = 0.472392 res = 7.501E-08 delta-k (pcm) = [ NORMAL ] ... 1086 D.R. = 1.9375 [ NORMAL ] Iteration 39: k_eff = 0.483657 res = 6.533E-08 delta-k (pcm) = [ NORMAL ] ... 1126 D.R. = 0.8710 [ NORMAL ] Iteration 40: k_eff = 0.495292 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 1163 D.R. = 0.5926 [ NORMAL ] Iteration 41: k_eff = 0.507260 res = 3.388E-08 delta-k (pcm) = [ NORMAL ] ... 1196 D.R. = 0.8750 [ NORMAL ] Iteration 42: k_eff = 0.519528 res = 4.598E-08 delta-k (pcm) = [ NORMAL ] ... 1226 D.R. = 1.3571 [ NORMAL ] Iteration 43: k_eff = 0.532058 res = 4.598E-08 delta-k (pcm) = [ NORMAL ] ... 1253 D.R. = 1.0000 [ NORMAL ] Iteration 44: k_eff = 0.544820 res = 8.469E-09 delta-k (pcm) = [ NORMAL ] ... 1276 D.R. = 0.1842 [ NORMAL ] Iteration 45: k_eff = 0.557781 res = 1.089E-08 delta-k (pcm) = [ NORMAL ] ... 1296 D.R. = 1.2857 [ NORMAL ] Iteration 46: k_eff = 0.570908 res = 6.775E-08 delta-k (pcm) = [ NORMAL ] ... 1312 D.R. = 6.2222 [ NORMAL ] Iteration 47: k_eff = 0.584174 res = 7.864E-08 delta-k (pcm) = [ NORMAL ] ... 1326 D.R. = 1.1607 [ NORMAL ] Iteration 48: k_eff = 0.597549 res = 9.074E-09 delta-k (pcm) = [ NORMAL ] ... 1337 D.R. = 0.1154 [ NORMAL ] Iteration 49: k_eff = 0.611006 res = 2.662E-08 delta-k (pcm) = [ NORMAL ] ... 1345 D.R. = 2.9333 [ NORMAL ] Iteration 50: k_eff = 0.624518 res = 3.085E-08 delta-k (pcm) = [ NORMAL ] ... 1351 D.R. = 1.1591 [ NORMAL ] Iteration 51: k_eff = 0.638062 res = 7.501E-08 delta-k (pcm) = [ NORMAL ] ... 1354 D.R. = 2.4314 [ NORMAL ] Iteration 52: k_eff = 0.651612 res = 6.654E-08 delta-k (pcm) = [ NORMAL ] ... 1355 D.R. = 0.8871 [ NORMAL ] Iteration 53: k_eff = 0.665146 res = 2.057E-08 delta-k (pcm) = [ NORMAL ] ... 1353 D.R. = 0.3091 [ NORMAL ] Iteration 54: k_eff = 0.678645 res = 1.512E-08 delta-k (pcm) = [ NORMAL ] ... 1349 D.R. = 0.7353 [ NORMAL ] Iteration 55: k_eff = 0.692087 res = 1.210E-09 delta-k (pcm) = [ NORMAL ] ... 1344 D.R. = 0.0800 [ NORMAL ] Iteration 56: k_eff = 0.705453 res = 1.028E-08 delta-k (pcm) = [ NORMAL ] ... 1336 D.R. = 8.5000 [ NORMAL ] Iteration 57: k_eff = 0.718729 res = 9.074E-09 delta-k (pcm) = [ NORMAL ] ... 1327 D.R. = 0.8824 [ NORMAL ] Iteration 58: k_eff = 0.731896 res = 6.049E-10 delta-k (pcm) = [ NORMAL ] ... 1316 D.R. = 0.0667 [ NORMAL ] Iteration 59: k_eff = 0.744940 res = 1.149E-08 delta-k (pcm) = [ NORMAL ] ... 1304 D.R. = 19.0000 [ NORMAL ] Iteration 60: k_eff = 0.757847 res = 2.057E-08 delta-k (pcm) = [ NORMAL ] ... 1290 D.R. = 1.7895 [ NORMAL ] Iteration 61: k_eff = 0.770604 res = 1.149E-08 delta-k (pcm) = [ NORMAL ] ... 1275 D.R. = 0.5588 [ NORMAL ] Iteration 62: k_eff = 0.783200 res = 3.146E-08 delta-k (pcm) = [ NORMAL ] ... 1259 D.R. = 2.7368 [ NORMAL ] Iteration 63: k_eff = 0.795624 res = 3.448E-08 delta-k (pcm) = [ NORMAL ] ... 1242 D.R. = 1.0962 [ NORMAL ] Iteration 64: k_eff = 0.807866 res = 2.964E-08 delta-k (pcm) = [ NORMAL ] ... 1224 D.R. = 0.8596 [ NORMAL ] Iteration 65: k_eff = 0.819919 res = 6.715E-08 delta-k (pcm) = [ NORMAL ] ... 1205 D.R. = 2.2653 [ NORMAL ] Iteration 66: k_eff = 0.831774 res = 2.238E-08 delta-k (pcm) = [ NORMAL ] ... 1185 D.R. = 0.3333 [ NORMAL ] Iteration 67: k_eff = 0.843424 res = 1.633E-08 delta-k (pcm) = [ NORMAL ] ... 1165 D.R. = 0.7297 [ NORMAL ] Iteration 68: k_eff = 0.854864 res = 1.633E-08 delta-k (pcm) = [ NORMAL ] ... 1143 D.R. = 1.0000 [ NORMAL ] Iteration 69: k_eff = 0.866087 res = 2.359E-08 delta-k (pcm) = [ NORMAL ] ... 1122 D.R. = 1.4444 [ NORMAL ] Iteration 70: k_eff = 0.877091 res = 2.299E-08 delta-k (pcm) = [ NORMAL ] ... 1100 D.R. = 0.9744 [ NORMAL ] Iteration 71: k_eff = 0.887870 res = 1.875E-08 delta-k (pcm) = [ NORMAL ] ... 1077 D.R. = 0.8158 [ NORMAL ] Iteration 72: k_eff = 0.898423 res = 2.420E-09 delta-k (pcm) = [ NORMAL ] ... 1055 D.R. = 0.1290 [ NORMAL ] Iteration 73: k_eff = 0.908747 res = 7.864E-09 delta-k (pcm) = [ NORMAL ] ... 1032 D.R. = 3.2500 [ NORMAL ] Iteration 74: k_eff = 0.918839 res = 1.633E-08 delta-k (pcm) = [ NORMAL ] ... 1009 D.R. = 2.0769 [ NORMAL ] Iteration 75: k_eff = 0.928699 res = 4.174E-08 delta-k (pcm) = [ NORMAL ] ... 986 D.R. = 2.5556 [ NORMAL ] Iteration 76: k_eff = 0.938326 res = 4.779E-08 delta-k (pcm) = [ NORMAL ] ... 962 D.R. = 1.1449 [ NORMAL ] Iteration 77: k_eff = 0.947719 res = 1.210E-09 delta-k (pcm) = [ NORMAL ] ... 939 D.R. = 0.0253 [ NORMAL ] Iteration 78: k_eff = 0.956880 res = 6.049E-09 delta-k (pcm) = [ NORMAL ] ... 916 D.R. = 5.0000 [ NORMAL ] Iteration 79: k_eff = 0.965808 res = 1.512E-08 delta-k (pcm) = [ NORMAL ] ... 892 D.R. = 2.5000 [ NORMAL ] Iteration 80: k_eff = 0.974505 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 869 D.R. = 1.2800 [ NORMAL ] Iteration 81: k_eff = 0.982972 res = 1.452E-08 delta-k (pcm) = [ NORMAL ] ... 846 D.R. = 0.7500 [ NORMAL ] Iteration 82: k_eff = 0.991211 res = 5.445E-09 delta-k (pcm) = [ NORMAL ] ... 823 D.R. = 0.3750 [ NORMAL ] Iteration 83: k_eff = 0.999224 res = 3.630E-09 delta-k (pcm) = [ NORMAL ] ... 801 D.R. = 0.6667 [ NORMAL ] Iteration 84: k_eff = 1.007014 res = 5.445E-09 delta-k (pcm) = [ NORMAL ] ... 778 D.R. = 1.5000 [ NORMAL ] Iteration 85: k_eff = 1.014581 res = 4.537E-08 delta-k (pcm) = [ NORMAL ] ... 756 D.R. = 8.3333 [ NORMAL ] Iteration 86: k_eff = 1.021932 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 735 D.R. = 1.2800 [ NORMAL ] Iteration 87: k_eff = 1.029067 res = 6.049E-08 delta-k (pcm) = [ NORMAL ] ... 713 D.R. = 1.0417 [ NORMAL ] Iteration 88: k_eff = 1.035990 res = 7.078E-08 delta-k (pcm) = [ NORMAL ] ... 692 D.R. = 1.1700 [ NORMAL ] Iteration 89: k_eff = 1.042705 res = 2.662E-08 delta-k (pcm) = [ NORMAL ] ... 671 D.R. = 0.3761 [ NORMAL ] Iteration 90: k_eff = 1.049215 res = 3.569E-08 delta-k (pcm) = [ NORMAL ] ... 650 D.R. = 1.3409 [ NORMAL ] Iteration 91: k_eff = 1.055524 res = 1.149E-08 delta-k (pcm) = [ NORMAL ] ... 630 D.R. = 0.3220 [ NORMAL ] Iteration 92: k_eff = 1.061635 res = 3.327E-08 delta-k (pcm) = [ NORMAL ] ... 611 D.R. = 2.8947 [ NORMAL ] Iteration 93: k_eff = 1.067553 res = 1.149E-08 delta-k (pcm) = [ NORMAL ] ... 591 D.R. = 0.3455 [ NORMAL ] Iteration 94: k_eff = 1.073282 res = 1.815E-09 delta-k (pcm) = [ NORMAL ] ... 572 D.R. = 0.1579 [ NORMAL ] Iteration 95: k_eff = 1.078825 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 554 D.R. = 16.0000 [ NORMAL ] Iteration 96: k_eff = 1.084186 res = 4.235E-09 delta-k (pcm) = [ NORMAL ] ... 536 D.R. = 0.1458 [ NORMAL ] Iteration 97: k_eff = 1.089370 res = 1.694E-08 delta-k (pcm) = [ NORMAL ] ... 518 D.R. = 4.0000 [ NORMAL ] Iteration 98: k_eff = 1.094381 res = 2.299E-08 delta-k (pcm) = [ NORMAL ] ... 501 D.R. = 1.3571 [ NORMAL ] Iteration 99: k_eff = 1.099224 res = 3.569E-08 delta-k (pcm) = [ NORMAL ] ... 484 D.R. = 1.5526 [ NORMAL ] Iteration 100: k_eff = 1.103901 res = 2.299E-08 delta-k (pcm) [ NORMAL ] ... = 467 D.R. = 0.6441 [ NORMAL ] Iteration 101: k_eff = 1.108418 res = 4.779E-08 delta-k (pcm) [ NORMAL ] ... = 451 D.R. = 2.0789 [ NORMAL ] Iteration 102: k_eff = 1.112777 res = 4.235E-09 delta-k (pcm) [ NORMAL ] ... = 435 D.R. = 0.0886 [ NORMAL ] Iteration 103: k_eff = 1.116986 res = 2.480E-08 delta-k (pcm) [ NORMAL ] ... = 420 D.R. = 5.8571 [ NORMAL ] Iteration 104: k_eff = 1.121046 res = 1.573E-08 delta-k (pcm) [ NORMAL ] ... = 405 D.R. = 0.6341 [ NORMAL ] Iteration 105: k_eff = 1.124962 res = 7.320E-08 delta-k (pcm) [ NORMAL ] ... = 391 D.R. = 4.6538 [ NORMAL ] Iteration 106: k_eff = 1.128738 res = 5.082E-08 delta-k (pcm) [ NORMAL ] ... = 377 D.R. = 0.6942 [ NORMAL ] Iteration 107: k_eff = 1.132377 res = 6.049E-10 delta-k (pcm) [ NORMAL ] ... = 363 D.R. = 0.0119 [ NORMAL ] Iteration 108: k_eff = 1.135884 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 350 D.R. = 48.0000 [ NORMAL ] Iteration 109: k_eff = 1.139264 res = 3.509E-08 delta-k (pcm) [ NORMAL ] ... = 337 D.R. = 1.2083 [ NORMAL ] Iteration 110: k_eff = 1.142519 res = 1.633E-08 delta-k (pcm) [ NORMAL ] ... = 325 D.R. = 0.4655 [ NORMAL ] Iteration 111: k_eff = 1.145654 res = 5.505E-08 delta-k (pcm) [ NORMAL ] ... = 313 D.R. = 3.3704 [ NORMAL ] Iteration 112: k_eff = 1.148671 res = 2.178E-08 delta-k (pcm) [ NORMAL ] ... = 301 D.R. = 0.3956 [ NORMAL ] Iteration 113: k_eff = 1.151575 res = 9.074E-09 delta-k (pcm) [ NORMAL ] ... = 290 D.R. = 0.4167 [ NORMAL ] Iteration 114: k_eff = 1.154371 res = 4.235E-09 delta-k (pcm) [ NORMAL ] ... = 279 D.R. = 0.4667 [ NORMAL ] Iteration 115: k_eff = 1.157059 res = 1.512E-08 delta-k (pcm) [ NORMAL ] ... = 268 D.R. = 3.5714 [ NORMAL ] Iteration 116: k_eff = 1.159645 res = 2.843E-08 delta-k (pcm) [ NORMAL ] ... = 258 D.R. = 1.8800 [ NORMAL ] Iteration 117: k_eff = 1.162132 res = 4.658E-08 delta-k (pcm) [ NORMAL ] ... = 248 D.R. = 1.6383 [ NORMAL ] Iteration 118: k_eff = 1.164522 res = 3.025E-09 delta-k (pcm) [ NORMAL ] ... = 239 D.R. = 0.0649 [ NORMAL ] Iteration 119: k_eff = 1.166820 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 229 D.R. = 16.0000 [ NORMAL ] Iteration 120: k_eff = 1.169029 res = 3.630E-09 delta-k (pcm) [ NORMAL ] ... = 220 D.R. = 0.0750 [ NORMAL ] Iteration 121: k_eff = 1.171150 res = 7.864E-09 delta-k (pcm) [ NORMAL ] ... = 212 D.R. = 2.1667 [ NORMAL ] Iteration 122: k_eff = 1.173188 res = 1.331E-08 delta-k (pcm) [ NORMAL ] ... = 203 D.R. = 1.6923 [ NORMAL ] Iteration 123: k_eff = 1.175145 res = 2.057E-08 delta-k (pcm) [ NORMAL ] ... = 195 D.R. = 1.5455 [ NORMAL ] Iteration 124: k_eff = 1.177024 res = 1.452E-08 delta-k (pcm) [ NORMAL ] ... = 187 D.R. = 0.7059 [ NORMAL ] Iteration 125: k_eff = 1.178828 res = 1.149E-08 delta-k (pcm) [ NORMAL ] ... = 180 D.R. = 0.7917 [ NORMAL ] Iteration 126: k_eff = 1.180560 res = 3.388E-08 delta-k (pcm) [ NORMAL ] ... = 173 D.R. = 2.9474 [ NORMAL ] Iteration 127: k_eff = 1.182222 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 166 D.R. = 0.5714 [ NORMAL ] Iteration 128: k_eff = 1.183817 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 159 D.R. = 0.0000 [ NORMAL ] Iteration 129: k_eff = 1.185346 res = 1.875E-08 delta-k (pcm) [ NORMAL ] ... = 152 D.R. = inf [ NORMAL ] Iteration 130: k_eff = 1.186813 res = 4.658E-08 delta-k (pcm) [ NORMAL ] ... = 146 D.R. = 2.4839 [ NORMAL ] Iteration 131: k_eff = 1.188220 res = 1.270E-08 delta-k (pcm) [ NORMAL ] ... = 140 D.R. = 0.2727 [ NORMAL ] Iteration 132: k_eff = 1.189569 res = 2.299E-08 delta-k (pcm) [ NORMAL ] ... = 134 D.R. = 1.8095 [ NORMAL ] Iteration 133: k_eff = 1.190862 res = 2.843E-08 delta-k (pcm) [ NORMAL ] ... = 129 D.R. = 1.2368 [ NORMAL ] Iteration 134: k_eff = 1.192102 res = 4.658E-08 delta-k (pcm) [ NORMAL ] ... = 123 D.R. = 1.6383 [ NORMAL ] Iteration 135: k_eff = 1.193290 res = 2.178E-08 delta-k (pcm) [ NORMAL ] ... = 118 D.R. = 0.4675 [ NORMAL ] Iteration 136: k_eff = 1.194428 res = 6.049E-10 delta-k (pcm) [ NORMAL ] ... = 113 D.R. = 0.0278 [ NORMAL ] Iteration 137: k_eff = 1.195519 res = 2.420E-08 delta-k (pcm) [ NORMAL ] ... = 109 D.R. = 40.0000 [ NORMAL ] Iteration 138: k_eff = 1.196563 res = 3.932E-08 delta-k (pcm) [ NORMAL ] ... = 104 D.R. = 1.6250 [ NORMAL ] Iteration 139: k_eff = 1.197564 res = 5.505E-08 delta-k (pcm) [ NORMAL ] ... = 100 D.R. = 1.4000 [ NORMAL ] Iteration 140: k_eff = 1.198522 res = 2.420E-09 delta-k (pcm) [ NORMAL ] ... = 95 D.R. = 0.0440 [ NORMAL ] Iteration 141: k_eff = 1.199440 res = 8.348E-08 delta-k (pcm) [ NORMAL ] ... = 91 D.R. = 34.5000 [ NORMAL ] Iteration 142: k_eff = 1.200317 res = 3.993E-08 delta-k (pcm) [ NORMAL ] ... = 87 D.R. = 0.4783 [ NORMAL ] Iteration 143: k_eff = 1.201159 res = 5.263E-08 delta-k (pcm) [ NORMAL ] ... = 84 D.R. = 1.3182 [ NORMAL ] Iteration 144: k_eff = 1.201963 res = 6.352E-08 delta-k (pcm) [ NORMAL ] ... = 80 D.R. = 1.2069 [ NORMAL ] Iteration 145: k_eff = 1.202733 res = 5.686E-08 delta-k (pcm) [ NORMAL ] ... = 77 D.R. = 0.8952 [ NORMAL ] Iteration 146: k_eff = 1.203470 res = 6.654E-09 delta-k (pcm) [ NORMAL ] ... = 73 D.R. = 0.1170 [ NORMAL ] Iteration 147: k_eff = 1.204175 res = 3.448E-08 delta-k (pcm) [ NORMAL ] ... = 70 D.R. = 5.1818 [ NORMAL ] Iteration 148: k_eff = 1.204849 res = 2.541E-08 delta-k (pcm) [ NORMAL ] ... = 67 D.R. = 0.7368 [ NORMAL ] Iteration 149: k_eff = 1.205494 res = 2.178E-08 delta-k (pcm) [ NORMAL ] ... = 64 D.R. = 0.8571 [ NORMAL ] Iteration 150: k_eff = 1.206111 res = 3.993E-08 delta-k (pcm) [ NORMAL ] ... = 61 D.R. = 1.8333 [ NORMAL ] Iteration 151: k_eff = 1.206700 res = 5.324E-08 delta-k (pcm) [ NORMAL ] ... = 58 D.R. = 1.3333 [ NORMAL ] Iteration 152: k_eff = 1.207264 res = 1.391E-08 delta-k (pcm) [ NORMAL ] ... = 56 D.R. = 0.2614 [ NORMAL ] Iteration 153: k_eff = 1.207804 res = 1.210E-09 delta-k (pcm) [ NORMAL ] ... = 53 D.R. = 0.0870 [ NORMAL ] Iteration 154: k_eff = 1.208319 res = 5.021E-08 delta-k (pcm) [ NORMAL ] ... = 51 D.R. = 41.5000 [ NORMAL ] Iteration 155: k_eff = 1.208811 res = 6.654E-09 delta-k (pcm) [ NORMAL ] ... = 49 D.R. = 0.1325 [ NORMAL ] Iteration 156: k_eff = 1.209282 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 47 D.R. = 1.4545 [ NORMAL ] Iteration 157: k_eff = 1.209732 res = 6.049E-10 delta-k (pcm) [ NORMAL ] ... = 44 D.R. = 0.0625 [ NORMAL ] Iteration 158: k_eff = 1.210162 res = 3.690E-08 delta-k (pcm) [ NORMAL ] ... = 42 D.R. = 61.0000 [ NORMAL ] Iteration 159: k_eff = 1.210573 res = 1.149E-08 delta-k (pcm) [ NORMAL ] ... = 41 D.R. = 0.3115 [ NORMAL ] Iteration 160: k_eff = 1.210964 res = 7.259E-08 delta-k (pcm) [ NORMAL ] ... = 39 D.R. = 6.3158 [ NORMAL ] Iteration 161: k_eff = 1.211339 res = 1.010E-07 delta-k (pcm) [ NORMAL ] ... = 37 D.R. = 1.3917 [ NORMAL ] Iteration 162: k_eff = 1.211697 res = 5.263E-08 delta-k (pcm) [ NORMAL ] ... = 35 D.R. = 0.5210 [ NORMAL ] Iteration 163: k_eff = 1.212039 res = 6.110E-08 delta-k (pcm) [ NORMAL ] ... = 34 D.R. = 1.1609 [ NORMAL ] Iteration 164: k_eff = 1.212365 res = 4.356E-08 delta-k (pcm) [ NORMAL ] ... = 32 D.R. = 0.7129 [ NORMAL ] Iteration 165: k_eff = 1.212676 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 31 D.R. = 0.4444 [ NORMAL ] Iteration 166: k_eff = 1.212973 res = 4.235E-09 delta-k (pcm) [ NORMAL ] ... = 29 D.R. = 0.2187 [ NORMAL ] Iteration 167: k_eff = 1.213258 res = 1.815E-08 delta-k (pcm) [ NORMAL ] ... = 28 D.R. = 4.2857 [ NORMAL ] Iteration 168: k_eff = 1.213529 res = 5.747E-08 delta-k (pcm) [ NORMAL ] ... = 27 D.R. = 3.1667 [ NORMAL ] Iteration 169: k_eff = 1.213787 res = 8.530E-08 delta-k (pcm) [ NORMAL ] ... = 25 D.R. = 1.4842 [ NORMAL ] Iteration 170: k_eff = 1.214034 res = 6.049E-10 delta-k (pcm) [ NORMAL ] ... = 24 D.R. = 0.0071 [ NORMAL ] Iteration 171: k_eff = 1.214270 res = 8.469E-09 delta-k (pcm) [ NORMAL ] ... = 23 D.R. = 14.0000 [ NORMAL ] Iteration 172: k_eff = 1.214494 res = 3.206E-08 delta-k (pcm) [ NORMAL ] ... = 22 D.R. = 3.7857 [ NORMAL ] Iteration 173: k_eff = 1.214709 res = 3.751E-08 delta-k (pcm) [ NORMAL ] ... = 21 D.R. = 1.1698 [ NORMAL ] Iteration 174: k_eff = 1.214913 res = 1.089E-08 delta-k (pcm) [ NORMAL ] ... = 20 D.R. = 0.2903 [ NORMAL ] Iteration 175: k_eff = 1.215108 res = 4.537E-08 delta-k (pcm) [ NORMAL ] ... = 19 D.R. = 4.1667 [ NORMAL ] Iteration 176: k_eff = 1.215295 res = 3.267E-08 delta-k (pcm) [ NORMAL ] ... = 18 D.R. = 0.7200 [ NORMAL ] Iteration 177: k_eff = 1.215472 res = 3.690E-08 delta-k (pcm) [ NORMAL ] ... = 17 D.R. = 1.1296 [ NORMAL ] Iteration 178: k_eff = 1.215641 res = 3.085E-08 delta-k (pcm) [ NORMAL ] ... = 16 D.R. = 0.8361 [ NORMAL ] Iteration 179: k_eff = 1.215803 res = 2.178E-08 delta-k (pcm) [ NORMAL ] ... = 16 D.R. = 0.7059 [ NORMAL ] Iteration 180: k_eff = 1.215957 res = 3.932E-08 delta-k (pcm) [ NORMAL ] ... = 15 D.R. = 1.8056 [ NORMAL ] Iteration 181: k_eff = 1.216103 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 14 D.R. = 0.2462 [ NORMAL ] Iteration 182: k_eff = 1.216243 res = 8.469E-09 delta-k (pcm) [ NORMAL ] ... = 14 D.R. = 0.8750 [ NORMAL ] Iteration 183: k_eff = 1.216377 res = 6.049E-09 delta-k (pcm) [ NORMAL ] ... = 13 D.R. = 0.7143 [ NORMAL ] Iteration 184: k_eff = 1.216504 res = 2.299E-08 delta-k (pcm) [ NORMAL ] ... = 12 D.R. = 3.8000 [ NORMAL ] Iteration 185: k_eff = 1.216625 res = 4.053E-08 delta-k (pcm) [ NORMAL ] ... = 12 D.R. = 1.7632 [ NORMAL ] Iteration 186: k_eff = 1.216741 res = 2.238E-08 delta-k (pcm) [ NORMAL ] ... = 11 D.R. = 0.5522 [ NORMAL ] Iteration 187: k_eff = 1.216851 res = 5.565E-08 delta-k (pcm) [ NORMAL ] ... = 11 D.R. = 2.4865 [ NORMAL ] Iteration 188: k_eff = 1.216955 res = 6.049E-08 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 1.0870 [ NORMAL ] Iteration 189: k_eff = 1.217056 res = 5.445E-09 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 0.0900 [ NORMAL ] Iteration 190: k_eff = 1.217151 res = 7.864E-09 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 1.4444 [ NORMAL ] Iteration 191: k_eff = 1.217242 res = 2.299E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 2.9231 [ NORMAL ] Iteration 192: k_eff = 1.217328 res = 6.049E-10 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 0.0263 [ NORMAL ] Iteration 193: k_eff = 1.217410 res = 4.114E-08 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 68.0000 [ NORMAL ] Iteration 194: k_eff = 1.217489 res = 2.420E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 0.5882 [ NORMAL ] Iteration 195: k_eff = 1.217563 res = 3.569E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 1.4750 [ NORMAL ] Iteration 196: k_eff = 1.217635 res = 1.210E-09 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 0.0339 [ NORMAL ] Iteration 197: k_eff = 1.217703 res = 7.864E-09 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 6.5000 [ NORMAL ] Iteration 198: k_eff = 1.217768 res = 1.149E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 1.4615 [ NORMAL ] Iteration 199: k_eff = 1.217829 res = 2.238E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 1.9474 [ NORMAL ] Iteration 200: k_eff = 1.217887 res = 4.235E-09 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.1892 [ NORMAL ] Iteration 201: k_eff = 1.217943 res = 3.993E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 9.4286 [ NORMAL ] Iteration 202: k_eff = 1.217996 res = 2.843E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.7121 [ NORMAL ] Iteration 203: k_eff = 1.218047 res = 7.441E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 2.6170 [ NORMAL ] Iteration 204: k_eff = 1.218095 res = 1.089E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.1463 [ NORMAL ] Iteration 205: k_eff = 1.218141 res = 1.754E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 1.6111 [ NORMAL ] Iteration 206: k_eff = 1.218184 res = 4.356E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 2.4828 [ NORMAL ] Iteration 207: k_eff = 1.218225 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.2222 [ NORMAL ] Iteration 208: k_eff = 1.218265 res = 1.210E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.2500 [ NORMAL ] Iteration 209: k_eff = 1.218302 res = 3.146E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 2.6000 [ NORMAL ] Iteration 210: k_eff = 1.218338 res = 5.626E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.7885 [ NORMAL ] Iteration 211: k_eff = 1.218372 res = 1.815E-09 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.0323 [ NORMAL ] Iteration 212: k_eff = 1.218404 res = 6.291E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 34.6667 [ NORMAL ] Iteration 213: k_eff = 1.218435 res = 4.356E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.6923 [ NORMAL ] Iteration 214: k_eff = 1.218465 res = 6.836E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.5694 [ NORMAL ] Iteration 215: k_eff = 1.218493 res = 4.719E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.6903 [ NORMAL ] Iteration 216: k_eff = 1.218519 res = 6.654E-09 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.1410 [ NORMAL ] Iteration 217: k_eff = 1.218544 res = 1.210E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.8182 [ NORMAL ] Iteration 218: k_eff = 1.218568 res = 1.573E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.3000 [ NORMAL ] Iteration 219: k_eff = 1.218591 res = 1.875E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.1923 [ NORMAL ] Iteration 220: k_eff = 1.218613 res = 3.388E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.8065 [ NORMAL ] Iteration 221: k_eff = 1.218634 res = 3.751E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.1071 [ NORMAL ] Iteration 222: k_eff = 1.218654 res = 1.815E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0484 [ NORMAL ] Iteration 223: k_eff = 1.218672 res = 5.445E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 3.0000 [ NORMAL ] Iteration 224: k_eff = 1.218690 res = 1.815E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.3333 [ NORMAL ] Iteration 225: k_eff = 1.218707 res = 6.291E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 34.6667 [ NORMAL ] Iteration 226: k_eff = 1.218723 res = 7.864E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.1250 [ NORMAL ] Iteration 227: k_eff = 1.218738 res = 6.896E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 8.7692 [ NORMAL ] Iteration 228: k_eff = 1.218753 res = 6.715E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.9737 [ NORMAL ] Iteration 229: k_eff = 1.218766 res = 1.512E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.2252 [ NORMAL ] Iteration 230: k_eff = 1.218779 res = 1.573E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.0400 [ NORMAL ] Iteration 231: k_eff = 1.218792 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.2308 [ NORMAL ] Iteration 232: k_eff = 1.218804 res = 4.840E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.2500 [ NORMAL ] Iteration 233: k_eff = 1.218815 res = 4.174E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 8.6250 [ NORMAL ] Iteration 234: k_eff = 1.218826 res = 4.114E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.9855 [ NORMAL ] Iteration 235: k_eff = 1.218836 res = 3.630E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.8824 [ NORMAL ] Iteration 236: k_eff = 1.218846 res = 7.804E-08 delta-k (pcm) [ NORMAL ] ... = 0 D.R. = 2.1500
We report the eigenvalues computed by OpenMC and OpenMOC here together to summarize our results.
In [25]:
# Print report of keff and bias with OpenMC
openmoc_keff = solver.getKeff()
openmc_keff = sp.keff.n
bias = (openmoc_keff - openmc_keff) * 1e5
print('openmc keff = {0:1.6f}'.format(openmc_keff))
print('openmoc keff = {0:1.6f}'.format(openmoc_keff))
print('bias [pcm]: {0:1.1f}'.format(bias))
openmc keff = 1.222044 openmoc keff = 1.218846 bias [pcm]: -319.8
In [ ]:
As a sanity check, let's run a simulation with the coarse 2-group cross sections to ensure that they also produce a reasonable result.
In [26]:
openmoc_geometry = get_openmoc_geometry(sp.summary.geometry)
openmoc_cells = openmoc_geometry.getRootUniverse().getAllCells()
# Inject multi-group cross sections into OpenMOC Materials
for cell_id, cell in openmoc_cells.items():
# Ignore the root cell
if cell.getName() == 'root cell':
continue
openmoc_material = cell.getFillMaterial()
openmoc_material.setNumEnergyGroups(coarse_groups.num_groups)
# Extract the appropriate cross section objects for this cell
transport = xs_library[cell_id]['transport']
nufission = xs_library[cell_id]['nu-fission']
nuscatter = xs_library[cell_id]['nu-scatter']
chi = xs_library[cell_id]['chi']
# Perform group condensation
transport = transport.get_condensed_xs(coarse_groups)
nufission = nufission.get_condensed_xs(coarse_groups)
nuscatter = nuscatter.get_condensed_xs(coarse_groups)
chi = chi.get_condensed_xs(coarse_groups)
# Inject NumPy arrays of cross section data into the Material
openmoc_material.setSigmaT(transport.get_xs(nuclides='sum').flatten())
openmoc_material.setNuSigmaF(nufission.get_xs(nuclides='sum').flatten())
openmoc_material.setSigmaS(nuscatter.get_xs(nuclides='sum').flatten())
openmoc_material.setChi(chi.get_xs(nuclides='sum').flatten())
In [27]:
# Generate tracks for OpenMOC
track_generator = openmoc.TrackGenerator(openmoc_geometry, num_azim=128, azim_spacing=0.1)
track_generator.generateTracks()
# Run OpenMOC
solver = openmoc.CPUSolver(track_generator)
solver.computeEigenvalue()
[ NORMAL ] Initializing a default angular quadrature... [ NORMAL ] Initializing 2D tracks... [ NORMAL ] Initializing 2D tracks reflections... [ NORMAL ] Initializing 2D tracks array... [ NORMAL ] Ray tracing for 2D track segmentation... [ NORMAL ] Progress Segmenting 2D tracks: 0.09 % [ NORMAL ] Progress Segmenting 2D tracks: 10.02 % [ NORMAL ] Progress Segmenting 2D tracks: 19.94 % [ NORMAL ] Progress Segmenting 2D tracks: 29.87 % [ NORMAL ] Progress Segmenting 2D tracks: 39.80 % [ NORMAL ] Progress Segmenting 2D tracks: 49.72 % [ NORMAL ] Progress Segmenting 2D tracks: 59.65 % [ NORMAL ] Progress Segmenting 2D tracks: 69.58 % [ NORMAL ] Progress Segmenting 2D tracks: 79.50 % [ NORMAL ] Progress Segmenting 2D tracks: 89.43 % [ NORMAL ] Progress Segmenting 2D tracks: 100.00 % [ NORMAL ] Initializing FSR lookup vectors [ NORMAL ] Total number of FSRs 3 [ NORMAL ] Initializing MOC eigenvalue solver... [ NORMAL ] Initializing solver arrays... [ NORMAL ] Centering segments around FSR centroid... [ NORMAL ] Max boundary angular flux storage per domain = 0.10 MB [ NORMAL ] Max scalar flux storage per domain = 0.00 MB [ NORMAL ] Max source storage per domain = 0.00 MB [ NORMAL ] Number of azimuthal angles = 128 [ NORMAL ] Azimuthal ray spacing = 0.100000 [ NORMAL ] Number of polar angles = 6 [ NORMAL ] Source type = Flat [ NORMAL ] MOC transport undamped [ NORMAL ] CMFD acceleration: OFF [ NORMAL ] Using 1 threads [ NORMAL ] Computing the eigenvalue... [ NORMAL ] Iteration 0: k_eff = 0.366644 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... -63335 D.R. = 0.0000 [ NORMAL ] Iteration 1: k_eff = 0.390955 res = 1.210E-07 delta-k (pcm) = [ NORMAL ] ... 2431 D.R. = 12.5000 [ NORMAL ] Iteration 2: k_eff = 0.392706 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... 175 D.R. = 0.0800 [ NORMAL ] Iteration 3: k_eff = 0.380770 res = 8.711E-08 delta-k (pcm) = [ NORMAL ] ... -1193 D.R. = 9.0000 [ NORMAL ] Iteration 4: k_eff = 0.374646 res = 5.324E-08 delta-k (pcm) = [ NORMAL ] ... -612 D.R. = 0.6111 [ NORMAL ] Iteration 5: k_eff = 0.369186 res = 6.775E-08 delta-k (pcm) = [ NORMAL ] ... -546 D.R. = 1.2727 [ NORMAL ] Iteration 6: k_eff = 0.365104 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... -408 D.R. = 1.4286 [ NORMAL ] Iteration 7: k_eff = 0.362589 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... -251 D.R. = 0.8000 [ NORMAL ] Iteration 8: k_eff = 0.360985 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... -160 D.R. = 0.5000 [ NORMAL ] Iteration 9: k_eff = 0.360771 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... -21 D.R. = 1.0000 [ NORMAL ] Iteration 10: k_eff = 0.361478 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 70 D.R. = 0.0000 [ NORMAL ] Iteration 11: k_eff = 0.363179 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... 170 D.R. = inf [ NORMAL ] Iteration 12: k_eff = 0.365787 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 260 D.R. = 3.0000 [ NORMAL ] Iteration 13: k_eff = 0.369244 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 345 D.R. = 2.0000 [ NORMAL ] Iteration 14: k_eff = 0.373421 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 417 D.R. = 0.6667 [ NORMAL ] Iteration 15: k_eff = 0.378350 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 492 D.R. = 1.5000 [ NORMAL ] Iteration 16: k_eff = 0.383902 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 555 D.R. = 1.0000 [ NORMAL ] Iteration 17: k_eff = 0.390057 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 615 D.R. = 1.0000 [ NORMAL ] Iteration 18: k_eff = 0.396756 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 669 D.R. = 0.3333 [ NORMAL ] Iteration 19: k_eff = 0.403951 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 719 D.R. = 1.0000 [ NORMAL ] Iteration 20: k_eff = 0.411603 res = 1.355E-07 delta-k (pcm) = [ NORMAL ] ... 765 D.R. = 7.0000 [ NORMAL ] Iteration 21: k_eff = 0.419673 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 807 D.R. = 0.1429 [ NORMAL ] Iteration 22: k_eff = 0.428109 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 843 D.R. = 2.0000 [ NORMAL ] Iteration 23: k_eff = 0.436887 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 877 D.R. = 1.5000 [ NORMAL ] Iteration 24: k_eff = 0.445966 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 907 D.R. = 0.6667 [ NORMAL ] Iteration 25: k_eff = 0.455315 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 934 D.R. = 0.5000 [ NORMAL ] Iteration 26: k_eff = 0.464905 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 958 D.R. = 2.0000 [ NORMAL ] Iteration 27: k_eff = 0.474705 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 980 D.R. = 0.0000 [ NORMAL ] Iteration 28: k_eff = 0.484690 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 998 D.R. = inf [ NORMAL ] Iteration 29: k_eff = 0.494835 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1014 D.R. = 0.2500 [ NORMAL ] Iteration 30: k_eff = 0.505115 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1028 D.R. = 1.0000 [ NORMAL ] Iteration 31: k_eff = 0.515510 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 1039 D.R. = 0.0000 [ NORMAL ] Iteration 32: k_eff = 0.525998 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 1048 D.R. = inf [ NORMAL ] Iteration 33: k_eff = 0.536561 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 1056 D.R. = 2.0000 [ NORMAL ] Iteration 34: k_eff = 0.547180 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... 1061 D.R. = 1.2500 [ NORMAL ] Iteration 35: k_eff = 0.557840 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 1065 D.R. = 0.4000 [ NORMAL ] Iteration 36: k_eff = 0.568524 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 1068 D.R. = 0.0000 [ NORMAL ] Iteration 37: k_eff = 0.579219 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 1069 D.R. = -nan [ NORMAL ] Iteration 38: k_eff = 0.589911 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 1069 D.R. = -nan [ NORMAL ] Iteration 39: k_eff = 0.600586 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1067 D.R. = inf [ NORMAL ] Iteration 40: k_eff = 0.611235 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1064 D.R. = 1.0000 [ NORMAL ] Iteration 41: k_eff = 0.621847 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... 1061 D.R. = 5.0000 [ NORMAL ] Iteration 42: k_eff = 0.632410 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1056 D.R. = 0.2000 [ NORMAL ] Iteration 43: k_eff = 0.642917 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 1050 D.R. = 4.0000 [ NORMAL ] Iteration 44: k_eff = 0.653360 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1044 D.R. = 0.2500 [ NORMAL ] Iteration 45: k_eff = 0.663729 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 1036 D.R. = 2.0000 [ NORMAL ] Iteration 46: k_eff = 0.674019 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 1028 D.R. = 1.5000 [ NORMAL ] Iteration 47: k_eff = 0.684223 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 1020 D.R. = 1.0000 [ NORMAL ] Iteration 48: k_eff = 0.694335 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 1011 D.R. = 1.0000 [ NORMAL ] Iteration 49: k_eff = 0.704350 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 1001 D.R. = 0.3333 [ NORMAL ] Iteration 50: k_eff = 0.714262 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 991 D.R. = 2.0000 [ NORMAL ] Iteration 51: k_eff = 0.724068 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 980 D.R. = 1.0000 [ NORMAL ] Iteration 52: k_eff = 0.733764 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 969 D.R. = 0.5000 [ NORMAL ] Iteration 53: k_eff = 0.743346 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 958 D.R. = 2.0000 [ NORMAL ] Iteration 54: k_eff = 0.752809 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 946 D.R. = 2.0000 [ NORMAL ] Iteration 55: k_eff = 0.762154 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... 934 D.R. = 1.2500 [ NORMAL ] Iteration 56: k_eff = 0.771376 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... 922 D.R. = 1.0000 [ NORMAL ] Iteration 57: k_eff = 0.780473 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 909 D.R. = 0.6000 [ NORMAL ] Iteration 58: k_eff = 0.789445 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 897 D.R. = 1.3333 [ NORMAL ] Iteration 59: k_eff = 0.798288 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 884 D.R. = 1.0000 [ NORMAL ] Iteration 60: k_eff = 0.807003 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 871 D.R. = 0.5000 [ NORMAL ] Iteration 61: k_eff = 0.815587 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 858 D.R. = 0.5000 [ NORMAL ] Iteration 62: k_eff = 0.824040 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 845 D.R. = 0.0000 [ NORMAL ] Iteration 63: k_eff = 0.832361 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 832 D.R. = inf [ NORMAL ] Iteration 64: k_eff = 0.840551 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 818 D.R. = 1.5000 [ NORMAL ] Iteration 65: k_eff = 0.848608 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 805 D.R. = 1.0000 [ NORMAL ] Iteration 66: k_eff = 0.856534 res = 0.000E+00 delta-k (pcm) = [ NORMAL ] ... 792 D.R. = 0.0000 [ NORMAL ] Iteration 67: k_eff = 0.864327 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 779 D.R. = inf [ NORMAL ] Iteration 68: k_eff = 0.871988 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 766 D.R. = 1.0000 [ NORMAL ] Iteration 69: k_eff = 0.879518 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 752 D.R. = 1.0000 [ NORMAL ] Iteration 70: k_eff = 0.886917 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 739 D.R. = 1.5000 [ NORMAL ] Iteration 71: k_eff = 0.894186 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 726 D.R. = 0.3333 [ NORMAL ] Iteration 72: k_eff = 0.901326 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 713 D.R. = 2.0000 [ NORMAL ] Iteration 73: k_eff = 0.908336 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 701 D.R. = 1.0000 [ NORMAL ] Iteration 74: k_eff = 0.915219 res = 1.161E-07 delta-k (pcm) = [ NORMAL ] ... 688 D.R. = 3.0000 [ NORMAL ] Iteration 75: k_eff = 0.921976 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 675 D.R. = 0.1667 [ NORMAL ] Iteration 76: k_eff = 0.928607 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 663 D.R. = 1.0000 [ NORMAL ] Iteration 77: k_eff = 0.935114 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 650 D.R. = 2.0000 [ NORMAL ] Iteration 78: k_eff = 0.941498 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 638 D.R. = 0.5000 [ NORMAL ] Iteration 79: k_eff = 0.947759 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 626 D.R. = 1.0000 [ NORMAL ] Iteration 80: k_eff = 0.953900 res = 9.679E-08 delta-k (pcm) = [ NORMAL ] ... 614 D.R. = 5.0000 [ NORMAL ] Iteration 81: k_eff = 0.959922 res = 8.711E-08 delta-k (pcm) = [ NORMAL ] ... 602 D.R. = 0.9000 [ NORMAL ] Iteration 82: k_eff = 0.965827 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 590 D.R. = 0.4444 [ NORMAL ] Iteration 83: k_eff = 0.971615 res = 4.840E-08 delta-k (pcm) = [ NORMAL ] ... 578 D.R. = 1.2500 [ NORMAL ] Iteration 84: k_eff = 0.977288 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 567 D.R. = 0.6000 [ NORMAL ] Iteration 85: k_eff = 0.982848 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... 555 D.R. = 0.3333 [ NORMAL ] Iteration 86: k_eff = 0.988297 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 544 D.R. = 3.0000 [ NORMAL ] Iteration 87: k_eff = 0.993635 res = 4.840E-08 delta-k (pcm) = [ NORMAL ] ... 533 D.R. = 1.6667 [ NORMAL ] Iteration 88: k_eff = 0.998865 res = 3.872E-08 delta-k (pcm) = [ NORMAL ] ... 523 D.R. = 0.8000 [ NORMAL ] Iteration 89: k_eff = 1.003988 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 512 D.R. = 0.5000 [ NORMAL ] Iteration 90: k_eff = 1.009006 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 501 D.R. = 1.0000 [ NORMAL ] Iteration 91: k_eff = 1.013921 res = 6.775E-08 delta-k (pcm) = [ NORMAL ] ... 491 D.R. = 3.5000 [ NORMAL ] Iteration 92: k_eff = 1.018732 res = 8.711E-08 delta-k (pcm) = [ NORMAL ] ... 481 D.R. = 1.2857 [ NORMAL ] Iteration 93: k_eff = 1.023444 res = 6.775E-08 delta-k (pcm) = [ NORMAL ] ... 471 D.R. = 0.7778 [ NORMAL ] Iteration 94: k_eff = 1.028057 res = 1.936E-08 delta-k (pcm) = [ NORMAL ] ... 461 D.R. = 0.2857 [ NORMAL ] Iteration 95: k_eff = 1.032573 res = 6.775E-08 delta-k (pcm) = [ NORMAL ] ... 451 D.R. = 3.5000 [ NORMAL ] Iteration 96: k_eff = 1.036994 res = 2.904E-08 delta-k (pcm) = [ NORMAL ] ... 442 D.R. = 0.4286 [ NORMAL ] Iteration 97: k_eff = 1.041321 res = 7.743E-08 delta-k (pcm) = [ NORMAL ] ... 432 D.R. = 2.6667 [ NORMAL ] Iteration 98: k_eff = 1.045554 res = 5.807E-08 delta-k (pcm) = [ NORMAL ] ... 423 D.R. = 0.7500 [ NORMAL ] Iteration 99: k_eff = 1.049699 res = 9.679E-09 delta-k (pcm) = [ NORMAL ] ... 414 D.R. = 0.1667 [ NORMAL ] Iteration 100: k_eff = 1.053753 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 405 D.R. = 2.0000 [ NORMAL ] Iteration 101: k_eff = 1.057721 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 396 D.R. = 0.5000 [ NORMAL ] Iteration 102: k_eff = 1.061602 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 388 D.R. = 3.0000 [ NORMAL ] Iteration 103: k_eff = 1.065399 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 379 D.R. = 3.0000 [ NORMAL ] Iteration 104: k_eff = 1.069113 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 371 D.R. = 0.8889 [ NORMAL ] Iteration 105: k_eff = 1.072747 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 363 D.R. = 0.2500 [ NORMAL ] Iteration 106: k_eff = 1.076301 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 355 D.R. = 4.5000 [ NORMAL ] Iteration 107: k_eff = 1.079776 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 347 D.R. = 0.1111 [ NORMAL ] Iteration 108: k_eff = 1.083176 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 339 D.R. = 6.0000 [ NORMAL ] Iteration 109: k_eff = 1.086499 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 332 D.R. = 0.3333 [ NORMAL ] Iteration 110: k_eff = 1.089750 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 325 D.R. = 0.5000 [ NORMAL ] Iteration 111: k_eff = 1.092928 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 317 D.R. = 5.0000 [ NORMAL ] Iteration 112: k_eff = 1.096035 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 310 D.R. = 2.2000 [ NORMAL ] Iteration 113: k_eff = 1.099073 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 303 D.R. = 0.2727 [ NORMAL ] Iteration 114: k_eff = 1.102043 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 297 D.R. = 2.6667 [ NORMAL ] Iteration 115: k_eff = 1.104946 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 290 D.R. = 0.2500 [ NORMAL ] Iteration 116: k_eff = 1.107783 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 283 D.R. = 1.0000 [ NORMAL ] Iteration 117: k_eff = 1.110557 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 277 D.R. = 5.0000 [ NORMAL ] Iteration 118: k_eff = 1.113268 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 271 D.R. = 0.0000 [ NORMAL ] Iteration 119: k_eff = 1.115919 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 265 D.R. = inf [ NORMAL ] Iteration 120: k_eff = 1.118508 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 258 D.R. = 1.0000 [ NORMAL ] Iteration 121: k_eff = 1.121039 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 253 D.R. = 0.0000 [ NORMAL ] Iteration 122: k_eff = 1.123513 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 247 D.R. = inf [ NORMAL ] Iteration 123: k_eff = 1.125930 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 241 D.R. = 0.3333 [ NORMAL ] Iteration 124: k_eff = 1.128291 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 236 D.R. = 1.0000 [ NORMAL ] Iteration 125: k_eff = 1.130599 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 230 D.R. = 6.0000 [ NORMAL ] Iteration 126: k_eff = 1.132854 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 225 D.R. = 0.1667 [ NORMAL ] Iteration 127: k_eff = 1.135057 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 220 D.R. = 3.0000 [ NORMAL ] Iteration 128: k_eff = 1.137210 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 215 D.R. = 3.3333 [ NORMAL ] Iteration 129: k_eff = 1.139313 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 210 D.R. = 0.4000 [ NORMAL ] Iteration 130: k_eff = 1.141367 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 205 D.R. = 1.0000 [ NORMAL ] Iteration 131: k_eff = 1.143374 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 200 D.R. = 0.0000 [ NORMAL ] Iteration 132: k_eff = 1.145334 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 195 D.R. = inf [ NORMAL ] Iteration 133: k_eff = 1.147250 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 191 D.R. = 0.4545 [ NORMAL ] Iteration 134: k_eff = 1.149120 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 187 D.R. = 2.0000 [ NORMAL ] Iteration 135: k_eff = 1.150948 res = 1.549E-07 delta-k (pcm) [ NORMAL ] ... = 182 D.R. = 1.6000 [ NORMAL ] Iteration 136: k_eff = 1.152733 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 178 D.R. = 0.2500 [ NORMAL ] Iteration 137: k_eff = 1.154476 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 174 D.R. = 2.0000 [ NORMAL ] Iteration 138: k_eff = 1.156179 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 170 D.R. = 1.1250 [ NORMAL ] Iteration 139: k_eff = 1.157842 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 166 D.R. = 0.4444 [ NORMAL ] Iteration 140: k_eff = 1.159466 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 162 D.R. = 1.7500 [ NORMAL ] Iteration 141: k_eff = 1.161053 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 158 D.R. = 1.4286 [ NORMAL ] Iteration 142: k_eff = 1.162602 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 154 D.R. = 0.1000 [ NORMAL ] Iteration 143: k_eff = 1.164115 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 151 D.R. = 5.0000 [ NORMAL ] Iteration 144: k_eff = 1.165592 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 147 D.R. = 1.4000 [ NORMAL ] Iteration 145: k_eff = 1.167035 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 144 D.R. = 0.7143 [ NORMAL ] Iteration 146: k_eff = 1.168444 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 140 D.R. = 0.8000 [ NORMAL ] Iteration 147: k_eff = 1.169819 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 137 D.R. = 0.5000 [ NORMAL ] Iteration 148: k_eff = 1.171163 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 134 D.R. = 4.0000 [ NORMAL ] Iteration 149: k_eff = 1.172475 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 131 D.R. = 0.6250 [ NORMAL ] Iteration 150: k_eff = 1.173756 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 128 D.R. = 1.6000 [ NORMAL ] Iteration 151: k_eff = 1.175006 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 125 D.R. = 0.5000 [ NORMAL ] Iteration 152: k_eff = 1.176227 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 122 D.R. = 0.2500 [ NORMAL ] Iteration 153: k_eff = 1.177420 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 119 D.R. = 4.0000 [ NORMAL ] Iteration 154: k_eff = 1.178584 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 116 D.R. = 1.0000 [ NORMAL ] Iteration 155: k_eff = 1.179720 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 113 D.R. = 2.0000 [ NORMAL ] Iteration 156: k_eff = 1.180830 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 111 D.R. = 0.1250 [ NORMAL ] Iteration 157: k_eff = 1.181914 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 108 D.R. = 13.0000 [ NORMAL ] Iteration 158: k_eff = 1.182971 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 105 D.R. = 0.4615 [ NORMAL ] Iteration 159: k_eff = 1.184004 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 103 D.R. = 0.6667 [ NORMAL ] Iteration 160: k_eff = 1.185012 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 100 D.R. = 0.5000 [ NORMAL ] Iteration 161: k_eff = 1.185997 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 98 D.R. = 1.5000 [ NORMAL ] Iteration 162: k_eff = 1.186957 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 96 D.R. = 2.0000 [ NORMAL ] Iteration 163: k_eff = 1.187895 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 93 D.R. = 0.5000 [ NORMAL ] Iteration 164: k_eff = 1.188811 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 91 D.R. = 2.0000 [ NORMAL ] Iteration 165: k_eff = 1.189705 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 89 D.R. = 0.3333 [ NORMAL ] Iteration 166: k_eff = 1.190578 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 87 D.R. = 1.0000 [ NORMAL ] Iteration 167: k_eff = 1.191430 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 85 D.R. = 2.0000 [ NORMAL ] Iteration 168: k_eff = 1.192261 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 83 D.R. = 0.5000 [ NORMAL ] Iteration 169: k_eff = 1.193073 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 81 D.R. = 1.0000 [ NORMAL ] Iteration 170: k_eff = 1.193865 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 79 D.R. = 4.5000 [ NORMAL ] Iteration 171: k_eff = 1.194638 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 77 D.R. = 0.8889 [ NORMAL ] Iteration 172: k_eff = 1.195394 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 75 D.R. = 0.2500 [ NORMAL ] Iteration 173: k_eff = 1.196130 res = 1.355E-07 delta-k (pcm) [ NORMAL ] ... = 73 D.R. = 7.0000 [ NORMAL ] Iteration 174: k_eff = 1.196849 res = 1.452E-07 delta-k (pcm) [ NORMAL ] ... = 71 D.R. = 1.0714 [ NORMAL ] Iteration 175: k_eff = 1.197551 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 70 D.R. = 0.1333 [ NORMAL ] Iteration 176: k_eff = 1.198236 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 68 D.R. = 2.5000 [ NORMAL ] Iteration 177: k_eff = 1.198905 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 66 D.R. = 1.0000 [ NORMAL ] Iteration 178: k_eff = 1.199558 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 65 D.R. = 1.0000 [ NORMAL ] Iteration 179: k_eff = 1.200195 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 63 D.R. = 0.0000 [ NORMAL ] Iteration 180: k_eff = 1.200818 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 62 D.R. = inf [ NORMAL ] Iteration 181: k_eff = 1.201424 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 60 D.R. = 1.5000 [ NORMAL ] Iteration 182: k_eff = 1.202017 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 59 D.R. = 0.0000 [ NORMAL ] Iteration 183: k_eff = 1.202595 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 57 D.R. = inf [ NORMAL ] Iteration 184: k_eff = 1.203159 res = 1.452E-07 delta-k (pcm) [ NORMAL ] ... = 56 D.R. = 1.6667 [ NORMAL ] Iteration 185: k_eff = 1.203710 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 55 D.R. = 0.7333 [ NORMAL ] Iteration 186: k_eff = 1.204247 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 53 D.R. = 0.6364 [ NORMAL ] Iteration 187: k_eff = 1.204772 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 52 D.R. = 1.5714 [ NORMAL ] Iteration 188: k_eff = 1.205284 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 51 D.R. = 1.0909 [ NORMAL ] Iteration 189: k_eff = 1.205784 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 50 D.R. = 0.1667 [ NORMAL ] Iteration 190: k_eff = 1.206273 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 48 D.R. = 0.5000 [ NORMAL ] Iteration 191: k_eff = 1.206748 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 47 D.R. = 0.0000 [ NORMAL ] Iteration 192: k_eff = 1.207212 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 46 D.R. = inf [ NORMAL ] Iteration 193: k_eff = 1.207666 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 45 D.R. = 1.6667 [ NORMAL ] Iteration 194: k_eff = 1.208109 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 44 D.R. = 1.0000 [ NORMAL ] Iteration 195: k_eff = 1.208540 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 43 D.R. = 0.4000 [ NORMAL ] Iteration 196: k_eff = 1.208962 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 42 D.R. = 6.5000 [ NORMAL ] Iteration 197: k_eff = 1.209373 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 41 D.R. = 0.6923 [ NORMAL ] Iteration 198: k_eff = 1.209775 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 40 D.R. = 0.4444 [ NORMAL ] Iteration 199: k_eff = 1.210167 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 39 D.R. = 0.5000 [ NORMAL ] Iteration 200: k_eff = 1.210549 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 38 D.R. = 3.0000 [ NORMAL ] Iteration 201: k_eff = 1.210922 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 37 D.R. = 2.0000 [ NORMAL ] Iteration 202: k_eff = 1.211286 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 36 D.R. = 0.5000 [ NORMAL ] Iteration 203: k_eff = 1.211641 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 35 D.R. = 0.0000 [ NORMAL ] Iteration 204: k_eff = 1.211988 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 34 D.R. = inf [ NORMAL ] Iteration 205: k_eff = 1.212326 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 33 D.R. = 1.0000 [ NORMAL ] Iteration 206: k_eff = 1.212656 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 33 D.R. = 2.3333 [ NORMAL ] Iteration 207: k_eff = 1.212979 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 32 D.R. = 1.5714 [ NORMAL ] Iteration 208: k_eff = 1.213293 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 31 D.R. = 0.4545 [ NORMAL ] Iteration 209: k_eff = 1.213600 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 30 D.R. = 0.6000 [ NORMAL ] Iteration 210: k_eff = 1.213899 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 29 D.R. = 0.3333 [ NORMAL ] Iteration 211: k_eff = 1.214192 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 29 D.R. = 1.0000 [ NORMAL ] Iteration 212: k_eff = 1.214477 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 28 D.R. = 3.0000 [ NORMAL ] Iteration 213: k_eff = 1.214755 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 27 D.R. = 2.6667 [ NORMAL ] Iteration 214: k_eff = 1.215027 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 27 D.R. = 0.0000 [ NORMAL ] Iteration 215: k_eff = 1.215292 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 26 D.R. = -nan [ NORMAL ] Iteration 216: k_eff = 1.215551 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 25 D.R. = inf [ NORMAL ] Iteration 217: k_eff = 1.215803 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 25 D.R. = 1.1667 [ NORMAL ] Iteration 218: k_eff = 1.216049 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 24 D.R. = 0.1429 [ NORMAL ] Iteration 219: k_eff = 1.216289 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 23 D.R. = 5.0000 [ NORMAL ] Iteration 220: k_eff = 1.216524 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 23 D.R. = 1.0000 [ NORMAL ] Iteration 221: k_eff = 1.216753 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 22 D.R. = 0.2000 [ NORMAL ] Iteration 222: k_eff = 1.216976 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 22 D.R. = 5.0000 [ NORMAL ] Iteration 223: k_eff = 1.217193 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 21 D.R. = 0.8000 [ NORMAL ] Iteration 224: k_eff = 1.217406 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 21 D.R. = 0.5000 [ NORMAL ] Iteration 225: k_eff = 1.217613 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 20 D.R. = 4.0000 [ NORMAL ] Iteration 226: k_eff = 1.217816 res = 1.645E-07 delta-k (pcm) [ NORMAL ] ... = 20 D.R. = 2.1250 [ NORMAL ] Iteration 227: k_eff = 1.218013 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 19 D.R. = 0.3529 [ NORMAL ] Iteration 228: k_eff = 1.218206 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 19 D.R. = 0.3333 [ NORMAL ] Iteration 229: k_eff = 1.218394 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 18 D.R. = 3.0000 [ NORMAL ] Iteration 230: k_eff = 1.218578 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 18 D.R. = 2.1667 [ NORMAL ] Iteration 231: k_eff = 1.218758 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 17 D.R. = 0.7692 [ NORMAL ] Iteration 232: k_eff = 1.218932 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 17 D.R. = 0.3000 [ NORMAL ] Iteration 233: k_eff = 1.219103 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 17 D.R. = 0.0000 [ NORMAL ] Iteration 234: k_eff = 1.219269 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 16 D.R. = inf [ NORMAL ] Iteration 235: k_eff = 1.219431 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 16 D.R. = 0.2500 [ NORMAL ] Iteration 236: k_eff = 1.219590 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 15 D.R. = 7.0000 [ NORMAL ] Iteration 237: k_eff = 1.219745 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 15 D.R. = 0.2857 [ NORMAL ] Iteration 238: k_eff = 1.219896 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 15 D.R. = 1.5000 [ NORMAL ] Iteration 239: k_eff = 1.220043 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 14 D.R. = 3.3333 [ NORMAL ] Iteration 240: k_eff = 1.220187 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 14 D.R. = 0.2000 [ NORMAL ] Iteration 241: k_eff = 1.220327 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 13 D.R. = 3.0000 [ NORMAL ] Iteration 242: k_eff = 1.220464 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 13 D.R. = 0.6667 [ NORMAL ] Iteration 243: k_eff = 1.220597 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 13 D.R. = 0.5000 [ NORMAL ] Iteration 244: k_eff = 1.220727 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 13 D.R. = 4.5000 [ NORMAL ] Iteration 245: k_eff = 1.220854 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 12 D.R. = 0.4444 [ NORMAL ] Iteration 246: k_eff = 1.220978 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 12 D.R. = 1.0000 [ NORMAL ] Iteration 247: k_eff = 1.221099 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 12 D.R. = 1.7500 [ NORMAL ] Iteration 248: k_eff = 1.221217 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 11 D.R. = 1.8571 [ NORMAL ] Iteration 249: k_eff = 1.221333 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 11 D.R. = 0.9231 [ NORMAL ] Iteration 250: k_eff = 1.221445 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 11 D.R. = 0.1667 [ NORMAL ] Iteration 251: k_eff = 1.221555 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 3.5000 [ NORMAL ] Iteration 252: k_eff = 1.221662 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 0.2857 [ NORMAL ] Iteration 253: k_eff = 1.221766 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 3.0000 [ NORMAL ] Iteration 254: k_eff = 1.221868 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 10 D.R. = 0.8333 [ NORMAL ] Iteration 255: k_eff = 1.221968 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 0.4000 [ NORMAL ] Iteration 256: k_eff = 1.222064 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 1.0000 [ NORMAL ] Iteration 257: k_eff = 1.222159 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 1.0000 [ NORMAL ] Iteration 258: k_eff = 1.222251 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 2.0000 [ NORMAL ] Iteration 259: k_eff = 1.222342 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 9 D.R. = 2.2500 [ NORMAL ] Iteration 260: k_eff = 1.222429 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 0.5556 [ NORMAL ] Iteration 261: k_eff = 1.222515 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 1.2000 [ NORMAL ] Iteration 262: k_eff = 1.222599 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 0.1667 [ NORMAL ] Iteration 263: k_eff = 1.222681 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 8 D.R. = 1.0000 [ NORMAL ] Iteration 264: k_eff = 1.222760 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 2.0000 [ NORMAL ] Iteration 265: k_eff = 1.222838 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 1.5000 [ NORMAL ] Iteration 266: k_eff = 1.222914 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 0.3333 [ NORMAL ] Iteration 267: k_eff = 1.222988 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 9.0000 [ NORMAL ] Iteration 268: k_eff = 1.223060 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 0.7778 [ NORMAL ] Iteration 269: k_eff = 1.223130 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 7 D.R. = 0.1429 [ NORMAL ] Iteration 270: k_eff = 1.223199 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 13.0000 [ NORMAL ] Iteration 271: k_eff = 1.223266 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 0.6923 [ NORMAL ] Iteration 272: k_eff = 1.223331 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 0.2222 [ NORMAL ] Iteration 273: k_eff = 1.223395 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 0.5000 [ NORMAL ] Iteration 274: k_eff = 1.223457 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 2.0000 [ NORMAL ] Iteration 275: k_eff = 1.223518 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 6 D.R. = 2.0000 [ NORMAL ] Iteration 276: k_eff = 1.223578 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 2.0000 [ NORMAL ] Iteration 277: k_eff = 1.223636 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 1.5000 [ NORMAL ] Iteration 278: k_eff = 1.223692 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.5833 [ NORMAL ] Iteration 279: k_eff = 1.223747 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.1429 [ NORMAL ] Iteration 280: k_eff = 1.223801 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 13.0000 [ NORMAL ] Iteration 281: k_eff = 1.223853 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.6923 [ NORMAL ] Iteration 282: k_eff = 1.223905 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 5 D.R. = 0.3333 [ NORMAL ] Iteration 283: k_eff = 1.223955 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 4.3333 [ NORMAL ] Iteration 284: k_eff = 1.224003 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.6923 [ NORMAL ] Iteration 285: k_eff = 1.224050 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 1.1111 [ NORMAL ] Iteration 286: k_eff = 1.224097 res = 1.355E-07 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 1.4000 [ NORMAL ] Iteration 287: k_eff = 1.224142 res = 1.452E-07 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 1.0714 [ NORMAL ] Iteration 288: k_eff = 1.224186 res = 1.258E-07 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.8667 [ NORMAL ] Iteration 289: k_eff = 1.224229 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.6923 [ NORMAL ] Iteration 290: k_eff = 1.224272 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 0.4444 [ NORMAL ] Iteration 291: k_eff = 1.224313 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 4 D.R. = 1.2500 [ NORMAL ] Iteration 292: k_eff = 1.224352 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.8000 [ NORMAL ] Iteration 293: k_eff = 1.224392 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.1111 [ NORMAL ] Iteration 294: k_eff = 1.224430 res = 1.355E-07 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.4000 [ NORMAL ] Iteration 295: k_eff = 1.224467 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.2857 [ NORMAL ] Iteration 296: k_eff = 1.224503 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.5000 [ NORMAL ] Iteration 297: k_eff = 1.224538 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.5000 [ NORMAL ] Iteration 298: k_eff = 1.224573 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.0000 [ NORMAL ] Iteration 299: k_eff = 1.224607 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 2.0000 [ NORMAL ] Iteration 300: k_eff = 1.224640 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 1.1667 [ NORMAL ] Iteration 301: k_eff = 1.224672 res = 1.645E-07 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 2.4286 [ NORMAL ] Iteration 302: k_eff = 1.224703 res = 1.355E-07 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.8235 [ NORMAL ] Iteration 303: k_eff = 1.224734 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 3 D.R. = 0.0000 [ NORMAL ] Iteration 304: k_eff = 1.224763 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = inf [ NORMAL ] Iteration 305: k_eff = 1.224792 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.6667 [ NORMAL ] Iteration 306: k_eff = 1.224821 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 4.5000 [ NORMAL ] Iteration 307: k_eff = 1.224849 res = 1.549E-07 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.7778 [ NORMAL ] Iteration 308: k_eff = 1.224876 res = 7.743E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.5000 [ NORMAL ] Iteration 309: k_eff = 1.224902 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.1250 [ NORMAL ] Iteration 310: k_eff = 1.224928 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.2222 [ NORMAL ] Iteration 311: k_eff = 1.224953 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.5455 [ NORMAL ] Iteration 312: k_eff = 1.224977 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.1667 [ NORMAL ] Iteration 313: k_eff = 1.225001 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 3.0000 [ NORMAL ] Iteration 314: k_eff = 1.225025 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.6667 [ NORMAL ] Iteration 315: k_eff = 1.225047 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.5000 [ NORMAL ] Iteration 316: k_eff = 1.225069 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 0.6667 [ NORMAL ] Iteration 317: k_eff = 1.225091 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.5000 [ NORMAL ] Iteration 318: k_eff = 1.225112 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.3333 [ NORMAL ] Iteration 319: k_eff = 1.225133 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 3.0000 [ NORMAL ] Iteration 320: k_eff = 1.225153 res = 1.161E-07 delta-k (pcm) [ NORMAL ] ... = 2 D.R. = 1.0000 [ NORMAL ] Iteration 321: k_eff = 1.225173 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0000 [ NORMAL ] Iteration 322: k_eff = 1.225192 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = inf [ NORMAL ] Iteration 323: k_eff = 1.225210 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.3333 [ NORMAL ] Iteration 324: k_eff = 1.225228 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 2.2500 [ NORMAL ] Iteration 325: k_eff = 1.225246 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.5556 [ NORMAL ] Iteration 326: k_eff = 1.225264 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.2000 [ NORMAL ] Iteration 327: k_eff = 1.225280 res = 9.679E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.6667 [ NORMAL ] Iteration 328: k_eff = 1.225297 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0000 [ NORMAL ] Iteration 329: k_eff = 1.225313 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = inf [ NORMAL ] Iteration 330: k_eff = 1.225329 res = 4.840E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.5556 [ NORMAL ] Iteration 331: k_eff = 1.225344 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0000 [ NORMAL ] Iteration 332: k_eff = 1.225359 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = inf [ NORMAL ] Iteration 333: k_eff = 1.225374 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.6667 [ NORMAL ] Iteration 334: k_eff = 1.225388 res = 2.904E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 1.5000 [ NORMAL ] Iteration 335: k_eff = 1.225402 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 2.0000 [ NORMAL ] Iteration 336: k_eff = 1.225416 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.3333 [ NORMAL ] Iteration 337: k_eff = 1.225429 res = 5.807E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 3.0000 [ NORMAL ] Iteration 338: k_eff = 1.225442 res = 1.452E-07 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 2.5000 [ NORMAL ] Iteration 339: k_eff = 1.225455 res = 6.775E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.4667 [ NORMAL ] Iteration 340: k_eff = 1.225467 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.2857 [ NORMAL ] Iteration 341: k_eff = 1.225479 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.5000 [ NORMAL ] Iteration 342: k_eff = 1.225491 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0000 [ NORMAL ] Iteration 343: k_eff = 1.225502 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = inf [ NORMAL ] Iteration 344: k_eff = 1.225513 res = 8.711E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 9.0000 [ NORMAL ] Iteration 345: k_eff = 1.225524 res = 1.936E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.2222 [ NORMAL ] Iteration 346: k_eff = 1.225535 res = 0.000E+00 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.0000 [ NORMAL ] Iteration 347: k_eff = 1.225545 res = 1.065E-07 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = inf [ NORMAL ] Iteration 348: k_eff = 1.225555 res = 3.872E-08 delta-k (pcm) [ NORMAL ] ... = 1 D.R. = 0.3636 [ NORMAL ] Iteration 349: k_eff = 1.225565 res = 9.679E-09 delta-k (pcm) [ NORMAL ] ... = 0 D.R. = 0.2500
In [28]:
# Print report of keff and bias with OpenMC
openmoc_keff = solver.getKeff()
openmc_keff = sp.keff.n
bias = (openmoc_keff - openmc_keff) * 1e5
print('openmc keff = {0:1.6f}'.format(openmc_keff))
print('openmoc keff = {0:1.6f}'.format(openmoc_keff))
print('bias [pcm]: {0:1.1f}'.format(bias))
openmc keff = 1.222044 openmoc keff = 1.225565 bias [pcm]: 352.2
In [ ]:
There is a non-trivial bias in both the 2-group and 8-group cases. In the case of a pin cell, one can show that these biases do not converge to <100 pcm with more particle histories. For heterogeneous geometries, additional measures must be taken to address the following three sources of bias:
- Appropriate transport-corrected cross sections
- Spatial discretization of OpenMOC's mesh
- Constant-in-angle multi-group cross sections
Visualizing MGXS Data¶
It is often insightful to generate visual depictions of multi-group cross sections. There are many different types of plots which may be useful for multi-group cross section visualization, only a few of which will be shown here for enrichment and inspiration.
One particularly useful visualization is a comparison of the continuous-energy and multi-group cross sections for a particular nuclide and reaction type. We illustrate one option for generating such plots with the use of the openmc.plotter module to plot continuous-energy cross sections from the openly available cross section library distributed by NNDC.
The MGXS data can also be plotted using the openmc.plot_xs command, however we will do this manually here to show how the openmc.Mgxs.get_xs method can be used to obtain data.
In [29]:
# Create a figure of the U-235 continuous-energy fission cross section
fig = openmc.plot_xs(reactions={'U235': ['fission']})
# Get the axis to use for plotting the MGXS
ax = fig.gca()
# Extract energy group bounds and MGXS values to plot
fission = xs_library[fuel_cell.id]['fission']
energy_groups = fission.energy_groups
x = energy_groups.group_edges
y = fission.get_xs(nuclides=['U235'], order_groups='decreasing', xs_type='micro')
y = np.squeeze(y)
# Fix low energy bound
x[0] = 1.e-5
# Extend the mgxs values array for matplotlib's step plot
y = np.insert(y, 0, y[0])
# Create a step plot for the MGXS
ax.plot(x, y, drawstyle='steps', color='r', linewidth=3)
ax.set_title('U-235 Fission Cross Section')
ax.legend(['Continuous', 'Multi-Group'])
ax.set_xlim((x.min(), x.max()))
Out[29]:
(1e-05, 20000000.0)
Another useful type of illustration is scattering matrix sparsity structures. First, we extract Pandas DataFrames for the H-1 and O-16 scattering matrices.
In [30]:
# Construct a Pandas DataFrame for the microscopic nu-scattering matrix
nuscatter = xs_library[moderator_cell.id]['nu-scatter']
df = nuscatter.get_pandas_dataframe(xs_type='micro')
# Slice DataFrame in two for each nuclide's mean values
h1 = df[df['nuclide'] == 'H1']['mean']
o16 = df[df['nuclide'] == 'O16']['mean']
# Cast DataFrames as NumPy arrays
h1 = h1.values
o16 = o16.values
# Reshape arrays to 2D matrix for plotting
h1.shape = (fine_groups.num_groups, fine_groups.num_groups)
o16.shape = (fine_groups.num_groups, fine_groups.num_groups)
Matplotlib's imshow routine can be used to plot the matrices to illustrate their sparsity structures.
In [31]:
# Create plot of the H-1 scattering matrix
fig = plt.subplot(121)
fig.imshow(h1, interpolation='nearest', cmap='jet')
plt.title('H-1 Scattering Matrix')
plt.xlabel('Group Out')
plt.ylabel('Group In')
# Create plot of the O-16 scattering matrix
fig2 = plt.subplot(122)
fig2.imshow(o16, interpolation='nearest', cmap='jet')
plt.title('O-16 Scattering Matrix')
plt.xlabel('Group Out')
plt.ylabel('Group In')
# Show the plot on screen
plt.show()
In [32]:
# close statepoint file to release HDF5 file handles
sp.close()